D indicates a neutral charm meson reconstructed in final states common to both D-meson decays inclusively, which was performed by the LHCb collaboration in a recent measurement [D decays, a strategy that requires knowledge of the variation of the decay amplitudes of the charm mesons.The decaysmentclass2pt{minimsurement . AlternaStudies of charm mixing and searches for lusively , will alThe decay 9±0.20)% , which i05)×10-3  comparedpp collision data collected at centre-of-mass energies of 7 and 8 TeV with the LHCb experiment, corresponding to an integrated luminosity of 3.0 fbIn this paper, time-integrated amplitude models of both decay modes are constructed using The paper is organised as follows. In Sect. pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about The LHCb detector  is a sinpp interaction vertices. At least one charged particle must have a transverse momentum The trigger  consistslgorithm  is used pp collisions are generated using Pythia  [EvtGen  [Geant4 toolkit [In the simulation,  Pythia   with a s Pythia  . Particl[EvtGen  . The int toolkit , 15 as d toolkit .Q-value of the decay. The charge of the muon and slow pion are used to infer the flavour of the neutral D meson. Candidates are only accepted if these charges lead to a consistent hypothesis for the flavour of the neutral D meson. All other aspects of the reconstruction and selection criteria are identical between the RS and WS samples.The decay chain The two-dimensional plane It is required that the hardware trigger decision is either due to the muon candidate or is independent of the particles constituting the reconstructed decay products of the The WS sample is contaminated by a category of RS decays in which the kaon is mis-identified as a pion, and a pion as a kaon. To suppress this background, it is required that the kaon is well identified by the RICH detectors. The residual contamination from this background is removed by recalculating the mass of the combinatorial background. Candidates where the mistag background. This latter source of background is dominated by RS decays. Both of these backgrounds are suppressed using a multivariate classifier based on a Boosted Decision Tree (BDT) [Remaining background from random combinations of particles can be divided into two categories. Candidates where the ee (BDT) –19 algorp, a are determined by the fit. The background shape parameters, including those for the polynomial in The signal and background yields in the signal region for each sample is determined by simultaneously fitting the two-dimensional  Cruijff  functionmentclass2pt{minimmentclass2pt{minimFor the amplitude analysis, a kinematic fit is performed constraining the wn value , which iisobars and this approximation as the isobar model. Isobars can be described in terms of resonances, typically using the relativistic Breit-Wigner amplitude for narrow vector and tensor states. For scalar states, there typically are multiple broad overlapping resonances, in addition to significant nonresonant scattering amplitudes between the constituent particles of the state. Such states cannot be described in terms of Breit-Wigner amplitudes and instead the K-matrix formalism [The amplitudes contributing to the decays ormalism , 23 is aCascade decays have the topology X. The unstable state then decays to three pseudoscalars Y). There are three distinct possibilities for cascade decays. The resonance X can either have isospin Y can either be in  Two complex parameters can be used to describe cascade decays: the coupling between the Quasi two-body decays have the topology X, Y form resonances of conventional quark content is Decay chains are described using a product of dynamical functions for each isobar and a spin factor. The amplitude for each decay chain is explicitly made to respect Bose symmetry by summing over both possible permutations of same-sign pions. The total amplitude is then modelled as a coherent sum of these processes. Spin factors are modelled using the Rarita–Schwinger formalism following the prescription in Ref. [The following decay chains are considered: in Ref. ; the dets, takes the formL is given by the normalised Blatt–Weisskopf function [q is the three-momentum of either decay product in the rest frame of the resonance, and is normalised to unity at zero momentum transfer. The factor k normalises the lineshape integrated over all values of s if the Blatt–Weisskopf form-factor and energy dependence of the width are neglected, and is included to reduce correlations between the coupling to the channel and the mass and width of the resonance.Resonances are modelled with the relativistic Breit-Wigner function unless otherwise stated, which as a function of the invariant-mass squared, function  \documenR decaying into three bodies abc can be expressed in terms of the spin-averaged matrix element of the decay r characterises the radius of the decaying resonance.For a resonance that decays via a single channel to two stable particles, such as rrow a_110^{+}{{\oThe K-matrix formalism  providesy decays , 28 of tThe rom Ref. , 29, whiThe boration . The \doThe Q-vector  approximQ-vector  approximinto Eq. , and the theorem  holds foIndependent fits are performed on the The probability density functions (PDFs) are functions of position in The PDF that describes the combinatorial background in the WS sample is fixed to the results of a fit to the two sidebands of the integration sample. The values of the normalisation integrals are independent of the generator distribution of the integration sample, however the uncertainties on the integrals are minimised when integration events approximate the function being integrated, which is known as importance sampling. Therefore, integration samples are generated using preliminary models that do not include efficiency effects.The function to minimise isi and j. The The quality of fits is quantified by computing a  in Ref. . The divi ispartial fit fractions for each sub-process are then defined as the fit fraction with only the contributions from the parent isobar included in the denominator.The values of coupling parameters depend strongly on various choices of convention in the formalism. Therefore, it is common to define the fractions in the data sample associated with each component of the amplitudes (fit fractions). In the limit of narrow resonances, the fit fractions are analogous to relative branching fractions. The fit fraction for component The number of possible models that could be used to fit the amplitudes is extremely large due to the large number of possible decay chains (A model of “reasonable” complexity typically contains boration . The twoFor Take a model and a set of possible additional decay chains, initially the complete set discussed in Appendix. B. Perform a fit to the data using this model adding one of these decay chains.If adding this decay chain improves the On the first iteration, restrict the pool of decay chains that are added to the model to those 40 contributions that give the largest improvements to the fit.Reiterate the model-building procedure, using the 15 models with the best fit quality from step 2 as starting points. Finish the procedure if no model has improved significantly.The model-building procedure therefore results in an ensemble of parametrisations of comparable fit quality.The steps of the model-building procedure areThis section presents fit results and systematic uncertainties, with the latter discussed first in Sect. Several sources of systematic uncertainty are considered. Experimental issues are discussed first, followed by uncertainties related to the model and the formalism.All parameters in the fit have a systematic uncertainty originating from the limited size of the integration sample used in the likelihood minimisation. This effect is reduced by importance sampling. The remaining uncertainty is estimated using a resampling technique. Half of the integration sample is randomly selected, and the fit performed using only this subsample. This procedure is repeated many times, and the systematic uncertainty from the finite integration statistics is taken to be There is an additional systematic uncertainty due to the imperfect simulation, which affects the efficiency corrections. The RS data are divided into bins in the The uncertainty associated with the determination of the signal fraction and mistag fraction in each sample is measured by varying these fractions within the uncertainties found in the fit to the Parameters that are fixed in the fit, such as the  in Ref. , and theThe uncertainty due to the background model in the WS fit is estimated using pseudo-experiments. A combination of simulated signal events generated with the final model and candidates from outside of the The choice of model is an additional source of systematic uncertainty. It is not meaningful to compare the coupling parameters between different parametrisations, as these are by definition the parameters of a given model. It is however useful to consider the impact the choice of parametrisation has on fit fractions and the fitted masses and widths. Therefore, the model choice is not included in the total systematic uncertainty, but considered separately in Sect. The total systematic uncertainty is obtained by summing the components in quadrature. The total systematic uncertainty is significantly larger than the statistical uncertainty on the RS fit, with the largest contributions coming from the form factors that account for the finite size of the decaying mesons. For the WS fit, the total systematic uncertainty is comparable to the statistical uncertainty, with the largest contribution coming from the parametrisation of the combinatorial background. A full breakdown of the different sources of systematic uncertainty for all parameters is given in Appendix C.Invariant mass-squared projections for entclass1pt{minimaentclass1pt{minimaW-emission diagram that is expected to dominate this final state.The largest contribution is found to come from the axial vector There are also large contributions from the different orbital angular momentum configurations of the quasi two-body processes  in Ref. , where tA significant contribution is found from the pseudoscalar state the kaon . Evidenc→K±π+π-p , 35, manboration , 37. The splines . The ArgV and ab,Four-body weak decays contain amplitudes that are both even, such as mmetries . Both soP-even and P-odd amplitudes averages to zero when integrated over the entire phase space. Therefore, the angle P-odd amplitude is the decay The interference between Invariant mass-squared distributions for W-emission diagram that dominates the RS decay, where it manifests itself in the Dominant contributions are found from the axial kaons, t}$$K _110^{+}$$\eThe coupling and shape parameters of the A large contribution is found from The model-finding procedure outlined in Sect. The coupling parameters cannot strictly be compared between different models, as in many cases these coupling parameters have a different interpretation depending on the choice of the model. However, it is instructive to consider how the fit fractions vary depending on the choice of model, which is shown in Table The The coherence factor fined as 19\documecument}γ , and canO-c data , and thrO-c data . A globaO-c data  yields\d in Ref. . This anThe stability of the local phase description can also be verified by evaluating the model-derived coherence factor and associated parameters in different regions of phase space. This is equivalent to changing the definition of Eq.  such thaIn order to define these regions, the phase space is divided into hypercubes using the algorithm described in Sect. The four-body decay modes W-emission topologies are crucial in describing these decays. Interference between the parity-even and parity-odd amplitudes causes large local parity violations, which are shown to be reasonably well modelled in the RS decay. A significant contribution from the pseudoscalar resonance Both amplitude models are found to have large contributions from axial resonances, the decays The coherence factor is calculated using the models, and is found to be consistent with direct measurements. It is found that the calculated value is relatively stable with respect to the parametrisation of subdominant amplitudes in the WS model. These models therefore provide a valuable input to future binned measurements of the


Building on past research, we here develop an analytic framework for describing the dynamics of the transmission of soil-transmitted helminth (STH) parasitic infections near the transmission breakpoint and equilibria of endemic infection and disease extinction, while allowing for perturbations in the infectious reservoir of the parasite within a defined location. This perturbation provides a model for the effect of infected human movement between villages with differing degrees of parasite control induced by mass drug administration (MDA). Analysing the dynamical behaviour around the unstable equilibrium, known as the transmission ‘breakpoint’, we illustrate how slowly-varying the dynamics are and develop an understanding of how discrete ‘pulses’ in the release of transmission stages , due to infected human migration between villages, can lead to perturbations in the deterministic transmission dynamics. Such perturbations are found to have the potential to undermine targets for parasite elimination as a result of MDA and/or improvements in water and sanitation provision. We extend our analysis by developing a simple stochastic model and analytically investigate the uncertainty this induces in the dynamics. Where appropriate, all analytical results are supported by numerical analyses. This isR0) and other factors associated with the population biology of the parasite such as adult parasite life expectancy  do the parasite transmission dynamics move away from the unstable breakpoint towards either attractor? This question is of practical significance since in monitoring and evaluating parasite prevalence and mean intensity trends as MDA coverage increase, public health workers need to understand how these epidemiological measures might be expected to change over time as the system moves towards parasite transmission interruption.The second factor is the influence of the migration of infected individuals into areas where the parasite population is set to cross the boundary of transmission cessation. This issue arises due to the observed heterogeneity in MDA coverage between adjacent or nearby villages or towns, due to various factors influencing the delivery and acceptance of MDA. Such migrations can potentially modify the reservoir of infectious material (eggs and larvae for STH) and hence render the transmission dynamics uncertain. This, in turn, poses the obvious question: how uncertain are the trajectories of transmission dynamics in the presence of migration? This issue is again of practical significance since an understanding of the impact of human movement between population centres in a landscape of heterogeneous MDA coverage will inform policy formulation and focus attention on attaining high and uniform coverage.We examine both of these questions using mathematical models of parasite transmission and control and employing analytical and numerical approaches. Our focus is on the control of the soil-transmitted helminths, but the conclusions are more broadly applicable to other human helminth infections. Throughout our focus shall be on the applied significance of the predicted dynamical properties of human-helminth parasite interactions to the design of effective control policies and their monitoring and evaluation.2M(t)  and infectious reservoir L(t) is given by Anderson and May (1992)β quantifies the contact rate of an individual with respect to L; μ, μ1 and μ2 are the death rates associated to humans, worms and infectious material in the reservoir (eggs and larvae), respectively; λ is the rate of egg production per female worm; γ is the density-dependent fecundity power index which accounts for a decreased egg rate per female worm in the hosts with a large number of worms aggregated together; and we have defined k is the ‘clumping factor’ .The nonlinear dynamical system of equations describing the time evolution of the mean total worm burden M(t) can be obtained by taking the time derivative of Eq. (1)M(t), L(t), M′(t), L′(t)]. With a specified reservoir behaviour L(t), M(t) towards stable ‘equilibria’ — the latter term corresponding to regions of the phase space where the first time derivatives M′(t) and L′(t) vanish.The second derivative of 2.1Ascaris lumbricoides or Trichuris trichuria — or larvae in the case of the hookworms: Necator americanus and Ancylostoma duodenale) is at equilibrium. This assumption is justified by the relatively long life span of the adult worm in the human host (1 to 2 years) versus the life expectancy of the eggs or larvae outside the human host which is in terms of weeks to a few months — see Ref. Ascaris suum, and by possible extension Ascaris lumbricoides, where the exceptional hardiness of their eggs to environmental factors can lead to very long lifespans dMdt=μ+μ{R0ϕf and, with some initial time t0 set, we have used the approximate solutionNotice that by perturbing the system away from reservoir equilibrium by 3In this section, we shall introduce the concept of a ‘saddle-node bifurcation’, which is found to be present at the point when the two equilibria collide in, e.g., We illustrate the point at which the stable endemic equilibrium (solid black line) and unstable breakpoint equilibrium (dashed black line) meet, known as a saddle-node bifurcation, in 3.1M† we may expand the system (suppressing dependencies and defining (ϕf)† ≡ ϕf for brevity) such thatz, the g† function takes negative values which decrease in magnitude with increasing k.Given the existence of this saddle-node bifurcation, locally about Now by truncating the expansion in M(t) ) when the dynamics are confined within the grey region representing M at the stable endemic equilibrium (upper) and unstable breakpoint equilibrium (lower) numerically obtained from Note that when Our analysis has now reached the point where we are in a position to address the initial question posed in the introduction. Moving from left to right between the two sets of panels in Another way to quantify the rate of change in the human-helminth system near the disease breakpoint is to compute the timescales over which the dynamics evolve. For completeness, we shall consider one such timescale directly in the next section.3.2In the previous sections we have been able to obtain approximate solutions to the dynamical behaviour parameterically near the point of saddle-node bifurcation. In contrast to this, if one wishes to compute the timescales towards fixed values over large regions of the phase plane, a numerical approach is necessary to avoid significant error.Mend in the absence of migration, for instance, one must compute the following integralμ1.In order to compute the time it takes for the transmission dynamics to travel between values of Motivated by the good agreement in the previous section between our analytic approximations and the full numerical solution to the STH transmission dynamics within a controlled range of initial conditions, we shall proceed to develop an equivalent approach with the inclusion of a perturbation from the infectious reservoir such that we may begin to address our second question.3.3Consider a perturbation of the form given by tpul and δL(tpul) is the maximal amplitude of the perturbation in the infectious reservoir.By truncating an expansion of tpul onwards, Remarkably, evolving the elapsed time from M(t0) and two choices for R0 (separated by the left and right panels). The upper panels display the dynamics under the influence of a positive-valued migration-driven perturbation, and conversely, the lower panels display the dynamics under the influence of a negative-valued migration-driven perturbation.Using As in the case without migration, t ≫ t0, It is important to note here how, at much later times With our analysis in this subsection, we have begun to address the second of our two questions posed in the introduction. The main limitation of this approach so far is that we have only considered a single discrete migratory event. Therefore, in order to further evaluate the degree to which the unstable breakpoint and stable endemic equilibria are robust to the effects of migration and hence draw more concrete conclusions, we will need to develop a model of multiple migratory events. Before doing so we will need to introduce another expansion.3.4ϕf) ≡ ϕf, such thatM* , we may thus describe the transmission dynamics parameterically near to the stable or unstable equilibrium points, given a value for R0.In parallel with the expansion we have used previously, one may also derive an expansion around either the stable endemic equilibrium or unstable breakpoint equilibrium solutions M* — which is due to the fact that the rate of time evolution in the transmission dynamics increases with increasing R0. This latter point becomes consistent with our expectations when noting that the amplitude of M″(t) as given by R0 values.In Building from the formalism previously discussed, we may derive a theory of deterministic pulses around both equilibria as well, however the conclusions drawn from such an analysis would be the same as those of the previous section. As an extension to such a theory, it is possible that many such migratory events which perturb the reservoir may occur over the STH transmission period of interest. In the proceeding section we shall develop a theory which includes this possibility by utilising a stochastic process.44.1Extending our approach to modelling multiple migration events of the same type as in the previous section requires deliberate specification in settings with endemic infection. To date few large-scale epidemiological studies have attempted to measure these rates in settings where soil-transmitted helminth infections are endemic. However, two such studies are underway that are attempting to do so, and hence more precise parameterization will be possible in the near future . In the M, k and z.In order to calculate the effect of these migrating individuals on the infectious reservoir over this same time period, however, we must also derive a distribution for the typical number of eggs that an infected individual might release, which we may subsequently draw from at each migration ‘event’. We derive this distribution in the proceeding section where we shall essentially conclude that it is a negative binomial distribution with mean and variance parameters which can be determined by specifying the parameters M which arises from the stochastic migration event can be accurately modelled in an extremely simple manner, e.g., a Markov process, and on finding the critical rate of migration above which the dynamics are overrun with stochastic noise — making it extremely difficult to control transmission through measures such as MDA.Combining the above two jumps in reasoning, in this section we will conclude that a compound Poisson process given by 4.2In this subsection we shall focus on obtaining a realistic stochastic representation of the flux in egg and/or larvae count into (or out of) the infectious reservoir over time. In order to do this, it shall serve our purpose to first briefly review the current theory regarding the probabilistic modelling for STH infections  and subsϕf term, included in the force of infection of n carried by that individual which includes both the density (aggregation of worms) dependence of fecundity , which fluctuates around the deterministic dynamics in continuous time, becomes the followingt ∈ [ti ± ,, ∞) and value 0 otherwise.8The event-based approach to a stochastic model of migration to or from the region of interest suggests that the times at which individuals do so are drawn from a Poisson distribution, and hence the event intervals are exponentially distributedk is assumed to be a constant in time. If MDA control is applied to a region, then it is not necessarily only the mean worm burden of hosts  which decreases for all of the clustered communities collectively within the region .Using P distribution at the stable endemic (right column) and unstable breakpoint (left column) equilbrium values M* here is the solution for either of the equilibria from In r ≳ μ2.For illustration purposes, in Due to the properties of the stable and unstable equilibria we have already discussed, the reader may initially expect the variance of the distributions in the left panels of mean worm burden M.Lastly, we note here that there is an asymmetry in the tails of the distribution around the unstable equilibrium. This is as one might expect given that the disease extinction equilibrium is a hard condition on the left hand side of the plot as opposed to the physically allowable continuum on the right hand side. A similar asymmetry in the opposite direction exists around the stable equilibrium due to the presence of the unstable equilibrium, and ultimately the disease extinction equilibrium, on the left side of this plot. Such observations will be useful in our interpretation of the variance of the distribution as a function of time. We reiterate to the reader, so as to avoid confusion, that the distributions of  ± ,M(t), simplifies substantially toMaintaining choices as above for r. We have provided the time evolution curves for the variance computed numerically for the fully non-Markovian process (solid coloured lines) and numerically for the Markovian process (dotted coloured lines), where the latter process is also computed with the analytic approximation provided by In r ≳ μ2. In this range, due to the disagreement between the numerical solution to the Markovian process and our approximation, we deduce that the numerically-obtained apparent sub-linear growth in the variance is due to limitations imposed on the process by the presence of the disease extinction equilibrium The agreement between our analytic relation given by r is low when compared to the reservoir death rate r ≪ μ2 the deterministic transmission dynamics experience some degree of controlled uncertainty; when r ≫ μ2 our results indicate enormous variability in the dynamics may be potentially induced — as is indicated by the large variances illustrated in our We turn, finally, to readdressing the second of the two questions posed in the introduction. Our stochastic model of migratory perturbations has demonstrated that both the stable endemic and unstable breakpoint equilibria behave in a similar fashion under the influence of a symmetric migrating flux of people in and out of the infectious reservoir: when such a rate 5In this paper we have developed an analytic framework for describing the transmission dynamics of STH parasitic infections near the unstable equilibrium, or ‘breakpoint’ — the target for transmission elimination strategies using MDA and/or sanitation based programmes of soil-transmitted helminth control. Our analysis, in addition to extending the literature with new analytic insights, has also analytically and numerically investigated the effect that infected human migration can have on the dynamics of parasite transmission by developing the new models of discrete infectious reservoir ‘pulses’ and a stochastic theory of many migratory events. The tools we have developed, along with our specific findings, should have important ramifications for both policies for control and the design of monitoring and evaluation programmes, e.g., our results regarding the critical migration rate of infected individuals above which elimination may be extremely difficult to achieve. As control efforts for neglected tropical helminth infections increase, our results should be applicable to many programmes today and in the future.We assessed the rate of change in time for the transmission trajectories near the parasite transmission breakpoint (arising from the dieocious nature of helminth parasites), finding them to be extremely slowly varying. Illustrating this point quite clearly are our A secondary, yet no less important effect, was studied in conjunction with our earlier analysis and is perhaps best illustrated by the combination of In the limit where the migratory rate — the rate of people leaving and entering the region or community and introducing material into the infectious reservoir  per unit time — is much smaller than the rate of reservoir death (the rate at which the eggs or larvae die outside of a host), our results indicate that uncertainty in the dynamics is present but controlled to some degree such that elimination will eventually occur. In the opposite limit, where the average migratory rate greatly exceeds the average death rate of infectious eggs or larvae in the reservoir, our results suggest that great variability in the transmission dynamics is possible and, indeed, likely. We therefore find that infected human migration is an important effect to quantify in order to assess its ability to undermine targets for parasite elimination from control measures, such as MDA and/or improvements in water and sanitation provision.We wish to further clarify some of the assumptions we have made in building the stochastic model of egg pulses here: we have assumed that a discrete pulse of infectious stages enter or leave the reservoir with a Poisson event rate. The amplitude of these pulses — see, e.g., In addition to these important practical implications which may stem from human migration, our analysis has also yielded further insights into the theory of human helminth parasite transmission dynamics. The large differences in dynamical timescales present between the infectious reservoir, or vector hosts in the case of schistosomes, filarial worms (life expectancy a few weeks to months) and adult worms in the human host (one to many years) admits an accurate Markovian description to be formulated for the migration model. This in turn provides analytical insights into the key parameters that determine epidemiological outcomes within the dynamic transmission systems.Throughout this paper we have deliberately excluded the possible effects induced by the presence of an age-structured population. Many components of our analysis should be generalisable in this aspect and we leave this extension to future work.


Critical transitions are qualitative changes of state that occur when a stochastic dynamical system is forced through a critical point. Many critical transitions are preceded by characteristic fluctuations that may serve as model‐independent early warning signals, implying that these events may be predictable in applications ranging from physics to biology. In nonbiological systems, the strength of such early warning signals has been shown partly to be determined by the speed at which the transition occurs. It is currently unknown whether biological systems, which are inherently high dimensional and typically display low signal‐to‐noise ratios, also exhibit this property, which would have important implications for how ecosystems are managed, particularly where the forces exerted on a system are anthropogenic. We examine whether the rate of forcing can alter the strength of early warning signals in (1) a model exhibiting a fold bifurcation where a state shift is driven by the harvesting of individuals, and (2) a model exhibiting a transcritical bifurcation where a state shift is driven by increased grazing pressure. These models predict that the rate of forcing can alter the detectability of early warning signals regardless of the underlying bifurcation the system exhibits, but that this result may be more pronounced in fold bifurcations. These findings have important implications for the management of biological populations, particularly harvested systems such as fisheries, and suggest that knowing the class of bifurcations a system will manifest may help discriminate between true‐positive and false‐positive signals. As early warning signals are based on the change in leading indicators across a given time series, it is the relative instability of a system with respect to conditions at start of the time series that is important for forecastability. Consequently, slow rates of forcing where time‐series length is invariant limit the scope for detecting change in a leading indicator, whereas faster rates of change over the same period can push a system further from equilibrium within the same amount of time. Understanding how the rate of forcing of biological systems affects the strength of early warning signals is thus important to their proper use for conservation intervention and planning.Here we use models known to exhibit statistical signals of critical slowing down before to investigate how the rate of forcing of a system alters the strength of early warning signals of population collapse. Using two models, one exhibiting a fold bifurcation and the other a transcritical bifurcation, we simulate populations subject to a range of forcing speeds and show that the rate of forcing has the potential to alter the detectability of generic early warning signals in biological systems, both through the length of time series available to analyze and by directly affecting the dynamics of a system prior to a collapse.22.1c)  stochastic perturbation with mean = 0 and σ = 0.5 that was applied at each time step with expectation μ and intensity σ2. The abundance simulations were implemented with a time step (δt) of 0.025 using the Euler approximation.The first model describes a population that grows logistically and moves from an underexploited to an overexploited state via a fold catastrophe , while for the transcritical bifurcation, those values were c = . These values were chosen so that simulated populations from the two models collapsed over similar time frames , density ratio (ratio of low frequencies to high frequencies within a rolling window), first‐order autoregressive coefficient (ar1), return rate (rate of return to equilibrium after a perturbation), and the standard deviation of the abundance time series. A number of these leading indicators are theoretically highly correlated ; however, especially with noisy data, these indicators have been shown to often perform differently . This was achieved by analyzing the final 240 time points prior to collapse for each population independently. Standardizing the time series removed any effect of time‐series length varying with the rate of forcing of the system Figure . The sec33.1In both models, the rate of system forcing altered the population dynamics and timing of extinction, and thus the length of the time series prior to collapse Figure a, b. BecTime‐series length also altered the distribution of Kendall tau values in the constant treatments, where theory suggests that there should be no detectable trend in the five leading indicators . While in both the standardized and nonstandardized time series, Kendall tau values were approximately uniformly distributed around 0, the variance was much larger in the standardized time series, suggesting it might be difficult disentangling false‐positive from true‐positive signals.4The possibility of generic early warning signals gives hope that population collapse may be predicted prior to its occurrence, a potentially useful tool for conservation prioritization and management. Such approaches could be particularly applicable to harvested systems such as fisheries (Vasilakopoulos & Marshall, The rate of forcing of the system altered the trends of four of the five generic leading indicators in the models, regardless of the whether the time‐series length was standardized Figures , althougThe results presented here, using standardized time‐series lengths and lengths allowed to vary with the rate of forcing, mimic different potential real‐world scenarios. In the first instance, the length of the time series available to detect early warning signals is limited by the time that it takes for a population to collapse Figures  and 3. TIn conclusion, we show that the predictability of population collapse is likely to be not only a function of the rate at which a system is forced away from stability, but may also depend on the underlying dynamics. A more complete understanding of a system may therefore be required before we are able to identify whether signals generated by currently available generic leading indicators are likely reliable.None declared.


Ultrasound examinations are a standard procedure in the clinical diagnosis of many diseases. However, the efficacy of an ultrasound examination is highly dependent on the skill and experience of the operator, which has prompted proposals for ultrasound simulation systems to facilitate training and education in hospitals and medical schools. The key technology of the medical ultrasound simulation system is the probe tracking method that is used to determine the position and inclination angle of the sham probe, since this information is used to display the ultrasound images in real time. This study investigated a novel acoustic tracking approach for an ultrasound simulation system that exhibits high sensitivity and is cost-effective. Five air-coupled ultrasound elements are arranged as a 1D array in front of a sham probe for transmitting the acoustic signals, and a 5 × 5 2D array of receiving elements is used to receive the acoustic signals from the moving transmitting elements. Since the patterns of the received signals can differ for different positions and angles of the moving probe, the probe can be tracked precisely by the acoustic tracking approach. After the probe position has been determined by the system, the corresponding ultrasound image is immediately displayed on the screen. The system performance was verified by scanning three different subjects as image databases: a simple commercial phantom, a complicated self-made phantom, and a porcine heart. The experimental results indicated that the tracking and angle accuracies of the presented acoustic tracking approach were 0.7 mm and 0.5°, respectively. The performance of the acoustic tracking approach is compared with those of other tracking technologies.10.1007/s40846-017-0258-9) contains supplementary material, which is available to authorized users.The online version of this article (doi: Medical ultrasound examinations have become essential for diagnostic, therapeutic, and surgical procedures in hospitals and other clinical environments. An ultrasound system can provide high-resolution cross-section images of the abdomen and its internal organs that are useful in many clinical applications, such as cardiology, obstetrics, and gynecology, as well as of the breast, thyroid, and vascular and musculoskeletal systems. However, the efficacy of an ultrasound examination is highly dependent on the skill of the operator. Misjudgment can occur if the operator lacks sufficient experience, particularly when detecting rare disorders. It is therefore very important that junior sonographers receive a training course in ultrasound examinations . AccordiAn ultrasound simulation system can provide very effective training without impacting patient safety because it can simulate highly accurate scenarios, uses very realistic tools, and affords opportunities to manage patient complications . The higThe OT approach for ultrasound simulation systems provides high accuracy, high update rates, and a relatively large workspace –8. For iThe present study investigated a novel acoustic tracking approach for use in a medical ultrasound simulation system. Air-coupled ultrasound elements are embedded in the front of a sham ultrasound probe for transmitting the acoustic signals, and the position and orientation of the sham probe are tracked by receiving the acoustic signals using 2D air-coupled ultrasound elements. After the position of the sham probe is identified by the acoustic tracking approach, its corresponding ultrasound image is displayed according to the position of a real ultrasound examination in the image database as obtained previously via the mechanical scanning of subjects. The validity of this approach was verified in phantom and in vitro porcine heart experiments, and the system performance was compared with those of several commercial ultrasound simulation systems.Figure i) for orientating the position of the sham probe. In the figure, N means the total position situation that was obtained from the motor platform. Each X was subtracted from Yi, with the results squared and summed across all values to find Ri. The minimum value of Ri corresponds to the correct position in the calibration database, which means that the position of sham probe could be tracked effectively. The minimum value of Ri is close to 0. After Ri was calculated, minimum value search was used to find the value that closes to 0 between R1 and RN. As Rmin was found, the system would find the image that was assigned in this position. For example, if the minimum value happened in R50, the system would capture image assigned in position 50 and display it on the monitor.The sham probe was fixed on a four-axis motor platform and placed above the 2D array of receiving elements. As the sham probe is moved in the four-axis directions , the received acoustic signals and position information are recorded simultaneously in the position calibration database. Therefore, the spatial relationship between the estimated positions and orientations and their corresponding images was obtained as the image database. Figure i is determined, the corresponding ultrasound image is displayed on the user interface.After the position and orientation of the sham probe are identified using the acoustic tracking approach, the real ultrasound image from a specific cross section of an organ is displayed on the system screen. The image database was obtained using a clinical ultrasound scanner  with a linear array probe (12L5). The probe was fixed on a four-axis motor platform so that it can be moved freely in 3D space by a motor controller. Open-source software is available for the Terason t3000 scanner to allow applications to be developed that run on the Windows operating system, which allows real-time ultrasound images to be acquired on a frame-by-frame basis in the PC as the probe is moved across the area of interest. The position information from the motor and image information from the scanner were integrated together in the image database. When the minimum value of RThree different subjects were used to verify the performance of the acoustic tracking approach for an ultrasound simulation system. The first subject was a commercial ultrasound phantom  which allowed for evaluations over ultrasound frequencies ranging from 2 to 15 MHz. Since the structure of this commercial ultrasound phantom is quite simple, a second phantom was constructed that had a complicated structure. Figure The size of the receiver unit is 55 × 55 mm, including the 25 elements. The receiving elements were fixed into an acrylic holder and soldered on a circuit board. The transmitting elements were connected to the continuous-wave generator. Figure Figure While the experimental results showed that the simulation system performs well, comparison with commercial ultrasound systems revealed that the acoustic tracking approach still has the following limitations. The tracking accuracy is determined by measuring the minimum horizontal distance that causes the array to be indistinguishable between two adjacent positions. The sham probe was fixed on the motor to sweep the receiver unit at a step setting from 0.001 to 1 mm. The experimental results show that 0.7 mm is the minimum horizontal distance between two adjacent positions that can be tracked using the acoustic approach. In other words, the simulation system may display the same image even when the sham probe is moved by up to 0.7 mm. The accuracy of the probe angle was also measured, by inclining the probe from 0.2° to 2°. The experimental results show that a resolution of 0.5° is achievable. In a trial involving sonographers with 10 years of experience in ultrasound examinations, they considered that the moving speed and sensitivity of the sham probe kept up with the images display on the simulation system, and hence provided an accurate simulation of a real examination.Since many studies have used the OT  and EMT This study investigated a novel acoustic tracking approach for an ultrasound simulation system. Air-coupled ultrasound elements are key components in this approach. Based on the acoustic signals received from a sham ultrasound probe, the position and angle of the moving sham probe can be detected precisely in this system, and the corresponding ultrasound image is displayed simultaneously on the screen. The system performance was verified using three different subjects, with the results showing that the dynamic images from the simulator perfectly match those from an actual clinical ultrasound system. The tracking and angle accuracies of the presented acoustic tracking approach were 0.7 mm and 0.5°, respectively. Future studies should focus on constructing a database of clinical ultrasound images, particularly for rare disorders.Supplementary material 1 (AVI 35343 kb)Supplementary material 2 (AVI 35226 kb)Supplementary material 3 (AVI 35226 kb)Below is the link to the electronic supplementary material.


Time series analysis is applied to identify and analyze a transition in the groundwater regime in the aquifer below the sand ridge of Salland in the Netherlands, where groundwater regime refers to the range of head variations throughout the seasons. Standard time series analysis revealed a discrepancy between modeled and observed heads in several piezometers indicating a possible change in the groundwater regime. A new time series modeling approach is developed to simulate the transition from the initial regime to the altered regime. The transition is modeled as a weighted sum of two responses, one representing the initial state of the system, the other representing the altered state. The inferred timing and magnitude of the change provided strong evidence that the transition was the result of significant dredging works that increased the river bed conductance of the main river draining the aquifer. The plausibility of this explanation is corroborated by an analytical model. This case study and the developed approach to identify a change in the groundwater regime are meant to stimulate a more systematic application of time series analysis to detect and understand changes in groundwater systems which may easily go unnoticed in groundwater flow modeling. The worldwide increase in groundwater demand requires increased care in assessing groundwater reserves, especially in the context of a changing climate  at an observation well, resulting from a stress applied on a groundwater system  is obtained by convolution of the time series q(t)of the stress with a corresponding impulse response function θ(t):t is time. The dependence of the response function on spatial coordinates is omitted in this notation. The response function θ(t) describes the reaction of the groundwater head to an instantaneous stress event of unit magnitude. In this paper, the scaled Gamma distribution is used as the impulse response functionM is a scaling factor, a and n define the shape of the function, and Γ(n) is the Gamma function of n. The Gamma distribution is used frequently to simulate the response to recharge in time series models is the remaining residual, and ϕr is the response to recharge R:θris the impulse response function of recharge. The recharge in Equation 6 is approximated as  is the measured precipitation, E(τ) is the measured reference evaporation, and f is a scaling factor. Runoff is neglected given the absence of streams on the ridge, the high permeability of the soil, the flat to gently sloping relief of the sand ridge and its surroundings, and the moderate climate :θw is the impulse response function of pumping. Modeling the residuals with an exponential decay process transforms the time series of residuals into a noise time series n(t) that is approximately white is the remaining noise at time ti.The observed heads are modeled as the sum of the response to recharge, the response to pumping and a reference level h‾o minus the sum of the mean contributions of the stresses  as the response function, asThe mean response Mr is the final response of the groundwater head when the recharge is applied continuously with unit intensity. Similarly, ϕ‾w=Q‾Mw.S (p) defined as half of the sum of the squared noise terms nidefined in Equation 9:p is the vector of Np log‐transformed model parameters and No is the number of observations. The search for the minimum of the objective function was performed using a modified Gauss‐Newton algorithm . The main idea is to replace the response to recharge by a weighted sum of two responses, one representing the initial state and the other representing the altered state.θ1(t) to θ2(t). Convolution of these response functions with the recharge time series results in two different responses, ϕ1(t) and ϕ2(t). The transition from the first to the second state can be described by a weighted sum of the two responses:ϕ(t) is the weighted sum of the two responses and ω(t) is the weighting function. The weighing function ω(t) is chosen to be an S‐shaped curve that varies from 1 to 0:β is a shape factor that determines the smoothness of the transition and σis the middle of the transition time, when the function takes a value of 0.5.The transition from one response to another response is implemented as follows. Suppose that the response function changes from Mr, ar, and nr of the response function to recharge before the transition, Mr, ar, and nr of the response function to recharge after the transition, the factor f, the exponential noise decay factor α, and the parameter σ of the transition function (19). The solution is not sensitive to the sharpness of the transition for Piezometer 1 so that the shape factor β was fixed to 50 which corresponds to a sharp transition. For Piezometer 2, parameters Mw, aw, and nw of the response function to pumping are also included for a total of 13 parameters. The new model gives a good fit for the entire measurement period for both piezometers . For Piezometer 1, a time interval of 4 months leads to approximately uncorrelated residuals while for Piezometer 2, a time interval of 23 months must be used. With approximately uncorrelated residuals, the AIC drops from −229 to −306 for Piezometer 1 and from −25 to −55 for Piezometer 2, which confirms that using the model with the regime transition is justified.where The transition time was identified with reasonable confidence intervals for both piezometers. The sharpness of the transition was determined with statistical significance for Piezometer 2 and was fixed for Piezometer 1, as stated. The resulting weighting function for Piezometer 2, including the 95% limits, is shown in Figure Mr, μr, and σr .The response functions that prevails before and after the transition are shown in Figure The quicker recession of the response to recharge after the transition indicates that groundwater is drained faster. The next step is to search for an underlying physical reason.3 of sediments  were removed from the river bed over a distance of 8 km. A probably unintentional consequence was an increase of the river bed conductance and thus of the draining capacity of the river. This explanation is consistent with the reduction of the response to recharge shown in Figure The local waterboard reported that significant dredging works had been carried out in the river the “Regge” Figure  between k, approximate saturated thickness is D, storage coefficient is Sand length of the cross‐section is L. The aquifer is bounded on the left by a fixed head representing the drained meadows to the west of the study area. The aquifer is bounded to the right by a river representing the river “Regge.”As a final step in the investigation, a short theoretical analysis is presented to determine whether a change in the river bed conductance can indeed result in the change in the response function presented in Table Qs [L2/T] is the flux from the aquifer to the river per unit length of river, ϕ(x = L) is the head in the aquifer relative to the stream stage at the semipervious stream bank, and Cis the river bed conductance [L/T]. The base of the aquifer is impermeable and aquifer parameters are uniform and constant. Heads are measured with respect to the heads on the left and right sides of the cross‐section . Initially, the head is zero everywhere. The analytical solution for the response function due to a constant recharge starting at time t = 0 is given by Bruggeman (θ(t) is characterized by its moments of order k defined as:Flow into the stream is computed as:ruggeman , EquatioThe three first moments are considered here and evaluated by numerical integration of the solution of Bruggeman. Alternatively, the moments can be obtained by solving the differential equation for the moments of the response function (e.g., Bakker et al. μ and the standard deviationσof the response function (Weisstein The moments are recombined and expressed as the mean response time Mr which determines the final response to recharge. Values obtained for this parameter with the analytical solution should therefore correspond approximately to the values obtained with the time series model. In contrast, neglecting the passage through the unsaturated zone results in a smaller mean response time μr and standard deviation σr. However, the change of these two parameters as a result of variations of the river bed conductance remains comparable to the time series model.In the simplified model, precipitation reaches the groundwater table instantaneously, which implies that the time it takes for infiltrated water to percolate through the unsaturated zone is neglected. This approximation does not affect the estimation of parameter D = 30 m, S = 0.3, and L = 4000 m. The values corresponding to the magnitude of the final response to precipitation Mr, the mean time μr and standard deviation σr are evaluated for river bed conductance values C ranging from 10 to 80 m/d, at a distance x = L/2. The results are plotted in Figure Values that approximate the situation of Piezometer 2 are chosen with k = 40 m/d, C= 10 m/d to C= 50 m/d leads to a theoretical reduction of approximately 5% to 10% of the parameters Mr, μr, and σr of the response function to recharge. These reductions support the conjecture that the observed transition in groundwater regime is the result of dredging works that increased the conductance of the river bed.An increase of the river bed conductance from In this study, it is shown how time series analysis can be used as an investigative tool to identify and analyze changes in the groundwater regime that are otherwise unnoticed. Standard time series analysis revealed a systematic discrepancy between modeled and observed heads in the phreatic aquifer under the sand ridge of Salland in the Netherlands. The investigated piezometers exhibit two different fluctuation regimes that can be modeled accurately when considered separately. A new time series modeling approach is developed that incorporates a weighted sum of two modeled responses to recharge, one representing the initial state and the other representing the altered state. The new approach results in excellent fits of the heads over the entire observation period. The results of the new approach initiated a search for the physical causes of the regime change, leading to the conclusion that dredging works in the river draining the aquifer are most likely the cause of the groundwater regime change. The local water board was not aware of this change to the groundwater regime and the change had not been incorporated in any of the groundwater models used for water management purposes.Finally, it is pointed out that changes in climate, land use, or groundwater pumping, which are the usual suspects when changes in head variations are observed, do not appear to be involved here. Time series analysis of observed heads is an instrumental tool to understand the history of the dynamics of an aquifer and deserves a more systematic application in the analysis of groundwater systems.


Azimuthal asymmetries play an important role in scattering processes with polarized particles. This paper introduces a new procedure using event weighting to extract these asymmetries. It is shown that the resulting estimator has several advantages in terms of statistical accuracy, bias, assumptions on acceptance and luminosities compared to other estimators discussed in the literature. P if the analyzing power A is known, or vice versa. To cancel systematic effects, one usually takes two data sets with opposite polarisations, e.g. polarisation up  are discussed and compared. Section In this paper a new estimator using event weights and a entclass1pt{minimain Refs. , but it entclass1pt{minimaIn general one can distinguish two classes of estimators: estimators using event counts, discussed in Sect. L) part of the detector is given by:Here events around mentclass2pt{minimA can be derivedIn the cross ratioAnother possibility is to consider estimators of the typein Refs. .A, we will discuss the FOM of Common to these estimators is that they reach the same statistical error Error propagation from Eqs.  or 6) l l6) leadThe full line in Fig. In this section estimators are discussed which use event weights instead of event counts as in the previous subsection. In Ref.  weighted in Ref.  that wit in Ref. . It is nNow a new method, reaching the Cramér–Rao bound as well, is introduced. The advantage is that no knowledge about the acceptance is required  and no corrections concerning the luminosities have to be applied. On the contrary, information on the acceptance and luminosity factor We consider the following six observablesFor an arbitrary acceptance in mentclass2pt{minimC of the observables is given in Appendix Assuming that the polarisations The FOM, calculated using the same conditions as used for entclass1pt{minimaIn this subsection we make some general remarks about the FOM reachable for event distributions of the type in Ref.  the estin in Eq. , Sect. 2n in Eq. , Sect. 2A only in the case of uniform In this subsection we crosscheck the results of the previous subsections and discuss possible bias with the help of Monte Carlo simulations. A Monte Carlo simulation with mentclass2pt{minimmentclasspt{minima2 in Eq. . One seeThe circles in Fig. This subsection discusses some extensions which can be applied to the weighting/fitting method but in general not easily to the other methods.x-y plane, the observed signal isIf the polarisation vector points for example in an arbitrary unknown direction  at Eqs. –13), on, on\docuIt is interesting to note that the method introduced here, especially for the case were the number of equations exceeds the number of parameter is a special case of the “Generalized Method of Moments” (GMM) widely used in economics .Two types of estimators to extract azimuthal asymmetries have been compared. One is based on event counts and one on event weighting. It was shown that estimators just using event counts do not use the full information contained in the data. This is reflected in the fact that the figure of merit is smaller than in methods where events are weighted with an appropriate weight. The optimal weight for azimuthal asymmetries is Among the estimators using event weights the method introduced in this paper has the advantage that no knowledge about the acceptance is required and no correction due to possible difference in luminosity has to be applied. On the contrary, the method even provides information on the azimuthal dependence of the acceptance. The method is easily extendable to more observables.


The growth of salt crystal hydrates (CaCl2·2H2O) on the interface has been studied. It has been found that the change in the initial salt concentration leads to different crystallization rates. The crystallization rate on the droplet interface is many times lower than for a thin layer. The description of crystallization in the salt solution droplet should take into account the crystallization anisotropy, which is associated with the direction of crystallization. The crystallization rate along the contact line of the droplet is many times higher than in the direction of the droplet radius. For a long time of crystallization, the area of the crystal film (outside the drop) increases several times. Four characteristic modes of crystallization to a drop of salt solution have been distinguished. When modeling crystallization, it is necessary to take into account multiple changes in the growth rate of salt crystallohydrates over time, as well as the anisotropic nature of crystallization.Non-isothermal evaporation during crystallization of CaCl In industrial technologies, several processes are often implemented simultaneously during crystallization: dissolution, dilution, heat transfer and evaporation. At that, liquid temperature, salt concentration and supersaturation change over time. Changes in boundary conditions over time significantly complicate the simulation. Spatial limitations change the heat transfer coefficient and crystallization rate. For the correct physical description of the complex non-stationary and non-isothermal processes, it is essential to review the literature in several related fields.2; chemical technologies. When modeling high-temperature evaporation of droplets and films, the physical and chemical properties of the wall have to be taken into account. The presence of water droplets and water vapor in the multicomponent fuel leads to lower combustion temperature and reduces harmful emissions during combustion3.Non-isothermal evaporation of drops and films is also used in a wide range of technical problems: the fuel multicomponent systems with gas-droplet flows; the absorption heat pumps in power engineering7. The droplet evaporation rate may be effectively controlled by applying surfactants9. At that the evaporation rate becomes nonlinearly dependent on time. Characteristic modes of droplet evaporation with surfactant are considered in9.Modern technologies widely apply textured surfaces to control wettability and to intensify droplet and film evaporation10 and ion transport12. Evaporation of salt solutions differs from pure water. Since the salt concentration increases with time, the evaporation rate, on the contrary, can fall many times, and the evaporation kinetics depends on the salt type14. The rapid increase in the salt concentration during boiling leads to the degeneration of the nucleate boiling and to the implementation of four evaporation modes, successively replacing each other16. Changes in the physical properties of aqueous solutions of salts with time of evaporation, significantly complicate the modeling of solutions. The properties of the aqueous solution of CaCl2 salt and equilibrium diagrams were studied in17.Aqueous salt solutions are widely used in modern energy technologies: membrane technologies21. The regularities of crystallization in salt solution drops and in double solutions are presented in24. It is characteristic that over evaporation time the crystal forms on the free surface of the droplet can vary and depend on the wettability. The beginning of crystallization in the drop is realized in the precursor film of the salt solution25, where the maximum supersaturation occurs. Collective effects and spontaneous crystallization in water droplets on the surface of heavy oil are considered in26. The main points of the theory of crystallization of salt solutions and the driving forces of crystallization are considered in27.Regularities of crystallization of salt solutions are important for describing numerous technologies associated with the creation of new materials, nanofilms with high heat and electrical conductivity, having properties of semiconductors and high strength. The properties of materials change when the crystallization rate and crystal forms vary30, which significantly increases the evaporation rate. The role of free convection in salt solution drops decreases with increasing evaporation time, since the salt concentration increases33. In this case, the heat transfer coefficient may have an extremum when approaching the crystallization. The Marangoni flow on the surface of a water drop at room temperature is suppressed by micron particles of dirt, which may be a surfactant33. With increasing wall temperature and heat flux, the thermal and the solutal Marangoni forces lead to intensive circulation of salt solution inside the droplet31.When describing evaporation and crystallization, it is necessary to estimate not only the rate of heat transfer in the liquid, but also convection in the gas phaseThe analysis of the literature has shown that the non-isothermal crystallization at high heat fluxes is influenced by many key factors, and this impact changes with time. At that, the heat transfer coefficient cannot be taken constant, as it is done in most approximate theoretical works. Factors that lead to a higher metastable area have not been thoroughly investigated. The objectives of these studies are to determine the effect of the initial salt concentration on the salt solution supersaturation and the crystallization rate, to compare the crystallization rate in different directions of the droplet, to compare the crystallization kinetics for a droplet and layer salt solution.2 salt. The drop and layer evaporated on a horizontal metal hot wall. The wall roughness and the static contact angle θ0 of the droplet remained for a long time . When a sessile drop evaporates, various regimes are available for the behavior of the droplet contact line. For example, the constant contact radius (CCR) mode or the constant contact angle (CCA) mode . For all drops of salt solution , there was the CCR mode that was implemented before the crystallization began . Wettability affects induction time and crystallization rate. A significant increase in wettability will decrease free convection at the edges of the droplet, and will change the adhesion of impurity particles and microcrystalline nuclei relative to the solid wall. In this case, the induction period and the crystallization rate vary (since the supersaturation of solution will be higher). A change in wettability is not included in the purpose of this research. The change in wettability preserves the qualitative nature of the findings.Experiments were carried out for a droplet and a thin layer of an aqueous solution of CaClθ0, the salt solution was removed, and the wall was repeatedly cleaned with water and alcohol. The initial values of the droplet contact angle for the CaCl2 aqueous salt solution  varied within θ0 = 51–54°. For Cm0 = 50%, the contact angle varied in the range 60–66°. Changes in the wall roughness (standard deviation) were within 1–2 µm for all experiments. All experiments were carried out at a constant wall temperature Tw = 75 °C, which was maintained quasi-constant (with an accuracy of 0.6–0.7 °C) in the automatic mode by adjusting the power of the electric heater. The heater with tungsten wire was located inside the metal working cylinder. The surface temperature Tw was measured by a thermocouple. The total error of Tw measurement did not exceed 1–1.2 °C. The temperature Ts of the liquid interface was measured by a thermal imager NEC-San Instruments (640 × 512 pixels and the resolution of 10 µm) with a maximum error of 1.5 °C. A detailed scheme of the setup are given in14.The duration of each experiment did not exceed 30 minutes. The droplet contact angle was measured before and after the experiment. Before measuring Cm0 was measured using densimeters. Droplet was applied to the wall surface using automatic densimeter (the electronic dispenser of Finnpipette Novus with an error of 0.5–0.7%) with a given rate of liquid run out and a given droplet volume. The droplet application process provided good repeatability of the droplet geometry. The diameter and height of the droplet changed by no more than 5–7%. Since the water from the liquid solution continuously evaporated, the current mass concentration of salt Cm increased over time. Values of Cm were measured using the gravimetric method. Changes in the liquid mass were recorded by scales, and the current salt concentration was determined with a maximum error of less than 8–10%. For all experiments, the initial droplet and the layer height were constant (h = 2.8 ± 0.1 mm).The evaporation of aqueous salt solutions was realized at a relative air humidity of 34–40%. The temperature of the external air varied within 22–23 °C. The external air pressure was 1 bar. We used a particularly pure salt and distillate, which underwent a long degassing. The initial salt concentration jcr in the salt solution depends on the heat transfer, the heat transfer coefficients αs were measured in the experiments. During crystallization, αs changed slightly. In the calculations, the average values of αs were used for the time of crystallization. The heat transfer coefficient αs of the aqueous salt solution was determined experimentally on the basis of heat balance (Eq. αs(Tw − Ts)) due to heat exchange in the liquid was spent on cooling from water evaporation (reje) and from salt dilution (qs), as well as on cooling from convection in gas (αg(Ts − T0)) and radiation (qr),Since the crystallization rate ance Eq. . The there is the latent evaporation heat, rcr is the latent crystallization heat, je is the evaporation rate of the salt solution, jcr is the crystallization rate, αg is the heat transfer coefficient of the gas (air + water vapor), T0 is the air temperature, qr is the radiation heat, and qs is the dilution heat, and F is the surface area. Since the thickness of the crystalline crust was about 0.02 mm, and the temperature increase due to crystallization was less than 1 °C20, the value of the heat of crystallization will be of the second order of smallness compared to the evaporation heat. Then Eq. αs may be defined according to Eq. where je is determined experimentally by the gravimetric method. The temperature difference Tw − Ts is also determined experimentally. A detailed description of the method of determining αs is presented in14. The maximum relative measurement error of αs was less than 18% and corresponded to the minimum evaporation rate.where jcr), the average velocity (U) in the droplet horizontal section was measured using the Particle Image Velocity (PIV) method . Measurements of velocity fields were realized in a horizontal section of the drop at a distance of 0.6 mm from the wall surface. TiO2 particles were used to visualize the velocity field. The particles size was less than 1 μm. A detailed PIV method for the velocity measuring in a droplet of aqueous salt solution was presented in32.To assess the convection effect on the crystallization jcr is proportional to the temperature difference ∆Tcr between the solution temperature at the crystallization front and the equilibrium temperature34. The crystallization kinetics of the solution binds the crystallization rate jcr with the supersaturation S as follows (4)27,The crystallization rate T is the absolute solution temperature; k is the Boltzmann constant; σ is the interfacial tension of the solution; v is the molecular volume, and S is the supersaturation. S = Cs/Ccr, where Cs is the salt concentration in a supersaturated state of the salt solution and Ccr is the salt concentration for a saturated state of the aqueous salt solution. The principal difference between (4) and (3) is that the driving force of crystallization depends not only on the temperature, but also on the concentration of components. Supersaturation S is a function of temperature and concentration. To be more precise, the deviation from the saturation curve depends on the parameters T and C. The realization of spontaneous homogeneous crystallization requires extremely large deviations from the saturation curve. The present experiments consider the growth of the crystal film from one large crystal on the free surface of the droplet and layer. In this case, heterogeneous crystallization is realized. There are maximum three or four growing crystals along the contact line, rather than tens or hundreds of crystals. At the same time, during crystallization, the salt concentration and supersaturation change, but new crystal centers do not appear. In connection with the above, expression (4) can be used only for qualitative evaluation, which relates the crystal growth rate to supersaturation. In view of the above, a key role in the crystal growth is played not only by S, but the heat exchange. Curves in Fig. 34. This generalization allows taking into account the role of heat transfer and the role of supersaturation is more clearly visible, which explains the divergence of curves.where αs in accordance with expression (2).Table αs decreases, since the viscosity of the salt solution increases many times. The neglect of αs will result in incorrect interpretation of the results. The values of heat transfer coefficients in Table With the growth of the initial salt concentration Ts. The crystallization front for the layer has a direction from the center to the edge  increases. Thus, if crystallization depended only on the thermophysical properties of the solution and the heat transfer coefficient, the curves 1–4 would coincide. The divergence of the curves is probably related to the dependence of crystallization on S. Supersaturation S, in turn, depends on the initial salt concentration and on the direction of crystallization . For a drop, the first crystal center grows in the vicinity of the contact line, and for a layer – near the center. The higher crystallization rate for the layer than for the droplet can be explained by different induction time . For the droplet, supersaturation was lower because of the smaller induction time. It is well known that in the presence of the surface flow of Marangoni, a high concentration of microscopic particles in the form of surfactants occurs at the drop edges33. These particles can significantly lower the induction time. The influence of contamination on the induction crystallization time was recently experimentally investigated in35. In this paper, a detailed molecular analysis of the surface of different particles was carried out and correlation dependences for the time of crystallization occurrence were determined. The solution was in the supersaturation state all the time. When the surface of the nanoparticles was free of impurities, the particles did not reduce the time of crystallization beginning. In the presence of contaminations, the induction time decreased many times during repeated experiments. To identify the relation for the induction time for the droplet and the layer, further studies using different micron particles in the form of contaminants are required, which is not the subject of this article.Figure dge Fig. . As the yer Fig. . From FiK and P has the form (5)27,Another characteristic feature of the graphs in Fig. ls is the average distance that the crystallization front passes for time t. In logarithmic coordinates, all crystallization curves should have the form of a straight line with inclination c to the abscissa axis. With crystallization time, the salt concentration and the height of the drop change slightly (about 5%). Therefore, the thermal constants and the heat transfer coefficient will also vary slightly. In addition, the temperature jump on the crystallization front is less than 1 °C . However, from Fig. dK/dP ≠ const. For the droplet dK/dP > 0. For the solution layer dK/dP < 0. The absence of a constant can be explained by the change in the supersaturation S over time. A solution layer covers the entire surface of the heater. When the crystalline film covers most of the surface of the salt solution  corresponds to the beginning of crystallization; (a2) corresponds the end of crystallization). The dotted line shows the boundary of the crystal film. When the crust covers most of the surface of the liquid, the temperature of the surface of the crust Ts increases by 2–4 °C.Figure jcr on the initial salt concentration Cm0. The crystallization rate jcr = Δls/Δt was determined by the slope of the straight line at the initial moment of the crystal front movement. The displacement Δls was taken as the average displacement for the entire crystal front. Measurement of Δls was carried out by processing the photos of the camera. In the photos, the phase boundary  was always clearly distinguishable. The curve jcr = f(Cm0) has a power form. For Cm0 exceeding 30%, the crystallization rate slightly decreases. For Cm0 values less than 20%, jcr is very sensitive to changes in the initial salt concentration. Such a strong dependence of the crystallization kinetics on the concentration for low Cm0 values is due to a higher evaporation rate. At the time of crystallization for low Cm0 there was a small drop height h (less than 0.5 mm) and, accordingly, a higher heat flux from the wall. The higher jcr value results in a higher degree of supersaturation during crystallization. For higher Cm0 values, the induction time is weakly dependent on the initial salt concentration. As a result, supersaturation S and jcr are quasi-constant.Figure jcr depending on time under different initial mass concentrations of CaCl2. Crystallization is realized on the free surface of the layer , reaches a maximum and then falls. This behavior has been discussed above and is easily explained. When the crystal crust covers a negligible part of the liquid area , the temperature Ts is quasi-constant. The concentration at the crystallization front increases with time, since the solution continues to evaporate and the salt concentration increases. However, with the growth of the crust area, the temperature Ts begins to rise markedly and the crystallization curve reaches the point at which dS/dt = 0 (the maximum point). With further crystallization, the growth of Ts  leads to a noticeable drop in the supersaturation dS/dt < 0). When the crystallization front approaches the side wall of the heater, the crystallization curve tends to an extremum (minimum) when again dS/dt = 0.Figure yer Fig. . For Cm0Such a behavior with the presence of several extrema will always be observed in practice during the crystallization of solutions, if crystallization is accompanied by the following boundary conditions: (1) a thin film of a liquid solution or melt, (2) a high heat flux from the wall, (3) a relatively low crystallization rate and (4) a noticeable evaporation rate of volatile components.Cm0 = 13%. The high initial crystallization rate for t = 0 leads to a completely different behavior. The jcr curve drops down sharply at 0 < t < 40 s and only when approaching the side wall of the heater the value of the derivative djcr/dt approaches zero (dS/dt = 0). This behavior will be characteristic of solutions with a high initial crystallization rate and a low evaporation rate.Figure t ≈ 0) the ratio jcr/je < 1 (je – evaporation rate) should be performed, and for the second group (curve 2) jcr/je > 1. When modeling crystallization, it is important not only to determine the value of the heat transfer coefficient, but also to establish the crystallization group, as well as to estimate the time change in the wall temperature Tw and the heat flux qw. The rates of change dTw/dt and dqw/dt will determine the character of crystallization. Often, technologies require amorphous structures or crystals with no long-range order. It is obvious that crystals which should exclude long-term dendritic growth on a free surface, need high values of a heat flux, high initial supersaturation (or overcooling), high density of crystal centers at homogeneous crystallization, as well as small thickness of a film of a solution. Such conditions are well implemented in the plasma spraying of nanofilms. High crystallization rates can lead to a strong heating of the solution under the crystalline film and to a sharp decrease in supersaturation due to the thermal inertia of the wall. Therefore, the oxidation of the wall or the formation of a wall layer of crystalline hydrates can significantly reduce the rate of crystallization due to a decrease in thermal conductivity and heat flux.Thus, for the first group of solutions (curve 1) at the initial crystallization moment (jcr(l)/jcr(d)  is the crystallization rate for a thin layer of CaCl2 solution, and jcr(d) is the crystallization rate for a drop of salt solution. As shown in Fig. A = jcr(l)/jcr(d) has an extremum (maximum). For the time interval 0 < t < 40–50 s, the curve increases (dA/dt > 0) and reaches maximum (dA/dt = 0). Next for t > 50–60 s, dA/dt < 0. For time t = 110–115 s, the parameter A becomes approximately equal to one (jcr(l) ≈ jcr(d)). The maximum difference in the crystallization rates between the drop and the layer is approximately equal to 8. Such a non-linear behavior of the curve in Fig. S and Tw changes over time.Figure (d) Fig. , where jLet us consider the kinetics of growth of salt crystallohydrates in different directions on the surface of the droplet. Earlier it was indicated that the first active fast-growing crystallization centers occur near the contact line of the droplet. In the precursor film, the salt concentration and supersaturation are noticeably higher than at an insignificant distance from the contact line.The growth of crystals, whose size becomes higher than the critical, in the precursor film. In the solution  there are much more crystalline nano-micro nuclei that have not reached a critical size. Spontaneous rapid growth is realized for crystals whose size has reached more than a critical value . Thus, it can be reasonably assumed that the size of other crystals is several orders of magnitude smaller. The crystal growth time for a size of 0.1–1 mm is about 1 second. The growth of crystals along the contact line is one hundred seconds . Thus, the resulting visualization is quite enough.S ≈ 1. The growth is realized in the direction (lcl) of the contact line . The crystal enters the region with ine Fig. , where t0 s Fig.  correspoion Fig. . At t = ls) of the drop center . As a result of water evaporation from the surface of the droplet, the salt concentration and supersaturation increase and, accordingly, the crystallization rate increases with time. Due to the contact line curvature and the curvature of the droplet surface, the crystallization rate increases many times.After the entire precursor film is covered with salt crystallohydrates, the growth of the film is realized in the direction   Fig.   is formed due to the Marangoni flowrop Fig. . The forl(−s)  (dendrites are removed from the center of the drop). If crystallization lasts for more than an hour, the area of the crystal film will increase 3–4 times. Figure 2·H2O breaks up. With further heating of the film, the thermodynamic equilibrium is disturbed and the evaporation of water is replaced by adsorption of water vapor. The destruction of the crystallohydrates allows the salt molecules to diffuse towards the edges of the film. It is characteristic that the crystallization rate j−s)cr( in the direction l−s)( is much lower than towards l(s) (jcr(s)/j−s)cr( ~ 0.01–0.02).In fact, the direction of growth of crystallohydrates in Fig. −s) Fig. , oppositl(s)) is not always realized. If crystallization in the droplet occurs on the wall without heating (T = 20–25 °C) and at high air humidity, the evaporation of the droplet stops . The absence of evaporation will lead to the absence of supersaturation and stop the growth of dendrites in the direction of l(s). In this paper, supersaturation in the vicinity of the droplet center increases due to high heat flux and relatively high evaporation rate.It should be also noted that the growth of dendrites in the direction of the center of the drop  is taken along the contact line of the drop, and the rate jcr(s) – in the direction of the center of the drop (jcr(cl) = Δlcl/Δt, jcr(s) = Δls/Δt). Moreover, jcr(s) is the average value of the rate for the full crystallization time (jcr(s) = const). The lcl displacement is taken as the total displacement from all growing centers. For time 0 < t < 26 s, the ratio Y decreases as the concentration and S between adjacent growing centers decreases. At the moment of appearance of the third center there is a jump in the rate jcr(cl) and jcr(cl) further increases due to the increase in S.The ratio of crystallization rates in two directions t > 30 s is due to the extremely small height h1 of the solution in the precursor film (0.01–0.1 mm). As a result, convection in the film is suppressed. The free convention velocity in the precursor film has an order of vc = 0.0001–0.001 mm/s (Micro PIV measurements). The diffusion rate can be estimated as a ratio of the diffusion coefficient to the layer height vd = D/h1 = 0.0001 mm/s. Near the crystallization front (between neighboring growing centers), the salt concentration will fall. During crystallization, the salt concentration between closely spaced crystals decreases and this decrease does not have time to be compensated by diffusion. Away from the crystalline centers, the evaporation of water leads to the fact that the rate of evaporation (ve = 0.01 mm/s) exceeds the rate of convection (vc = 0.001 mm) (vev > vc). The slower the crystal front moves along the contact line, the greater the supersaturation at a distance from the front is.A significant increase in the salt concentration for ls), the solution height increases many times in comparison with the height of the precursor film. As a result, the role of convection increases many times and supersaturation in ls direction will be lower than in the vicinity of the contact line. Measurements using the PIV method show that the average solution velocity in the horizontal section of the droplet has the order of 0.03–0.04 mm/s /jcr(s) ≫ 1 will be realized. The maximum value of the Y parameter reflecting the crystallization anisotropy is approximately 20.During crystallization in the direction of the droplet center : the solution in the capillaries; the rod submerged in the liquid; the film of solution in contact with the side walls; a particle floating on a liquid surface, etc. These problems are frequent in modern technologies associated with crystallization and evaporation. Taking into account anisotropy will ensure a more correct modeling of the crystallization rate and the control over the properties of the obtained materials.Thus, an important conclusion may be formulated from the experimental data on crystallization in a drop of salt solution. In the vicinity of the precursor film of a drop, a higher supersaturation The kinetics of crystallization in the drop is found to be fundamentally different from the thin layer (film). The appearance of the first growing crystal in the drop occurs near the contact line. In the salt solution film, the beginning of crystallization takes place near the center of the layer. The crystallization rate in the layer is many times higher than the velocity of the crystal front in the drop.jcr on the initial mass concentration of salt Cm0 is highly nonlinear. At low initial salt concentrations (Cm0 < 20%), jcr is highly sensitive to changes in Cm0. For Cm0 > 30%, jcr is quasi-constant. This nonlinear character is determined by the supersaturation behavior in the solution.Experimental data show that the dependence of the crystallization rate S for the droplet and the layer, as well as with the dependence of the supersaturation on the initial salt concentration.For different experimental conditions, the heat transfer coefficients are determined to differ several times. Crystallization curves in dimensionless coordinates have been obtained taking into account the thermophysical properties of the solution and convection inside the liquid. A significant divergence of curves shows that it is not enough to take into account only the thermophysical properties and the heat transfer coefficient. The discrepancy between the experimental data is associated with a change in supersaturation At the crystallization front there is a growth of dendrites both for drops, and for a layer. The form of dendrites changes over the crystallization time.Anisotropy of crystallization is observed for a drop of salt solution. The rate of growth of salt crystallohydrate in the direction of the contact line is many times higher than the rate in the direction of the center of the droplet.jcr(cl)/jcr(−s) ≫ 1, for the third mode jcr(cl)/jcr(s) ≫ 1, the fourth mode is characterized jcr(s)/jcr(−s) ≫ 1).Four characteristic modes of crystallization to a drop of salt solution, which differ in the direction of dendrites motion and the rate of crystal growth, have been distinguished (for the second mode The maximum ratio of the crystallization rate in the direction of the contact line to the rate in the direction of the droplet center reaches 20 times.


One of the new methods in the removal of impurities from the wheat grains is the electrostatic separation of particles based on the differences in their conductivity and permittivity. The moisture content of particles directly influences their electrical properties. In this study, by developing a cylindrical capacitor in an electrical circuit, the electrical capacitance of wheat grain and cluster straw particles in two varieties at four levels of moisture content  and five frequency levels  is estimated and their dielectric constant is calculated. Results showed that increasing the moisture content of straw particles and reducing the frequency compared to the seeds had significant effects on dielectric constant. The dielectric constant of grain particles was higher than the straw at lower moisture content and in high values of moisture content, the dielectric constant of straw particles was higher than the seeds. This study shows that increasing the moisture content of straw particles and reducing the frequency compared to the seeds had significant effects on dielectric constant. The dielectric constant of grain particles was higher than the straw at lower moisture contents and in high values of moisture content, the dielectric constant of straw particles was higher than the seeds. According to the FAO reports, the annual production of wheat in all over the world and Iran is 750 and 11.1 million tons in 2016, respectively , as well as transportation and processing Baryeh, . One of Information on the dielectric constant of grain has resulted in the development of a capacitance type grain moisture meter. Knowledge of the dielectric properties of seeds, grains, and other products is useful in many applications, including the prediction of the behavior of materials when exposed to electrical fields. The dielectric properties of food and agricultural products are basically used to describe the thermal behavior of materials when exposed to high‐frequency electrical fields in dielectric thermal processes and the development of appropriate techniques for the rapid moisture content determination of agricultural products  is defined as the ratio of absolute permeability to the vacuum permittivity , impedance analyzer, and scalar and vector network analyzer  in four levels of moisture content  and five frequency levels  is measured and their dielectric constant is calculated.2The samples of wheat in the form of spikelet from two cultivars of Chamran2 and Mehregan were prepared from the farm of Lorestan Agricultural Research Center and were threshed and cleaned manually. Straw masses mostly included lemma and palea and less amount of straw, rachis, and pedicel. Initial moisture content of samples which included grain and straw were measured by oven method. The moisture content of the samples was increased by flooding method in distilled water in variable time (5–25 min) to obtain 5 levels of moisture C=2πεmC is the measured capacitance, PC1 and PC2 are the polyethylene capacitance, and eqC is the equivalent capacitance of the sample (sC) and air gap (airC) that existed among the grain and straw mass in the container. eqC is the sum of the capacity of the material and the air contained in its porosity space which is series with polyethylene coatings and can be calculated by Equations Ceq=1P), then the height of air gap (ah) is P × h and the height of materials in capacitor is (1 − P) × h. Therefore, the capacitance of air and materials and their dielectric coefficient can be calculated with the following equations.If the ratio of air gap volume to the total volume of capacitor that was filled by the material (wheat and straw) is defined as the porosity  and the moisture content (Mc %) data of different materials  in different frequencies were fitted to power, exponential, and polynomial models. The models were evaluated according to the statistical criterion R2 for verifying the goodness of fit. The best model with the highest R2 was selected to predict the rε of materials as a function of the moisture content. Table After measuring the moisture content of the samples (grain particles and straw) and transferring them to the cylindrical capacitor, the capacitor was placed in the circuit according to the Figures 3The obtained dielectric constants of wheat grain and cluster straw samples at 25°C and four moisture content levels and frequency range from 1 to 500 kHz are shown in Figure db) fitted by regression analysis to the experimental data in 5 levels of frequency using the general quadratic equation as: rε = a(Mc(%db))2 + b(Mc(%db)) + c based on model parameters  and R2 are given in Table Results of the polynomial model of dielectric constant as a function of moisture content  were also significant at 1% level.V1 at 1 kHz and V2 at 500 kHz, respectively.Tables T. dicoccum in the frequency range of 20–200 kHz in a moisture content of 11.4%, reducing the dielectric constant, conductivity, and capacitance of the particle. Guo et al. (Mc% from 10% to 20%. Similar results were obtained by Berber et al. (These results were similar to the results of other researches. Nelson, Guo, Trabelsi, and Kays  reportedo et al.  reportedr et al.  in reduc4Increasing moisture content in most agricultural products due to the presence of water molecules in the particles that have a high dielectric coefficient and high electrical conductivity reduces electrical capacities and increase electrical conductivity and their dielectric constant. This phenomenon is more significant in low frequencies. However, this process tends in straw to be faster than wheat grain particles, so making it difficult to separate straw and grain in electrical fields at straws with moisture content more than 12%.The authors declare that they do not have any conflict of interest.This study does not involve any human or animal testing.