Nonlinear interactions between X-rays and long wavelength radiation can be used as a powerful atomic-scale probe for light-matter interactions and for properties of valence electrons. However, reported X-ray nonlinear effects were small and their observations required tremendous efforts. Here we report the observation of strong nonlinearities in parametric down-conversion (PDC) of X-rays to long wavelength radiation in gallium arsenide and lithium niobate crystals, with efficiencies about 4 orders of magnitude stronger than the efficiencies measured in any material studied before. Furthermore, we show that the efficiency in the ferroelectric phase of strontium barium niobite is two orders of magnitude stronger than in its paraelectric phase. This observation suggests that the lack of inversion symmetry is the origin for the strong observed nonlinearity. Additionally, we demonstrate the ability to use the effect for the investigation of the spectral response of non-centrosymmetric materials at wavelengths ranging from infrared to soft X-rays. Here, the authors report parametric down-conversion of X-rays into long wavelength radiation in gallium arsenide and lithium niobate crystals, with efficiencies about 4 orders of magnitude stronger than the efficiencies measured in any material studied previously. They explore the lack of inversion symmetry as a possible physical mechanism. However, most approaches utilize long wavelength radiation, thus cannot probe microscopic scale information, such as the valence electron redistribution in response to the application of external electric field or illumination. This is due to the fundamental limit of resolution of waves, which limits the resolution to about the half of the wavelength. Although X-ray-based techniques are capable of probing atomic-scale structures, they interact mainly with core electrons, thus provide very limited information on valence electrons and on their atomic-scale interactions with long wavelength radiation2. There are several methods that utilize Bragg diffraction to reconstruct the valence charge density by subtracting the theoretical contribution of the core electrons from the measured intensity4. However, those methods are very limited3 and the experimental results exhibit large variance and are often not reproducible4. Moreover, those methods cannot provide any spectroscopic information about the optical response of valence electrons.Optics and photonics is a major field of research that is important for fundamental sciences and has led to many practical applications and inventions. This field, which covers a broad range of the electromagnetic spectrum is, to a large extent, based on light-matter interactions. It is clear that a better understanding of the light-matter interactions is crucial for further developing of photonics-based research and technologies. Indeed, the approaches and techniques aiming at improving the knowledge of light-matter interactions are diverse and attract a great deal of attention6 proposed a method to measure the microscopic properties of valence electrons in solids by using nonlinear wave mixing of X-rays and long wavelength radiation such as UV and visible. In essence, the effect can be viewed as X-ray scattering from optically modulated valence electrons, as is shown schematically in Fig. 16. The effect of difference frequency generation of two X-ray pulses was studied theoretically as a probe for microscopic properties at the atomic scale18. Moreover, the effect of two photon absorption has been used recently for nonlinear spectroscopy19. The nonlinearity in X-ray and long wavelength mixing was discussed by numerous theoretical works25. However, to date, nonlinear interactions between X-rays and long wavelength radiation have been observed only in simple crystals such as diamond and silicon15. The typical efficiencies and the signal-to-noise ratios that have been reported are very small and are barely sufficient for the measurements. The experimental results have been interpreted by using simple classical or semiclassical models for the nonlinearity with reasonable agreements where the long wavelengths are either in the range where the crystals are transparent14 or in the extreme ultraviolet regime with only one isolated resonance15.About half a century ago, Freundωp = ωs + ωi. Due to the high absorption in the UV range, the UV photons are completely absorbed and only the X-ray photon can be detected. However, since the photons are always generated in pairs, the rate of the X-rays depends also on the optical properties of the material in the UV range, hence the measurement of X-rays is sufficient to retrieve the information that can be probed by the UV photons. The selection of the wavelengths of the generated beams is done by using the requirement for momentum conservation (phase matching) that imposes a relation, which depends on the refractive indices of the material, between the propagation angles of the beams and their photon energies. Since the wavelengths of the X-ray photons are on the order of the distances between atomic planes, we utilize the reciprocal lattice vectors to achieve phase matching, which is given by kp + G = ks + ki where kp, ks, and ki are the wavevectors of the pump, signal, and idler beams, respectively and G is the reciprocal lattice vector.In the effect of PDC of X-rays into longer wavelength radiation, an input X-ray pump beam interacts with the vacuum fluctuations in the nonlinear crystal to generate photon pairs at lower frequencies. Energy conservation implies that the wavelength of one of the generated photons is in the X-ray regime  and the wavelength of the second photon is in the UV or visible range (denoted as idler) where the sum of the frequencies of the generated photons is equal to the frequency of the input X-ray photon, namely 3), which are stronger by orders of magnitude from the background. Our measurements of the effect of PDC of X-rays into the UV and optical regimes in these crystals exhibit efficiencies that are about four orders of magnitude stronger than the efficiencies measured in any crystal, in which X-ray PDC has been observed so far. This is in sharp contrast to the prediction of the existing theories. Our results indicate an unrevealed underlying physical mechanism that is responsible for the strong nonlinearity we observed. As a first step in the direction of understating the observed strong nonlinearity we explore the lack of inversion symmetry as a possible physical mechanism. In addition, we demonstrate the ability to perform spectroscopic measurements in a very broad wavelength range that enable the retrieval of information on the band structure, density of states, and atomic resonances in the crystals. As such, our work opens exciting possibilities for future research of nonlinear X-ray optics in complex non-centrosymmetric materials and surfaces, and for the development of advanced spectroscopy techniques that rely on these effects.In this work we report on the observation of prominent large nonlinear effects in the non-centrosymmetric crystals gallium arsenide (GaAs) and lithium niobate . The general trend far from atomic resonances is that the efficiency drops, as the idler photon energy increases. This is mainly because the current density, which is proportional to the joint density of states, decreases when the idler photon energy increases25. In addition, the theory, which led to a good agreement in the previous experiments15, underestimates the efficiencies for GaAs and LiNbO3 by about four orders of magnitude. This ratio is maintained in the whole range of measured photon energies. These pronounced discrepancies indicate on a new source for the strong nonlinearity, which was not considered in previous works.We begin by showing the very strong efficiencies of the signal of the PDC of X-rays into UV in both GaAs and LiNbOOf importance, the measured efficiencies presented in Figs. 3 with reciprocal lattice vectors of nearly equal magnitudes. Although the X-ray scattering factors for these reciprocal lattice vectors are comparable, the efficiencies of the PDC effect for reciprocal lattice vectors, which are parallel to the c-axis of the crystal, are considerably larger. For example, the effect measured for the (0 0 6) atomic planes is two orders of magnitude larger compared to the (1 1 0) atomic planes. This can indicate that the nonlinearity depends on the direction of the permanent dipoles in the crystal and on symmetry of unit cells or the molecules in the materials. It is remarkable to note that for the visible range, the nonlinear coefficient is the largest for polarizations along the c-axis27. It is very likely that the electric field of the idler that leads to the largest efficiencies we observed in LiNbO3 is also in the direction of the c-axis. This is consistent with the theories that predict that the largest efficiency for selected atomic planes is obtained when the electric field of the idler is parallel to the reciprocal lattice vector 15.Another interesting result becomes apparent when comparing the efficiencies for LiNbO28), but can be attributed to deeper atomic resonances of the arsenic atoms. The spectrum of the GaAs (4 0 0) atomic planes is shown in Fig. p valance electrons in gallium atoms. The spectrum measured for the GaAs (3 1 1) atomic planes shows again a maximal efficiency slightly above the band gap. In addition, we observe a sharp change in the trend of the spectrum near 20 eV. This feature is different than those discussed previously and cannot be interpreted as a resonance (from the band structure or atomic transitions).After we show the observation of the very strong nonlinearities, we elucidate the origin of the effect and demonstrate the ability of its application for broad range spectroscopic measurements by exploring the spectral dependencies of the effect that are shown in Figs. 3 crystal are shown. The peak at 5.9 eV for LiNbO3 (1 1 0) and LiNbO3 (3 3 0) atomic planes and the broad structures we observed for the LiNbO3 (−1 1 10) atomic planes, which are shown in Fig.29 or to the ionization energy for the 2s valance electrons in lithium atoms. The peak at 7.5 eV, which appears in Fig. s electrons in niobium atoms. The peaks at 12 and 15 eV, which appears for the LiNbO3 (−1 1 10) and the LiNbO3 (3 3 0) atomic planes relate either to higher band transitions or to a deeper atomic level. Figure 3 (0 0 6) atomic planes. In these measurements the atomic planes that participate in the effect are directed along the polarized direction on the crystal. This spectrum shows no prominent features.In Fig. 25. This suggests that PDC of X-rays into UV can be used for the study of electronic density of states and band structures in solids.The main implication of the measured spectra is that the effect of PDC of X-ray into longer wavelength radiation can be used as a powerful tool to investigate phenomena in solid-state physics and in atomic physics. Generally speaking, it is likely that the lower idler energies correspond to solid-state physics and the higher energies to atomic physics, but to exactly distinguish these effects, a more detailed theoretical model is needed. Actually, the transition between the range where the dominant physical mechanism is solid-state physics and the range where the atomic physics dominates has been rarely studied. Hence, we foresee that PDC of X-rays into UV will be used as a powerful tool for studying this range, which will open an opportunity to study a broad range of physical phenomena with one experimental setup. We note that the peaks at the band gap of the crystal that appear in most of the measurements can be explained by the divergence of the joint density of states3 are stronger than in GaAs. This can be explained by noting that in LiNbO3 there are fewer atomic resonances in the measured energy range. The different visible features in each of spectra can be explained by the nonlinearity, which depends also on the reciprocal lattice vectors themselves and on the distributions of the electronic wave functions. A comprehensive understanding of the spectra should include analysis of the nonlinear conductivity for different reciprocal lattice vectors while considering the selection rules between transitions.Another pronounced property that is common to all spectra is that apart from local enhancement near resonances, the efficiency decreases with the idler photon energies. However, the efficiency spectra are very different and depend on the atomic planes that are used for the phase matching. In addition, the efficiency dependencies on the idler energy in LiNbO11. This type of second-order nonlinearity is non-zero even in centrosymmetric martials but significantly weaker than the ordinary second-order nonlinearity in non-centrosymmetric materials in the optical regime. It is therefore possible that the lack of inversion symmetry contributes significantly to the strong nonlinear effects we report here, which mixes between X-rays and long wavelengths. While a comprehensive model that describes the interaction that we have measured in our experiments is still not available, we can test this hypothesis experimentally by comparing the PDC signal in the non-centrosymmetric and in centrosymmetric phases of the same crystal. A good example for such a crystal would be a ferroelectric crystal such as LiNbO3 since the ferroelectric phase is known to be non-centrosymmetric whereas the paraelectric phase is centrosymmetric. Since the Curie temperature (Tc) of LiNbO3 is 1145 °C, we choose to explore the dependence on the inversion symmetry in Sr0.6Ba0.4Nb2O6 crystals, where Tc is between 340 and 350 K30, thus more accessible with conventional heaters. We performed our measurements on beamline I16 of the Diamond Light Source26, with a setup, which is similar to that in Fig. Tc, SBN is ferroelectric and has a tetragonal non-centrosymmetric crystal structure. Above Tc, the structure of SBN is cubic. Although the crystal is not completely centrosymmetric in this phase, due to the presence of various types of atoms in its unit cell, the degree of the inversion symmetry is much higher compared to the ferroelectric phase.We note that both inspected crystals have non-centrosymmetric crystal structures. This is in contrast to silicon and diamond crystals that have been investigated before. This observation raises the question of the importance of inversion symmetry to nonlinear effects with X-rays, which has been ignored in all previous publications. It is well known that in the optical regime the lack of inversion symmetry is essential for second-order nonlinearities; however, thus far, X-ray nonlinearities have been considered as resulting from interactions beyond the diploe approximation that can be viewed as X-ray scattering from optically driven oscillationsThe angular dependence of the PDC signal in both phases is shown in Fig. 31. We have provided evidence that the lack of inversion symmetry is the physical mechanism for the strong nonlinearity in non-centrosymmetric crystals. Consequently, it is likely that our method can be applied to a large class of non-centrosymmetric materials and will lead to the development of advanced tools for the investigation of inversion symmetry breaking mechanisms, anharmonicity, and interfaces on the atomic scale. Our work demonstrates the possibility to utilize the effect of PDC of X-rays into visible and UV radiation as a powerful tool to probe numerous physical phenomena as it covers a large range of energies and provides structural and spectroscopic information in a single measurement. We expect that the full understanding of the effect will open a large range of opportunities to probe properties of solids and atoms, which are currently obscured due to the limitations of the present-day methods, hence advance the understanding of their functionality. Our work can be extended into the studying of the dynamics of the valence electrons and electronic excitations in a broad spectral range. This can be done by combining the X-ray input beam for the PDC with an additional optical laser in a pump-probe configuration. These types of experiments will be of interest with X-ray free-electron lasers, which provides femtosecond pulses as compared to picosecond pulses available with storage ring-based synchrotrons. We expect that the data acquisition time with the new emerging high repetition-rate free-electron lasers will be content32.In conclusion, we have reported the measurement of non-predicted strong nonlinearities leading to efficiencies that are larger by about four orders of magnitude than previously reported efficiencies of PDC of X-rays into long wavelength radiation. These high efficiencies cannot be explained by existing theories and indicate an unexplored physical underlying mechanism. We note that the angular dependence of the effect, the dependence on the pump photon energy, and the agreement with the phase-matching calculations constitute strong evidence that the effect we have measured is indeed PDC and not any other known inelastic effect. Furthermore, we have found that at the edges the PDC efficiency is reduced in contrast to inelastic scattering effects3 experiments. First, we describe the experimental setup for the GaAs experiment, which we performed at Diamond Light Source on beamline I16. The input power is approximately 1013 photons/s. The input beam is monochromatic at 10.3 keV and is polarized in the scattering plane. The dimensions of the beam at the input are 20 µm  × 180 µm . The nonlinear crystal is a GaAs crystal with a thickness of 350 µm. The analyzer is an Si (1 1 1) triple-bounce analyzer and the detector is a Medipix multipixel detector with pixel size of 55 µm × 55 µm. The overall spectral resolution of the system is about 1 eV. The experimental setup, which we use for the SBN measurements, is similar to that of the GaAs. A minor difference is the input energy, which is at 10 keV. Additionally, we use a nitrogen gas jet heater to heat the crystal.We provide further information on the experimental setups, which we used for both the GaAs and the LiNbO3 measurements at the ESRF on the ID20 beamline with a similar setup. The input power is approximately 5 × 1012 photons/s. The input beam is monochromatic at 10 keV and is polarized in the scattering plane. The dimensions of the beam at the input are 0.4 mm × 0.4 mm. The nonlinear crystal is a polished LiNbO3 crystal with dimensions of 7 mm × 7 mm × 5 mm. The analyzer is an Si (4 4 0) double-bounce analyzer and the detector is a Medipix multipixel detector with a pixel size of 55 µm × 55 µm. The overall spectral resolution of the system is about 0.3 eV.We performed the LiNbOIn all of the experiments the scattering plane of the analyzer was perpendicular to the scattering plane of the nonlinear crystal, in order to decouple the analyzer angle from the signal angle.We add further details on the data analysis procedure. We select the photon energy by tuning the analyzer angle. At each of the photon energies we scan the angle of the sample and record the intensity on the area detector for exposure times between 0.01 and 1 s. At each angle of the sample we sum over the counts in the area within full-width at half-maximum in the horizontal axis of the detector. We then plot the rocking curve (the dependence of the efficiency on the angle of the sample) and find its peak value. We repeat this procedure for the entire range of photon energies and plot the dependence of the peak value of the rocking curve as a function the photon energy to construct the spectra that we plot in Figs. ωp = ωs + ωi, we determine that this position corresponds to the idler energy of 0 eV, i.e. the elastic energy. Next, we detune the analyzer angle to fit for signal energy of 15 eV off the elastic energy. Energy conservation determines that this signal corresponds to idler energy of 15. We use linear interpolation to determine the idler energy along the vertical direction of the detector. The transformation of the horizontal position along the detector into degrees is performed as follows. We measure the Bragg horizontal position. This position is set to be the calculated Bragg angle. Next, we calculate the deviation from the Bragg angle by dividing the horizontal distance along the detector by the distance of the detector from the crystal. We repeat the calibration procedure for each of the atomic planes.To calibrate the vertical pixels of the detector with respect to the idler energy, we use the following procedure. We tune the sample and the detector arm to the Bragg angles and the crystal analyzer to observe the highest intensity. This condition corresponds to the elastic scattering. We then find the vertical position on the detector where the Bragg signal is observed. By using the energy conservation equation Supplementary InformationPeer Review File


The world is changing at a rapid rate, threatening extinction for a large part of the world's biota. One potential response to those altered conditions is to evolve so as to be able to persist in place. Such evolution includes not just traits themselves, but also the phenotypic plasticity of those traits. We used individual‐based simulations to explore the potential of an evolving phenotypic plasticity to increase the probability of persistence in the response to either a step change or continual, directional change in the environment accompanied by within‐generation random environmental fluctuations. Populations could evolve by altering both their nonplastic and plastic genetic components. We found that phenotypic plasticity enhanced survival and adaptation if that plasticity was not costly. If plasticity was costly, for it to be beneficial the phenotypic magnitude of plasticity had to be great enough in the initial generations to overcome those costs. These results were not sensitive to either the magnitude of the within‐generation correlation between the environment of development and the environment of selection or the magnitude of the environmental fluctuations, except for very small phenotypic magnitudes of plasticity. So, phenotypic plasticity has the potential to enhance survival; however, more data are needed on the ubiquity of trait plasticity, the extent of costs of plasticity, and the rate of mutational input of genetic variation for plasticity. For some of those threats—over‐exploitation of resources, exotic toxins, intense nuclear radiation, the complete destruction of habitat—there is little that species can do. But for some types of threats, especially climate change, there are some potential responses that permit persistence Holt, . ClimateThe effectiveness of both responses depends on the rate and magnitude of environmental change. Even with ample genetic variation, the rate of an evolutionary response can be outpaced by sufficiently rapid shifts in the environment. A potential solution is phenotypic plasticity . We varied the within‐generation correlation of the environment at the time of development and selection (ρ), as that determines the optimal amount of plasticity  added to both. Finally, because costs of plasticity can substantially constrain plasticity evolution  that determines its survival to adulthood (when selection takes place). Random mating (including the possibility of selfing) and reproduction then occur, after which all adults die.We used an individual‐based model (implemented in Fortran 90) to simulate the effects of phenotypic plasticity on environmental rescue of a population in response to a change in the environmental mean value that happens either once (a step change) or continuously (a linear change). Random variation was added to this changing mean. The model is based on that of Bürger and Lynch , to whic2.1ijT) of the ith individual developing in generation j is given by:ijkN are allelic values at the n (10) nonplastic loci and ijz is a zero‐mean, unit‐variance‐independent Gaussian random deviate (the random component of phenotype); these are the components of the original model of Bürger and Lynch  plastic loci of this individual and jE is the environment at the time of trait development in generation j. For a clone of genetically identical individuals, taking the expected value of Equation  with an intercept of a  and a slope (d) equal to the product of parameter b and the sum of plastic allelic values. The plasticity parameter (b) determines the magnitude of the plastic response by the phenotype for a given plastic genetic value, scaling the phenotypic variation due to plasticity relative to the variation due to the nonplastic alleles. For a value of b = 1, the sum of alleles at plastic loci would be 1 for individuals perfectly adapted by plasticity alone .An organism's total phenotype is the sum of three components: contributions from nonplastic loci, contributions from plastic loci whose effect depends on the developmental environment, and a random component. The phenotype  that was a Gaussian function of the difference between the individual's phenotype and an optimum phenotype for its environment :ω determined the strength of selection on the phenotype . Fitness is the product of ijW and fecundity. The survival probability was 1 for an individual with trait ijT equal to the optimum Topt,j and decreased as the absolute value of the difference between ijT and Topt,j increased. The effective selection was stabilizing when the population mean trait value was near the optimum, and directional when the mean was far from the optimum.Selection occurred during survival from juvenile to adult, which had a probability  the cost of plasticity . This cost of plasticity was independent of allelic expression; even when plasticity was not expressed , the plasticity loci still had an effect on fitness. An example of such an independent cost would be maintaining additional cellular or organismal machinery needed to translate an environmental signal into a phenotypic change  as in Chevin and Lande . Includi2.3Reproduction followed selection. Density was regulated by limiting the number of matings to a value of 256. If there were fewer than 256 adults, then all adults mated as a female; if there were more than 256, that number was chosen at random (without replacement) to act as females. µ, µ being the per‐locus mutation rate . If a mutation occurred, a random locus was selected and a zero‐mean Gaussian with variance α2  was added to the previous allelic value; the mutation rate and variance for plastic and nonplastic alleles were the same. After the alleles of each offspring were determined, the random component of its phenotype was chosen. Because the plasticity parameter (b) determines how genetic variation gets translated into phenotypic variation, a greater value means that the same mutational change has a greater phenotypic effect. A population with a higher plasticity parameter therefore would be expected to be able to plastically generate new phenotypic variation at a higher rate.During reproduction, there was free recombination. Allelic values could take on any real value. Each offspring haplotype mutated with probability  was determined by drawing an independent zero‐mean Gaussian with variance τ2. The optimum at the time of selection for that generation  was another zero‐mean Gaussian with variance τ2 and a correlation coefficient of ρ with lE, calculated as Topt,l=ρEl+τ1-ρ2ξl, where lξ is an independent zero‐mean, unit‐variance Gaussian deviate. This variation in the environment determined the amount of plasticity at the end of the equilibration period. We always set the cost of plasticity equal to 0 during the equilibration period, so the mean plasticity slope was expected to equilibrate at a value of ρ. The initial value of each allele was an independent Gaussian. We performed initial simulations over a range of parameter sets to determine the means and variances that would speed the approach to equilibrium within the 2000 generations. Initially, nonplastic alleles had a mean of 0 and a variance of 0.02/(2n), while plastic alleles had a mean of ρ/(2m) and a variance of the lower of either 0.375/(2m) or 0.05/(2mbτ). These initial values allowed the population genetics to equilibrate within the 2000‐generation period.For all simulations, a population was initiated with 256 adults with random nonplastic and plastic alleles. There was then a 2000‐generation equilibration period, with the mean phenotypic optimum held constant at 0, to allow the population to reach mutation–selection–drift equilibrium. For generation 2.5j was determined by taking the mean environment and adding a random value. The procedure was similar to that used during the equilibration period. The environment at the time of development was the sum of the mean environment and an independent zero‐mean Gaussian with variance τ2 (je), while the environment at the time of selection was the sum of the mean environment and ρej+τ1-ρ2ξj, where jξ is an independent zero‐mean, unit‐variance Gaussian deviate. In some cases, the variance of the random environmental component differed between the equilibration period and the environmental change period.  The magnitude of the step change varied from 2 to 6, while for continual change, the total change varied from 20 to 200, depending on the rate of change; for comparison, the width of the fitness function, ω, was 1. The difference between the environments at the time of selection and development was Gaussian with a mean of 0 and a variance of 2(1 – ρ)τ2, so the expected value of the magnitude of the difference was 2τ1-ρ/π. With our standard parameters, this is about 0.4, while its maximum value is less than 0.8, somewhat less than the step change but much less than the total continual change. Unless otherwise indicated, after the change occurred or started all simulations were continued for 1,000 generations or until the population went extinct. For continual change, in our model the phenotypic response of a plastic individual got larger, even if there were no additional genetic changes, because of the change in the environmental inducer. Thus, we assumed that there were no intrinsic morphological, physiological, or developmental limits to the plastic response.After the equilibration period, for the step change the mean environment was abruptly increased to a fixed positive value; for continual change, the mean environment increased by a fixed increment each generation, resulting in a linear change over time. In either case, the value of the environments at the time of development and at the time of selection in generation 2.6T¯opt,j, so that a perfectly adapted population has a relative phenotype of 1. Its relative plasticity is the mean plastic component of phenotype . These effects reversed for greater values of b, in which the plasticity benefit outweighed the cost. Not surprisingly, the final relative plasticity was lower than the no‐cost case and lower than when fluctuations were absent  had much larger effect on the probability of survival, compared to the no‐cost scenario, especially when the magnitude was the same before and after the step change  was greater than the no‐cost scenario (0.2), because those values were in a range to see the effects. Lower values of b with a cost would have resulted in almost no survival, and higher values for the no‐cost scenario would have resulted in no differences in the amount of plasticity .The magnitude of the environmental fluctuations  substantially increased the probability of survival for the first 1,000 generations  is not shown because it resulted in zero survival over the entire range of rate changes used here . Extinction, when it occurred, happened almost exclusively in the first 20 to 40 generations  That lag was close to zero for all rates of change, and little affected by the amount of plasticity, commensurate with a relative plasticity of 1.0 Figure e. This lτ is more complex, with only the highest τ showing clearly lower survival, likely because of contrasting effects of the magnitude of variation before and after the change. In both cases, τ had almost no effect on either the amount of plasticity, which was always close to 1.0  decreased the survival probability Figure A; as wit Figures C, S6C, o Figures E, S6E.3.4b = 0), except for the greatest amount of plasticity. This result is very similar to the model that lacked environmental fluctuations  before rising steadily again, giving a final plasticity approximately proportional to the value of b, again similar to the no‐fluctuation model  decreased the probability of survival  can often foster population persistence in temporally changing environments. In some circumstances, even though extinction ultimately occurs, plasticity can be selected for and act to delay that extinction  make simplifying assumptions about the genetic variation that permits evolution by natural selection. Our individual‐based simulations reveal that there can be strong, and at times surprising, patterns that emerge in or because of the dynamics of genetic variation. A species may show high plasticity over long spans of evolutionary history, not because of relentless selection for plasticity, but because a past bout of strong selection led to fixation of a plastic phenotype. At the same time, that selection may corrode available heritable variation in plasticity so that future reductions in plasticity are constrained. Moreover, the dynamics of genetic variation in the nonplastic and plastic components of a phenotype can be mutually interdependent, leading to complex temporal patterns in genetic variation . Our model allowed us to explore a variety of general scenarios. Models and information on particular species will be necessary to predict and manage climate change responses.Our results point to a need for additional information about phenotypic plasticity coupled with more specific models. The meta‐analysis of the frequency of plasticity (Palacio‐López et al., All authors contributed to the development of the ideas and the writing of the manuscript. The models were coded and run by MB. Click here for additional data file.


Arthrospira platensis and to assess the effectiveness of ethanol production from preconditioned biomass. The study is aimed at the selection of the most advantageous parameters of thermochemical hydrolysis to reach the experiment variant with the best effects, degree of polysaccharide degradation and effectiveness of alcohol fermentation. The experiment was divided into two stages; in stage I, the possibility of obtaining fermentable sugars by hydrothermal and chemical treatment of the substrate was tested. Stage II involved an assessment of the effectiveness of the pretreatment methods to produce bioethanol in alcohol fermentation. Yeast used in industrial ethanol production—Saccharomyces cerevisiae As4—was used in the alcohol fermentation. The results have shown that the temperature of 150 °C was the most beneficial for the process of thermohydrolysis, and the mash in the microwave-heated sample contained the highest concentration of alcohol (0.97 g/l), which is 98% more than in the control mash and 37% more than in the conventionally heated sample.The search for a balance between the energy-related challenges of the future and providing nutritional security has resulted in the development of a market for biofuels of successive generations. The larger their portion in biofuel production, the less the prices of agricultural products will increase. The use of algae, cyanobacteria and aquatic plants in the production of liquid fuels is an alternative. The aim of this study was to determine the effect of thermal hydrolysis on degradation of polysaccharides contained in biomass of cyanobacteria  The process efficiency in low-temperature microwave treatment depends largely on the type of material under treatment, its physical parameters, structure, conductivity and dielectric properties. In conventional thermal treatment, heat is supplied by convection and conduction; when microwave radiation is applied, energy is supplied directly to the material being heated. The application of microwave technology has a lot of potential benefits; microwaves pass through the material and they accumulate energy and generate heat in the whole volume of a material. Using microwave energy reduces the duration of heating a material, allows for process control and improves the energy efficiency. Budarin et al.  studied A comparison of microwave and conventional heating in a number of biological reactions has revealed various behaviours and properties which—as scientists argue—are proof of the nonthermal effects of microwave radiation. The difference between thermal and nonthermal effects lies in that an effect is regarded as thermal if it can be induced not only by microwave field but also by heat generated in a different way; an effect is nonthermal if it is induced by radiation of such intensity that the temperature increase it causes is negligible or if the effect cannot be achieved by increasing the temperature in a different manner .Saccharomyces cerevisiae As4. Inoculum of yeast S. cerevisiae was done with liquid YPG medium: 10 g of yeast extract, 20 g of peptone, 20 g of glucose and 20 g agar dissolved in 1000 cm3 of distilled water. The pH was brought to 5.2 by adding 1 M HCl and controlled by a universal pH meter.Alcohol fermentation was conducted with an industrial yeast strain used in the industrial production of ethanol: 3 of liquid YPG medium and incubated for 24 h in a shaker at a temperature of 30 °C.Five cubic centimetres of sterile distilled water was transferred into a tube with a yeast culture on YPG, and washout was performed. The cell suspension obtained in the process was introduced to a conical flask with 100 cmAlcohol fermentation was conducted in an SHF (separate hydrolysis and fermentation) system. After hydrolysis, the substrate was fermented. Stage II involved testing all variants of the experiment tested at stage I.The inoculum of the appropriate yeast strain was added to the prepared medium (substrate after pretreatment). Fermentation was conducted for 72 h under anaerobic conditions, at an appropriate temperature for the yeast strain, i.e. at 38 °C.The content of ethanol in the medium was determined after the fermentation was completed. This was done by the method using Hach Lange’s LCK 300 reagents.p = 0.05 was adopted in the tests.Statistical analysis of the results was done with the STATISTICA 12.0 PL; a one-way analysis of variance (ANOVA) was conducted in order to check the significance of the differences between variables. A RIR Tukey test was conducted in order to determine the significance of differences between the variables under analysis. The level of significance of The amount of produced glucose and phenolic compounds were analysed to assess the effectiveness of the pretreatment process.The amount of glucose released to the solution Fig.  was usedThere is a risk of formation of inhibitors of alcohol fermentation during the process of thermohydrolysis; taking this into consideration, the amount of phenolic compounds formed following the thermal treatment was determined Fig. .. The coThese results show that an increase in the concentration of phenolic compounds did not inhibit alcohol fermentation, but it was correlated with the concentration of produced glucose Fig. . The conThe literature provides examples of application of microwaves as a conditioning factor in alcohol fermentation. Substrate exposure to microwave radiation in various temperature ranges has shown that microwaves increase solubilisation of substrates and break the network of exopolysaccharides, thereby speeding up chemical processes  of the dry weight of the substrate used  and various pretreatment times . Maximum glucose yield 36.8 g/100 gGelidium amansii in autoclave at 120 °C at different time intervals—20, 40, 60, 80, and 60 min—caused an increase in glucose by 59% as a result of the control , which is more by 98% than in the control mash and more by 37% than in the conventionally heated sample. The literature presents different values of bioethanol depending on the type of applied microalgae or macroalgae and pretreatment methods. Bioethanol yields from Arthrospira platensis helped to achieve higher efficiency of glucose release and production of ethanol compared with conventional heating. The application of microwave technology increased the amount of produced glucose by a maximum of 62% compared with a sample with no pretreatment. The results have shown that 150 °C was the most beneficial for the thermohydrolysis process, both in the microwave and conventional heating. The results show that the increased concentration of phenolic compounds did not inhibit alcohol fermentation; the control mash yielded 0.49 g/l of bioethanol, the alcohol concentration in the conventionally preheated sample increased by 45% (to 0.71 g/l), and the mash in the microwave-heated sample contained the highest concentration of alcohol (0.97 g/l), which is 98% more than in the control mash and 37% more than in the conventionally heated sample.The application of microwave heating with a view to hydrothermal disintegration of cyanobacteria


Rotation is present in many physical and geophysical systems and its role in determining flow properties and modifying turbulent fluctuations is of crucial importance. Here we focus on the role of rotation on temperature fluctuations in turbulent thermal convection. The system used consists of a rotating half soap bubble heated from below. This system has features, curvature and a quasi two dimensional character, which are reminiscent of atmospheric and planetary systems. Our experiments and numerical simulations show that rotation changes the nature of turbulent fluctuations and a new scaling regime is obtained for the temperature field. This change in the scaling behavior of temperature fluctuations, due to rotation, is put forth by studying the so called second moment of temperature differences across different scales. For high enough rotation rates, these temperature differences display a transition from Bolgiano Obukhov scaling to a new scaling regime. This scaling is at odds with expectations from theory, numerics, and experiments in three dimensions, suggesting that the effects of rotation on turbulent flows depend strongly on geometry and spatial dimension. As for hydrodynamic turbulence6, large fluctuations of the temperature and of the velocity of the fluid characterize turbulent thermal convection. These fluctuations can be described by using scaling laws which, according to8, are of the Kolmogorov type while, according to others9, are similar to those suggested for stably stratified convection11. Several experiments have measured these statistical properties but a number of issues regarding these scaling laws, and notably whether the statistics are Kolmogorov like or Bolgiano like, remain unresolved9. Recently, two dimensional (2D) turbulent thermal convection has been demonstrated in either vertical soap films14 or soap bubbles16. A detailed examination of the statistical properties of the velocity fluctuations, the density variations15, as well as the temperature fluctuations16 showed that they displayed scaling laws predicted by Bolgiano and Obukhov in the 1950’s for turbulence in stably stratified media20. The presence of such scaling laws as well as the ease of measuring the spatial variations of different quantities  make such two dimensional versions ideal models for the study of scaling and self similarity of turbulent flows governed by Bolgiano-Obukhov scalings.Turbulent thermal convection is important for numerous processes of meteorological, geophysical, and industrial interest. Several experimental and theoretical studies have focused on the properties of this turbulent state24. This change in scaling for the velocity field has direct consequences on the scaling of scalar fields in rotating turbulent flows according to numerical simulations24 but no experiments exist so far. Rotation effects have also been studied in turbulent Rayleigh Bènard convection and a number of effects have been observed25 such as the enhancement of heat transport and its eventual decrease for high rotation rates26 as well as the existence of transitions between different turbulent states27. A novel aspect of the experiments described here is that the cell used has the advantage of allowing the full hemisphere to be subjected to a global rotation as shown in Fig. 128. Its quasi 2D nature provides possible parallels with large scale atmospheric and geophysical flows and allows simple measurements of the temperature field, a difficult task in 3D cells.Here, we investigate the role of rotation on the statistical properties of the temperature fluctuations, a scalar field, in a half soap bubble heated from below. Global rotation is inherent to a number of geophysical and planetary processes but how it affects scalar quantities such as the concentration of pollutants, the humidity or the temperature remains without experimental support. The examination of the role of rotation on the velocity fluctuations in three dimensional (3D) hydrodynamic turbulence has been shown to introduce novel features and changes in scaling behavior in experiments and simulationsr, raised to a power n and averaged over space and time) extracted from temperature fields on the surface of the bubble. In the absence of rotation, these structure functions follow a scaling law versus r, expected and found in earlier experiments16 namely Bolgiano-Obukhov scaling, with exponents of n/5 for the variation of the nth order moments of temperature differences across a scale r. For low rotation rates, this scaling barely changes. However, and above a certain threshold in rotation rate, the scaling exponents change and show an n/2 behavior. While no predictions exist for such a change, other experiments and phenomenological models have uncovered a similar transition for the velocity structure functions in rotating 3D hydrodynamic turbulence. The transition we find here, although bears the same features, is for temperature fluctuations in turbulent thermal convection so our results are new. We are not aware of other experiments where the effects of rotation on a scalar field are measured, but numerical simulations suggest a different scaling behavior so our results are at odds with expectations in 3D. The role of rotation is thus different in our geometry. Our own numerical simulations carried out for comparable conditions as the experiments suggest a similar result as our experiments namely a transition from n/5 to n/2 as found experimentally. Further increase in rotation rate shows another transition to exponents which increase with the rotation rate suggesting that for high rotations a new regime sets in. That rotation changes scaling exponents of turbulent fluctuations, be they in the hydrodynamic case or in the thermal convection case as shown here, has important consequences on the understanding of the energy content of such fluctuations across the scales, a question which is important in understanding energy transfers in a variety of situations29.Our diagnostics of the effects of rotation on the turbulent thermal convection is based on the so called temperature structure functions  shows that the rotation of the bubble introduces a first layer near the equator and extending up to about 10° above the equator where the local rotation rate decreases from its imposed value at the equator. At latitudes above roughly 15°, the local rotation rate remains constant and near 1/3 of the imposed rotation rate. Our measurements are carried out in the region above the first layer and for which the rotation rate is independent of latitude. In this region, the effects of the surrounding air on the dynamics of the flow on the surface of the bubble are estimated to be small (see Supp. Mat.). The temperature field measurements used a calibrated 14 bit infrared camera (640 × 512 pixels) working in the spectral range 2.5 μm to 5 μm with a sensitivity of 20 mK and an adjustable exposure time between 0.5 and 1 ms. The camera can also be fitted with different lenses to vary the spatial resolutions as well as different band pass filters allowing to work in conditions where variations of the emissivity of the soap film constituting the bubble due to variations in thickness are minimized (see Supp. Mat.). Images of the same region   were recorded and used to calculate temperature differences across different scales r. Averaging over the area of interest and over hundreds of images allowed us to improve the statistics (between 1 and 5 million points were used) and calculate the moments of these differences. The temperature field was recorded for periods of up to 30 s which is greater than the temperature correlation time (of order 0.1 s) and a few times the smallest rotation times considered. The error in r, introduced by the curved geometry of the bubble, is less than a few percent over a 1 cm region.The convection cell, described previously inFigure δT(rx) = T(x + rx) − T(x) and δT(ry) = T(y + ry) − T(y) and calculate the nth order moments as x and y refer to the horizontal and vertical coordinates and the brackets refer to an average over space and time. For simplicity, we will focus on the second moment n = 2 for the rest of the discussion. Structure functions are important quantities in the study of turbulence and different scaling relations have been proposed for their variation versus the scale r. In 3D turbulent flows, where Kolmogorov scaling for the velocity fluctuations is believed to prevail, Obukhov and Corrsin6 generalized the scaling arguments of Kolmogorov to a scalar field like the temperature and used both the energy dissipation rate ∈ and the scalar dissipation rate ∈T to predict that the nth order structure functions should scale as 11 for stably stratified turbulence, to the case of Rayleigh Bénard convection for which the fluid thermal expansion rate β, the gravity constant g, and the dissipation rate ∈T fix the scaling relation of the nth order structure function of the temperature as rn/5 9. The nth order moments are thus expected to vary as a power law of the separation distance r with an exponent n/5 in the Bolgiano-Obukhov regime. To compare the experimental conditions here to their classical counterparts, we estimate the Rayleigh number  to be between 7 107 and 3 108 while the Reynolds number  is estimated to be about 300016. In previous experiments using the soap bubble, and for ΔT > 35 °C, the exponent n/516 strongly suggesting the presence of a Bolgiano-Obukhov scaling. Here we examine how this scaling behavior changes with the global rotation of the bubble.From such spatial images, and besides the qualitative aspects just described, we extract the temperature difference Ro is introduced: Ro compares the advection to rotation time scales and is generally written as Ro = V/ΩR where V is a characteristic velocity, R a characteristic length (the radius of the bubble in our case) and Ω = 2πf is the angular rotation rate. For Ro values greater than 1, rotation plays a minor role but when Ro reaches values near 1 and smaller, rotation effects on the properties of the flow are expected to become important. This number can be recast, for thermal convection driven flows as 30. In the experiments described here Ro is varied down to values near 0.1.To gauge the effects of rotation, a non dimensional number, the so called Rossby number rx and ry are similar. These functions display power law scaling for spatial scales between roughly 1 mm and 10 mm. The scaling exponents are in agreement with predictions of Bolgiano and Obukhov as reported before16.Rotation effects are studied for temperature gradients >35° where the scaling of the temperature structure functions follows the Bolgiano-Obukhov regime. The structure functions of order 1 and 2 are displayed in Fig. r. The exponents turn out to be different from the above results. The scaling is observed in the range 1 to 10 mm as shown in Fig. π needs to be large enough (>0.1 Hz) for the transition from n/5 to n/2 behavior to occur. This corresponds to an Ro of roughly 1. Further increase in the rotation frequency, and therefore a decrease in the value of Ro, did not change the exponents. However, and for higher rotation frequencies such that Ro decreases below 0.25, a new increase in the value of The results for the structure functions in the presence of rotation are shown in Fig. 32. Briefly, a hemisphere of radius 1, subjected to thermal convection is described by the coupled Navier -Stokes and the heat equation in the Boussinesq approximation which are simulated using a stereographic projection. The results of these simulations are shown in Fig. Ra numbers and for Ro values smaller than 1 and comparable to those of the experiments. As Ro decreases below 0.25, the exponent The experimental results presented here are confronted to the results of direct numerical simulations (DNS) of thermal convection in a hemispherical geometry as explained inRo−1. Note that for Ro−1 < 1, the exponent is roughly the same as for no rotation. For Ro−1 > 1 and higher, Ro−1 increases: Ro−1 near 10. The plots on the right in Fig. Ro−1 > 4 and for which Ro decreases to small values of order 0.1 where rotation effects are supposed to dominate the flow, the scaling exponent becomes even steeper.This behavior and changes in the scaling of the temperature structure functions can be appreciated in Fig. 33 and Canuto and Dubovikov35 argued that if Ω−1 is used as the characteristic time scale for local energy transfers in rotating hydrodynamic turbulence as suggested in36, a scaling in n/2 can be obtained instead of n/3 for the velocity structure functions. Other arguments have been put forth in37 who introduces a new length scale determined by the rotation rate and the dissipation rate of the turbulent flow. These arguments mostly rely on the introduction of a new time scale, or a new length scale, both determined by the rotation rate, which change the scaling of the energy density spectra. Experimental evidence of the n/2 scaling has been obtained in21 while in23 a continuous increase of the exponent from n/3 at low rotations rates to steeper and steeper exponents has been observed. For a scalar field such as the temperature studied here, on the other hand, numerical simulations find an equivalent scaling in n/424 when the velocity structure functions scale as n/2. This scaling is consistent with the velocity scaling since both are related by 24. Our scaling exponents for n = 2 are clearly higher than the expected exponent both in experiments and in numerics making our quasi two dimensional system with a spherical geometry quite different from its three dimensional counterparts. The above relation between scaling exponents for the velocity and the scalar field suggests that the scaling exponent of the velocity structure function of order 2, in our case for moderate values of Ro, should be much smaller than 1 and rather close to zero. This is at odds with the three dimensional expectations and suggests that our geometry and the dimensionality of the experiments (quasi 2D instead of 3D) play an important role in how rotation modifies the statistical properties of turbulent flows. To further check these results we have carried out additional experiments to measure the velocity structure functions. These results show that the velocity structure functions display Bolgiano Obukhov scaling consistent with an exponent of 3n/5 as expected and observed experimentally before16. Under rotation, the scaling range diminishes and the structure function exponents become smaller, contrary to 3D experiments where the exponent increases. This is compatible with the expected exponent from the scalar measurements. In fact, the velocity structure functions are compatible with a logarithmic variation which again comforts the fact that we expect a small scaling exponent if any for the velocity structure functions. These results are shown in Supp. Mat. This result is only valid for Ro. In fact, a value of 38. In this particular case, the statistical properties of the temperature become of a diffusive character while the underlying velocity field loses spatial correlations. In any case, rotation makes for a large decrease of the velocity fluctuations as shown in Supp. Mat.So far, only results for the role of rotation on the velocity structure functions in 3D hydrodynamic turbulence have been obtained. ZhouRo values smaller than 0.2 the exponent increases to values higher than 1, the relation between Ro, the less plumes there are at the pole as shown in Fig. Further, for Our novel quasi 2D rotating convection cell allows for a detailed study of rotation effects on the statistical properties of temperature fluctuations in turbulent thermal convection. These properties show a transition from Bolgiano-Obukhov scaling to a new scaling regime with nearly n/2 scaling for moderate Rossby numbers. This transition is also obtained in direct numerical simulations. This new scaling is at odds with expected results from theoretical expectations and three dimensional numerical simulations and suggests that the dimensionality of the system used as well as its geometry play a role in setting how rotation affects the statistical properties of turbulent flows. Further decrease in Ro leads to even higher exponents suggesting a re-laminarization of the flow for high enough rotation rates. Considering that our system, which has a natural curvature with quasi two dimensional flow properties, bears similarities with geophysical systems for which rotation governs a number of properties, the results found here call for new thinking about the role of rotation in the modification of turbulence properties.Supplementary material


An indoor localization system based on off-the-shelf smartphone sensors is presented which employs the magnetometer to find user location. Further assisted by the accelerometer and gyroscope, the proposed system is able to locate the user without any prior knowledge of user initial position. The system exploits the fingerprint database approach for localization. Traditional fingerprinting technology stores data intensity values in database such as RSSI  values in the case of WiFi fingerprinting and magnetic flux intensity values in the case of geomagnetic fingerprinting. The down side is the need to update the database periodically and device heterogeneity. We solve this problem by using the fingerprint database of patterns formed by magnetic flux intensity values. The pattern matching approach solves the problem of device heterogeneity and the algorithm’s performance with Samsung Galaxy S8 and LG G6 is comparable. A deep learning based artificial neural network is adopted to identify the user state of walking and stationary and its accuracy is 95%. The localization is totally infrastructure independent and does not require any other technology to constraint the search space. The experiments are performed to determine the accuracy in three buildings of Yeungnam University, Republic of Korea with different path lengths and path geometry. The results demonstrate that the error is 2–3 m for 50 percentile with various buildings. Even though many locations in the same building exhibit very similar magnetic attitude, the algorithm achieves an accuracy of 4 m for 75 percentile irrespective of the device used for localization. The Global Positioning System (GPS) serves as the de facto technology due to its precisely accurate positioning information outdoor. However, GPS inability to work in the indoor environments necessitated the researchers to delve into other alternatives for indoor positioning. Indoor localization got a huge interest, especially during the last decade, primarily due to the excessive use of smartphones. In addition, various companies’ services, which are collectively called Location Based Services (LBS), also accelerated this endeavor as indoor localization serves as the backbone of these services. Not only that, such indoor localization can be extremely helpful to locate workers working in emergency situations such as fire, earthquake, etc. Indoor positioning technology can be broadly divided into two categories: infrastructure dependent systems and infrastructure independent systems. The former either makes the use of existing devices such as WiFi ,2,3 or iAn algorithm is presented to generate the patterns using the geomagnetic data. The generated patterns are computationally efficient to process.A deep learning based artificial neural network is presented to detect user states of walking and stationary using gyroscope data.An efficient infrastructure free user indoor localization algorithm is presented for when the user’s initial position is unknown.We focus on the infrastructure free approach as all smartphones have built in sensors which can easily be adopted for indoor localization. These sensors, developed using Micro-Electric Mechanical Systems (MEMS), are becoming more reliable than before. This research aims to use three such sensors: magnetometer, accelerometer and gyroscope. The contributions of this research work can be summarized as below:The rest of the paper is organized in the following manner. The earth’s geomagnetic field is the natural phenomenon which extends from the earth’s interior out until it meets the solar wind. The magnitude of magnetic field at earth surface extends between 25 and 65 x-axis indicates the measurements generated every 100 ms, while y-axis shows the total magnetic field strength.It is observed that magnetic field strength varies in space and over time , which iPrevious studies ,13 show Fingerprinting is the process of generating and storing fingerprint signatures associated with each location index. These fingerprints are normally the averaged RSSI  values in the case of WiFi. Fingerprinting has been utilized for localization systems during the last few decades and it comprises of two phases: the off-line phase, also called the training phase, and the on-line phase, also called the localization phase. The training phase is the survey of the buildings to collect the data for which we intend to develop localization system. Normally, several observations are collected for each point and their averaged values are stored in the database along with the unique index value of that point. Localization is performed when user sends the data of certain unknown point and that data are matched against the fingerprint database. Various matching techniques are used for the said purpose, including Euclidean distance, Manhattan distance, K nearest neighbor, etc. The process of fingerprinting is not a trivial task for a variety of reasons. First, since the fingerprint signatures are normalized values, many observations are needed to be taken for each point. Second, to achieve a good localization accuracy, the fingerprint database should be large enough. Last is the maintenance and updating of the database as any new instalment in an indoor environment requires updating the fingerprint database accordingly. Another very important factor which potentially affects the accuracy of localization system is the uniqueness of the signature. Each point should have a unique signature or the accuracy is compromised otherwise. This research aims to build a fingerprint based indoor localization system using geomagnetic sensor, accelerometer and gyroscope. We focus to resolve the last two problems mentioned above as well.The application of magnetic fields to solve the problem of indoor positioning and localization can be broadly categorized into two groups: active magnetic fields and passive magnetic fields. The former approach accomplishes this task by generating artificial magnetic fields. Sheinker et al. and Blankenbach & Norrdine in ,15 utiliChung et al. in  developeLi et al. in  investigLi et al. in  use HMR2Zhang et al. in  proposedJung, J., Lee, S.M., and Myung, H., in  addresseAn indoor navigation system based on WiFi and geomagnetic fingerprinting is presented in . The errMeng et al. in  introducA fingerprinting based localization scheme based on magnetic field strength and channel state information is discussed in . A Line x, y and z values and calculates representative features. The features including entropy, power of the coefficients, variance, variance of Fast Fourier Transform, intensity, Zero Crossing Rate, kurtosis, skewness and correlation coefficient are extracted and later used for localization process. The clustering is performed as well by taking into account the magnetic intensity. A classifier is designed to estimate the location based on the extracted features. The presented approach shows good results, however with a single device.An indoor localization system is presented in  which ut28 presented an indoor localization approach based on camera, WiFi and inertial sensors including accelerometer, gyroscope, compass and magnetometer. Initially, the scene is identified using the camera on the smartphone and deep learning has been utilized for the said purpose. Fingerprinting approach is used for WiFi and geomagnetism to aid the localization process. The proposed system is able to achieve an accuracy of 1.32 m at 95%. Even though the system achieves a very good accuracy, it is not always practical to hold the mobile phone in a position to acquire the image of the scene which is the very pivotal component of the proposed system. In addition, using mobile phone camera consumes the phone battery very quickly as well. Moreover, the draw back of using the camera is that it cannot work in dark environment. Another fact which cannot be undermined is that the system also uses the WiFi fingerprinting which makes it infrastructure dependent.This research presents an indoor localization system which benefits from the geomagnetic disturbances prevail in indoor environments. These disturbances are caused by ferromagnetic materials such as doors, elevators, concrete containing iron, etc. The majority of the already available indoor positioning and localization systems based on geomagnetism use fingerprinting technique. The main drawbacks of the traditional fingerprinting based techniques are that the database needs to be updated periodically otherwise the accuracy of the localization systems is affected. Secondly, the geomagnetic data are device dependent which means that measuring magnetic flux intensity using two different smart phones shows very different values. This makes it very difficult to use geomagnetism for indoor localization for all devices alike. The above mentioned problems are resolved using the geomagnetic patterns. Thus, instead of using magnetic flux intensity values, we use the patterns formed by these values. The indoor localization that this study presents leverages off-the-shelf sensors already available in smartphones. In the current study, the purpose of using the gyroscope is twofold: motion detection and the heading estimation. Even though accelerometer is used traditionally for the motion detection, we use gyroscope for the same purpose for two reasons. First, the gyroscope supports fast data rate than accelerometer so working at higher data rate is possible. Second, gyroscope is more tolerant to noise, so, with a little preprocessing, data quality is good to be used for the system. Various techniques exist that can be adopted for motion detection including Artificial Neural Networks (ANN), Support Vector Machines (SVM), Decision Trees (DT), Principal Component Analysis (PCA), etc. We use ANN in our work, as it is easy to implement and shows good performance as well.The ANN is the mathematical model based on the human brain neuron and it works well for pattern recognition, forecasting, data compression, etc. A typical ANN is consisted of an input layer, one or more hidden layers and an output layer each containing small units called neurons or nodes, as shown in The weights of the ANN are determined using the back-propagation algorithm  in whicht shows the time and m is the size of the input vector. For the current study, m is five because we use four features from the gyroscope and a bias node. The details of the features used as an input vector are given in The input vector n is the size of the output vector, which is two in our study. We use the gyroscope data to determine whether the use is walking or stationary at a particular time. We use sigmoid activation function for the ANN.The output vector The sensor data from smartphone sensors is collected at a sampling frequency of 10 Hz and is pre-processed using a low pass filter to reduce the noise effect. The selected features value varies significantly when the user changes its state from stationary to walking. For training the ANN, 5000 samples of every feature are used. The ANN for user state prediction achieves an accuracy of 95%.f where the size of f for this study is 1 s. The accelerometer provides three-axis acceleration values and the total acceleration is calculated as follows:The accelerometer is used to calculate the distance traveled by the user in a given time frame (1)iCompute the magnitude of the acceleration for a given sample (2)Compute the variance in acceleration using(3)Find the local maxima as step candidates and then apply Threshold 1 and Threshold 2. Threshold 1 We use step detection model to calculate the distance for each frame. A step detection algorithm is proposed as well which works on the acceleration data. The algorithm has the following steps:After step detection, we use Weinberg model  to measuWhen step detection and step length estimation is complete, we can calculate the position of the user using the following equation:The calculated distance using accelerometer module is used to assist the magnetometer module to find the exact position of the user. The details of this process are discussed in the next section.x, magnet y and magnetic z values for each point. Our experiments reveal that accuracy is higher if x, y and z magnetic values are matched as compared to magnetic field intensity B alone, so we store the patterns formed by x, y and z magnetic values. Since the orientation of the smart phone is fixed in front of the user, as shown in The magnetometer module is the key part of the system which decides the user location in the indoor environment. The location of the user is found by matching the user scan with the fingerprint database. The database contains patterns formed by magnet Algorithm 1 Generate geomagnetic pattern1:2:3:4:5:6:fordo7:    8:    9:end forThe fingerprint database approach has associated disadvantage of its need to be updated periodically. Moreover, various smartphones exhibit different geomagnetic values at the same time for the same place which makes it impossible to use the fingerprint approach for all smartphones. Preferably, we use the patterns formed by smartphones as compared to the geomagnetic values themselves. Pattern matching in itself is a computationally expensive process which may hinder the performance of the system, so we present the concept of Binary Grid (BG) which stores the patterns in a binary form. We call it binary as it contains only two integers: 0 and 1. The 1 is where we have a magnetic value and 0 otherwise. Algorithm 1 is proposed to generate the BG for given geomagnetic intensity values. It is easy and computationally efficient to convert the values to patterns and store and extract them. Here, we explain the algorithm with the help of a toy example.Let us say that we have to transform the geomagnetic values shown in M × N size is declared where M is number of rows and N is the number of columns. Then, each magnetic data point is taken and converted to a row number by subtracting it from the maximum data point and rounding it. Afterwards, a 1 is added to the calculated row and this process is repeated for all the data values. The BG shown in x axis for Galaxy S8 and its associated BG.First, a matrix containing zeros of Algorithm 2 User positioning using geomagnetic and acceleration data.1:fordo2:fordo    3:        4:         5:        6:end for     7:    8:    9:end for10:For the current study, magnetic data values from Samsung Galaxy S8 are gathered to make the BG. Afterwards, this grid is used to match the user scans for both Samsung Galaxy S8 and LG G6. We use a 1 s frame at a sampling rate of 10 Hz to perform the pattern matching. Each frame is taken, converted to the pattern using the given algorithm and then matched against the BG (geomagnetic pattern database). The point with the lowest error is selected as the user location and error is calculated using the Euclidean distance. Algorithm 2 is used as the localization algorithm. First, a user sample of geomagnetic values is taken and converted to a pattern using the given algorithm. Then, that sample pattern is matched against the pattern database. The point with the lowest Euclidean distance is taken as the geomagnetic position. This process is repeated for ten consecutive samples.The distance traveled by the user is also calculated using the acceleration data. Five such iterations are made and then the estimated positions using geomagnetic pattern matching for five iterations are considered for final location. The underlying reason for taking five windows is to reduce the error in matching caused by the similarity of magnetic values at different places. Even though that pattern matching performs very well in finding the user position, the user position is often miscalculated, which results in high errors. Each window is exactly one frame ahead of the previous window. This difference is used to infer the next location of the user. By taking user position for five consecutive windows, we are able to find the outliers and replace them with correct positions using the distance calculated using the accelerometer data. Since each window is separated by one frame and the average distance traveled by user in one frame is 0.85 to 0.95 m, the location calculated by the algorithm for each window should match the same, otherwise it is not correct. We follow the same logic to calculate the final location of the user. Toy example: Let us say that we have user taken geomagnetic values given in For the data values given in For simplicity, in this explanation, we only take x coordinate of geomagnetic estimate. The acceleration distance is in meters and show the distance for one frame. Thus, if we consider that the first geomagnetic estimate is correct, then the next positions can be calculated using the distance data and they will be 4.42, 5.25, 6.04, 6.97, 7.82, 8.72, 9.51, 10.39 and 11.2, respectively. We call these calculated positions as position candidates and we calculate all the possible candidates by considering each of these 10 geomagnetic estimates as the correct position. This yields ten sets of position candidates. The calculated candidate sets are then compared with geomagnetic estimates and positions are:x coordinate of five positions calculated for the above given example are 3.51, 4.46, 32.46, 6.88 and 7.76, respectively. Thus, using the outlier finding equation, the third position in this sequence is an outlier and it is replaced with the correct position using the distance data. The positions corrected after the removal of outliers are called the finalized positions.One set of position candidates is selected as the geomagnetic positions and its first position is the starting position of the user. This process is repeated for five windows. The size of the window is same, i.e., ten frames. The only difference is that the second window is one frame ahead of the first frame and so on, as shown in The experiment was performed using three different buildings located in Yeungnam University, Republic of Korea. Similarly, the third floor of the Electrical Engineering (EE) department was tested using the proposed algorithm. We tested with a different path for EE building and use a semi square path. The third building where the experiment was performed is Industry Academic Cooperation Technology Building (IACT) Floor 2. The path for IACT is a squared path where the ending point is from where we start the experiment. To check the performance of the system in more realistic and complicated environments, we adopted four different walking styles, as shown in In this part, we present the accuracy results of the proposed algorithm for the three buildings. The error for Galaxy S8 is 2.3 m 50% of the time while LG G6 has 3.3 m error. The maximum error for Galaxy S8 and LG G6 is now almost similar which is 11.22 m and 11.89 m respectively.The results for IACT building Floor 3, as shown in As shown in the This study presents an indoor localization system based on off-the-shelf smartphone geomagnetic sensor which is further assisted by accelerometer and gyroscope sensors. The fingerprinting approach is used for localization. However, unlike the traditional fingerprint approach where intensity values are stored, a fingerprint database of intensity data patterns is built. A pattern making algorithm is presented for fast transformation of data to patterns and computationally efficient for storing and retrieving of the patterns. In addition, deep learning method is adopted to identify user walking and stationary states using gyroscope sensor. The accuracy of the deep learning ANN is 95%. The experimental results illustrate that the mean error of the proposed system is 2–3 m for different buildings. It is apparent that the accuracy depends on the uniqueness of the pattern formed by geomagnetic values and errors rise when the pattern is similar for various locations. The proposed system has advantages over other solutions as it does not need any additional hardware. Furthermore, it does not rely on any infrastructure and works well without WiFi. Another important point to mention here is that the algorithm works without any knowledge of the initial position which means that the algorithm can predict the user position just using a few frames of user data. Even though the search space is big in some cases and there is no sensor to constrain the search space, the algorithm performs very well.This research proposes a system which works on smartphone built-in sensors to locate a pedestrian indoor. The system incorporates the data from three sensors, i.e., the accelerometer, magnetometer and gyroscope, for localization. The algorithm does not need any initial position to calculate the user current position. The algorithm is able to determine user position with 4 m accuracy at 75%. To evaluate the performance of the proposed system, four different walking styles are tested starting from a straight walk to more complex walk with turn through a semicircular walk. Additionally, the algorithm solves the problem of device heterogeneity as it has been tested with Samsung Galaxy S8 and LG G6 and it works in a similar fashion for both devices. Currently, it works with a fixed device behavior where the device is held in front of the user. In the future, we intend to work with varying behaviors of user for holding the device in various manners such as listening to phone call, walking with swinging device in hand, etc.


Absolute and relative dispersion are fundamental quantities employed in order to assess the mixing strength of a basin. There exists a time scale called Lagrangian Integral Scale associated to absolute dispersion that highlights the occurrence of the transition from a quadratic dependence on time to a linear dependence on time. Such a time scale is commonly adopted as an indicator of the duration needed to lose the influence of the initial conditions. This work aims to show that in a semi-enclosed basin the choice of the formulation in order to calculate the absolute dispersion can lead to different results. Moreover, the influence of initial conditions can persist beyond the Lagrangian Integral Scale. Such an influence can be appreciated by evaluating absolute and relative dispersion recursively by changing the initial conditions. Furthermore, finite-size Lyapunov exponents characterize the different regimes of the basin. TL, i.e. the integral of the auto-correlation function of residual velocities. This time defines the occurrence of the change in the slope of the absolute dispersion plot. For times smaller than TL, the absolute dispersion has a quadratic dependence on time whereas, for times larger than TL, a linear dependence on time is expected. We aim to evaluate such statistics varying the initial conditions, i.e. the time instance at which numerical particles are released and, consequently, the velocity at which they are subjected at the beginning of their trajectory. Indeed, the evaluation of the absolute dispersion varying the initial conditions can lead to results having one order of magnitude of difference, as it will be shown in the next paragraphs. Even TL could be influenced by initial conditions. However, the present case does not show any important impact over the computation of TL. Therefore, there is the need to further evaluate the time scale over which the influence of the initial conditions is lost.The Gulf of Trieste is a shallow semi-enclosed basin in the NE Adriatic Sea see  with a mIn the last years a network of HF-radars has been installed in the gulf of Trieste as part of a European cooperation project: Tracking Oil Spill and Coastal Awareness Network. The HF-radar network consists of three monostatic CODAR SeaSonde systems  and provU10 and water level η recorded from the tidal gauge of Trieste (source data from www.mareografico.it) are compared with the significant wave height Hs calculated from reanalysis A2(t), lea2(t). Two regimes are usually detected: for times smaller than the Lagrangian time scale TL an absolute dispersion function of square time is recovered, whereas for times greater than TL a linear dependence from time is obtained:i-th velocity component as /μ(t) over the computations of a2(t) with different initial conditions. r) curves present a subdiffusive regime (see next paragraph). Therefore, grey curves actually tend to collapse relatively to the average. Such a result suggests that the relative importance of the initial condition decreases as time elapses. As the Lagrangian time scale TL shows when there is a change of regime on the plot of the total absolute dispersion, the function σ(t) evaluates the influence of the initial conditions on the strength of the absolute total dispersion after a time t. In case the function σ(t) would not decrease, the influence of the initial conditions would persist even for long times.Furthermore, Panel a) shows that the grey curves tend to collapse one over each other for long times. For this reason, it is possible to quantify whether the curves tend to narrow by adopting a normalization with respect to the average d2(t) as a function of time. Compared with of σ(t) for d2(t). The periodicity is thus damped due the absence of mean drift.While autocorrelations and Lagrangian integral time scales are calculated once for all, the evaluation of absolute dispersion can be pursued taking into consideration the mean drift , 26. Ther0 and on the forcing injection scale in the flow rI. In particular it is possible to recollect the following:rI can be regarded as the Rossby radius of deformation and r is the separation. The first regime belongs to the enstrophy cascade in two-dimensional turbulence and corresponds to non-local dispersion where the particles are advected by structures greater than the initial separation. The second regime belongs to the energy cascade where the celebrated Richardson law is recovered. Particles disperse randomly in the third regime since they belong to different flow structures. Therefore, relative dispersion should behave asα is of order one and χ is the rate at which enstrophy is transferred to scales shorter than rI. [Relative dispersion regimes typically depend on the initial separation 2∝t3r0≥rI0where αr2 in logarithmic scale in order to visualize a linear relation of the type lnri = lnr0 + cit, where ci = αχ⅓. The procedure of changing recursively the initial condition is employed and the black curves represent the average trends. The other curves are omitted in favour of readability. Red curves are the best fit over the first 20h with values of ci ranging from 0.098 to 0.157 h−1.rI show large values of kurtosis, whereas at larger separations the kurtosis tends toward Gaussianity . Particles that undergo a random walk lead to Gaussian p.d.f. characterized by such a kurtosis. Particle pairs initially separated by a distance smaller than rI will experience dispersion that grows exponentially and cubically in time. On the contrary, particles pairs initially separated by a distance greater than rI will directly experience a cubic growth. It is possible to argue that the first case is a direct consequence of vortex merging [Relative diffusivity is plotted in  merging . Fig 1 s merging . Complexr) curves are here evaluated through original pairs. Since the measured velocity fields have a 1.5 km resolution in space, smaller scales will not be considered. Following [−1. The average strength is approximately 0.22 day−1, whose order of magnitude is in agreement with the findings of [r increases, the FSLE slope suggests the presence of both the Richardson regime (∼ 6 < r <∼ 10 km) and the linear regime (∼ 10 < r <∼ 13 km).FSLE Λ curvesrmax. Such a behavior is shown in For larger spatial scales, as pointed out by , the behTL, i.e. the integral of velocity auto-correlations. Besides, TL defines when the behaviour of absolute dispersion changes from a quadratic function of time to a linear function of time. However, it is possible to observe from this work the persistent importance of initial conditions over absolute dispersion even for long times. As a result, it is possible to recover another time scale associated to the fading of the influence of the initial conditions over the absolute dispersion. Such a time scale is evaluated with the function σ(t). This should be interpreted as a quantity that measures how strong could be the effect of initial conditions with respect to an average value. σ(t) could well be adopted in order to compare the absolute dispersion computed in different ways. The smaller σ(t) is as time elapses, the weaker initial conditions are on the outcome of absolute dispersion computations. This measure can well be evaluated alongside with TL in order to further characterize the mixing properties of a basin.Evaluation of absolute and relative dispersion is of great importance in order to assess the mixing properties of a basin. However, the evaluation of absolute dispersion is not independent from the initial conditions. This means that a specific evaluation of the time scale over which initial conditions are lost must be considered. This work shows a significant influence of the initial conditions on the absolute dispersion. It is possible to argue that a strong forcing that influences initial conditions is the tide. This can be deduced by the analysis of the velocity auto-correlations that tend to decrease for long times, as expected, but show a persistent and periodic, even if small, correlation. Usually, initial conditions are considered to be lost after a time equal to the Lagrangian Integral Time Scale Finally, relative dispersion is evaluated both as a function of the separation and as Finite-Size Lyapunov Exponent (FSLE) curves in order to unravel the several mixing regimes of the Gulf of Trieste. The approach pursued is the same: relative dispersion and FSLE are evaluated at the varying of the initial conditions and multiple results are obtained. Averages are evaluated and a mean behaviour is shown.