Self assembling wire networks typically evolve to minimize the resistance across electrical contacts which are frequently used in a manner comparable to Hebbian learning. In this work, we demonstrate that electrical fields can also be used to cause an increase in the resistance of the wire network. We show that if such a wire is exposed to a transverse electric field, the wire is deformed in a way that depends on it’s tensile strength. We measure the wire resistance as a function of transverse field for several field strengths and show that by deforming the wire, the amplitude of the resulting shape can be modified in a controllable fashion. At a critical value of the transverse field, we show that the wire loses stability. At this point we observe thresholding behavior in that the resistance increases abruptly to a maximum value and the wire is destroyed. This thresholding behavior suggests that self assembled wires may be manipulated via an transverse electric field and demonstrates that a mechanism exists for the destruction of undesirable connections. Self assembling particle wire networks have been studied recently as a potential means of producing complex electrical devices12571017The optimization in self-assembling wire networks can be viewed as the network learning the nature of its environment, analogous to Hebb’s learning ruleTo do this, we first expose a self assembled wire to a small electric field perpendicular to the wire, and observe the change in wire shape and resistance. We then explore the behavior of the wire in the presence of a large perpendicular electric field. It is in this regime in which the wire begins to break down and we find thresholding behavior. Then we discuss a theory that quantitatively describes the charge transport properties as well as the observed deformation and breaking of these wires which explains the behavior of a self-assembled wire subject to a transverse electric field. The resulting behavior of the device somewhat resembles that of a memristor in that the resistance is dependent on the past voltages across the wireV = 18 kV. We see that this resistance is increases nonlinearly with the distance between electrodes due to the charge carried by the shutting particle.In the absence of a transverse electric field, the particles form a wire connecting the two primary electrodes which is straight when averaged over multiple instances. However, when the transverse voltage is applied we observe a distortion of the wire. This behavior can be seen in We find that the amplitude of the distortion increases linearly with the transverse voltage. R = 250 GΩ for all transverse voltages up to V^ = 13 kV, and transitions abruptly to a resistance state of R = 750 GΩ between V^ = 7 kV and V^ = 10 kV when the wire is destroyed, after which the resistance is constant for increasing transverse voltages. Each data point is a measurement of the average resistance of the wire over five minutes. The critical voltage was defined as the transverse voltage at which the resistance more than doubled the value measured at the previous transverse voltage. We measured a critical Vc = 8.5 kV +/− 0.7 kV.We have observed that the particles in the wire shuttle charge along the wire in the manner of a bucket brigadeN particles each carrying a voltage Vi with i = 1, 2..., N as diagrammed in V0 and VN+1 respectively. We will consider the case of one positive electrode and one negative electrode such that V0 = −VN+1 = ΔV/2.We consider a chain of Ii,j is the current that flows from particle i to particle j. Since current only flows between nearest neighbors in the chain, conservation of charge then gives the equation of motion for the charge Qi on particle i asThe current σi,j between the nearest neighbor particles i and j and write the currents:Now we introduce the (possibly non-ohmic) conductivity This expression is simply Ohm’s law.Ii−1,i = Ii,i+1 for all i = 1, 2..., N. This implies that the currents between nearest neighbor particles has also reached a constant value I, and so equation Now we require that the system has reached the stationary state in which the time averaged particle charges are no longer varying. In this case, the left side of Eq. This equation can be solved for the voltage. The solution is linear, and after enforcing the boundary conditions we haveAnd equation σ on the gap size may be evaluated at least approximately by considering the dynamics of a single particle shuttling between two identical neighboring particles held at an electrode voltage difference ΔVe. Provided the gap is large compared to the radius of the particle, the leading order term in the force on the particle is simply the monopole termWhich only depends on the electrode voltages and the total number of particles. The dependence of the conductance c is the particle capacitance, γd is the damping coefficent due to the oil, and s is the separation between the center of the neighboring particles. From this we calculate the time t required for the particle to cross the gap once. Introducing the constant A = 2c3(ΔVe)2/(4πεγd) and the gap size d = s − 4r we findwhere cΔVe every time it crosses the gap, we have the conductivity as it depends on dSince the particle transfers a charge and the gap size dependent resistanceThis completes the description of the wire conductivity as it depends on the idealized shuttling motion of the equally spaced particles. However, during the real bucket brigade motion of many particles, much larger gaps may appear in the wire at the expense of smaller gaps. This causes the conductivity of the wire to momentarily drop as charge cannot be carried effectively across large gaps. When this happens, the particles that are still in contact with an electrode charge up to the electrode voltage, and particles that are no longer in contact with an electrode rapidly become neutral.N + 1 possible sites. Once the gap has formed, the particle to the left of the gap will have the left electrode voltage, and the particle to the right will have the right electrode voltage. Since current can no longer flow across the gap in the wire, the particles on either side of the gap will acquire a charge dependent upon their capacitance c and the voltage they reach. Therefore, these particles will experience a force Fi = cVi E^ perpendicular to the length of the wire if exposed to a perpendicular external electric field E^. The force Fi averaged over all possible gaps can be found by considering the probability that the gap is on either side of the particle. If we assume that the gap is equally likely to occur at any of the sites, then there are i sites on one side (left) of the particle, and N − i + 1 sites on the other side (right). Therefore there is a probability of i/(N + 1) that the gap is to the left of particle i and a probability of (N − i + 1)/(N + 1) that the gap is to the right. The magnitude of the perpendicular force on the particle is the same in either case, but the direction of the force is determined by which side of the particle the gap is on. If we say the force is positive when the gap is to the left of the particle, and negative when it is to the right, we find that the expectation value of the force averaged over all possible gaps isWe consider now the case of a single gap forming in the wire. We assume that the gap has an equal chance of occurring at any of the ori is determined by the probability that the gap is to the left of site i and the probability that the gap is to the right of site i. We see that this changes linearly along the length of the wire. This force acts perpendicular to the straight wireThat is, the average force on the particle at site L − 2Nr)/(N + 1). We may use this to calculate the force parallel to the direction of the wire. The force between a sphere of charge Q and an uncharged sphere of equal radius with a gap of size s between them isIf the stretch of the wire is small, then the total length is not significantly different from the unstretched length and the gap size may be approximated as /L so that 〈iF〉 → 〈F(x)〉 = −cΔVE^(1/2 − x/L) where L is the total length of the wire. Assuming a small displacement y(x) and a viscous damping term Which is the effective tension in the wire. From this, we can calculate the displacement of the wire in a transverse electric field. We will do this by taking the approximation of a continuous wire Where T is the restoring force acting as the tension in the wire from above. In the steady state, ymax of the wire should increase linearly with the perpendicular electric field.This shows that the maximum displacement Using the tension calculated above, and writing c ≈ 4πεr  which givesThis gives the average wire displacement to leading order in the number of gaps. We can gain one further simplification by approximating the capacitance of the charged particle as the capacitance of a single sphere This is entirely in terms of known quantities.We can also approximate the perpendicular electric field required to break the wire. As the wire distorts, the force due to the perpendicular field gains a component parallel to the wire that acts against the tension force. At the critical perpendicular field strength, this component becomes larger than the tension in the wire and the wire breaks. This condition can be written asθ is the angle that the wire makes with the x-axis. The lowest field at which the wire can break can be found by taking sin(θ) as a function of the electric fields. We find the value of sin(θ) using the derivative of eq. dy/dx = 24Fmax/T we find the relationship for the critical field to bewhere c ≈ 4πεr leads to a critical field ofUsing eq. c/T = 1.2 * 10−5 F/N which is much lower than our measured c/T = 9.1 * 10−5 F/N. We also calculate a critical field strength of E^ = 334 kN/C which corresponds to a perpendicular electrode voltage of Vc = 6.7 kV. This is somewhat lower than the measured Vc = 8.5 +/− 0.7 kV breaking voltage. While these estimates all differ from the experimental values, some discrepancy is expected since we have used the capacitance of an isolated sphere as an approximation to the capacitance of the particles in the wire. Since the particles in the wire are interacting, their capacitances may differ somewhat from the values used in this approximation.Using the parameter values from the experiment and the approximations above, we find the value of To summarize, we find that the conductivity of a self assembled particle wire can be related to the conductivity of a single particle charge shuttle. We can therefore view the wire as a chain of charge shuttling particles, similar to a bucket brigade. We also find that a self assembled particle wire can be distorted or even destroyed by a strong enough perpendicular electric field. This can be understood as being caused by gaps that form in the wire during the bucket brigade conduction motion of the particles which cause sections of the wire to have a nonzero time averaged charge. This effect may be exploited to use self assembled wires as a type of voltage controlled resistor, and demonstrates that self assembling wire connections are capable of increasing resistance in response to changes in the local environment.mm wide and separated by a distance of L = 40 mm. The electrodes are immersed in a dielectric fluid (castor oil) and a voltage (the primary voltage) is applied across them. The oil contains N = 25 steel conducting spheres of radius r = 0.775 mm which self assemble into a wire. The particles in the wire transport charge by undergoing a bucket brigade motion.L = 40 mm long secondary electrodes separated by a distance of d = 20 mm. A voltage (the transverse voltage) is applied to these electrodes and the wire changes its configuration, thus altering the displacement of the wire and its resistance.Parallel to the line connecting the two primary electrodes are two additional mm grid below the experiment was used to determine the pixel size and so convert the pixel position into to the real position of the particle in the experimental area. Particle positions were recorded using coordinates centered at the primary positive electrode. The line connecting the primary electrode was defined to be the x-axis.Wires were allowed to equilibriate in the applied fields for five minutes, after which digital images of the wires were taken by a camera mounted above the experiment. Two examples of these images can be seen in MΩ resistor was placed in series with the primary voltage source and the wire. The time averaged voltage across this series resistor was recorded and use to compute the current through the circuit and therefore the total resistance of the wire. The resistance of the formed wire was measured as a function of the secondary electrode voltage while the voltage across the main electrode remains fixed.The wire resistance measurements were taken using an identical setup with the addition of two porous nonconducting screens by the transverse electrodes to prevent the particles from forming a connection between this electrode pair at higher transverse voltages. A 0.5 d was varied in this experiment to find the resistance as a function of gap size. A 0.5 MΩ resistor was placed in series with the primary voltage source and the voltage across this resistor was measured to compute the resistance of the gap with the particle in it.How to cite this article: Stephenson, C. and Hubler, A. Stability and conductivity of self assembled wires in a transverse electric field. Sci. Rep.5, 15044; doi: 10.1038/srep15044 (2015).


Cassini spacecraft has patrolled Saturn's magnetosphere and observed its magnetopause boundary over a wide range of prevailing solar wind and interior plasma conditions. We now have data that enable us to resolve a significant dawn‐dusk asymmetry and find that the magnetosphere extends farther from the planet on the dawnside of the planet by 7 ± 1%. In addition, an opposing dawn‐dusk asymmetry in the suprathermal plasma pressure adjacent to the magnetopause has been observed. This probably acts to reduce the size asymmetry and may explain the discrepancy between the degree of asymmetry found here and a similar asymmetry found by Kivelson and Jia (2014) using MHD simulations. Finally, these observations sample a wide range of season, allowing the “intrinsic” polar flattening (14 ± 1%) caused by the magnetodisc to be separated from the seasonally induced north‐south asymmetry in the magnetopause shape found theoretically (5 ± 1% when the planet's magnetic dipole is tilted away from the Sun by 10–17°).For over 10 years, the  Saturn's magnetosphere extends farther at dawn than dusk by  7%The degree of asymmetry departs from MHD predictions, likely due to the suprathermal plasma pressureAn intrinsic polar flattening of  14% is found with an additional seasonally induced component Plumes of water ice grains and molecules are ejected from Enceladus [e.g., Arridge et al., Pilkington et al., Krimigis et al., Kanani et al., Pilkington et al. [The thermal component of this plasma is largely equatorially confined due to centrifugal forces and forms an extended magnetodisc structure [e.g., n et al.  found thPilkington et al. [Maurice et al. [Hansen et al. [XKSM axis points from the planet toward the Sun, the ZKSM axis is such that the magnetic dipole is contained within the XKSM‐ZKSM plane, and the YKSM points toward dusk to complete the right‐handed set. As such, this asymmetry will also be quantified in terms of the apparent polar flattening/inflation imposed by the orientation of the planetary dipole with respect to the solar wind flow direction, which changes with season.Here we will extend the analysis of n et al.  and conse et al.  and Hansn et al.  found th2Pilkington et al. [Dougherty et al., Young et al., Slavin et al., Arridge et al., Kanani et al., As detailed by n et al. , an extePetrinec and Russell, Krimigis et al., Sergis et al., To isolate the impact of internal plasma dynamics on magnetopause morphology, it is first necessary to remove the effects of external variability by correcting for changing solar wind dynamic pressure. In the absence of a dedicated upstream pressure monitor, a Newtonian approximation to supersonic flow about a body [Shue et al. [Here the empirical magnetopause model of e et al.  is used,r and θ are polar coordinates that describe a point on the magnetopause. The parameter r denotes the distance from the planet's center (the origin), and θ is the angle between the planet‐Sun line and the position of the point on the magnetopause with respect to the origin. The parameter r0 is the subsolar standoff distance and K is the “flaring parameter” which controls the downstream shape of the magnetopause surface. If K = 0.5, the magnetosphere is “open” with a constant tail radius. Above this value, the model shape expands with distance from the planet, and below this value the magnetosphere is “closed.” Coefficients a1 − 4 control, respectively, (1) the size scale of the magnetosphere; (2) its response to changes in solar wind dynamic pressure; (3) the nominal downstream flaring of the magnetosphere; and finally, (4) the effect of dynamic pressure on magnetopause flaring.Pilkington et al. [Z, by a factor E where E<1. Hence, the axisymmetric surface described by equations x=rcosθ, y=rsinθcosϕ, z=rsinθsinϕ, and ϕ is the angle between the projection of r onto the YKSM‐ZKSM plane and the YKSM axis.This model is rotationally symmetric about the planet‐Sun line, but a significant degree of polar flattening has been observed by n et al. . Hence, Pilkington et al.[−6RS. The Matlab Optimization Toolbox implementation of the interior‐point algorithm of Waltz et al. [Ugray et al. [This model is fitted iteratively to the magnetopause observations by minimizing the root‐mean‐square (RMS) distance between each observed magnetopause crossing and the model surface, constructed separately at the dynamic pressure estimated for each crossing assuming pressure balance. The distance between each crossings and each model surface is calculated near exactly by solving a set of four equations numerically as outlined by on et al.. This efz et al.  is employ et al.  is used 33.1K, were fixed to the values found by Pilkington et al. [In the first instance, to determine if a dawn‐dusk asymmetry could be present, all model coefficients besides those that control the extent of tail flaring, n et al. . SeparatK in each case implied that there is a statistically significant difference in the tail flaring on the dawn and dusk flanks with the magnetopause extending farther on the dawn flank. However, there are several problems with this methodology. First, imposing a different degree of flaring in this way leads to a discontinuous surface at the poles. Also, as pointed out by Petrinec and Russell [Joy et al.[The best fitting values of  Russell  and Joy oy et al., empiricXKSM and YKSM directions than the observations of the magnetopause at dusk, and the high‐latitude observations lie on the duskside of the planet only. As a result, the trajectory of the spacecraft has been considered and crossings that lie in a region that has not been adequately sampled on the opposite side of the planet have been removed. Specifically, crossings are accepted that satisfy the conditions |ZKSM|≤10 and −18≤XKSM≤24, the latter of which also accounts for potential biases in YKSM due to the trajectory of the spacecraft. This left 989 magnetopause crossings with which to proceed with the analysis. The mean magnetopause position found in previous studies is still captured despite these restrictions, e.g., Achilleos et al. [Pilkington et al. [To minimize the impact of observational bias, the data were reduced in order to provide equal spacecraft sampling on either side of the planet. It can be seen in Figure s et al.  and Pilkn et al. .Massey, σ significance level, indicating that the probability that the dynamic pressure distributions are significantly different is less than 69.1%, the lowest level of significance usually considered. This indicates that systematic differences in the pressure distributions on either side of the planet are insignificant.Since the observations on the dawnside and duskside of the planet are typically separated in time by years, long‐terms trends in the dynamic pressure due to the solar cycle, for example, could potentially affect the results of this study. To ensure that the upstream conditions were similar when the observations on each side of the magnetopause were made, the Kolmogorov‐Smirnov test Massey,  has beenThroughout the period that this study encompasses, the spacecraft spent approximately 3 years sampling the dawnside of the planet, but one of these years was primarily spent traversing the magnetotail during which the magnetopause could not be observed. It spent approximately 5 years sampling the duskside of the planet, so naturally there were more observations of the magnetopause here. If an empirical model were fitted to the reduced set of magnetopause crossings outlined above, the fit would be artificially weighted to the dusk magnetopause as a result. Such a weighting is removed by randomly sampling the data on the duskside to balance the number of crossings on either side. A technique known as “stratified sampling” is used to mirror the local time distribution of crossings to prevent artificial weighting to “overpopulated” local time sectors.The procedure is as follows: the dawn crossings are separated into local time bins with a width of 1 h and the percentage of crossings within each bin is calculated. The probability of a crossing occurring within each local time bin on the dawnside of the planet is then calculated and imposed on the random sample drawn from crossings on the duskside. In any cases where there are fewer crossings on the duskside in a particular mirrored local time bin, the dawn crossings in that particular bin are randomly sampled instead. The end result is an equivalent number of dawn and dusk crossings equally dispersed in terms of local time, to which the model is fitted. 716 magnetopause crossings remained in total.ϕ is the angle between the YKSM axis and the projection of the radial vector onto the YKSM−ZKSM plane, and a5 is a free parameter found by fitting the empirical surface to the data. The magnitude of a5 hence controls the size of the dawn‐dusk asymmetry and cosϕ increases the tail flaring on one side of the planet and reduces it on the opposite side depending on the sign of a5 with a smooth transition between them. As such, the asymmetry in terms of the flaring parameter will be of magnitude 2a5 at the equator in the XKSM−YKSM plane.The functional form of the flaring parameter has been modified to introduce a dawn‐dusk asymmetry, a5=−0.024 ± 0.007 and reduced the RMS residual by ∼10% relative to a fit without the asymmetry term in equation a3=0.688 ± 0.006. A significance test, such as the F test, can be used to test the hypothesis that adding the extra free parameter significantly improves the predictive power of the model and simply relies on the improvement in the model prediction being large enough to outweigh the cost of adding extra free parameters. Employing this test, the probability that this improvement was caused by random scatter in the data is negligible.Repeating the fitting using This asymmetry may be caused physically by the intrinsic asymmetry in plasma flow around the planet with respect to the direction of solar wind flow. Plasma generally flows in the same direction as the planet rotates, so it flows against the direction of the solar wind at dawn and in the same direction as the solar wind at dusk. Hence, the magnetopause may be pushed farther from the planet at dawn than at dusk.Kivelson and Jia [RS at the terminator plane compared to our empirically derived asymmetry of 1.47 ± 0.49RS when the surface is constructed at the same standoff distance (26.61RS). The surfaces have been compared at the same standoff distance rather than the same dynamic pressure, because we have found that the asymmetry is insensitive to changes in the dynamic pressure within the limitations of the data used in this study, whereas the absolute size of the asymmetry changes with system size. It should be noted though that the empirical model predicts that a dynamic pressure of 0.011 ± 0.01 nPa is necessary for Saturn's magnetosphere to have a standoff distance of 26.61RS, which is significantly different from the dynamic pressure used in the simulation of 0.013 nPa. A comparison between the MHD and the empirical surface is shown in Figure MHD simulations by  and Jia  predict distance 6.61RS. Pilkington et al. [β, the ratio of suprathermal pressure to the magnetic pressure, just inside the magnetopause. The plasma β indicates the control that plasma has on the system. Plasma is confined by the magnetic field to varying degrees depending on the particle energy, so for the system to change in size as a result of a sudden influx of hot plasma, for example, [e.g., Krimigis et al., The largest discrepancy between these surfaces is at dusk, where the empirical surface lies farther from the planet than the theoretical MHD surface. The discrepancy between these results can be explained by considering the effect that suprathermal plasma has on the magnetopause. n et al.  found thβ. This is in the opposite sense to the aforementioned asymmetry in the distance from the planet to the magnetopause at dawn and dusk. As such, the suprathermal plasma can perturb the magnetopause more at dusk than at dawn, pushing the magnetopause farther out at dusk than where it would otherwise be located. A similar asymmetry is seen in the ring current . The cause of this asymmetry is unknown but may be caused by the change in the flux tube configuration as they move around the planet. As expanded flux tubes in the dawn sector flow around the planet through noon, they are forced into a smaller volume because they move from the spacious magnetotail and into the dayside magnetosphere [Kivelson and Southwood, Delamere and Bagenal, Khurana and Schwarzl, An asymmetry in the suprathermal plasma pressure has been observed and is shown in Figure Kivelson and Jia [XKSM‐ZKSM plane such that the solar wind is preferentially flowing into the dawnside of the planet. This may also be expected to produce a small dawn‐dusk asymmetry in the opposite sense to that detected here and probably reduces the asymmetry somewhat. Kivelson and Jia [XKSM direction. If the aberration of flow does, indeed, cause a small asymmetry, then including it in the simulation would partially reduce the discrepancy between the observations and the MHD prediction.This effect is not present in the results of  and Jia  as the s and Jia  assume t3.2Maurice et al. [Voyager 1 and Voyager 2. They were able to derive the shape of the magnetopause from this information assuming a fixed solar wind dynamic pressure. They found that the magnetopause geometry changed with planetary season due to variations in the angle between the magnetic dipole and the ZKSM axis, λ. When their surface is recast into the KSM coordinate system, there is a significant difference in its geometry in opposite hemispheres in the presence of a significant dipole tilt. The smallest dipole tilt tested by Maurice et al. [λ. Specifically, their surface is flatter in the north and more elongated in the south under conditions similar to those when Cassini arrived at Saturn (λ=–26.7°). Similar results were obtained by Hansen et al. [e et al.  construce et al.  was 15°,n et al.  through E to vary, the same degree of flattening is found within the uncertainties. Hence, for this data set, seasonal variability cannot be quantified through modification of the functional form of the empirical model as was done in section Such a study is hampered by the fact that the high‐latitude observations utilized here were all observed at similar hemispheric season; i.e., the crossings in both hemispheres experience a similar “effective” dipole tilt in both hemispheres. The observations of the northern hemisphere took place when the dipole was tilted away from the Sun by ∼10–14° in the northern hemisphere. The observations in the southern hemisphere took place 5–6 years later when the dipole was similarly tilted away from the Sun in the southern hemisphere by ∼14–17°. As these observations are in opposite hemispheres, a similar effective dipole tilt is experienced and, hence, no north‐south asymmetry would be expected. Indeed, when the fitting is repeated for crossings in the north and south separately allowing only Tsyganenko [Arridge et al. [Tsyganenko [RH, the current sheet is gradually deflected out of the magnetic equator and is aligned parallel to solar wind flow at distances much larger than RH.However, seasonal variations may be taken into account using the “general deformation method” proposed by yganenko , who dese et al. . The foryganenko  employedTsyganenko [λ∗ is the effective tilt angle, which is radially dependent and given by, r is the planet‐crossing distance and λ is the dipole tilt as defined above. Note that the change in notation from Tsyganenko [RH, is the standoff distance of the surface that passes directly through the crossing [Arridge et al., E is then the degree of polar flattening intrinsic to the shape of the obstacle.yganenko  describeyganenko  remains Pilkington et al. [Fitting with this transformation reduced the RMS residual by ∼5% and yielded a polar flattening of 14 ± 1%, which is significantly different from the 19 ± 1% determined by n et al.  who fitt4Magnetometer and plasma data have been analyzed to construct an extended set of magnetopause crossings comprising coverage over most regions of Saturn's dayside magnetopause. These have been used to probe the structure of Saturn's magnetopause in greater detail than ever before.Kivelson and Jia [β was also observed adjacent to the magnetopause, which likely acts to reduce the extent of the size asymmetry as the magnetopause can be perturbed more by internal plasma pressure on the duskside of the planet. This additional asymmetry may account for the discrepancy between the two results since the MHD simulation does not include a suprathermal plasma population.This analysis has revealed a significant dawn‐dusk asymmetry in the size of the magnetosphere, with the magnetopause extending farther from the planet on the dawnside. It is suggested that this is caused by the intrinsic asymmetry in plasma flow around the planet with respect to the direction of solar wind flow.  and Jia  have derTsyganenko [Pilkington et al. [Pilkington et al. [In addition, since these measurements span a wide range of planetary season, it has been ascertained that a north‐south asymmetry is introduced during phases of the planetary season away from equinox, in agreement with theoretical work. This can be interpreted as an additional component of polar flattening and inflation in opposite hemispheres in addition to the intrinsic flattening due to the presence of the magnetodisc. These contributions have been separated using the general deformation method of yganenko , and a fn et al.  and Pilkn et al.  can be a


The present work presents the comparative simulation of a diesel engine fuelled on diesel fuel and biodiesel fuel. Two models, based on tabulated chemistry, were implemented for the simulation purpose and results were compared with experimental data obtained from a single cylinder diesel engine. The first model is a single zone model based on the Krieger and Bormann combustion model while the second model is a two-zone model based on Olikara and Bormann combustion model. It was shown that both models can predict well the engine's in-cylinder pressure as well as its overall performances. The second model showed a better accuracy than the first, while the first model was easier to implement and faster to compute. It was found that the first method was better suited for real time engine control and monitoring while the second one was better suited for engine design and emission prediction. The modeling of internal combustion engines has been largely developed during past years. For this purpose, a multitude of industrial codes dedicated to the simulation of the engines is available on market . These codes, despite the fact that they can be useful for predicting engine performances, are expensive for third world's university laboratory and their source codes are practically impossible to modify to implement new model or functions.When modeling compression engine different approaches can be used with different level of complexity, such as thermodynamic 0D models, quasi-dimensional multizone models, and computational fluid dynamics (CFD) models , 2.For this study a quasi-dimensional approach was selected; these models allows to compute efficient, economic, and fast calculations of engine performances as a function of different engine parameters. Using these types of models we can compute the different stages of a diesel engine cycle as in compression, injection, ignition delay, and combustion and exhaust stage.The evaluated models in this study will be evaluated in terms of accuracy and speed of calculation.For both models the fuel spray characteristic is modeled using the phenomenological model of Razleytsev  and Lyshqc is the cyclic fuel supply in Kg/cycle; RPM is the crankshaft rotational speed in rpm; ρf is the density of the fuel in kg/m3; dc is the diameter of the injector hole in mm; φinj is the duration of injection in degree of rotation of the crankshaft.First the average outflow velocity of fuel from the injector is calculated in m/s byM characterizing the relationship between the surface tension force, inertia, and viscosity is calculated as follows:μf is the coefficient of dynamic viscosity of the fuel at a temperature of 323 K in Pa·s; σf is the coefficient of surface tension of the fuel at a temperature of 323 K in N/m.The criterion Weber number characterizing the relationship between surface tension force and inertia is determined asμair = 28.9 Kg/Kmole is the molecular mass of air; ρair is the density of air.The density of the charge at the end of the compression before the TDC is calculated as follows:We then determine the fuel/air density ratio byE32 is an empirical factor depending on designs of the injector, whose recommended value is 1.7.Finally the Sauter mean diameter of the atomized fuel is calculated in micron byAt this point the finesse of the pulverized fuel is determined and we can see it mainly depends on physical properties of the fuel such as viscosity and density. The next step of the model is to determine the kinetic of combustion of the atomized fuel, whose kinetic will be dependent of the earlier found Sauter mean diameter.This part of the elaborated model will permit us to determine parameters of the process such as the evaporation rate of the atomized fuel, its ignition delay, and the duration of combustion.P0 is the reference pressure which in our case corresponds to the inlet manifold pressure.Pressure in the cylinder at the end of the compression before the TDC isK = 1/Pc · 106 is the evaporation constant related to cylinder pressure in m2/sAz is a constant characterizing the duration of evaporation of large drops in diesel engine in 1/s and its value is given as  2.4 in [λ is the coefficient of excess air.We then determine the theoretical constant of evaporation of the fuel by  2.4 in  used it The full duration of combustion is then calculated asEa in this correlation is given by Ea = 618840/(CN + 25); however, this value was computed for the particular experiment reported in [The value of the apparent activation energy orted in , where tFor the two models, we used a double Wiebe function  to modelThis method is a single zone model based on the first law of thermodynamics, mass conservation, and ideal gas laws. Following that we can write the governing equation for calculating variation of in-cylinder pressure with respect to crank angle as (12)dQinThe Krieger and Bormann algorithm is based on polynomial fitting constant to compute the adiabatic index (ratio of specific heat) as function of crank angle. The fitting coefficients can be found in the Appendix.ucorr = cuexp(Dλ + Eλ + FPTλ) is the correction factor for the internal energy accounting for dissociationThe internal energy of combustion products at equilibrium for a reaction between air and a hydrocarbon CnH2n is given asRcorr = crexp(r0logλ + ((r1 + r2/T) + r3log(f6P))/λ).The gas constant is computed ascv = ∂u/∂T.The adiabatic index (ratio of specific heat) is computed asThis model is a two-zone thermodynamic model where the thermodynamics properties of combustion products and fuel are determined using polynomial curve fitted data from the Chemkin  or JANAFThe in-cylinder pressure and temperature of burned and unburned gases derivative can be calculated following Ferguson's algorithm , 16 by(h/∂T)P = cP.The equations of state of the mixture are given byThe combustion products are evaluated assuming that they are in equilibrium at a given temperature and pressure. Using Olikara and Borman  method wyi is the mole fraction of the ith combustion specie at equilibrium and Tm the total number of mole. Following that we can write ∑i=110yi − 1 = 0.Considering the combustion reaction of a hydrocarbonp representing the pressure at which the reaction occurs in atmosphere. The reactions constants are computed using the following expression:A, B, C, D, and E given in with the constants The system of equation comprises 10 unknowns and 4 equations; we then need 6 complementary equations in order to be able to solve the system. For that we introduce six gas phase equilibrium reactions constantWe find ourselves with a set of 11 nonlinear equations with 11 unknowns which are solved using Newton Raphson iteration. A detailed description of the resolution algorithm can be found in . The metFor validation purposes the two models were implemented and compared with experimental results from , the engP-V diagram using the trapezoidal rule, and the formula used was thenVd being the displaced volume of the engine, in m3.The experimental imep (indicative mean effective pressure) was not given in the experimental work reported by , it was Simulations were computed at rated engine speed and the pressure plot was made and compared with the experimental results Figures , and 4. The pressure traces obtained from the two model show that they reproduce well the in cylinder pressure for both type of fuels in the given engine configuration. It can be seen that the maximum pressure decreases when biodiesel fuel is used for the two simulations, which is equally the trend observed experimentally and in other works such as –22. ThisThe values of computed parameters are given in Another assessment made for the two models was the speed of computation; the first model was computed in 6 seconds, while the second took about 40 to 45 second to run completely on 2 Ghz dual core Pentium personal computer.With this assessment, we can say that the first model could be suitable for real time engine control while the second could be used for engine's design and also emission evaluation since it computes in cylinder pressure by determining combustion species states at each time step. Another development that could be made for the second model can be the implementation of the Zeldovich mechanism , 11 to cThe aim of the present study was to develop and implement two different models for diesel engine fuelled on biodiesel based on tabulated chemistry. The two models showed good predictability of engine performance, with the second approach giving a better accuracy. The first approach was faster to compute the cylinder pressure than the second and was found more suitable for engine monitoring and control while the second one was found better suited for engine design and emission prediction.


In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. The signals, with majority of the components are zero, are called sparse signals. Like majority of the signals in the nature, the ocean waves are sparse either in the time or in the frequency domain. Therefore the compressive sampling technique can be thought as a very efficient tool for measuring or simulating the ocean waves. In this paper it is shown that the efficiency of the compressive sampling technique can also be used for the improvement of the computational simulation efforts of the ocean waves.th order Runge-Kutta method. The proposed approach, which can be named as compressive spectral method, depends on the idea of using smaller number of spectral components compared to the classical spectral method. Performing time integration with smaller number of spectral components and using the compressive sampling technique, it shown that the ocean wave field can be modeled with a significantly better efficiency compared to the classical spectral method. The sparsity property of the wave field in the frequency domain which has the Jonswap form is used and l1 minimization step of the compressive sampling algorithm is applied in the frequency domain.The linear and fully nonlinear ocean gravity waves are considered in this study. Ocean waves are simulated by implementation of a high order spectral method in which the spectral derivatives are evaluated using the fast Fourier transforms (FFT) over the periodic domain. Time integration is carried out using a 4It is shown that by using a smaller number of spectral components and the compressive sampling technique, ocean waves can be simulated very efficiently compared to the classical spectral simulation with a larger number of spectral components. Also it is shown that the accuracy difference between two models is of negligible importance. Therefore it is shown that the proposed compressive spectral method can be a very efficient tool in simulations of fully nonlinear ocean waves.z = 0 are given asMany different approximate equations are developed to model the ocean waves. Also there are various models which solve the fully nonlinear kinematic and dynamic boundary conditionsη and φ denote the water surface fluctuation and the velocity potential, respectivelyh, the velocity potential φ can be expressed bywhere φz at z = 0 can be written aswhere F and F−1 denote the Fourier and inverse Fourier transformations respectively. In this paper only one dimensional waves are studied.where th order Runge-Kutta method for time integration in order to simulate the linear ocean waves for various initial linear ocean wave profiles. Initial linear ocean wave fields are constructed by an inverse FFT algorithm using random spectral components with total energy described by the Jonswap spectrum. Details and further discussion can be seen inThis set of equations are solved with a 4The high order spectral method summarized in this section is first presented in123η is the water surface fluctuation and ϕ is the velocity potential. Using ϕs, it is possible to show that potential flow of water waves on an deep fluid can be formulated as a canonical Hamiltonian system;FollowingH is the Hamiltonian which is the total energy of the wavefield. The details of this derivation can be seen inwhere andthe classical kinematic and dynamic boundary conditions can be written as1andPa is the atmospheric pressure, ρ is the density of water and the horizontal gradient is where ψ takes the form of a decaying exponential so that14For deep water the shape function whereas for shallow waterh is the water depth1S, the ϕz can be written aswhere ϕz using (10–12). So that  can be solved numerically. In this study time integration is performed by a 4th order Runge-Kutta method8By utilizing the efficient FFTs on a periodic domain one can evaluate  So that ,8 can beϕz using 0–12. So After it has been introduced to the scientific community with a seminal paperη be a signal of length N and a K-sparse signal, that is only K out of N elements of the signal are nonzero. Using orthonormal basis functions with transformation matrix ψ, η can be represented in terms of basis functions. Typical transformation used today are the Fourier, wavelet or discrete cosine transforms just to mention few. Therefore it is possible to write η which is a K-sparse signal one can obtain ηs is the signal with non-zero components only.Let K-sparse signal η of length N can exactly be reconstructed from M ≥ Cμ2K log(N) random measurements with a very high probability, where C is a positive constant and μ2 is the mutual coherence between the sensing basis ξ and transform basis ψM samples are taken in physical domain or for the recovery of the sparse signal in the physical domain the M samples are taken in the spectra. Taking M random projections and by using the sensing matrix ξ one obtains g = ξη. Therefore the problem can be formulated asThe underlying idea of the CS is that a l1 solution of the CS problem is given as where l1 minimization is only one of the alternatives which can be used for this optimization problem. There are some other algorithms in literature to recover the sparse solutions such as reweighted l1 minimization or greedy pursuit algorithms10N be the number of the spectral components used for the representation of a signal. N is generally desired to be as large as possible that the computational effort allows. Here we introduce the compressive spectral method which states that by using M spectral components with M << N and using the CS technique to construct the N-component signal at the last step of the time evolution from M components, it is possible to obtain a very efficient computational method especially for very long time evolutions. The selection of the M spectral components has to be done carefully depending on the width of the K-sparse wave profile in order to satisfy the lower limit of M = O(K log(N/K)) condition of the CS algorithm where O denotes the order of symbol. For example for a 10-sparse signal with 1000 elements, that is for K = 10 and N = 1000 one would need M = O(20) components for the exact recovery of the 10-sparse signal by the CS. If a smaller M is used then the exact recovery of the sparse signal may become impossible. If a higher M is used that exact recovery can be done but one starts to lose the undersampling ratio advantage of the CS.In a classical spectral method let M samples has to be chosen randomly. However for the many of the phenomena we encounter in the oceanography we have the priori knowledge about which spectral components will be nonzero. Some examples are sideband waves with few nonzero spectral components, Jonswap spectrum with more energy in the smallers wavenumbers, triangular spectrum of the rational rogue wave solutions of the nonlinear Schrödinger equationM equally spaced samples in the physical ocean surface. Our undersampling ratio becomes r = N/M. This deterministic uniform sampling causes r replicas to appear in the recovered spectrum by the CS. We only need and keep the energy in the smaller wavenumber components and filter out the r − 1 aliasing high wavenumber replicas of the spectrum.The CS theory states that M spectral components. After the time stepping, the N point signal is reconstructed from M components with the help of the l1 minimization technique of the CS theory. It is shown that the methodology offered in here can reduce the computational effort significantly compared to the classical spectral method with N components while the accuracy difference in the results is negligible. In order to ensure the stability of the schemes both for the classical and the proposed compressive spectral methods, a small dt must be selected to satisfy the CFL condition. For example for L = 500 m, N = 2048, M = 256 the dt = 10−5 value is selected. This strict requirement is imposed by the classical spectral method, not by the proposed compressive spectral method. That is dxN = L/N is smaller than dxM = L/M, so in order to satisfy CFL condition (upper bounded dt/dx), smaller dt must be selected for the classical method. The proposed method also relaxes this restriction.Starting from the initial conditions, time stepping is performed for only selected A similar approach has been introduced by us and discussed in13N = 1024 component classical spectral method and the M = 256 component compressive spectral method proposed are compared. The two methods are in excellent agreement as it can be seen in the figure. The normalized root-mean-squared difference between two spectra is 0.0045 for this simulation.In the N = 1024 component spectral method and the M = 256 component compressive spectral method proposed are compared. The two methods are in excellent agreement as it can be seen in the figure. The normalized root-mean-square difference between two profiles is 0.0052 for this simulation.By means of an inverse FFT, it is possible to construct the ocean surface with linear waves which is not necessarily sparse. In the N = 2048 component classical spectral method and the M = 256 component compressive spectral method proposed are compared. The two methods are in excellent agreement as it can be seen in the figure. The normalized root-mean-square difference between two spectra is 0.0044 for this simulation.In the N = 1024 component classical spectral method and the M = 256 component compressive spectral method proposed are compared. Again the two methods are in excellent agreement in terms of accuracy. The normalized root-mean-square difference between two profiles is 0.0048 for this simulation.Again by means of an inverse FFT, it is possible to construct the ocean surface with linear waves which is not necessarily sparse. In the N = 1024 component classical spectral method and the M = 128 component compressive spectral method proposed are compared in the M causes the difference to increase although still it is of negligible importance. This is mainly due to the fact that for a smaller M the sparsity condition becomes critical. The normalized root-mean-square difference between two spectra is 0.0036 for this simulation.The Jonswap spectra of the N = 1024 component classical spectral method and the M = 128 component compressive spectral method proposed are compared. The two methods are in very good agreement as it can be seen in the figure. The normalized root-mean-square difference between two profiles is 0.0165 for this simulation.Again by means of an inverse FFT, it is possible to construct the ocean surface with linear waves which is not necessarily sparse. In the All of the results presented above show promising evidence for the accuracy of the proposed method for the linear ocean wave simulations. Additionally the computational efforts required to run the various configurations for the linear ocean wave simulations are summarized in the l1 minimization. However as the number of time steps gets bigger, the computational effort significantly reduces while the differences in the wave profiles are of negligible importance. Therefore compressive spectral method provides a great computational efficiency compared to the classical spectral method for the ocean wave simulations which are sparse in frequency domain.The average computation times of 50 realizations given in the N = 1024 component classical spectral method and the M = 256 component compressive spectral method proposed are compared for a monochromatic wave. The two methods are in excellent agreement as it can be seen in the figure. The normalized root-mean-square difference between two profiles is 0.0230 for this simulation. Water surface fluctuation is obtained by taking the inverse FFT of this spectra and is shown in the N = 1024 component classical spectral method and the M = 256 component compressive spectral method proposed are compared. The two methods are in excellent agreement as it can be seen in the figure. The normalized root-mean-square difference between two profiles is 0.0006 for this simulation.In this section we solve the governing equations for the fully nonlinear model described above by the classical spectral method and by the proposed compressive spectral method for a monochromatic wave. In the N = 1024 component classical spectral method and the M = 256 component compressive spectral method proposed are compared for a trichromatic profile, that is a wavefield with three wavenumber components. This is also known as the sidebands example, a wavefield with one central wavenumber component and two side neighbour components of this central wavenumber. The steepness for this surface is ka ≈ 0.1. The two methods are in excellent agreement as it can be seen in the figure. The normalized root-mean-square difference between two profiles is 0.0034 for this simulation. In the N = 1024 component classical spectral method and the M = 256 component compressive spectral method proposed are compared for the trichromatic wavefield. The normalized root-mean-square difference between two profiles is 0.0059 for this simulation and agreement is excellent.In this section we solve the governing equations for the fully nonlinear model described above by the classical spectral method and by the proposed compressive spectral method for a trichromatic wave. In the M = O(K log(N/K)) samples are needed for the exact reconstruction. Therefore it is important to analyze how the proposed method will perform in the case of spectral broadening. For this purpose we consider the nonlinear wave interactions. We test the proposed method with longer temporal runs. Generally speaking, a time scale of 25Tp is sufficient for nonlinear interactions to be developed5Tp is the peak wave period. We test the method with a run time of 50Tp. The resulting spectra for this simulation is presented in the As discussed in the review of compressive sampling section above, for a K-sparse frequency series at least M = O(K log(N/K)) condition of the compressive sampling is not strict because initially only three wavenumbers has energy and after the time stepping long enough to cause some interactions (for this example 50Tp is used) the energy has spread to only few other wavenumber components. Although there is spectral broadening, the spectra still satisfies the M = O(K log(N/K)) condition of the compressive sampling since K remains small, therefore the proposed compressive spectral method works well.As it can be realized from the figures above, the method also works well in the case of spectral broadening due to nonlinear interactions. The spectra exhibits energy increase in higher and lower wavenumbers. For trichromatic waves, the η and ϕs in the Fourier domain. The effects of the smoothing filter such as the decay of the total wave energy is discussed in1M components and those components are the first M components of the classical smoothing filter with N terms.In this section we solve the governing equations for the fully nonlinear model described above by the classical spectral method and the proposed compressive spectral method for a wave field described by a Jonswap spectra. For small evolution times the results are no different than the results presented in linear wave simulations sections since nonlinear interaction do not develop within short time. Therefore we concentrate on runs with time scales long enough for the nonlinear interactions to be developed. However it is known that high order spectral method is subjected to high wavenumber instability in the form of a sawtooth function in the spatial domain which becomes more critical for longer runs. Therefore in order to obtain stable solutions smoothing filter must be applied. One possible form of the smoothing filter is given in1N = 2048 component classical spectral method and the M = 256 component compressive spectral method proposed are compared for a fully nonlinear ocean wave surface defined by a Jonswap spectrum. The two methods are in excellent agreement as it can be seen in the figure. The normalized root-mean-square difference between two profiles is 0.0099 for this simulation. The corresponding water surface fluctuation which is obtained by applying inverse FFT on for this spectra can be seen in the M = O(K log(N/K)) condition of the compressive sampling. As a numerical check; for a peak period of Tp = 12 s and significant wave height of Hs = 1 m, the N component Jonswap spectra decreases almost to zero at the 80th point of the wavenumber vector. Therefore for this case the two sided Jonswap spectra can be thought as 160-sparse function. Therefore for N = 1024 at least M = O(160 log(1024/160)) = O(129) sampling points are necessary. Although this requirement forces M to be bigger in the case of spectral broadening, the proposed method still performs significantly better in terms of computation time as discussed in the coming sections.In the Tp is used. As it can realized from the M = O(K log(N/K)) condition of the compressive sampling therefore proposed compressive spectral method works well. If longer runs are performed with various configurations higher values for M may be needed due on the restrictions on M. In that case the proposed compressive spectral method would be less efficient than itself with a smaller M, but still more efficient than the classical spectral method. However with the examples presented above it is shown the proposed compressive sampling method can accurately model the fully nonlinear ocean waves in the typical temporal and frequency range including the spectral broadening.As a further check on the spectral broadening, we consider a Jonswap type spectrum with energy concentrated around two peak periods initially. Such simulations can be beneficial for modeling shorter waves with more energy superimposed on longer wave trains as well as swell simulations. Again smoothing filter is applied in this simulation and a run time of 50In reality, for example in very shallow water with many wave interactions and capillary components the spectrum would be too wide for the CS to make the exact recovery. So in that case since the sparsity property is not satisfies the proposed method would fail. However as the spectrum gets wider, the actual surface profile would get narrower and more sparse. Therefore in that case by means of a hybrid method it would be possible to switch to perform the CS in the physical domain by taking samples in the frequency domain. However this is a part of future study and not addressed in this paper.l1 minimization. However for the bigger number of time steps, the computational time is significantly improved while the differences in the wave profiles are of negligible importance. Therefore by reducing the computation time the compressive spectral method provides a great computational efficiency compared to the classical spectral method and can be used as a tool in not only for ocean wave simulations but also many other phenomena in applied mathematics and physics.All of the results presented above show promising evidence for the accuracy of the proposed method. Additionally the computational efforts required to run the various configurations are summarized in the In this study compressive spectral method for the simulation of the linear and the fully nonlinear ocean gravity waves is introduced. The sparsity property of Jonswap frequency spectrum of the ocean waves is used for this purpose. It is shown that by using a smaller number of spectral components and the compressive sampling technique, it is possible to reconstruct the ocean surface with negligible difference in accuracy compared to the classical spectral method which uses a bigger number of spectral components. It is shown that the proposed compressive spectral method improves the computational effort significantly compared to the classical spectral method while still correctly models the nonlinear ocean waves including spectral broadening. This improvement becomes more significant especially for large time evolutions.How to cite this article: Bayındır, C. Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves. Sci. Rep.6, 22100; doi: 10.1038/srep22100 (2016).


With the popularity of smart handheld devices and the emergence of cloud computing, users and companies can save various data, which may contain private data, to the cloud. Topics relating to data security have therefore received much attention. This study focuses on data stream environments and uses the concept of a sliding window to design a reversible privacy-preserving technology to process continuous data in real time, known as a continuous reversible privacy-preserving (CRP) algorithm. Data with CRP algorithm protection can be accurately recovered through a data recovery process. In addition, by using an embedded watermark, the integrity of the data can be verified. The results from the experiments show that, compared to existing algorithms, CRP is better at preserving knowledge and is more effective in terms of reducing information loss and privacy disclosure risk. In addition, it takes far less time for CRP to process continuous data than existing algorithms. As a result, CRP is confirmed as suitable for data stream environments and fulfills the requirements of being lightweight and energy-efficient for smart handheld devices. With the rapid advances in network technologies and the popularity of smart handheld devices, user habits are gradually changing. Cloud computing is the emerging concept in response to these changes. The objective of cloud computing is to provide better services through the Internet and network computing so that computers can collaborate with each other and share hardware and software resources and data Kshetri .In recent years, users and companies have been collecting and saving various data to the cloud, which they analyse to find hidden business opportunities. Owing to the enormous volume of data in a cloud environment, it is impossible to use a manual process to sort the data into the information that can be understood by people. Data mining based on big data has become an important service for cloud computing  algorithm, can recover the protected data and extract the embedded watermark to verify whether the protected data has been tampered with. The requirements for protecting private information and performing data mining of the continuous data can be fulfilled at the same time. The details are explained in the following sections.To protect the content in the data in a data stream environment while meeting the requirements for data mining, we use the concept of a sliding window and propose the CRP algorithm, which can effectively process this type of data. The algorithm has a data protection phase and a data recovery phase. In the data protection phase, a sliding window model is used to protect the content in the continuous data, and the watermarks customised by users are embedded. On the other hand, in the data recovery phase, in addition to recovering the original data from the protected data, one can also extract the embedded watermark to verify whether the protected data has been tampered with. The data protection and recovery phases in CRP are detailed below.s is 3, and the watermark w is (0000111101001…)2. First, since the window size s is 3, the current sliding window has the first three rows of data. According to Step 2, these data in the window are not required to go through the protection process and can be directly saved to the cloud. In Step 3, the average value for Heartbeat in the sliding window is calculated to be 76 diff is 2 (= 78 − 76). Since diff = 2, the fourth value in Heartbeat after data protection is 79 (= 78 + 1). Next, using a similar method, the fourth values in blood pressure, blood glucose, and oxygen content after data protection are calculated and saved to the cloud. The sliding window then slides to the second, third and fourth rows. The above method is used to obtain the values after data protection of the fifth row. Table The example in Table w is 000011101001…After the data protection, if users have concerns about the protected data, the protected data can be recovered and the watermark can be extracted to compare whether the watermark is the same as the watermark configured by the users. This is to verify the integrity of the protected data. The process for the data recovery phase is shown below.s is 3, the current sliding window has the first three rows of data. According to Step 2, these data are not required to go through the recovery process and are thus directly configured as the recovered data. In Step 3, the average value for Heartbeat in the sliding window is calculated to be 76 diff is 3 (= 79 − 76). For the fourth value of Heartbeat, the value after data recovery is 78 (= 79 − 1). Next, using a similar method, the values for Blood pressure, Blood glucose, and Oxygen content after data recovery for the fourth values of data are calculated. Then, the sliding window will slide to the second, third and fourth rows of data. The above method is then used to obtain the value after data recovery of the fifth row of data. Table w is (0000111101001…)2.Table mentclass2pt{minimIn the experiment, we use the assessment method for measuring (Herranz et al. The objective of PPDM is to reduce the disclosure risk of the privacy in the original data while considering the value of data mining for the protected data (Hao et al. DR = 0.5 × ID + 0.5 × DLD (Herranz et al. In terms of knowledge reservation, our assessment is usually based on the classification used in financial and medical estimations (Zhu et al. In our experiments, five test datasets included in UCI Machine Learning Repository (Frank and Asuncion diff. As a result, the content of the original data and that of the protected data are similar.Figure In the following experiments, the default value for the sliding window size is set to be 3 based on experimental observations.In Fig. Figures To show the effectiveness of CRP in regards to the continuous data process, we calculated the execution time required for CRP to protect and recover data; the results are shown in Fig. With the popularity of smart handheld devices and the emergence of cloud computing, users and companies are saving various data to the cloud. Data companies collect data and perform data analysis to find hidden business opportunities. These data may contain private data, making a serious issue data security. To protect private data, our study targeted a data stream environment and designed the CRP algorithm based on the sliding window model to protect continuous data. After CRP protection, the original data can be accurately restored using the data recovery program. In addition, data integrity can be verified using an embedded watermark. For our experiments, we used data for knowledge reservation, information loss, and privacy disclosure risk to assess the effectiveness of CRP. The processing times required for data protection and data recovery were calculated. The experiment results confirmed that, from knowledge reservation and privacy disclosure risk analysis, CRP had better performance than the existing PDE algorithm. In terms of information loss, CRP also had better stability than PDE. In addition, CRP required less execution time than the PDE algorithm in regards to data protection and data recovery, indicating that CRP can effectively protect the privacy in continuous data and can also meet the requirements for knowledge analysis; it is therefore suitable for a cloud computing environment and smart handheld devices.


The aim of the current study was to evaluate the sensitivity of the lever sign test and the widely used basic tests of the Lachman, anterior drawer and pivot shift tests, both under anaesthesia and without anaesthesia, according to the gold standard diagnostic arthroscopic results in patients undergoing anterior cruciate ligament reconstruction. The study included 117 patients, diagnosed with ACL tear which was definitively determined during an arthroscopic surgical procedure applied. Before anaesthesia and while under anaesthesia, the Lachman, anterior drawer, pivot shift and lever sign tests were applied to all patients. Evaluation was made of MR images for each patient and documented. The patients comprised 96 males and 21 females, witha mean age of 25.8 ± 5.9 years . Total tear was determined in 82 cases, anteromedial (AM) bundle in 14, posterolateral (PL) bundle in 13 and elongation in 8. Pre-anaesthesia positivity was found in lever sign at 94.2 %, Lachman at 80.5 %, pivot shift at 62.3 % and anterior drawer at 60.1 %. These rates were determined after anaesthesia as lever sign 98.4 %, Lachman 88.7 %, pivot shift 88.3 % and anterior drawer 84.2 %. The lever sign test can be easily applied clinically and it seems to have higher sensitivity than the Lachman test which is the basis of classic information, it should be included in routine clinical practice. In the light of the results of this study, further studies are required to review the accepted view that the Lachmann test is the most reliable test. Anterior cruciate ligament (ACL) injuries are the most frequently seen ligament injuries of the knee joint  with a 33 mT/m maximum gradient capacity.Following the trauma, all patients were given cold pack therapy, anti-inflammatory medical treatment and weight-bearing was not permitted in the first week. Before the arthroscopic procedure, quadriceps and hamstring strengthening exercises were applied for at least 3 weeks. The mean period between trauma and surgery was 8.7 weeks . All patients were admitted for surgery under spinal anaesthesia without the application of muscle relaxant. The cases for which ACL reconstruction procedures were applied after the 4th week were grouped as acute or chronic. Patients were excluded if there was medial meniscus posterior root tear, bilateral ACL tear, multiple ligament injuries or previous arthroscopic surgery.The lever sign test was applied as described by Lelli . The patDescriptive statistics were used to characterize the sample. Sensitivity was calculated by measuring the proportion of actual positives in the total sample and formulated as true positives/. All calculations were performed with SPSS 20.0 software .The patients comprised 96 males and 21 females, with a mean age of 25.8 ± 5.9 years  Table MRI sensitivity was determined as 92.3 %. In 9 patients determined with total ACL tear in the arthroscopic evaluation, it was reported as intact in the MRI evaluation.According to these results, the lever sign test has much higher sensitivity than the other tests both before anaesthesia and under anaesthia. The sensitivity value under anaesthesia was even found to be higher than the MRI evaluation. In the pre-anaesthesia evaluation, the examination method with the lowest reliability was seen to be the anterior drawer test. The test with the lowest sensitivity under anaesthesia was determined to be the pivot shift test.The most significant finding of this study was that the lever sign test is a new test with higher sensitivity than the Lachman test which can be applied easily both under anaesthesia and without anaesthesia.Due to the stress of the trauma and patient resistance, it may be difficult to apply the standard physical examination methods effectively. Secondly, if the tear is partial or if the ruptured ACL is attached to another point, false negative results may be given (Lintner et al. As 85 % of ACL injuries are from the femoral attachment and there can be considered to be a possibility of attachment of the ruptured ligament to the PCL or structures within the femoral notch, it is more correct for manipulation to be made from the femur.In the study by Lelli, it was determined that the lever sign test had high sensitivity regardless of the degree of the ACL tear or the time of injury (Lelli et al. In literature, the Lachman test has been reported as the test with the highest sensitivity and the pivot shift as that with the highest specificity (Benjaminse et al. The high sensitivity value of the Lachman test in the current study may be due to low patient resistance as there was no acute trauma group. The lever sign test was seen to have much higher sensitivity compared to the other tests in both the evaluation pre-anaesthesia and under anaesthesia. Under anaesthesia, an increase was seen in the sensitivity of the lever sign test and of the other tests. Although this change was significant, it was not at a very high rate in the lever sign test. This shows that the test was affected less than the other tests by patient-related factors.In a meta-analysis by Carola F. Van Eck et al., the sensitivity of the Lachman, anterior drawer and pivot shift tests applied without anaesthetic was found to be 0.81, 0.38 and 0.28 respectively (van Eck et al. In the Lelli study, the sensitivity of the examination method was evaluated according to the MRI diagnosis of the ACL tear (Lelli et al. A limitation of the current study was the small sample size as the evaluation was only of arthroscopic surgery cases. For the same reason, no acute cases were evaluated and therefore the study only included chronic cases. As the number of cases with partial tear was extremely low, test reliability could not be evaluated in respect of partial and full tear cases. Evaluation was not made according to different types of anaesthesia. As the number of females in the sample was low, differences in terms of gender were not evaluated. Finally, when evaluating the sensitivity of the tests, no examination was made of specificity.Diagnosis of ACL tear is made by a combined evaluation of the patient history, physical examination and MRI. Accurate diagnosis is made by interpretation of these 3 steps together. The physical examination methods are indispensable as practical, cheap, non-invasive methods.The lever sign test can be easily applied clinically and it seems to have higher sensitivity than the Lachman test which is the basis of classic information, it should be included in routine clinical practice. In the light of the results of this study, further studies are required to review the accepted view that the Lachmann test is the most reliable test.