Diffuse Part Research Articles

Comparison principles and applications to mathematical modelling of vegetal meta-communities

<abstract><p>This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance). Actually we plan to study the effect of the <italic>fragmentation</italic> of the habitat on biodiversity. A simple neutral model for the evolution of abundances in a vegetal metacommunity is introduced. Migration between the communities is explicitely modelized in a deterministic way, while the reproduction process is dealt with using Wright-Fisher models, independently within each community. The large population limit of the model is considered. The hydrodynamic limit of this split-step method is proved to be the solution of a partial differential equation with a deterministic part coming from the migration process and a diffusion part due to the Wright-Fisher process. Finally, the diversity of the metacommunity is adressed through one of its indicators, the mean extinction time of a species. At the limit, using classical comparison principles, the exchange process between the communities is proved to slow down extinction. This shows that the existence of corridors seems to be good for the biodiversity.</p></abstract>

Unified Stability Analysis for Itô Stochastic Systems: From Almost Surely Asymptotic to Finite-Time Convergence

This technical note proposes a unified Lyapunov framework for analyzing the stochastic asymptotic and finite-time convergence/stability for Ito stochastic nonlinear systems. By exploring the coupling effect between the drift and the diffusion parts of the system, novel almost sure convergence/stability criteria are established. For the finite-time case, the stability criteria not only capture the stabilizing effect of stochastic noise but also include the existing finite-time stability criteria as special cases. For the asymptotic case, it removes the local Lipschitz conditions and the non-zero property of the solution demanded by the existing results. The proposed theoretical results are further applied to solve the sliding mode control and the optimal finite-time/asymptotic stabilization problems.

Approximation of a degenerate semilinear PDE with a nonlinear Neumann boundary condition

We consider a system of semilinear partial differential equations (PDEs) with a nonlinearity depending on both the solution and its gradient. The Neumann boundary condition depends on the solution in a nonlinear manner. The uniform ellipticity is not required for the diffusion coefficient. We show that this problem admits a viscosity solution which can be approximated by a penalization. The Lipschitz condition is required for the coefficients of the diffusion part. The nonlinear part as well as the Neumann condition are Lipschitz. Moreover, the nonlinear part is monotone in the solution variable. Note that the existence of a viscosity solution to this problem has been established in [13] then completed in [15]. In the present paper, we construct a sequence of penalized systems of decoupled forward backward stochastic differential equations (FBSDEs) then we directly show its strong convergence. This allows us to deal with the case where the nonlinearity depends on both the solution and its gradient. Our work extends, in particular, the result of [4] and, in some sense, those of [1, 3]. In contrast to works [1, 3, 4], we do not pass by the weak compactness of the laws of the stochastic system associated to our problem.

Unraveling the coherent dynamic structure factor of liquid water at the mesoscale by molecular dynamics simulations.

We present an investigation by molecular dynamics (MD)-simulations of the coherent dynamic structure factor, S(Q, t) (Q: momentum transfer), of liquid water at the mesoscale (0.1 Å-1 ≤ Q ≤ Qmax) [Qmax ≈ 2 Å-1: Q-value of the first maximum of the static structure factor, S(Q), of water]. The simulation cell-large enough to address the collective properties at the mesoscale-is validated by direct comparison with recent results on the dynamic structure factor in the frequency domain obtained by neutron spectroscopy with polarization analysis [Arbe et al., Phys. Rev. Res. 2, 022015 (2020)]. We have not only focused on the acoustic excitations but also on the relaxational contributions to S(Q, t). The analysis of the MD-simulation results-including the self- and distinct contributions to the diffusive part of S(Q, t)-nicely explains why the relaxation process hardly depends on Q in the low Q-range (Q ≤ 0.4 Å-1) and how it crosses over to a diffusion-driven process at Q ≈ Qmax. Our simulations also give support to the main assumptions of the model used to fit the experimental data in the above mentioned paper. The application of such a model to the simulation S(Q, t) data delivers (i) results for the relaxation component of S(Q, t) in agreement with those obtained from neutron experiments and (ii) longitudinal and transverse hydrodynamic-like components with similar features than those identified in previous simulations of the longitudinal and transverse current spectra directly. On the other hand, in general, our MD-simulations results of S(Q, t) qualitatively agree with the viscoelastic transition framework habitually used to describe inelastic x-ray scattering results.

On the generation mechanisms of low-frequency synchronous pressure pulsations in a simplified draft-tube cone

This paper focuses on the generation mechanisms of synchronous pressure pulsations featuring a lower frequency than the rotating frequency of a vortex core which are observed in a simplified draft-tube cone through analyzing the results of experiments along with unsteady-state numerical simulations. A Venturi-tube is selected as a simplified geometry of hydro-turbine draft-tube; and a stationary-blades swirl generator is installed upstream to generate a uniform swirling flow in the Venturi cone (diffuser part). The experiments, including the dynamic pressure measurements, are conducted for several flowrates to determine the characteristics of pressure fluctuations in the Venturi cone. Two types of pressure fluctuations are identified, namely convective and synchronous. Both cover wide ranges of different frequencies, revealing that the phenomena responsible for generation of these pressure fluctuations feature a stochastic component. The synchronous pressure pulsations, which feature lower frequencies than the convective fluctuations, are identified as the product of self-excited oscillations of vortex breakdown. High-speed visualization of the vortex shape reveals that the vortex features three states: an axisymmetric vortex, a breakdown, and appearance of several helical vortices generated downstream of the breakdown location; while the location of the vortex breakdown fluctuates in time. By using the results of unsteady CFD simulation, it is confirmed that the location of the vortex breakdown fluctuates with the same frequency (Strouhal numbers 0 to 1) as the low-frequency synchronous pressure pulsations observed in the Venturi cone. Moreover, it is observed that the volume of the stagnation region produced due to the counterflow downstream of the breakdown location fluctuates with the same low frequency. Further analysis of the CFD results showed that the flow field at the location of the vortex breakdown experiences a severe shear layer formation around the center of the Venturi. This shear layer stretches the vortex center spatially on the plane perpendicular to the vortex axis. It is also observed that several intermittent helical vortices are generated downstream the breakdown location and rotate periodically in the Venturi while featuring a stochastic nature, as well.

Coarse‐graining via EDP‐convergence for linear fast‐slow reaction‐diffusion systems

AbstractIn [7] a fast‐reaction limit for a linear reaction‐diffusion system consisting of two diffusion equations coupled by a linear reaction is performed. The linear reaction‐diffusion system is understood as a gradient flow of the free energy in the space of probability measures equipped with a geometric structure, which contains the Wasserstein metric for the diffusion part and cosh‐type functions for the reaction part. The fast‐reaction limit is done on the level of the gradient system by proving EDP‐convergence with tilting. The limit gradient system induces a diffusion system with Lagrange multipliers on the linear slow‐manifold. Moreover, the limit gradient system can be equivalently described by a coarse‐grained gradient system, which induces a scalar diffusion equation with a mixed diffusion constant for the coarse‐grained slow variable.

Diffusion gravity and its consequences

Diffusion quantum mechanics (DQM), proposed recently (Zakir, 2020-21), describes a conservative diffusion of classical particles in a fluctuating classical scalar field and, in a homogeneous field, derives the formalism of quantum mechanics. In an inhomogeneous scalar field, DQM reproduces gravitation, and in the present paper, the following theory of diffusion gravity and its various consequences are considered. In DQM a part of the energy of the scalar field is transferred to particles as their fluctuation energy (“thermal” energy), appearing as their rest energy (mass). The resulting local decrease in the field’s energy density around a macroscopic body generates “thermal” diffusion flux of particles to this region. The properties of this “thermal” part of conservative diffusion are similar to gravitation. A high matter concentration in some region reduces the local energy density of scalar field sufficiently to reduce the local intensity of fluctuations. Due to the conservativity of diffusion, the increments in the drift velocity of particles are cumulative, and “thermal” diffusion acceleration arises, independent on the particle’s mass. The world lines become curved, and all processes with particles slowdown, which means time dilation. On hypersurfaces of simultaneity t = const, where the scalar field is defined, effective metrics, connection, and curvature arise. They obey to Einstein’s equations following from balance between energies of matter and background scalar field.

Generation of mean flows in rotating anisotropic turbulence: The case of solar near-surface shear layer

Context.Results from helioseismology indicate that the radial gradient of the rotation rate in the near-surface shear layer (NSSL) of the Sun is independent of latitude and radius. Theoretical models using the mean-field approach have been successful in explaining this property of the NSSL, while global direct or large-eddy magnetoconvection models have so far been unable to reproduce this.Aims.We investigate the reason for this discrepancy by measuring the mean flows, Reynolds stress, and turbulent transport coefficients under conditions mimicking those in the solar NSSL.Methods.Simulations with as few ingredients as possible to generate mean flows were studied. These ingredients are inhomogeneity due to boundaries, anisotropic turbulence, and rotation. The parameters of the simulations were chosen such that they matched the weakly rotationally constrained NSSL. The simulations probe locally Cartesian patches of the star at a given depth and latitude. The depth of the patch was varied by changing the rotation rate such that the resulting Coriolis numbers covered the same range as in the NSSL. We measured the turbulent transport coefficient relevant for the nondiffusive (Λ-effect) and diffusive (turbulent viscosity) parts of the Reynolds stress and compared them with predictions of current mean-field theories.Results.A negative radial gradient of the mean flow is generated only at the equator where meridional flows are absent. At other latitudes, the meridional flow is comparable to the mean flow corresponding to differential rotation. We also find that the meridional components of the Reynolds stress cannot be ignored. Additionally, we find that the turbulent viscosity is quenched by rotation by about 50% from the surface to the bottom of the NSSL.Conclusions.Our local simulations do not validate the explanation for the generation of the NSSL from mean-field theory where meridional flows and stresses are neglected. However, the rotational dependence of the turbulent viscosity in our simulations agrees well with theoretical predictions. Moreover, our results agree qualitatively with global convection simulations in that an NSSL can only be obtained near the equator.

Knudsen type group for time in ℝ and related Boltzmann type equations

We consider certain Boltzmann type equations on a bounded physical and a bounded velocity space under the presence of both reflective as well as diffusive boundary conditions. We introduce conditions on the shape of the physical space and on the relation between the reflective and the diffusive part in the boundary conditions such that the associated Knudsen type semigroup can be extended to time [Formula: see text]. Furthermore, we provide conditions under which there exists a unique global solution to a Boltzmann type equation for time [Formula: see text] or for time [Formula: see text] for some [Formula: see text] which is independent of the initial value at time 0. Depending on the collision kernel, [Formula: see text] can be arbitrarily small.

A weighted discontinuous Galerkin method for diffusion equations with non-smooth coefficients on distorted polygonal meshes

The elliptic equations with heterogeneous and anisotropic diffusion coefficients play an important role in many physical applications such as radiation hydrodynamics and reservoir simulations. Usually the distorted meshes are considered since the 解 of the diffusion part involves the hydro part. The discontinuous Galerkin (DG) method is an important class of methods in computational mathematics. Thefeatures of DG methods can be implemented flexibly on large deformation quadrilateral meshes anddiscontinuous coefficients. In this study, we present a weighted discontinuous Galerkin (WDG) method for numerically solving the elliptic 问题 with non-smooth coefficients. The WDG method is based on the symmetric interior penalty technique. We give the proof of the coercivity and continuity of bilinear forms in the WDG scheme. The convergence analysis for the energy norm is presented based on the coercivity and continuity. Next, we prove an error estimate in the $L^2$ norm based on the duality argument. Numerical examples demonstrate the validity of the WDG method for elliptic problems with discontinuous and anisotropic diffusion coefficients. Some types of distorted meshes such as random, sinusoidal, Shestakov, and Z meshes are used.

Linear-Quadratic Stochastic Delayed Control and Deep Learning Resolution

We consider a simple class of stochastic control problems with a delayed control, in both the drift and the diffusion part of the state stochastic differential equation. We provide a new characterization of the solution in terms of a set of Riccati partial differential equations. Existence and uniqueness of a solution are obtained under a sufficient condition expressed directly as a relation between the time horizon, the drift, the volatility and the delay. Furthermore, a deep learning scheme (The code is available in a IPython notebook.) is designed and used to illustrate the effect of the delay feature on the Markowitz portfolio allocation problem with execution delay.

Numerical studies for effect of geometrical parameters on water jet pump performance via entropy generation analysis

This paper presented an implementation of entropy generation analysis in the main flow field of a water jet pump via the CFD method. This study aimed to identify the inefficient location of energy conversion and to analyse entropy generation sources in each region of the water jet pump. The 2D-axisymmetric model and realisable k-ε (RKE) turbulence model at steady-state conditions were performed to validate jet pump performance and to assess the entropy generation. Likewise, the effects of the projection ratio and throat-aspect ratio as independent parameters were investigated. As a result, the throat is the most inefficient part due to the high total entropy generation rate, following by diffuser part. Also, the entropy generation rate was assessed dominant than viscous dissipation due to the turbulent dissipation, which was caused by a turbulent shear stress layer of mixing the streams. In conclusion, the projection ratio influenced the growth of the shear stress layer as well as the entropy generation. Further, the throat-aspect ratio affected the distribution of entropy generation in the throat section. An appropriate combination of both parameters has an impact on the jet pump performance improvements reducing the entropy generation rate in the future.

EDP-convergence for a linear reaction-diffusion system with fast reversible reaction

We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We understand the linear reaction-diffusion system as a gradient flow of the free energy in the space of probability measures equipped with a geometric structure, which contains the Wasserstein metric for the diffusion part and cosh-type functions for the reaction part. The fast-reaction limit is done on the level of the gradient structure by proving EDP-convergence with tilting. The limit gradient system induces a diffusion system with Lagrange multipliers on the linear slow-manifold. Moreover, the limit gradient system can be equivalently described by a coarse-grained gradient system, which induces a diffusion equation with a mixed diffusion constant for the coarse-grained slow variable.

Increasing Boiling Fluid Flowing Efficiency from Motive Nozzles of Two-Phase Ejectors

The article contains the possibility of increasing boiling fluid flowing efficiency from expanding channels. This process takes place in the motive flow nozzle of a liquid-vapor ejector, working on the principle of thermal stream compression. Efficiency increasing by profiling the diffuser part of the nozzle. Modern industry uses nozzles, which are like de Laval nozzles, with straight walls of the diffusers. The authors suggest paying closer attention to profiling these nozzles, which might increase their efficiency and improve their gas-dynamic characteristics. For comparison, we choose a channel of a traditional form (with straight walls of the diffuser) and a channel of parabolic shape. The article contains a mathematical model to calculate the process of flowing the boiling fluid from the authors-designed channels – the peculiarities of this model that appear after changing the geometry of its streaming part. We obtain comparative analysis calculation results based on the mathematical model and the Ansys CFX workflow model. As a result of numerical calculation using the authors mathematical model and modelling in the Ansys CFX software package, it concludes that the parabolic shape of the diffuser is the most favourable. In the boiling process, the liquid central core is boiling at the optimum distance from the nozzle throat, and the flow of a stable vapor structure with the required pressure value for each regime forming at the outlet.

Thermal transport in CuCr2X4 ( X=S , Se, Te): Experiment and ab initio calculations

We present a combined experimental and theoretical study of the longitudinal and transverse thermoelectric properties of ferrimagnetic spinels $\mathrm{Cu}{\mathrm{Cr}}_{2}{X}_{4}$ ($X=\mathrm{S}$, Se, Te). The thermoelectric power of all studied phases is positive and consists of two contributions; an almost linear diffusive thermopower observed at high temperature, and a strong enhancement below ${T}_{C}$ attributed to magnon drag. The diffusive part of thermopower and resistivity decreases from $X=\mathrm{S}$ to Te, whereas the magnon drag enhancement is the biggest for $X=\mathrm{Se}$, which has also the highest ${T}_{C}$. The thermopower was calculated by DFT method using GGA, $\mathrm{GGA}+U, \mathrm{GGA}+\text{oeeHyb}$, and mBJ potentials. A good agreement with the experimental thermopower was achieved using GGA potential for $X=\mathrm{S}$ and with mBJ potential for $X=\mathrm{Te}$. The mBJ potential, which was designed for $sp$-type semiconductors, better describes the valence bands of $\mathrm{Cu}{\mathrm{Cr}}_{2}{\mathrm{Te}}_{4}$ that exhibit stronger $sp$-orbitals character than sulfide and selenide. The anomalous Nernst effect (ANE) is negative at room temperature for all phases, the highest absolute value $\ensuremath{\sim}1.5 \ensuremath{\mu}\mathrm{V}$/K is observed for $X=\mathrm{Te}$ and Se around room temperature, whereas ANE for $X=\mathrm{S}$ is much smaller. A sign change of ANE to positive is observed at 285 K for $X=\mathrm{S}$ and at 65 K for $X=\mathrm{Se}$. The trend of anomalous Nernst conductivity is reproduced by Berry phase calculations if the renormalization of the bands due to the strong correlation effects is taken into account.

Structural Attack (and Repair) of Diffused-Input-Blocked-Output White-Box Cryptography

In some practical enciphering frameworks, operational constraints may require that a secret key be embedded into the cryptographic algorithm. Such implementations are referred to as White-Box Cryptography (WBC). One technique consists of the algorithm’s tabulation specialized for its key, followed by obfuscating the resulting tables. The obfuscation consists of the application of invertible diffusion and confusion layers at the interface between tables so that the analysis of input/output does not provide exploitable information about the concealed key material.Several such protections have been proposed in the past and already cryptanalyzed thanks to a complete WBC scheme analysis. In this article, we study a particular pattern for local protection (which can be leveraged for robust WBC); we formalize it as DIBO (for Diffused-Input-Blocked-Output). This notion has been explored (albeit without having been nicknamed DIBO) in previous works. However, we notice that guidelines to adequately select the invertible diffusion ∅and the blocked bijections B were missing. Therefore, all choices for ∅ and B were assumed as suitable. Actually, we show that most configurations can be attacked, and we even give mathematical proof for the attack. The cryptanalysis tool is the number of zeros in a Walsh-Hadamard spectrum. This “spectral distinguisher” improves on top of the previously known one (Sasdrich, Moradi, Güneysu, at FSE 2016). However, we show that such an attack does not work always (even if it works most of the time).Therefore, on the defense side, we give a straightforward rationale for the WBC implementations to be secure against such spectral attacks: the random diffusion part ∅ shall be selected such that the rank of each restriction to bytes is full. In AES’s case, this seldom happens if ∅ is selected at random as a linear bijection of F322. Thus, specific care shall be taken. Notice that the entropy of the resulting ∅ (suitable for WBC against spectral attacks) is still sufficient to design acceptable WBC schemes.

Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability

Evolution of the nonequilibrium thermodynamic entities corresponding to dynamics of the Hopf instabilities and traveling waves at a nonequilibrium steady state of a spatially extended glycolysis model is assessed here by implementing an analytically tractable scheme incorporating a complex Ginzburg-Landau equation (CGLE). In the presence of self and cross diffusion, a more general amplitude equation exploiting the multiscale Krylov-Bogoliubov averaging method serves as an essential tool to reveal the various dynamical instability criteria, especially Benjamin-Feir (BF) instability, to estimate the corresponding nonlinear dispersion relation of the traveling wave pattern. The critical control parameter, wave-number selection criteria, and magnitude of the complex amplitude for traveling waves are modified by self- and cross-diffusion coefficients within the oscillatory regime, and their variabilities are exhibited against the amplitude equation. Unlike the traveling waves, a low-amplitude broad region appears for the Hopf instability in the concentration dynamics as the system phase passes through minima during its variation with the control parameter. The total entropy production rate of the uniform Hopf oscillation and glycolysis wave not only qualitatively reflects the global dynamics of concentrations of intermediate species but almost quantitatively. Despite the crucial role of diffusion in generating and shaping the traveling waves, the diffusive part of the entropy production rate has a negligible contribution to the system's total entropy production rate. The Hopf instability shows a more complex and colossal change in the energy profile of the open nonlinear system than in the traveling waves. A detailed analysis of BF instability shows a contrary nature of the semigrand Gibbs free energy with discrete and continuous wave numbers for the traveling wave. We hope the Hopf and traveling wave pattern around the BF instability in terms of energetics and dissipation will open up new applications of such dynamical phenomena.

Electrophoretic mobility and stability of SiO2 nanoparticles in the solutions of AOT in n-hexadecane-chloroform mixtures.

Electrophoretic mobility of SiO2 nanoparticles in a n-hexadecane-chloroform mixture depending on AOT concentration and chloroform content was determined. It was shown that an increase in chloroform content and a decrease in AOT concentration cause a growth in electrophoretic mobility. The use of the values of Debye lengths (characteristic thickness) of the diffuse part of the electric double layer (EDL) that were determined previously allowed us to calculate the electrokinetic potential and to evaluate the stability of organosols. The obtained data were in good correlation with the dynamics of temporal changes of hydrodynamic radius and the intensity of light scattering. Organosols may be used for heteroaggregation (sorption) of Au and Ag nanoparticles on SiO2 .

Temperature-dependent dynamic structure factors for liquid water inferred from inelastic neutron scattering measurements.

Temperature-dependent dynamic structure factors S(Q, ω) for liquid water have been calculated using a composite model, which is based on the decoupling approximation of the mean square displacement of the water molecules into diffusion and solid-like vibrational parts. The solid-like vibrational part Svib(Q, ω) is calculated with the phonon expansion method established in the framework of the incoherent Gaussian approximation. The diffusion part Sdiff(Q, ω) relies on the Egelstaff-Schofield translational diffusion model corrected for jump diffusions and rotational diffusions with the Singwi-Sjölander random model and Sears expansion, respectively. Systematics of the model parameters as a function of temperature were deduced from quasi-elastic neutron scattering data analysis reported in the literature and from molecular dynamics (MD) simulations relying on the TIP4P/2005f model. The resulting S(Q, ω) values are confronted by means of Monte Carlo simulations to inelastic neutron scattering data measured with IN4, IN5, and IN6 time-of-flight spectrometers of the Institut Laue-Langevin (ILL) (Grenoble, France). A modest range of temperatures (283-494K) has been investigated with neutron wavelengths corresponding to incident neutron energies ranging from 0.57 to 67.6 meV. The neutron-weighted multiphonon spectra deduced from the ILL data indicate a slight overestimation by the MD simulations of the frequency shift and broadening of the librational band. The descriptive power of the composite model was suited for improving the comparison to experiments via Bayesian updating of prior model parameters inferred from MD simulations. The reported posterior temperature-dependent densities of state of hydrogen in H2O would represent valuable insights for studying the collective coupling interactions in the water molecule between the inter- and intramolecular degrees of freedom.

Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions

We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation is solved with the Crank-Nicolson method, while order reduction occurs in general if using other Runge-Kutta schemes or even the exact flow itself for the diffusion part. We prove these results when the source term only depends on the space variable, an assumption which makes the splitting scheme equivalent to the Crank-Nicolson method itself applied to the whole problem. Numerical experiments suggest that the second order convergence persists with general nonlinearities.