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This paper mainly deals with the (non)existence, asymptotic behaviors and uniqueness of traveling waves to a nonlocal diffusion system with asymmetric kernels and delays for quasi-monotone case. The difference from some previous works is the asymmetry reflected in both diffusion and reaction terms, and this not only has an impact on the positivity of minimal wave speed and the wave profiles of traveling waves with the same speed spreading from the left and right of the x-axis, but also leads to some difficulties for the nonexistence and asymptotic behaviors of traveling waves, which are overcome by using new techniques. Thereby, the results for traveling waves of nonlocal diffusion equations with symmetric kernels and with (or without) delays are improved to equations with asymmetric kernels, and those conclusions for scalar equations and systems with Laplace diffusion and local nonlinearities are also generalized to the nonlocal case. Finally, some concrete applications and numerical simulations are shown to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

Scanning the whole writing, we discuss a stochastic cooperative species system with distributed delays under the influences of Ornstein–Uhlenbeck process of mean regression. We successfully obtain the existence and uniqueness of positive solutions for stochastic system at first. Secondly, by studying the Lyapunov function, we present the existence of the stationary distribution of the system. We are relatively familiar with the understanding of the density function of random systems. This paper also gives the expression of the density function of the random system near the unique positive equilibrium. In addition, the asymptotic properties of the p-moment boundedness and solution of the stochastic population system are also studied. In particular, we use numerical simulation to verify the theoretical results in the last section. [ABSTRACT FROM AUTHOR]

We study emergent behaviors of Cucker–Smale (CS) flocks on the hyperboloid H d in any dimensions. In a recent work [Ha et al., J. Math. Phys. 61(4), 042701 (2020)], a first-order aggregation model on the hyperboloid was proposed and sufficient conditions for emergent dynamics were proposed in terms of initial configuration and system parameters. In this paper, we are interested in the second-order modeling of CS flocks on the hyperboloid. For this, we derive our second-order model from the abstract CS model on complete and smooth Riemannian manifolds via explicit identifications of geodesic and parallel transport. Velocity alignment has been shown by combining general velocity alignment estimates for the abstract CS model on manifolds and verifications of the a priori estimate of the second derivative of the energy functional. For the two-dimensional case H 2 , similar to the recent result by Ahn, Ha, and Shim [Kinet. Relat. Models 14(2), 323–351 (2021)], asymptotic flocking admits only two types of asymptotic scenarios, either convergence to a rest state or a state lying on the same plane (coplanar state). We also provide several numerical simulations to illustrate an aforementioned dichotomy on the asymptotic dynamics of the hyperboloid CS model on H 2 . [ABSTRACT FROM AUTHOR]

We study the emergence of the mono-cluster flocking due to the interplay between the unit-speed constraint and time-delayed interactions in the evolution of the Cucker-Smale ensemble. Several flocking models with unit-speed constraint have been extensively used in the flocking modeling of self-propelled multi-agent systems in the control theory community. Time-delayed interactions can be caused by the finite propagation speed constraint in communications. In the previous literature, these two physical mechanisms have been studied separately. In this paper, we investigate these combined physical effects in a common framework and study how the interplay between these mechanisms affects asymptotic flocking dynamics. For this, we provide a sufficient framework for a mono-cluster flocking in terms of system parameters (e.g., time-delay, coupling strength, particle numbers) and initial data. We also provide several numerical simulations and compare them with analytical results. [ABSTRACT FROM AUTHOR]

In this paper, the authors investigate the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas, which are the set of all rarefaction waves, shock waves, and contact discontinuity. For these Riemann solutions, the authors further consider their limiting behavior. In the process of analyzing the limiting behavior, the authors found that the delta shock wave is contained in the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas. Consequently, up to some appropriate conditions, there is unidirectional transformation from non-isentropic Euler equations for the modified Chaplygin gas to Chaplygin gas. On the basis of numerical simulations, the authors verified the reasonability of the theoretical analysis. [ABSTRACT FROM AUTHOR]

We study the robustness and asymptotic stability of the unique equilibrium for the Winfree model on a general network under the effect of small time-delay. Time-delay is a ubiquitous mechanism in classical and quantum many-body systems, and it is due to the finite speed of communication. In this paper, we further investigate the robustness of the equilibrium under the effects of small time-delay and general network topology. For this, we present several sufficient frameworks formulated in terms of the network topology, coupling strength, time-delay, and initial configuration. In the proposed framework, we present a positively invariant arc which contains the unique equilibrium independent of strength of time-delay. By using energy estimates, we show that the unique equilibrium in the invariant arc is asymptotically stable. We also provide several numerical simulations and compare them with analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in the limit of Riemann solutions to the Aw-Rascle model with a two-parameter flux approximation including pressure. It is proved that the limit of solutions tends to a special delta-shock rather than the classical one to the transport equations. In order to further study this problem, we consider a perturbed flux approximation system and proceed to investigate the limits of solutions. We rigorously proved that, as the flux approximation vanishes, any Riemann solution containing two shock waves tends to a delta-shock to the transport equations; any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the transport equations and the nonvacuum intermediate state in between tends to a vacuum state. Moreover, some representative numerical simulations are exhibited to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper studied the planar, solitary, and spiral waves of the coupled Burgerscomplex Ginzburg-Landau (Burgers-CGL) equations, which were derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chemical reaction having two flame fronts corresponding to two reaction zones with a finite separation distance between them. First, some exact solutions including the planar and solitary waves for the one-dimensional Burgers-CGL equations that are obtained by subtle transforms and the hyperbolic tangent function expansion method. Second, some spiral waves for the two-dimensional Burgers-CGL equations are investigated. The existence of the spiral waves is proved rigorously by Schauder's fixed point theorem applied to a class of functions, and the approximate solutions are also obtained by the power series expansion method. Furthermore, some numerical simulations are carried out near 0 < r < 1, since the core of the spiral wave is a singular point in the view of mathematics, and the results verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

Quantum cellular automata (QCA) are models of quantum computation of particular interest from the point of view of quantum simulation. Quantum lattice gas automata (QLGA - equivalently partitioned quantum cellular automata) represent an interesting subclass of QCA. QLGA have been more deeply analyzed than QCA, whereas general QCA are likely to capture a wider range of quantum behavior. Discriminating between QLGA and QCA is therefore an important question. In spite of much prior work, classifying which QCA are QLGA has remained an open problem. In the present paper we establish necessary and sufficient conditions for unbounded, finite QCA (finitely many active cells in a quiescent background) to be QLGA. We define a local condition that classifies those QCA that are QLGA, and we show that there are QCA that are not QLGA. We use a number of tools from functional analysis of separable Hilbert spaces and representation theory of associative algebras that enable us to treat QCA on finite but unbounded configurations in full detail. [ABSTRACT FROM AUTHOR]

The wavelet transform method originated by Wei et al. [Phys. Rev. Lett. 89, 284103.4 (2002)] was proved [Juang and Li, J. Math. Phys. 47, 072704.16 (2006); Juang et al., J. Math. Phys. 47, 122702.11 (2006); Shieh et al., J. Math. Phys. 47, 082701.10 (2006)] to be an effective tool to reduce the order of coupling strength for coupled chaotic systems to acquire the synchrony regardless the size of oscillators. In Juang et al., [IEEE Trans. Circuits Syst., I: Regul. Pap. 56, 840 (2009)] such method was applied to coupled map lattices (CMLs). It was demonstrated that by adjusting the wavelet constant of the method can greatly increase the applicable range of coupling strengths, the parameters, range of the individual oscillator, and the number of nodes for local synchronization of CMLs. No analytical proof is given there. In this paper, the optimal or near optimal wavelet constant can be explicitly identified. As a result, the above described scenario can be rigorously verified. [ABSTRACT FROM AUTHOR]

Chern insulators are periodic band insulators with the property that their projector onto the occupied bands has a nonzero Chern number. From numerical calculations, it is known that a Chern insulator with a homogeneous boundary displays a continuum spectrum that fills the entire insulating gap. The local density of states corresponding to this part of the spectrum is localized near the boundary, hence the terminology edge spectrum. An interesting question arises, namely, if a rough boundary, which can be seen as a strong random potential acting on these quasi-one-dimensional states, would destroy the continuum edge spectrum. Numerical simulations seem to indicate that the answer is no. The present paper shows how the question can be answered analytically by connecting the expectation value of the charge edge current to the index of a Fredholm operator, which remains invariant under arbitrary deformations of the boundary. [ABSTRACT FROM AUTHOR]

We are concerned about the averaging principle for the stochastic Burgers equation with slow-fast time scale. This slow-fast system is driven by Lévy processes. Under some appropriate conditions, we show that the slow component of this system strongly converges to a limit, which is characterized by the solution of stochastic Burgers equation whose coefficients are averaged with respect to the stationary measure of the fast-varying jump-diffusion. To illustrate our theoretical result, we provide some numerical simulations. [ABSTRACT FROM AUTHOR]

We consider gravitational lensing of a background source by a finite system of point-masses. The problem of determining the maximum possible number of lensed images has been completely resolved in the single-plane setting (where the point masses all reside in a single lens plane), but this problem remains open in the multiplane setting. We construct examples of K-plane point-mass gravitational lens ensembles that produce ∏ i = 1 K (5 g i − 5) images of a single background source, where gi is the number of point masses in the ith plane. This gives asymptotically (for large gi with K fixed) 5K times the minimal number of lensed images. Our construction uses Rhie's single-plane examples and a structured parameter-rescaling algorithm to produce preliminary systems of equations with the desired number of solutions. Utilizing the stability principle from the differential topology, we then show that preliminary (nonphysical) examples can be perturbed to produce physically meaningful examples while preserving the number of solutions. We provide numerical simulations illustrating the result of our construction, including positions of lensed images and the structure of critical curves and caustics. We observe an interesting "caustic of multiplicity" phenomenon that occurs in the nonphysical case and has a noticeable effect on the caustic structure in the physically meaningful perturbative case. [ABSTRACT FROM AUTHOR]

The Navier–Stokes–Voigt equations are a regularization of the Navier–Stokes equations. Sharing some asymptotic and statistical properties, they have been used in direct numerical simulations of the latter. In this article, we characterize the decay rate of the solutions to the Navier–Stokes–Voigt equations with damping. Applying the Fourier splitting method, we prove the H1 decay of weak solutions for α > 0, β > 2, and μ > ν2. [ABSTRACT FROM AUTHOR]

When aiming to apply mathematical results of non-commutative geometry to physical problems, the following question arises: How they translate to a context in which only a part of the spectrum is known? In this article, we aim to detect when a finite-dimensional triple is the truncation of the Dirac spectral triple of a spin manifold. To this end, we numerically investigate the restriction that the higher Heisenberg equation [A. H. Chamseddine et al., J. High Energy Phys. 2014, 98] places on a truncated Dirac operator. We find a bounded perturbation of the Dirac operator on the Riemann sphere that induces the same Chern class. [ABSTRACT FROM AUTHOR]

We show that the invariant measures of point vortices, when conditioning the Hamiltonian to a finite interval, converge weakly to the enstrophy measure by conditioning the renormalized energy to the same interval. We also prove the existence of solutions to 2D Euler equations having the energy conditional measure as an invariant measure. Some heuristic discussions and numerical simulations are presented in Sec. VI. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical scatterers. To model this, we consider two optically random media, with the second medium obtained by shifting the first medium in some local region. We derive the radiative transfer equation for the cross-correlation of the wave fields in the media. Then we derive its diffusion approximation. In both the radiative transfer and the diffusion regimes, we relate the correlation of speckle patterns to the solutions of the radiative transfer and the diffusion equations. We present numerical simulations based on our model which are in agreement with recent experimental measurements. [ABSTRACT FROM AUTHOR]

In this paper, we numerically investigate the dynamics of the solitary waves in the presence of damping and external stochastic forces for the improved Boussinesq equation. The hydrodynamical and Stokes damping will be considered respectively. Since the analytic solutions for the considered problems are not available, Monte Carlo method will be used in random space and finite volume element method will be used in physical space. Numerical results demonstrate that solitary wave profile is not strongly affected by the Gaussian white noise in our study. The average of the velocity of the solitary waves is very close to that for the deterministic case. [ABSTRACT FROM AUTHOR]

The inverse Henderson problem of statistical mechanics is the theoretical foundation for many bottom-up coarse-graining techniques for the numerical simulation of complex soft matter physics. This inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction potential given the equilibrium pair correlation function of the system. In 1974, Henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system. Here, we provide a rigorous proof of a slightly more general version of the latter statement using Georgii's variant of the Gibbs variational principle. [ABSTRACT FROM AUTHOR]

We show that the quantum state diffusion equation of Gisin and Percival, driven by complex Wiener noise, is equivalent up to a global stochastic phase to quantum trajectory models. With an appropriate feedback scheme, we set up an analog continuous measurement model which exactly simulates the Gisin-Percival quantum state diffusion. [ABSTRACT FROM AUTHOR]

This article presents a new example intended to showcase limitations of computer simulations in the study of random processes with local interaction. For this purpose, we examine a new version of the well-known Stavskaya process, which is a discretetime analog of the well-known contact processes. Like the bulk of random processes studied till now, the Stavskaya process is constant-length, that is, its components do not appear or disappear in the course of its functioning. The process, which we study here and call Variable Stavskaya, VS, is similar to Stavskaya; it is discrete-time; its states are bi-infinite sequences, whose terms take only two values (denoted here as "minus" and "plus"), and the measure concentrated in the configuration "all pluses" is invariant. However, it is a variable length, which means that its components, also called particles, may appear and disappear under its action. The operator VS is a composition of the following two operators. The first operator, called "birth," depends on a real parameter β; it creates a new component in the state "plus" between every two neighboring components with probability β independently from what happens at other places. The second operator, called "murder," depends on a real parameterα and acts in the following way: whenever a plus is a left neighbor of a minus, this plus disappears (as if murdered by that minus which is its right neighbor) with probabilityα independently from what happens to other particles. We prove for anyα < 1 and any β > 0 and any initial measure μ that the sequence μ(VS)t (the result of t iterative applications of VS to μ) tends to the measure δ⊕ (concentrated in "all pluses") as t→∞. Such a behavior is often called ergodic. However, the Monte Carlo simulations and meanfield approximations, which we performed, behaved as if μ(VS)t tended to δ⊕ much slower for someα, β, μ than for some others. Based on these numerical results, we conjecture that VS has phases, but not in that simple sense as the classical Stavskaya process. Published [ABSTRACT FROM AUTHOR]

We present a product formula to approximate the exponential of a skew-Hermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm with respect to the dimension of the Lie algebra, or when the norm of the effective operator resulting from nested commutators is less than the product of the norms, the number of terms in the product is significantly less than that obtained from well-known results. We apply our results to construct product formulas useful for the quantum simulation of some continuous-variable and bosonic physical systems, including systems whose potential is not quadratic. For many of these systems, we show that the number of terms in the product can be sublinear or even subpolynomial in the dimension of the relevant local Hilbert spaces, where such a dimension is usually determined by the energy scale of the problem. Our results emphasize the power of quantum computers for the simulation of various quantum systems. [ABSTRACT FROM AUTHOR]

We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the onedimensional harmonic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion. [ABSTRACT FROM AUTHOR]

The new classes of periodic solutions of nonlinear self-dual network equations describing the breather and soliton lattices, expressed in terms of the Jacobi elliptic functions have been obtained. The dependences of the frequencies on energy have been found. Numerical simulations of soliton lattice demonstrate their stability in the ideal lattice and the breather lattice instability in the dissipative lattice. However, the lifetime of such structures in the dissipative lattice can be extended through the application of ac driving terms. [ABSTRACT FROM AUTHOR]

The time-dependent Ginzburg-Landau formalism for (d + s)-wave superconductors and their representation using auxiliary fields is investigated. By using the link variable method, we then develop suitable discretization of these equations. Numerical simulations are carried out for a mesoscopic superconductor in a homogeneous perpendicular magnetic field which revealed peculiar vortex states. [ABSTRACT FROM AUTHOR]

We study by computer simulations the complex solutions of the two-dimensional Burgers equations in the whole plane in absence of external forces. For such model the existence of singularities, corresponding to a divergence of the total energy at a finite time, is proved by Li and Sinai ['Singularities of complex-valued solutions of the two-dimensional Burgers system,' J. Math. Phys. 51, 015205 (2010)] for a large class of initial data. The simulations show that the blow-up takes place in a very short time, of the order of 10-5 time units. Moreover near the blow-up time the support of the solution in Fourier space moves out to infinity along a straight line. In x-space the solutions are concentrated in a finite region, with large space derivatives, as one would expect for physical phenomena such as tornadoes. [ABSTRACT FROM AUTHOR]

We develop an analytical method for calculating the geometric wakefield and impedances of an ultrarelativistic beam propagating on- and off-axis through an axially symmetric geometry with slowly varying circular cross-section, such as a transition. Unlike previous analytical methods, our approach permits detailed perturbative investigation of geometric wakefields, and detailed perturbative investigation of impedance as a function of frequency. We compare the accuracy of the results of our approach with numerical simulations performed using the code ECHO and determine parameters in which there is good agreement with our asymptotic analysis. [ABSTRACT FROM AUTHOR]

Nested Uhrig dynamical decoupling (NUDD) is a highly efficient quantum error suppression scheme that builds on optimized single axis UDD sequences. We prove the universality of NUDD and analyze its suppression of different error types in the setting of generalized control pulses. We present an explicit lower bound for the decoupling order of each error type, which we relate to the sequence orders of the nested UDD layers. We find that the error suppression capabilities of NUDD are strongly dependent on the parities and relative magnitudes of all nested UDD sequence orders. This allows us to predict the optimal arrangement of sequence orders. We test and confirm our analysis using numerical simulations. [ABSTRACT FROM AUTHOR]

We consider passive scalar mixing by a prescribed divergence-free velocity vector field in a periodic box and address the following question: Starting from a given initial inhomogeneous distribution of passive tracers, and given a certain energy budget, power budget, or finite palenstrophy budget, what incompressible flow field best mixes the scalar quantity? We focus on the optimal stirring strategy recently proposed by Lin et al. ['Optimal stirring strategies for passive scalar mixing,' J. Fluid Mech. 675, 465 (2011)] that determines the flow field that instantaneously maximizes the depletion of the H-1 mix-norm. In this work, we bridge some of the gap between the best available a priori analysis and simulation results. After recalling some previous analysis, we present an explicit example demonstrating finite-time perfect mixing with a finite energy constraint on the stirring flow. On the other hand, using a recent result by Wirosoetisno et al. ['Long time stability of a classical efficient scheme for two dimensional Navier-Stokes equations,' SIAM J. Numer. Anal. 50(1), 126-150 (2012)] we establish that the H-1 mix-norm decays at most exponentially in time if the two-dimensional incompressible flow is constrained to have constant palenstrophy. Finite-time perfect mixing is thus ruled out when too much cost is incurred by small scale structures in the stirring. Direct numerical simulations in two dimensions suggest the impossibility of finite-time perfect mixing for flows with fixed power constraint and we conjecture an exponential lower bound on the H-1 mix-norm in this case. We also discuss some related problems from other areas of analysis that are similarly suggestive of an exponential lower bound for the H-1 mix-norm. [ABSTRACT FROM AUTHOR]