Physica D: Nonlinear Phenomena最新文献

In this note, we provide two results concerning the global well-posedness and decay of solutions to an asymptotic model describing the nonlinear wave propagation in the troposphere, namely, the morning glory phenomenon. The proof of the first result combines a pointwise estimate together with some interpolation inequalities to close the energy estimates in Sobolev spaces. The second proof relies on suitable Wiener-like functional spaces.

We study the comparison between the phenomenological and kinetic models for a mixture of gases from the viewpoint of collective dynamics. In the case in which constituents are Eulerian gases, balance equations for mass, momentum, and energy are the same in the main differential part, but production terms due to the interchanges between constituents are different. They coincide only when the thermal and mechanical diffusion are sufficiently small. In this paper, we first verify that both models satisfy the universal requirements of conservation laws of total mass, momentum, and energy, Galilean invariance and entropy principle. Following the work of Ha and Ruggeri (ARMA 2017), we consider spatially homogeneous models which correspond to the generalizations of the Cucker Smale model with thermal effect. In these circumstances, we provide analytical results for the comparison between two resulting models and also present several numerical simulations to complement analytical results.

We construct the approximate solutions to the Vlasov–Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of plasma physics. The quasi-neutrality is an important characteristic of plasmas and its scale is characterized by a small parameter, called the Debye length. We present the approximate equations obtained by a formal expansion in the parameter and study the properties of the approximate solutions. Moreover, we present numerical experiments demonstrating that the approximate solutions converge to those of the Vlasov–Poisson system as the parameter goes to zero.

We have simulated the motion of a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates consisting of alternating hydrophilic and hydrophobic stripes, using a multicomponent pseudopotential lattice Boltzmann method. This extends our earlier work where the substrates were uniformly hydrophilic or hydrophobic. In steady-state conditions, we calculate the following, as functions of pattern wavelength: (i) the velocity fields of moving bridges, in particular their (time-averaged) terminal velocities; (ii) the deformation of moving bridges, as measured by the deviation of bridge contact angles from their equilibrium values; (iii) the minimum applied force that breaks a moving bridge. In addition, we found that a bridge moving between patterned substrates cannot be mapped onto a bridge moving between uniform substrates endowed with some effective contact angle, even in the limit of very small pattern wavelength compared to bridge width.

Key network motifs searching in complex networks is one of the crucial aspects of network analysis. There has been a series of insightful findings and valuable applications for various scenarios through the analysis of network structures. However, in dynamic systems, slight changes in the choice of dynamic equations and parameters can alter the significance of motifs. The known methods are insufficient to address this issue effectively. In this paper, we introduce a concept of perturbation energy based on the system’s Jacobian matrix, and define motif centrality for dynamic systems by seamlessly integrating network topology with dynamic equations. Through simulations, we observe that the key motifs obtained by the proposed energy method present better effective and accurate than them by integrating network topology methods, without significantly increasing algorithm complexity. The finding of key motifs can be used to apply for system control, such as formulating containment policies for the spread of epidemics and protecting fragile ecosystems. Additionally, it makes substantial contribution to a deeper understanding of concepts in physics, such as signal propagation and system’s stability.

Hele-Shaw problems are prototypes to study the interface dynamics. Linear theory suggests the existence of self-similar patterns in a Hele-Shaw flow. That is, with a specific injection flux the interface shape remains unchanged while its size increases. In this paper, we explore the existence of self-similar patterns in the nonlinear regime and develop a nonlinear theory characterizing their fundamental features. Using a boundary integral formulation, we pose the question of self-similarity as a generalized nonlinear eigenvalue problem, involving two nonlinear integral operators. The nonlinear flux constant $C_f$ is the eigenvalue and the corresponding self-similar pattern $\tilde{x}$ is the eigenvector. We develop a quasi-Newton method to solve the problem and show the existence of nonlinear shapes with $k$-fold dominated symmetries. Nonlinear results are compared with the established linear theory, demonstrating a divergence between the two due to non-linear effects absent in the linear stability analysis. Further, we investigate how sensitive the shape of the interface is to the viscosity. Additionally, we conduct numerous numerical experiments using a wide range of initial guesses and initial flux constants. Through these experiments, one is able to obtain a diagram of self-similar shapes and the corresponding flux. It could be used to verify possible self-similar shapes with a proper initial guess and initial flux constant. Our results go beyond the predictions of linear theory and establish a bridge between the linear theory and simulations.

Here, we explore the phase transitions triggered by the implementation of social distancing in a basic spatiotemporal model of a qualitative SIS-type infectious disease. We consider human decisions made based on spatiotemporal information regarding the disease spread. This information can be either local, nonlocal with a finite range, or global in scope.

We show that nonlocal and global feedbacks, while resulting in the same spatially homogeneous equilibria, lead to a dynamic behavior that is fundamentally distinct from what is observed when decisions are made based on local information.

Various phenomena arise due to the nonlocal nature of the feedback: (i) Instabilization of Otherwise Stable Homogeneous Equilibria; (ii) Nucleation/Invasion Phenomena; (iii) Onset of Standard and Generalized Traveling Waves, which can incur in wave-pinning; iv) in case of Global Information Feedback, onset of locally stable Far From Equilibrium Patterns that coexist with a locally stable disease-elimination equilibrium. Thus, the nonlocal nature of the human behavior-related feedback introduces a rich array of dynamic behaviors and patterns in the system.

Hodograph equations for the $n$-dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form and information on existence or absence of gradient catastrophes. It is shown that in even dimensions the constructed solutions are periodic in time for particular subclasses of external forces. Several particular examples in one, two and three dimensions are considered, including the case of Coriolis external force.

The aim of this work is multifold. Firstly, it intends to present a complete, quantitative and self-contained description of the periodic traveling wave solutions and Whitham modulation equations for the Toda lattice, combining results from different previous works in the literature. Specifically, we connect the Whitham modulation equations and a detailed expression for the periodic traveling wave solutions of the Toda lattice. Along the way, some key details are filled in, such as the explicit expression of the characteristic speeds of the genus-one Toda–Whitham system. Secondly, we use these tools to obtain a detailed quantitative characterization of the dispersive shocks of the Toda system. Lastly, we validate the relevant analysis by performing a detailed comparison with direct numerical simulations.

This paper investigates a continuous time model for the baleen whale population, which is a diverse and widely distributed parvorder of carnivorous marine mammals. We use theoretical and schematic designs to explore stability charts, rightmost characteristic roots, and supercritical Hopf bifurcation of the positive equilibrium. Our research on the Hopf bifurcation and stability of the bifurcating periodic solutions is based on the center manifold reduction and Poincaré normal form theory. Interestingly, the characteristic equation has pure imaginary roots at the second, third, and subsequent critical values. However, Hopf bifurcation theorem is not satisfied because all other characteristic roots of the characteristic equation at these critical values do not have strictly negative real parts, except the pure imaginary roots. We also use the parameter values reported in the previous studies to simulate the unstable periodic solutions at the second and third critical values through bifurcation diagrams. The numerical results obtained under specific parameter values align closely with our theoretical derivations.