Physica D: Nonlinear Phenomena最新文献

This paper investigates the dynamics of crystalline clusters observed in Molecular Dynamics (MD) studies conducted earlier (Yadav et al., 2023) for ultra-cold neutral plasmas. An external oscillatory forcing is applied for this purpose, and the evolution is tracked with the help of MD simulations using the open-source LAMMPS software. Interesting observations relating to cluster dynamics are presented. The formation of a pentagonal arrangement of particles is also reported.

In public opinion events, the breeding of negative sentiment has a serious negative impact on the network environment and even offline lives. Hence, establishing an emotion-based propagation dynamic model to catch the sentiment development patterns is essential for helping public opinion management. We propose an E-SLFI (Emotion-driven Susceptible-Latent-Forwarding-Immune) model, which describes the dynamics of the sentiment propagation of ternary polarities under the promoting effect of the conscious emotional contagion mechanism. An empirical case composed of 16,354 pieces of forwarding information and two phases verifies the effectiveness of the proposed sentiment propagation dynamic model, due to the fitting optimization indicator MAPE equals 0.0942 % and 0.0066 % respectively. Further, we simulate the model and implement sensitivity analysis of the important parameters of the model. Combining the results of experiments, we find that enhancing the emotional consensus of recipients and inducers can decide the main sentiment in the system, and anti-emotional consensus can improve the existence of weak sentiments. Our work here is conducive to designing online public sentiment guidance strategies to manage public opinion and calming the network atmosphere to a certain extent.

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.