Related papers: From Phase Space Representation to Amplitude Equat…
We consider a two-dimensional problem in nonlinear elasticity which corresponds to the cubic-to-tetragonal phase transformation. Our model is frame invariant and the energy density is given by the squared distance from two potential wells.…
Lattice relaxation profoundly reshapes electronic structures in twisted materials. Prevailing treatments, however, typically rely on large-scale density functional theory (DFT), which is computationally costly and mechanistically opaque.…
We consider the development of instabilities of homogeneous stationary solutions of discrete time lattice maps. Under some generic hypothesis we derive an amplitude equation which is the space-time continuous Ginzburg-Landau equation. Using…
Rayleigh-Taylor (RT) instability commonly arises in compressible systems with time-dependent acceleration in practical applications. To capture the complex dynamics of such systems, a two-component discrete Boltzmann method is developed to…
We investigate nonlinear aggregation dynamics of phase elements distributed on the unit circle under parametrically modulated external fields. Our model, inspired by flaky particle rotation in fluids, employs the equation ${d\alpha/dt} =…
By using a generalization of the multiple scales technique we develop a method to derive amplitude equations for zero--dimensional forced systems. The method allows to consider either additive or multiplicative forcing terms and can be…
In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude…
This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. This paper outlines the stability analysis and a procedure to reduce and simplify the non-linear…
The phase field crystal (PFC) approach extends the notion of phase field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance…
This paper presents a combined numerical-theoretical study of the macroscopic behavior and local field distributions in a special class of two-dimensional periodic composites with viscoplastic phases. The emphasis is on strongly nonlinear…
Placed slightly out of dynamical equilibrium, an isolated stellar system quickly returns towards a steady virialized state. We study this process of collisionless relaxation using the matrix method of linear response theory. We show that…
New method for ab initio calculations of the properties of large size system based on phase-amplitude functional is presented. It is shown that Schrodinger equation for many electrons complex system including large size molecules, or…
The Enskog-like kinetic approach, recently introduced by us to study strongly inhomogeneous flu- ids, is reconsidered in order to improve the description of the transport coefficients. The approach is based on a separation of the…
We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…
We consider a nonlinear autonomous random dynamical system of $N$ degrees of freedom coupled by Gaussian random interactions and characterized by a continuous spectrum $n_{\mu}(\lambda)$ of real positive relaxation rates. Using Kac-Rice…
We study the detailed out of equilibrium time evolution of a homogeneous Bose-Einstein condensate.We consider a nonrelativistic quantum theory for a self-interacting complex scalar field, immersed in a thermal bath, as an effective…
The dynamics of non-equilibrium closed quantum systems and their route to thermalization are of fundamental interest to several fields, from cosmology to particle physics. However, a comprehensive description of non-equilibrium phenomena…
We investigate the dissipative dynamics of linear and nonlinear waves in harmonic traps by means of engineered complex non-Hermitian potentials. By combining an analytical mapping between real and complex Schr\"odinger equations with direct…
We present an analytical and numerical study of a nonlinear diffusion model which describes density relaxation of loosely packed particles under gravity and weak random (thermal) vibration, and compare the results with Monte Carlo…