相关论文: Stretched Exponential Decay in the Edwards-Wilkins…

In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of…

We study the global existence and decay estimates for nonlinear wave equations with the space-time dependent dissipative term in an exterior domain. The linear dissipative effect may vanish in a compact space region. Moreover the nonlinear…

By refining a recent result of Xie and Zhang, we prove the exponential ergodicity under a weighted variation norm for singular SDEs with drift containing a local integrable term and a coercive term. This result is then extended to singular…

The time-elapsed model for neural networks is a nonlinear age structured equationwhere the renewal term describes the network activity and influences the dischargerate, possibly with a delay due to the length of connections.We solve a long…

We propose a general method for deriving one-dimensional models for nonlinear structures. It captures the contribution to the strain energy arising not only from the macroscopic elastic strain as in classical structural models, but also…

In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of…

Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and…

As the possibility to decouple temporal and spatial variations of the electromagnetic field, leading to a wavelength stretching, has been recognized to be of paramount importance for practical applications, we generalize the idea of…

In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent…

Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…

This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…

We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are…

Elasto-plastic models are among the most successful ways to study the critical properties of the plastic yielding transition of amorphous solids. Typically these models are studied under a condition of constant transition rates from one…

We present results on dynamical processes that exhibit a stretched exponential relaxation. When the relaxation is a result of two competing exponential processes, the size of the system, although macroscopic, play a dominant role. There…

The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems…

This paper studies, in fine details, the long-time asymptotic behavior of decaying solutions of a general class of dissipative systems of nonlinear differential equations in complex Euclidean spaces. The forcing functions decay, as time…

Extended Self-Similarity (ESS) is a widely used tool for uncovering universal power-law scaling in systems dominated by nonlinear interactions. This work demonstrates that ESS scaling can also emerge in a system governed by purely linear…

In this work, with the help of fractional calculus, it is shown a time dependence of entropy more general than the well known Pesin relation is derived. Here the equiprobability postulate is not assumed, the system dynamic in the phase…

We consider an analytical approach that involves the complex poles of the propagator to investigate the effect due to the lack of time reversal invariance on the time evolution of decay for purely absorptive potentials. We find that the…

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…