相关论文: A model of viscoelasticity with time-dependent mem…

The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in…

Sequential deep learning models such as RNN, causal CNN and attention mechanism do not readily consume continuous-time information. Discretizing the temporal data, as we show, causes inconsistency even for simple continuous-time processes.…

Models of active nematics in biological systems normally require complexity arising from the hydrodynamics involved at the microscopic level as well as the viscoelastic nature of the system. Here we show that a minimal, space-independent,…

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…

Soft solids with tunable mechanical response are at the core of new material technologies, but a crucial limit for applications is their progressive aging over time, which dramatically affects their functionalities. The generally accepted…

This paper develops a three-dimensional decomposition of volatility memory into orthogonal components of level, shape, and tempo. The framework unifies regime-switching, fractional-integration, and business-time approaches within a single…

We investigate nonlinear stochastic Volterra equations in space and time that are driven by L\'evy bases. Under a Lipschitz condition on the nonlinear term, we give existence and uniqueness criteria in weighted function spaces that depend…

The phenomenon of local dynamical inhomogeneity of time is predicted, which implies that the course of time along the trajectory of motion of a particle in the inertial reference frames moving relative to each other depends on the state of…

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…

In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…

The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal…

An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…

Point process data are becoming ubiquitous in modern applications, such as social networks, health care, and finance. Despite the powerful expressiveness of the popular recurrent neural network (RNN) models for point process data, they may…

Renewable energy is essential for energy security and global warming mitigation. However, power generation from renewable energy sources is uncertain due to volatile weather conditions and complex equipment operations. To improve…

Memory effects are ubiquitous in nature and are particularly relevant at the nanoscale where the dynamical properties of electrons and ions strongly depend on the history of the system, at least within certain time scales. We review here…

Most materials age, and their properties change over time. The aging of materials is reflected in their mechanical responses to external stress and strain, which exhibit logarithmic relaxation and universal power-law creep. Those responses…

Discrete dynamics arise naturally in systems with broken temporal translation symmetry and are typically described by first-order recurrence relations representing classical or quantum Markov chains. When memory effects induced by hidden…

Lack of memory (locality in time) is a major limitation of almost all present time-dependent density functional approximations. By using semiclassical dynamics to compute correlation effects within a density-matrix functional approach, we…

We study the behaviour of the solutions to a dynamic evolution problem for a viscoelastic model with long memory, when the rate of change of the data tends to zero. We prove that a suitably rescaled version of the solutions converges to the…

Fractional calculus has been proved to be very effective in representing the visco-elastic relaxation response of materials with memory such as polymers. Moreover, in modelling the temperature dependency of the material functions in…