相关论文: An Efficient and Accurate Method for Modeling Nonl…

The logistic growth model is a classical framework for describing constrained growth phenomena, widely applied in areas such as population dynamics, epidemiology, and resource management. This study presents a generalized extension using…

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…

We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…

Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…

In the field of brittle fracture animation, generating realistic destruction animations using physics-based simulation methods is computationally expensive. While techniques based on Voronoi diagrams or pre-fractured patterns are effective…

This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More…

Fractional partial differential equations (FDEs) are used to describe phenomena that involve a "non-local" or "long-range" interaction of some kind. Accurate and practical numerical approximation of their solutions is challenging due to the…

The assembly of virus capsids from free coat proteins proceeds by a complicated cascade of association and dissociation steps, the great majority of which cannot be directly experimentally observed. This has made capsid assembly a rich…

We introduce complex order fractional derivatives in models that describe viscoelastic materials. This can not be carried out unrestrictedly, and therefore we derive, for the first time, real valued compatibility constraints, as well as…

We present a novel method to improve pharmacokinetics modeling, an essential step of drug development. Conventional models frequently fail to fully represent the intricacies of drug absorption and distribution, which limits their predictive…

History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of…

Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretised in time using collocation methods, which assume that the Caputo derivative of the computed solution is piecewise-polynomial. For…

This paper presents a new iterative reconstruction method to provide high-resolution images of shear modulus and viscosity via the internal measurement of displacement fields in tissues. To solve the inverse problem, we compute the…

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

In this work, we propose a framework that constructs reduced order models for nonlinear structural mechanics in a nonintrusive fashion, and can handle large scale simulations. We identify three steps that are carried out separately in time,…

We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and…

This paper is devoted to the study of a hemivariational inequality modeling the quasistatic bilateral frictional contact between a viscoelastic body and a rigid foundation. The damage effect is built into the model through a parabolic…

Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…

This letter proposes a fractional-order battery model based on the Caputo definition. A closed-form time-domain solution is derived, enabling a simple recursive expression for discrete-time implementation. The model requires only the…

Earth introduces strong attenuation and dispersion to propagating waves. The time-fractional wave equation with very small fractional exponent, based on Kjartansson's constant-Q theory, is widely recognized in the field of geophysics as a…