Related papers: A generalised distributed-order Maxwell model
Spatial non-locality of space-fractional viscoelastic equations of motion is studied. Relaxation effects are accounted for by replacing second-order time derivatives by lower-order fractional derivatives and their generalizations. It is…
In this paper, a new fractional order generalization of the classical Windkessel arterial model is developed to describe the aortic input impedance as an assessment of the left ventricular after-load. The proposed models embeds…
It has recently been discovered that the viscoelastic properties of cells are inherent markers reflecting the complex biological states, functions and malfunctions of the cells. Although the extraction of model parameters from the…
We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Maxwell-Stefan closure approach. Mechanical forces result into…
A theory for the non-local shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence…
This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations of Scott-Blair elements to construct a series of well-known…
The theory of evolving natural configurations is an effective technique to model dissipative processes. In this paper, we use this theory to revisit nonlinear constitutive models of viscoelastic solids. Particularly, a Maxwell and a…
A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to…
This paper presents a reduced-order model for the Reynolds equation for deformable structure and large displacements. It is based on the model established in [11] which is piece-wise linearized using two different methods. The advantages…
This paper considers weak Galerkin finite element approximations for a quasistatic Maxwell viscoelastic model. The spatial discretization uses piecewise polynomials of degree $k \ (k\geq 1)$ for the stress approximation, degree $k+1$ for…
This short chapter provides a fractional generalization of gradient mechanics, an approach (originally advanced by the author in the mid 80s) that has gained world-wide attention in the last decades due to its capability of modeling pattern…
We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems in continuum mechanics concern mathematical…
We develop a global setting for modeling thermo-visco-elastic materials that satisfy the principles of thermodynamics and are properly invariant. This setting encompasses many known solid and fluid models, as well as new models with…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
Dielectric measurements on molecular liquids just above the glass transition indicate that alpha relaxation is characterized by a generic high-frequency loss varying as $\omega^{-1/2}$, whereas deviations from this come from one or more…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent…