Related papers: An Efficient Approach to Fractional Analysis for N…
It is known that a finite-size homogeneous granular fluid develops an hydrodynamic-like instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term…
A novel modeling approach for viscoelastic hydraulic cylinders, with negligible inertial forces, is proposed, based on the extended fractional-order Jeffreys model. Analysis and physical reasoning for the parameter constraints and order of…
We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…
This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the…
In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential…
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…
This paper proposes a thermodynamically consistent phase-field damage model for viscoelastic materials. Suitable free-energy and pseudo-potentials of dissipation are developed to build a model leading to a stress-strain relation, under the…
This paper introduces an analytical formula for the fractional-order conditional moments of nonlinear drift constant elasticity of variance (NLD-CEV) processes under regime switching, governed by continuous-time finite-state irreducible…
This study proposes and explores a linear hydrodynamic thermo-elasticity system within mixture models, comprising fluid and solid phases, with a focus on biological tissues, particularly tumor-related phenomena. Although tumor growth is not…
The methods of non-equilibrium thermodynamics of systems with an interface have been applied to the study of transport processes in semiconductor junctions. A complete phenomenological model for drift-diffusion processes in a junction has…
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville…
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…
We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of Dynamic Density Functional Theory. The discretized equation preserves the structure…
In this letter, we develop a framework to study the mechanical response of athermal amorphous solids via a coupling of mesoscale and microscopic models. Using measurements of coarse grained quantities from simulations of dense disordered…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last…
This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…