Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations
Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass
transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of …
transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of …
Viscoelastic Cahn–Hilliard models for tumor growth
We introduce a new phase field model for tumor growth where viscoelastic effects are taken
into account. The model is derived from basic thermodynamical principles and consists of a …
into account. The model is derived from basic thermodynamical principles and consists of a …
90 Years of Galbrun's Equation: An Unusual Formulation for Aeroacoustics and Hydroacoustics in Terms of the Lagrangian Displacement
The field of aeroacoustics has gained much attention since the well-known acoustic
analogies were first published in the 1950s. In parallel, the continuous growth of …
analogies were first published in the 1950s. In parallel, the continuous growth of …
Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion
We prove that there exists a weak solution to a system governing an unsteady flow of a
viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is …
viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is …
[HTML][HTML] On determining Navier's slip parameter at a solid boundary in flows of a Navier–Stokes fluid
J Málek, KR Rajagopal - Physics of Fluids, 2024 - pubs.aip.org
While the assumption of the “no-slip” condition at a solid boundary is unquestioningly
applied to study the flow characteristics of a Navier–Stokes fluid, there was considerable …
applied to study the flow characteristics of a Navier–Stokes fluid, there was considerable …
Thermodynamics of viscoelastic rate-type fluids with stress diffusion
We propose thermodynamically consistent models for viscoelastic fluids with a stress
diffusion term. In particular, we derive variants of compressible/incompressible …
diffusion term. In particular, we derive variants of compressible/incompressible …
Non-isothermal general Ericksen–Leslie system: derivation, analysis and thermodynamic consistency
F De Anna, C Liu - Archive for Rational Mechanics and Analysis, 2019 - Springer
We derive a model describing the evolution of a nematic liquid–crystal material under the
action of thermal effects. The first and second laws of thermodynamics lead to an extension …
action of thermal effects. The first and second laws of thermodynamics lead to an extension …
Derivation of the variants of the Burgers model using a thermodynamic approach and appealing to the concept of evolving natural configurations
Viscoelastic rate-type fluid models involving the stress and frame-indifferent time derivatives
of second order, like those in Burgers' model, are used to describe the complicated …
of second order, like those in Burgers' model, are used to describe the complicated …
On thermodynamics of incompressible viscoelastic rate type fluids with temperature dependent material coefficients
We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type
models for incompressible viscoelastic fluids. In particular, we study the models that allow …
models for incompressible viscoelastic fluids. In particular, we study the models that allow …
Approximation and existence of a viscoelastic phase-field model for tumour growth in two and three dimensions
H Garcke, D Trautwein - arXiv preprint arXiv:2305.14915, 2023 - arxiv.org
In this work, we present a phase-field model for tumour growth, where a diffuse interface
separates a tumour from the surrounding host tissue. In our model, we consider transport …
separates a tumour from the surrounding host tissue. In our model, we consider transport …