Related papers: Special Cosserat rods with rate-dependent evolving…
Filtered budgets for anelastic turbulence and a general expression of the turbulent sensible heat flux are derived for a multicomponent fluid with an arbitrary equation of state. A family of subgrid-scale closures is then found under the…
Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004), we consider a variational plate model for an elastic cone under compression in the direction of the cone symmetry axis. Assuming radial symmetry,…
According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal compressible two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable,…
We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary…
In 1995, Kazhikhov and Vaigant introduced a particular class of isentropic compressible Navier-Stokes equations with variable viscosity coefficients and, for the first time, established the existence of global smooth solutions for…
The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was…
In this paper, we develop a non-singular continuum theory of point defects based on a second strain gradient elasticity theory, the so-called gradient elasticity of bi-Helmholtz type. Such a generalized continuum theory possesses a weak…
The Gibbs distribution universally characterizes states of thermal equilibrium. In order to extend the Gibbs distribution to non-equilibrium steady states, one must relate the self-information $\mathcal{I}(x) = -\log(P_\text{ss}(x))$ of…
A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on…
When thermodynamics is understood as the science (or art) of constructing effective models of natural phenomena by choosing a minimal level of description capable of capturing the essential features of the physical reality of interest, the…
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…
The essence of the second law of classical thermodynamics is the `entropy principle' which asserts the existence of an additive and extensive entropy function, S, that is defined for all equilibrium states of thermodynamic systems and whose…
We study the topology and geometry of two dimensional coarsening foams with arbitrary liquid fraction. To interpolate between the dry limit described by von Neumann's law, and the wet limit described by Marqusee equation, the relevant…
We study the weakly nonlinear saturation of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. This instability, established in our preceding work as a Hopf bifurcation of a…
The weak-field limit of Einstein--Cartan (EC) relativity is studied. The equations of EC theory are rewritten such that they formally resemble those of Einstein General Relativity (EGR); this allows ideas from post-Newtonian theory to be…
Spontaneous transitions between non-equilibrium patterns are characterised by hydrodynamic calculations of ideal straight roll steady state heat convection. The calculations are tested quantitatively against existing experimental data. It…
Hooke's law states that the forces or stresses experienced by an elastic object are proportional to the applied deformations or strains. The number of coefficients of proportionality between stress and strain, i.e., the elastic moduli, is…
We study the initial value problem for a system of equations describing the motion of two-dimensional non-homogeneous incompressible fluids exhibiting odd (non-dissipative) viscosity effects. We consider the complete odd viscous stress…
In this study, an inhomogeneous Cosserat rod theory is introduced and compared to the conventional homogeneous rod for modeling soft manipulators. The inhomogeneity is addressed by considering the pressure actuation as part of the rod's…
The result that closed systems evolve toward equilibrium is derived entirely on the basis of quantum field theory for a model system, without invoking any of the common extra-mathematical notions of particle trajectories, collapse of the…