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The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…
This work deals with the evaluation of the flow curve of colloidal systems that develop fluid phases with different mechanical properties, namely shear-banding fluids. The problem involved is that, as different fluid phases coexist in the…
We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
In this lectures given at the Morning side center of Mathematics in October 2016, we present in a very simple framework Hilbertian hypocoercive methods in the case of 1d kinetic inhomogeneous equations, and some illustrations concerning…
Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…
Under inhomogeneous flow, dense suspensions exhibit complex behaviour that violates the conventional homogenous rheology. Specifically, one finds flowing regions with a macroscopic friction coefficient below the yielding criterion, and…
We have measured the nonlinear rheological response of a model transient network over a large range of steady shear rates. The system is built up from an oil in water droplet microemulsion into which a telechelic polymer is incorporated.…
During the past few years, nonextensive statistics has been successfully applied to explain many different kinds of systems. Through these studies some interpretations of the entropic parameter q, which has major role in this statistics, in…
In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non--Newtonian coefficient. According to a recently…
In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
The note is about some nonlinear curvature conditions which arise naturally in conformal geometry.
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
Constitutive equations are developed for a polymer fluid, which is treated as a permanent network of strands bridged by junctions. The junctions are assumed to slide with respect to their reference positions under loading. Governing…
We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…