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We report the complete statistical treatment of a system of particles interacting via Newtonian forces in continuous boundary-driven flow, far from equilibrium. By numerically time-stepping the force-balance equations of a model fluid we…
Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply…
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…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
Being based on V. Konoplev's axiomatic approach to continuum mechanics, the paper broadens its frontiers in order to bring together continuum mechanics with classical mechanics in a new theory of mechanical systems. There are derived motion…
In the classical theory of fluid mechanics a linear relationship between the shear stress and the symmetric velocity gradient tensor is often assumed. Even when a nonlinear relationship is assumed, it is typically formulated in terms of an…
Using mode-coupling theory, we derive a constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full…
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…
Finding an accurate stress-strain relation, able to describe the mechanical behavior of metals during {forming} and machining processes, is an important challenge in several fields of mechanics, with significant repercussions in the…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
A non-perturbative approach to the time-averaging of nonlinear, autonomous ODE systems is developed based on invariant manifold methodology. The method is implemented computationally and applied to model problems arising in the mechanics of…
Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the…
In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
General features of nonlinear quantum mechanics are discussed in the context of applications to two-level atoms.
Constitutive laws relate fluid stress to deformation and underpin predictions of non-Newtonian behavior in industrial and biological fluids. Standard characterization relies on measurements in idealized flows that often miss physics…
Slow and dense granular flows often exhibit narrow shear bands, making them ill-suited for a continuum description. However, smooth granular flows have been shown to occur in specific geometries such as linear shear in the absence of…