Related papers: Opportunities for use of exact statistical equatio…
We derive an exact contrast-expansion formalism for the effective conductivity of heterogeneous materials (media) with local properties described by arbitrary continuous random fields, significantly generalizing the widely used binary-field…
We investigate the three-dimensional incompressible Navier-Stokes equations. The equations are discretized with Fourier spectral method and a fourth-order Runge-Kutta scheme in time. The spectral accuracy, resolution conditions, and an…
Stochastic field theories are often constructed phenomenologically, without a systematic assessment of thermodynamic consistency or local detailed balance. This may hinder a physical description of irreversibility at the field-theoretic…
Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…
Loops are pervasive in robotics problems, appearing in mapping and localization, where one is interested in finding loop closure constraints to better approximate robot poses or other estimated quantities, as well as planning and…
The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness…
Local analysis of the two dimensional Navier-Stokes equations is used to obtain estimates on the energy and enstrophy fluxes involving Taylor and Kraichnan length scales and the size of the domain. In the framework of zero driving force and…
The present work proposes a theory of isotropic and homogeneous turbulence for incompressible fluids, which assumes that the turbulence is due to the bifurcations associated to the velocity field. The theory is formulated using a…
The basic concepts and equations of classical fluid mechanics are presented in the form necessary for the formulation of Newtonian cosmology and for derivation and analysis of a system of the averaged Navier-Stokes-Poisson equations. A…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
The presence of defects in solids formed by active particles breaks their discrete translational symmetry. As a consequence, many of their properties become space-dependent and different from those characterizing perfectly ordered…
An analytic model for steady state turbulence is employed to obtain the inertial range power spectrum of compressible turbulence. We assume that for homogeneous turbulence, the timescales controlling the energy injected at a given…
The goal of this article is to present -- in a cohesive, and somewhat self-contained fashion -- several recent results revealing an experimentally, numerically, and mathematical analysis-supported \emph{geometric scenario} manifesting…
We construct an exact relativistic cosmology in which an inhomogeneous but isotropic local region has fractal number counts and matches to a homogeneous background at a scale of the order of $10^2$ Mpc. We show that Einstein's equations and…
In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role…
We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular…
Based on the Schrodinger equation, exact expressions for the non-relativistic particle energy in the local external field and the external field potential are derived as inhomogeneous density functionals. On this basis, it is shown that,…
New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are…
The completeness of solutions of homogeneous as well as non-homogeneous unsteady Stokes equations are examined. A necessary and sufficient condition for a divergence-free vector to represent the velocity field of a possible unsteady Stokes…
A simple procedure to approximate the noncommutation terms that arise whenever it is necessary to use a variable scale filtering of the motion equations and to compensate directly the flow solutions from the commutation error is here…