Related papers: On the material time derivative of volume, surface…
The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential…
This paper presents a collection of useful formulas of dynamic derivatives on time scales, systematically collected for reference purposes. As an application, we define trigonometric and hyperbolic functions on time scales in such a way the…
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general…
We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows. The scheme is intended to work robustly in the lubrication regime when the distance between two particles…
The transformation of the partial fractional derivatives under spatial rotation in $R^2$ are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed…
A simple connection between mass M of a particle or a body and time t is proposed. The flow of time t depends on the relativechange of mass, i.e \frac{\Delta M}{M}=- \mu dt, where \mu is unknown parameter. Some of the simplest consequences…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
Traditional approaches to the study of the dynamics of spacetime curvature in a very real sense hide the intricacies of the nonlinear regime. Whether it be huge formulae, or mountains of numerical data, standard methods of presentation make…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
We discuss exterior and classical interior alternatives for evaluating fluid flow induced forces on bodies. The discussion aims at a reduction of the total shape derivative, achieved through a decoupling of control and objective in the…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
The question on expansion of moving volume inside of a smooth flow of the compressible liquid is under consideration. We find a condition on initial data such that if it holds, then within a finite time either the boundary of the moving…
It is known from both experiments and molecular dynamics simulations that chemically patterning a solid surface has an effect on the flow of an adjacent liquid. This fact is in stark contrast with predictions of classical fluid mechanics…
In many applications free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical applications. Albeit the frequent applications, slight…
The space-time foam formulas, quoted below in Eqs (1) and (3), express the minimal amount of quantum uncertainty to be introduced into the structure of the Einsteinian space-time in order to make that structure compatible with quantum…
Discontinuous time derivatives are used to model threshold-dependent switching in such diverse applications as dry friction, electronic control, and biological growth. In a continuous flow, a discon- tinuous derivative can generate multiple…
An analysis is performed of the role played by physical intuition in expressing the electromagnetic field in terms of its sources in the time-dependent case. The conclusion is that it is dangerous to dissociate physical intuition from the…
This paper discusses a general formulation of the material point method in the context of additive decomposition rate-independent plasticity. The process of generating the weak form shows that volume integration over deforming particles can…
Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space. This means, for example, that the flux of matter energy through a…
We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…