Related papers: Two problems in Classical Mechanics
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
We consider the question of how to distinguish quantum from classical transport through nanostructures. To address this issue we have derived two inequalities for temporal correlations in nonequilibrium transport in nanostructures weakly…
In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.
This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…
We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems in continuum mechanics concern mathematical…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
This is a commentary on two recent experimental papers in PNAS by Vivek et al. and Illing et al. that convincingly address an issue at the junction of two fundamental questions in glass physics: the role of the dimensionality of space on…
The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…
Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the…
This paper proves that protomechanics, previously introduced in quant-ph/9909025, deduces both quantum mechanics and classical mechanics. It does not only solve the problem of the arbitrariness on the operator ordering for the quantization…
Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…
This article attempts to use the ideas from the field of complexity sciences to revisit the classical field of fluid mechanics. For almost a century, the mathematical self-consistency of Navier-Stokes equations has remained elusive to the…
Several classic one-dimensional problems of variational calculus originating in non-relativistic particle mechanics have solutions that are analogues of spatially homogeneous and isotropic universes. They are ruled by an equation which is…
The aim of this paper is twofold: First, we give a formal introduction to the basics of the mathematical framework of classical mechanics. Along the way, we prove a Hamiltonian and a Lagrangian version of Noether's Theorem, an important…
In spite of its long history and classical character which goes back even to d'Alembert and Lagrange, the problems of constraints in mechanics of continua is still mysterious and full of misunderstandings. Let us mention the problem of…
Modern physics is based on three major theories - general relativity, quantum field theory, and (quantum) thermodynamics. Classical acoustics in fluids is usually regarded and studied as a part of classical mechanics, more precisely fluid…
Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of an inverse-quadratic potential in 1D is…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
The basic physical problems that necessitated the emergence of quantum physics are summarized, along with the elements of wave mechanics and its traditional statistical interpretation. Alternative interpretations to the statistical one,…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…