Related papers: The Darboux Classification of Curl Forces
Radial tidal forces can be compressive instead of disruptive, a possibility that is frequently overlooked in high level physics courses. For example, radial tidal compression can emerge in extended stellar systems containing a smaller…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
We numerically examine the dynamics of a probe particle driven at a constant force through an assembly of particles with competing long-range repulsion and short-range attraction that forms a bubble or stripe state. In the bubble regime, we…
We investigate the collective dynamics of multivortex assemblies in a two dimensional (2D) toroidal fluid film of distinct curvature and topology. The incompressible and inviscid nature of the fluid allows a Hamiltonian description of the…
We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…
Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Ref. [Phys. Rev. X 8(1), 011047 (2018)]…
Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in…
Capture, selective collection and flight manipulation of airborne particulate are three important functional requirements in various actively growing aerosol technology applications. Aerodynamic drag, particle inertia and dielectrophoretic…
The curvature of the inertial or gravitational potentials defined as a Hodge-Helmholtz decomposition of acceleration into an irrotational and a solenoidal components, enable to federate certain domains of macroscopic physics. After two…
A geometric approach to derive the Nambu brackets for ideal two-dimensional (2D) hydrodynamics is suggested. The derivation is based on two-forms with vanishing integrals in a periodic domain, and with resulting dynamics constrained by an…
Considering trajectory curves, integral of n-dimensional dynamical systems, within the framework of Differential Geometry as curves in Euclidean n-space, it will be established in this article that the curvature of the flow, i.e. the…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
In a wide range of physical phenomena, we find propagating surfaces {\Omega}t which need mathematical treatment. In this article, we review the theory of the system of kinematical conservation laws (KCL), which govern the evolution of these…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
When considering how self-interaction affects an object's motion, it can be convenient to decompose the self-force into conservative and dissipative pieces. As a toy model for understanding such decompositions of the gravitational…
Two-dimensional driven dissipative flows are generally integrable via a conservation law that is singular at equilibria. Nonintegrable dynamical systems are confined to n*3 dimensions. Even driven-dissipative deterministic dynamical systems…
A three-dimensional mathematical model of a viscous incompressible fluid with two stiff particles is investigated in the near-contact regime. When one of the particles approaches the other motionless particle with prescribed translational…
The friction force is derived using fractional calculus by considering the non-uniform flow of time in dissipative processes. The approach incorporates inhomogeneous velocity without unphysical approximations, resulting in a Lagrangian…
We give some theoretical as well as computational results on Laplace and Maxwell constants. Besides the classical de Rham complex we investigate the complex of elasticity and the complex related to the biharmonic equation and general…
We construct a class of closed timelike curves (CTCs) using a compactified extra dimension $u$. A nonzero metric element $g_{tu}(u)$ enables particles to travel backwards in global time $t$. The compactified dimension guarantees that the…