Related papers: Problem of Metrizability for the Dynamical Systems…
The equations of motion for a fully ionized hydrogenic plasma in applied coaxial electric and magnetic fields are analyzed, where the term for the Hall effect in the generalized Ohm's law equation picks up a factor of 1/2 relative to its…
Interatomic-force measurements are regularly performed using frequency-modulation atomic force microscopy. This requires conversion of the observed shift in the resonant frequency of a force-sensing cantilever, to the actual force…
The momentum of a free massive particle, invariant under translation, thereby realizes a trivial representation of the translation group. By allowing nontrivial reps of translations, momentum changes with translation, a recipe for force.…
The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is…
Recently [J. Haro and E. Elizalde, Phys. Rev. Lett. {\bf 97}, 130401 (2006)], a Hamiltonian formulation has been introduced in order to address some longstanding severe problems associated with the physical description of the dynamical…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
A Lagrangian derivation of the Equation of Motion (EOM) for static spherically symmetric metrics in F(R) modified gravity is presented. For a large class of metrics, our approach permits to reduce the EOM to a single equation and we show…
A new systematic correction for Casimir force measurements is proposed and applied to the results of an experiment that was performed more than a decade ago. This correction brings the experimental results into good agreement with the Drude…
We investigate the problem of how to obtain the force field between atoms of an experimentally determined structure. We show how this problem can be efficiently solved, even at finite temperature, where the position of the atoms differs…
In this paper we address the problem of identifying contracting systems among dynamical systems appearing in mechanics. First, we introduce a sufficient condition to identify contracting systems in a general Riemannian manifold. Then, we…
Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
A functional calculus approach is applied to the derivation of evolution equations for the moments of the magnetization dynamics of systems subject to stochastic fields. It allows us to derive a general framework for obtaining the master…
In this paper we analyze the dynamic stability of the hovering magnetic top from first principles without using any preliminary assumptions. We write down the equations of motion for all six degrees of freedom and solve them analytically…
In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a…
We consider the problem of building numerically stable algorithms for computing Discrete Fourier Transform (DFT) of $N$- length signals with known frequency support of size $k$. A typical algorithm, in this case, would involve solving…
Multi-system interaction is an important and difficult problem in physics. Motivated by the experimental result of an electronic circuit element "Fractor", we introduce the concept of dynamic-order fractional dynamic system, in which the…
Mechanical quantum systems, such as resonators and levitated particles, offer unique opportunities for quantum metrology. Particularly, their significant mass and quantum-level control enable applications in measuring gravitational effects.…
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…
The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…