Related papers: Radiative Damping and Functional Differential Equa…
Constrained mechanical multibody systems arise in many important applications like robotics, vehicle and machinery dynamics and biomechanics of locomotion of humans. These systems are described by the Euler-Lagrange equations which are…
We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses St\"urmer's extrapolation formula and assumes…
The paper provides the fractional integrals and derivatives of the Rie\-mann-Liouville and Caputo type for the five kinds of radial basis functions (RBFs), including the powers, Gaussian, multiquadric, Matern and thin-plate splines, in one…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
We introduce a type of quantum dissipation -- local quantum friction -- by adding to the Hamiltonian a local potential that breaks time-reversal invariance so as to cool the system. Unlike the Kossakowski-Lindblad master equation, local…
The problem of self forces and radiation reaction is solved by conservation of energy methods. The longstanding problem of constant acceleration is solved, and it is shown that the self force does indeed affect the particle's motion, as…
We discuss the general three-particle quantum scattering problem, for motion restricted to the full line. Specifically, we formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As a…
Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of…
It is argued that, contrary to conventional wisdom, no trustworthy universal self-force/radiative corrections to the Lorentz force equation, can be derived from the basic tenets of classical electrodynamics. This concords with the apparent…
A three-body semiclassical model is proposed to describe the nucleon transfer and emission reactions in a heavy-ion collision. In this model the two heavy particles, i.e. nuclear cores A$_1(Z_{A_1}, M_{A_1})$ and A$_2(Z_{A_2}, M_{A_2})$,…
This paper proposes four fundamental requirements for establishing PDEs (partial differential equations) modeling irreversible processes. We show that the PDEs derived via the CDF (conservation-dissipation formalism) meet all the…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
In classical electrodynamics, an accelerating charged body emits radiation and experiences a corresponding radiation-reaction force, or self force. We extend to higher order in the total charge a previous rigorous derivation of the…
Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…
At present there are two vastly different ab initio approaches to the description of the the many-body dynamics: the Density Functional Theory (DFT) and the functional integral (path integral) approaches. On one hand, if implemented…
Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…
The construction of predictive models of atomic nuclei from first principles is a challenging (yet necessary) task towards the systematic generation of theoretical predictions (and associated uncertainties) to support nuclear data…
We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical problem, to which contributions range over…