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There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…
We make an observation about Galilean transformation on a 1-D mass variable systems which leads us to the right way to deal with mass variable systems. Then using this observation, we study two-bodies gravitational problem where the mass of…
The full three-body problem, on the motion of three celestial bodies under their mutual gravitational attraction, is one of the oldest unsolved problems in classical mechanics. The main difficulty comes from the presence of unstable and…
The correlated motion of a positron surrounded by electrons is a fundamental many-body problem. We approach this by modeling the momentum density of annihilating electron-positron pairs using the framework of reduced density matrices,…
We investigate here the interactions of waves governed by a Boussinesq system with a partially immersed body allowed to move freely in the vertical direction. We show that the whole system of equations can be reduced to a transmission…
The momentum conservation law for general dissipationless reduced-fluid (e.g., gyrofluid) models is derived by Noether method from a variational principle. The reduced-fluid momentum density and the reduced-fluid canonical momentum-stress…
We relate the breakdown of equations of states for the mechanical pressure of generic dry active systems to the lack of momentum conservation in such systems. We show how sources and sinks of momentum arise generically close to confining…
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. And conversely, the relative scarcity of solutions for non-equilibrium models greatly limits our…
We discuss a piecewise-conserved constant of motion for a simple dissipative oscillatory mechanical system. The system is a harmonic oscillator with sliding (dry) friction. The piecewise-conserved constant of motion corresponds to the time…
We revisit the dynamics of the post-Newtonian (PN) two-body problem for two inspiraling compact bodies. Starting from a matter-only reduced Hamiltonian, we present an adapted framework based on the Lie series approach, enabling the…
The potential energy problem in a gravitationally bound two-body system has recently been studied in the framework of a proposed impact model of gravitation \citep{WilDwi}. The result was applied to the free fall of the so-called…
Pair potentials that are bounded at the origin provide an accurate description of the effective interaction for many systems of dissolved soft macromolecules (e.g., flexible dendrimers). Using numerical free-energy calculations, we…
A new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method is relatively fast, and allows us to solve the full rigid two-body problem for…
We analyze the angular momentum balance for a particle undergoing Thomas precession. The relationships among relativistic torque, the center of mass, and the center of inertia for a spinning particle are clarified. We show that spin…
I study the joint effect of dynamical friction, tidal torques and cosmological constant on clusters of galaxies formation I show that within high-density environments, such as rich clusters of galaxies, both dynamical friction and tidal…
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…
In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…
A mathematical model describing the flow of two-phase fluids in a bounded container $\Omega$ is considered under the assumption that the phase transition process is influenced by inertial effects. The model couples a variant of the…
We revisit the problem of flux-balance equations for isolated post-Newtonian matter systems due to the emission of gravitational waves. In particular we show by a local derivation confined to the system, using the expression of…
This paper considers the energy required for collections of finite density bodies to undergo escape under internal gravitational interactions alone. As the level of the system energy is increased there are different combinations of…