Related papers: Explicit Solution to the Constant Radial Accelerat…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…
This paper investigates rotating star solutions to the Euler-Poisson equations with a non-isentropic equation of state. As a first step, the equation for gas density with a prescribed entropy and angular velocity distribution is studied.…
A global existence result is established for a free boundary problem of planar magnetohydrodynamic fluid flows with radiation and large initial data. Particularly, it is novelty to embrace the constant transport coefficient. As a…
Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted…
In (Commun Pure Appl Math 2(4):331-407, 1949), Grad proposed a Hermite series expansion for approximating solutions to kinetic equations that have an unbounded velocity space. However, for initial boundary value problems, poorly imposed…
In the article we introduce an analytical solution for Reissner's large-deflection finite-strain planar beam subject to an end force and a bending moment. The solution is given in terms of Jacobi elliptical functions. The obtained…
In a recent series of papers new exact analytical solutions of the field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been…
Gyration radius of individual's trajectory plays a key role in quantifying human mobility patterns. Of particular interests, empirical analyses suggest that the growth of gyration radius is slow versus time except the very early stage and…
The Tolman VII solution (an exact static spherically symmetric perfect fluid solution) to the Einstein equations is reexamined, and a closed form equation of state (EOS) is deduced for the first time. This EOS allows further analysis…
We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These…
High-precision astrometric and radial-velocity observations require accurate modelling of stellar motions in order to extrapolate measurements over long time intervals, and to detect deviations from uniform motion caused for example by…
This paper is concerned with radially symmetric solutions of systems of the form \[ u_t = -\nabla V(u) + \Delta_x u \] where space variable $x$ and and state-parameter $u$ are multidimensional, and the potential $V$ is coercive at infinity.…
We provide a self-contained analysis, based entirely on pde methods, of the exponentially long time behavior of solutions to linear uniformly parabolic equations which are small perturbations of a transport equation with vector field having…
We present a relativistic treatment of the problem of soft electromagnetic structure by the modified instant form of relativistic Hamiltonian dynamics. Our approach uses relativistic parametrization and so picks out the relativistic…
Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…
We compare three approaches to posing the index 3 set of differential algebraic equations (DAEs) associated with the constrained multibody dynamics problem formulated in absolute coordinates. The first approach works directly with the…
In the last years, a growing number of challenging applications in navigation, logistics, and tourism were modeled as orienteering problems. This problem has been proposed in relation to a sport race where certain control points must be…
This letter presents a novel method for estimating the position, velocity, and acceleration of a moving target using range-based measurements. Although most existing studies focus on position and velocity estimation, the framework of this…
New exact solvable elliptic potentials with free constants for the spectral problems of the third order are found. A time dependence of such potentials gives their isospectral deformations and solutions of nonlinear integrable equations.
Warp drives are exotic solutions of general relativity that offer novel means of transportation. In this study, we present a solution for a constant-velocity subluminal warp drive that satisfies all of the energy conditions. The solution…