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The relativistic Lagrangian for a spinning particle in an electromagnetic field is derived from the known Lagrangian in the particle's rest frame. The resulting relativistic Stern-Gerlach and Thomas precession forces on the particle are…
The Lagrangian average (LA) of the ideal fluid equations preserves their fundamental transport structure. This transport structure is responsible for the Kelvin circulation theorem of the LA flow and, hence, for its potential vorticity…
The formal derivation of Langevin equations (and, equivalently Fokker-Planck equations) with projection operator techniques of Mori, Zwanzig, Kawasaki and others apparently not has widely found its way into textbooks. It has been reproduced…
We prove asymptotic stability of the Poisson homogeneous equilibrium among solutions of the Vlassov-Poisson system in the Euclidean space $\mathbb{R}^3$. More precisely, we show that small, smooth, and localized perturbations of the Poisson…
A relativistic self-gravitating equilibrium system with steady flow as well as spherical symmetry is discovered. The energy-momentum tensor contains the contribution of a current related to the flow and the metric tensor does an…
We propose a simple mechanism that may explain the observed particle-antiparticle asymmetry in the Universe. In the Einstein-Cartan-Sciama-Kibble theory of gravity, the intrinsic spin of matter generates spacetime torsion. Classical Dirac…
Dispersion forces between neutral material bodies are due to fluctuations of the polarization of the bodies. For bodies in equilibrium these forces are often referred to as Casimir-Lifshitz forces. For bodies in relative motion, in addition…
Vlasov kinetic theory is extended by adopting an extra one particle distribution function as an additional state variable characterizing the micro-turbulence internal structure. The extended Vlasov equation keeps the reversibility, the…
Regarding a recent dispute about the symmetry of the stress tensor of fluids, more considerations are presented. The usual proofs of this symmetry are reviewed, and contradictions between this symmetry and the mechanism of gas viscosity are…
In special relativity a gyroscope that is suspended in a torque-free manner will precess as it is moved along a curved path relative to an inertial frame S. We explain this effect, which is known as Thomas precession, by considering a real…
The classical problem of attitude stability in a central gravity field is generalized to that on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied in the framework of geometric mechanics. Based on…
Finsler geometry is a natural generalization of (pseudo-)Riemannian geometry, where the line element is not the square root of a quadratic form but a more general homogeneous function. Parameterizing this in terms of symmetric tensors…
We observe clear precessional motion of highly birefringent liquid crystal (LC) particles trapped in a spherically aberrated optical trap which is built around a tilted refractive index stratified medium. For input circularly polarized…
We consider the physically relevant fully compressible setting of the Rayleigh Benard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to the gravitational force. Under suitable restrictions…
We investigate the gravitational wake due to, and dynamical friction on, a perturber moving on a circular orbit in a uniform gaseous medium using a semi-analytic method. This work is a straightforward extension of Ostriker (1999) who…
The Kepler problem in classical mechanics exhibits a rich structure of conserved quantities, highlighted by the Laplace--Runge--Lenz (LRL) vector. Through Noether's theorem in reverse, the LRL vector gives rise to a corresponding…
Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction…
To estimate influence of the "dark energy" on the Keplerian orbits, we solve the general relativistic equations of motion of a test particle in the field of a point-like mass embedded in the cosmological background formed by the Lambda-term…
The classical theory of linear response applies to statistical mechanics close to equilibrium. Away from equilibrium, one may describe the microscopic time evolution by a general differentiable dynamical system, identify nonequilibrium…
We report on the application of chaos control to the irregular motion of an electron under the combined influence of a Coulomb and a magnetic field, the so-called ``diamagnetic Kepler problem'' (DKP). We show how to stabilize the classical…