Related papers: Stochastic Gauss Equations
A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a…
Many phenomena such as stellar variability, stellar explosions, behavior of different kind of X-ray and gamma-ray sources, processes in active galactic nuclei and other astrophysical objects show stochastic features. Brief description of…
It is shown that the Bohm equations for the phase $S$ and squared modulus $\rho$ of the quantum mechanical wave function can be derived from the classical ensemble equations admiting an aditional momentum $p_s$ of the form proportional to…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
We use the basic equations that predict the emission of gravitational waves according to the Einstein gravitation theory to calculate the luminosities and the amplitudes of the waves generated by binary stars, pulsations of neutron stars,…
We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component $\phi_j$ of the wave vector is understood as a…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
A stochastic theory of gravity is described in which the metric tensor is a random variable such that the spacetime manifold is a fluctuating physical system at a certain length scale. A general formalism is described for calculating…
Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
The Einstein vacuum equations on an (n+1)-dimensional toroidal manifold $\mathbb{M}^{n+1}=\mathbb{T}^{n}\times\mathbb{R}^{+}$ reduce to a system of n-dimensional nonlinear ODEs in terms of the set of toroidal radii $(a_{i})_{i=1}^{n}$ or…
This two-paper series addresses and fixes the long-standing gauge invariance problem of angular momentum in gauge theories. This QED part reveals: 1) The spin and orbital angular momenta of electrons and photons can all be consistently…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the…
The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
Investigations of spherically symmetric motions of self-gravitating gaseous stars governed by the non-relativistic Newtonian gravitation theory or by the general relativistic theory lead us to a certain type of non-linear hyperbolic…
The paths of stars in galaxies have circular velocity independent of their distance from the centre of the galaxy. Newtonian mechanics with a logarithmic potential has such paths. In relativity these paths can be taken to be geodesics and…
Several mechanisms exist for generating a stochastic background of gravitational waves in the period following inflation. These mechanisms are generally classical in nature, with the gravitational waves being produced from inhomogeneities…
In orbital and attitude dynamics the coordinates and the Euler angles are expressed as functions of the time and six constants called elements. Under disturbance, the constants are endowed with time dependence. The Lagrange constraint is…