Joint probability distribution of composite quantum systems

We determine the joint probability distribution for two observables attached to two systems in weak interaction, by minimizing the entropic measure of interdependence subject to constraints given by marginal expected values and by the correlation coefficient between the two observables.     

Joint probability distribution beyond the Smoluchowski limit for brownian motion in position space

We obtain a time convolutionless partial differential equation for the joint probability distribution in position space of a non-markovian brownian particle under the influence of some potential. We discuss the corrections to the Smoluchowski limit in this context.     

Probability Density and Joint Probability Density of SDE with General Nonlinear Gaussian Noise

We consider a stochastic differential equation with a general nonlinearity in Gaussian noise; With both D (fluctuation intensity) and γ (correlation time) small quantities with D/γ < 1/10, approximate equations for the probability density p(q, t) and the joint probability density p(q, t, q^t, t^p) are derived. As applications of our general equations, quadratic noise, exponential noise and triangle function noise are studied.     

Fokker-Planck approximation for N-dimensional nonmarkovian langevin equations

The Fokker-Planck approximation for n-dimensional nonmarkovian Langevin equations is discussed through an expansion in powers of the correlation time of the noise. Exact cases are considered and an application to brownian motion is presented.     

q-deformed probability and binomial distribution

We introduce the concept ofq-deformed probability and discuss theq-deformed binomial distribution.     

Response probability distribution of built-up vibro-acoustic systems

The vibro-acoustic response of built-up structures, consisting of stiff components with low modal density and flexible components with high modal density, is sensitive to small imperfections in the flexible components. In this paper, the uncertainty of the response is considered by modeling the low modal density master system as deterministic and the high modal density subsystems in a nonparametric stochastic way, i.e., carrying a diffuse wave field, and by subsequently computing the response probability density function. The master system's mean squared response amplitude follows a singular noncentral complex Wishart distribution conditional on the subsystem energies. For a single degree of freedom, this is equivalent to a chi-square or an exponential distribution, depending on the loading conditions. The subsystem energies follow approximately a chi-square distribution when their relative variance is smaller than unity. The results are validated by application to plate structures, and good agreement with Monte Carlo simulations is found.     

Singularity spectrum of the resolvent in a nonmarkovian master equation

The well-known standard nonmarkovian master equation is used to describe the damping of a harmonic macroscopic coordinate coupled to a thermally equilibrated Fermi gas. The time evolution of the phonon distribution is expressed in terms of a resolvent whose spectrum of singularities is computed and analyzed. It is seen that an apparent limitation of the model related to the appearance of undesired oscillations does not inhibit the expected behavior of the average phonon number and phonon number dispersion.     

Steady state probability distribution for turbulence fluctuations

An incompressible and viscous fluid is represented by a complex scalar field. In terms of, the hydrodynamic mode interaction v. grad v can be described canonically, i.e. as a functional derivative of a Hamiltonian. By introducing noise and stochastic damping a Langevin equation and its corresponding Fokker-Planck equation is obtained. Both are expected to describe a turbulent flow. The stochastic process approximately obeys detailed balance. This allows to derive, as a main result, the stationary distribution function of a turbulent fluid. It is non Gaussian, contains a 4^th order (transverse) current-current interaction, and has mass (~ ²) zero.     

Polarization mode dispersion probability distribution for arbitrary distances

The probability distribution of the differential group delay (DGD) at any fiber length is determined by use of a physically reasonable model of the fiber birefringence. We show that if the fiber correlation length is of the same order as or larger than the beat length, the DGD distribution approaches a Maxwellian in roughly 30 fiber correlation lengths, corresponding to a couple of kilometers in realistic cases. We also find that the probability distribution function of the polarization dispersion vector at the output of the fiber depends on the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.     

A non self-referential expression of Tsallis' probability distribution function

The canonical probability distribution function (pdf) obtained by optimizing the Tsallis entropy under either the linear mean energy constraint U or the escort mean energy constraint U_q suffer self-referentiality. In a recent paper [Phys. Lett. A 335, 351 (2005)] the authors have shown that the pdfs obtained with either U or U_q are equivalent to the pdf in a non self-referential form. Based on this result we derive an alternative expression for the Tsallis distributions, employing either U or U_q, which is non self-referential.     

The exact probability distribution of a two-dimensional random walk

A calculation is made of the exact probability distribution of the two-dimensional displacement of a particle at timet that starts at the origin, moves in straight-line paths at constant speed, and changes its direction after exponentially distributed time intervals, where the lengths of the straight-line paths and the turn angles are independent, the angles being uniformly distributed. This random walk is the simplest model for the locomotion of microorganisms on surfaces. Its weak convergence to a Wiener process is also shown.     

Moment analysis of the probability distribution of different sandpile models

We reconsider the moment analysis of the Bak-Tang-Wiesenfeld and the stochastic sandpile model introduced by Manna [J. Phys. A 24, L363 (1991)] in two and three dimensions. In contrast to recently performed investigations our analysis reveals that the models are characterized by different scaling behavior, i.e., they belong to different universality classes.     

A macro traffic flow model with probability distribution function

In this paper, we introduce three probability distribution functions into the dynamic equation and propose a macro traffic flow model to investigate the impacts of the probability distribution functions on the evolutions of traffic flow under three typical states (i.e., uniform flow, shock, rarefaction wave, and small perturbation). The numerical results indicate that the probability distribution functions do not change the density and speed distributions of uniform flow, produce a two-layer shock but have no prominent effects on rarefaction wave, and have little effect on small perturbation.