Some integrable models in quantized spaces

It is shown that in a quantized space determined by the $B_2\quad (O(5)=Sp(4))$ algebra with three dimensional parameters of the length $L^2$, momentum $(Mc)^2$, and action $S$, the spectrum of the Coulomb problem with conserving Runge-Lenz vector coincides with the spectrum found by Schr\"odinger for the space of constant curvature but with the values of the principal quantum number limited from the side of higher values. The same problem is solved for the spectrum of a harmonic oscillator.Comment: 11 pages, LaTe

Is the mean-field approximation so bad? A simple generalization yelding realistic critical indices for 3D Ising-class systems

Modification of the renormalization-group approach, invoking Stratonovich transformation at each step, is proposed to describe phase transitions in 3D Ising-class systems. The proposed method is closely related to the mean-field approximation. The low-order scheme works well for a wide thermal range, is consistent with a scaling hypothesis and predicts very reasonable values of critical indices.Comment: 4 page

Yakhot's model of strong turbulence: A generalization of scaling models of turbulence

We report on some implications of the theory of turbulence developed by V. Yakhot [V. Yakhot, Phys. Rev. E {\bf 57}(2) (1998)]. In particular we focus on the expression for the scaling exponents $\zeta_{n}$. We show that Yakhot's result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L'vov and I. Procaccia [V. L'vov & I. Procaccia, Phys. Rev. E {\bf 62}(6) (2000)]. The model furthermore yields a theoretical justification for the method of extended self--similarity (ESS).Comment: 8 page

Model Flames in the Boussinesq Limit: The Effects of Feedback

We have studied the fully nonlinear behavior of pre-mixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. Key results include the establishment of criterion for when such flames propagate as simple planar flames; elucidation of scaling laws for the effective flame speed; and a study of the stability properties of these flames. The simplicity of some of our scalings results suggests that analytical work may further advance our understandings of buoyant flames.Comment: 11 pages, 14 figures, RevTex, gzipped tar fil

Effect of quantum noise on Coulomb blockade in normal tunnel junctions at high voltages

We have investigated asymptotic behavior of normal tunnel junctions at voltages where even the best ohmic environments start to look like RC transmission lines. In the experiments, this is manifested by an exceedingly slow approach to the linear behavior above the Coulomb gap. As expected on the basis of the quantum theory taking into account interaction with the environmental modes, better fits are obtained using 1/sqrt{V}- than 1/V- dependence for the asymptote. These results agree with the horizon picture if the frequency-dependent phase velocity is employed instead of the speed of light in order to determine the extent of the surroundings seen by the junction.Comment: 9 pages, 4 figures, submitted to Phys. Rev.

Randomness in Classical Mechanics and Quantum Mechanics

The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations, i.e. the uncertainty (errors of observation) in the determination of coordinate and momentum is always positive (non zero). A "functional" formulation of classical mechanics was suggested. The fundamental equation of the microscopic dynamics in the functional approach is not the Newton equation but the Liouville equation for the distribution function of the single particle. Solutions of the Liouville equation have the property of delocalization which accounts for irreversibility. The Newton equation in this approach appears as an approximate equation describing the dynamics of the average values of the position and momenta for not too long time intervals. Corrections to the Newton trajectories are computed. An interpretation of quantum mechanics is attempted in which both classical and quantum mechanics contain fundamental randomness. Instead of an ensemble of events one introduces an ensemble of observers.Comment: 12 pages, Late

Scaling Relations for Collision-less Dark Matter Turbulence

Many scaling relations are observed for self-gravitating systems in the universe. We explore the consistent understanding of them from a simple principle based on the proposal that the collision-less dark matter fluid terns into a turbulent state, i.e. dark turbulence, after crossing the caustic surface in the non-linear stage. The dark turbulence will not eddy dominant reflecting the collision-less property. After deriving Kolmogorov scaling laws from Navier-Stokes equation by the method similar to the one for Smoluchowski coagulation equation, we apply this to several observations such as the scale-dependent velocity dispersion, mass-luminosity ratio, magnetic fields, and mass-angular momentum relation, power spectrum of density fluctuations. They all point the concordant value for the constant energy flow per mass: $0.3 cm^2/sec^3$, which may be understood as the speed of the hierarchical coalescence process in the cosmic structure formation.Comment: 26 pages, 6 figure

On Properties of Vacuum Axial Symmetric Spacetime of Gravitomagnetic Monopole in Cylindrical Coordinates

We investigate general relativistic effects associated with the gravitomagnetic monopole moment of gravitational source through the analysis of the motion of test particles and electromagnetic fields distribution in the spacetime around nonrotating cylindrical NUT source. We consider the circular motion of test particles in NUT spacetime, their characteristics and the dependence of effective potential on the radial coordinate for the different values of NUT parameter and orbital momentum of test particles. It is shown that the bounds of stability for circular orbits are displaced toward the event horizon with the growth of monopole moment of the NUT object. In addition, we obtain exact analytical solutions of Maxwell equations for magnetized and charged cylindrical NUT stars.Comment: 16 pages, 3 figures, 1 tabl

Action at a distance as a full-value solution of Maxwell equations: basis and application of separated potential's method

The inadequacy of Li\'{e}nard-Wiechert potentials is demonstrated as one of the examples related to the inconsistency of the conventional classical electrodynamics. The insufficiency of the Faraday-Maxwell concept to describe the whole electromagnetic phenomena and the incompleteness of a set of solutions of Maxwell equations are discussed and mathematically proved. Reasons of the introduction of the so-called ``electrodynamics dualism concept" (simultaneous coexistence of instantaneous Newton long-range and Faraday-Maxwell short-range interactions) have been displayed. It is strictly shown that the new concept presents itself as the direct consequence of the complete set of Maxwell equations and makes it possible to consider classical electrodynamics as a self-consistent and complete theory, devoid of inward contradictions. In the framework of the new approach, all main concepts of classical electrodynamics are reconsidered. In particular, a limited class of motion is revealed when accelerated charges do not radiate electromagnetic field.Comment: ReVTeX file, 24pp. Small corrections which do not have influence results of the paper. Journal reference is adde

Unilateral interactions in granular packings: A model for the anisotropy modulus

Unilateral interparticle interactions have an effect on the elastic response of granular materials due to the opening and closing of contacts during quasi-static shear deformations. A simplified model is presented, for which constitutive relations can be derived. For biaxial deformations the elastic behavior in this model involves three independent elastic moduli: bulk, shear, and anisotropy modulus. The bulk and the shear modulus, when scaled by the contact density, are independent of the deformation. However, the magnitude of the anisotropy modulus is proportional to the ratio between shear and volumetric strain. Sufficiently far from the jamming transition, when corrections due to non-affine motion become weak, the theoretical predictions are qualitatively in agreement with simulation results.Comment: 6 pages, 5 figure