Kinematically Extended Continuum Theories: Correlation Between Microscopical Deformation and Macroscopical Strain Measures

The present work investigates the correlation between macrocscopical deformation modes and microscopical deformation modes. Thereby, the macroscopical deformation is represented by the strain-like quantities of the according macroscopical continuum theory while the microscopical deformation is expressed in the form of a Taylor series expansion. The use of an energy criterion makes it possible to derive a quantitative relation between microscopical and macroscopical deformation. The procedure is applied to different kinematically extended continuum theories on the macroscopical level. The investigation may help to select an optimal macroscopical continuum theory instead of choosing a theory based on phenomenological observations, whereby the optimal theory ist that one, which reflects the microscopical deformation behaviour best. The microscopical deformation behaviour depends on the topology of the microstructure under consideration. Thus, the optimal theory is affected by the topology of the microstructure

Non-abelian plane waves and stochastic regimes for (2+1)-dimensional gauge field models with Chern-Simons term

An exact time-dependent solution of field equations for the 3-d gauge field model with a Chern-Simons (CS) topological mass is found. Limiting cases of constant solution and solution with vanishing topological mass are considered. After Lorentz boost, the found solution describes a massive nonlinear non-abelian plane wave. For the more complicate case of gauge fields with CS mass interacting with a Higgs field, the stochastic character of motion is demonstrated.Comment: LaTeX 2.09, 13 pages, 11 eps figure

Painlev\'{e} test of coupled Gross-Pitaevskii equations

Painlev\'{e} test of the coupled Gross-Pitaevskii equations has been carried out with the result that the coupled equations pass the P-test only if a special relation containing system parameters (masses, scattering lengths) is satisfied. Computer algebra is applied to evaluate j=4 compatibility condition for admissible external potentials. Appearance of an arbitrary real potential embedded in the external potentials is shown to be the consequence of the coupling. Connection with recent experiments related to stability of two-component Bose-Einstein condensates of Rb atoms is discussed.Comment: 13 pages, no figure

Function reconstruction as a classical moment problem: A maximum entropy approach

We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we reconstruct a set of functions using an iterative entropy optimization scheme, and study the convergence profile as the number of moments is increased. We consider a wide variety of functions that include a distribution with a sharp discontinuity, a rapidly oscillatory function, a distribution with singularities, and finally a distribution with several spikes and fine structure. The last example is important in the context of the determination of the natural density of the logistic map. The convergence of the method is studied by comparing the moments of the approximated functions with the exact ones. Furthermore, by varying the number of moments and iterations, we examine to what extent the features of the functions, such as the divergence behavior at singular points within the interval, is reproduced. The proximity of the reconstructed maximum entropy solution to the exact solution is examined via Kullback-Leibler divergence and variation measures for different number of moments.Comment: 20 pages, 17 figure

The Partition Function and Level Density for Yang-Mills-Higgs Quantum Mechanics

We calculate the partition function $Z(t)$ and the asymptotic integrated level density $N(E)$ for Yang-Mills-Higgs Quantum Mechanics for two and three dimensions ($n = 2, 3$). Due to the infinite volume of the phase space $\Gamma$ on energy shell for $n= 2$, it is not possible to disentangle completely the coupled oscillators ($x^2 y^2$-model) from the Higgs sector. The situation is different for $n = 3$ for which $\Gamma$ is finite. The transition from order to chaos in these systems is expressed by the corresponding transitions in $Z(t)$ and $N(E)$, analogous to the transitions in adjacent level spacing distribution from Poisson distribution to Wigner-Dyson distribution. We also discuss a related system with quartic coupled oscillators and two dimensional quartic free oscillators for which, contrary to YMHQM, both coupling constants are dimensionless.Comment: 10 pages, LaTeX; minor changes; version accepted for publication as a Letter in J. Phys.

A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page

Pore-scale tomography and imaging: applications, techniques and recommended practice

No abstract available

Experimental Evaluation of Fluid Connectivity in Two-Phase Flow in Porous Media During Drainage

This study aims to experimentally investigate the possibility of combining two extended continuum theories for two-phase flow. One of these theories considers interfacial area as a separate state variable, and the other explicitly discriminates between connected and disconnected phases. This combination enhances our potential to effectively model the apparent hysteresis, which generally dominates two-phase flow. Using optical microscopy, we perform microfluidic experiments in quasi-2D artificial porous media for various cyclic displacement processes and boundary conditions. Specifically for a number of sequential drainage processes, with detailed image (post-)processing, pore-scale parameters such as the interfacial area between the phases (wetting, non-wetting, and solid), and local capillary pressure, as well as macroscopic parameters like saturation, are estimated. We show that discriminating between connected and disconnected clusters and the concept of the interfacial area as a separate state variable can be an appropriate way of modeling hysteresis in a two-phase flow scheme. The drainage datasets of capillary pressure, saturation, and specific interfacial area, are plotted as a surface, given by f (Pc, sw, awn) = 0. These surfaces accommodate all data points within a reasonable experimental error, irrespective of the boundary conditions, as long as the corresponding liquid is connected to its inlet. However, this concept also shows signs of reduced efficiency as a modeling approach in datasets gathered through combining experiments with higher volumetric fluxes. We attribute this observation to the effect of the porous medium geometry on the phase distribution. This yields further elaboration, in which this speculation is thoroughly studied and analyzed

Chaos and Preheating

We show evidence for a relationship between chaos and parametric resonance both in a classical system and in the semiclassical process of particle creation. We apply our considerations in a toy model for preheating after inflation.Comment: 7 pages, 9 figures; uses epsfig and revtex v3.1. Matches version accepted for publication in Phys. Rev.