333 research outputs found
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 and the asymptotic integrated
level density for Yang-Mills-Higgs Quantum Mechanics for two and three
dimensions (). Due to the infinite volume of the phase space
on energy shell for , it is not possible to disentangle completely the
coupled oscillators (-model) from the Higgs sector. The situation is
different for for which is finite. The transition from order
to chaos in these systems is expressed by the corresponding transitions in
and , 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)Â =Â 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.
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