Modeling the behavior of elastic materials with stochastic microstructure

Even in the simple linear elastic range, the material behavior is not deterministic, but fluctuates randomly around some expectation values. The knowledge about this characteristic is obviously trivial from an experimentalist’s point of view. However, it is not considered in the vast majority of material models in which “only” deterministic behavior is taken into account. One very promising approach to the inclusion of stochastic effects in modeling of materials is provided by the Karhunen-Lo`eve expansion. It has been used, for example, in the stochastic finite element method, where it yields results of the desired kind, but unfortunately at drastically increased numerical costs. This contribution aims to propose a new ansatz that is based on a stochastic series expansion, but at the Gauß point level. Appropriate energy relaxation allows to derive the distribution of a synthesized stress measure, together with explicit formulas for the expectation and variance. The total procedure only needs negligibly more computation effort than a simple elastic calculation. We also present an outlook on how the original approach in [7] can be applied to inelastic material

Coherent states for polynomial su(1,1) algebra and a conditionally solvable system

In a previous paper [{\it J. Phys. A: Math. Theor.} {\bf 40} (2007) 11105], we constructed a class of coherent states for a polynomially deformed $su(2)$ algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed $su(1,1)$ algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1,1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1,1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.Comment: 2 figure

Full-analytic frequency-domain 1pN-accurate gravitational wave forms from eccentric compact binaries

The article provides ready-to-use 1pN-accurate frequency-domain gravitational wave forms for eccentric nonspinning compact binaries of arbitrary mass ratio including the first post-Newtonian (1pN) point particle corrections to the far-zone gravitational wave amplitude, given in terms of tensor spherical harmonics. The averaged equations for the decay of the eccentricity and growth of radial frequency due to radiation reaction are used to provide stationary phase approximations to the frequency-domain wave forms.Comment: 28 pages, submitted to PR

Phase Coherence and Superfluid-Insulator Transition in a Disordered Bose-Einstein Condensate

We have studied the effects of a disordered optical potential on the transport and phase coherence of a Bose-Einstein condensate (BEC) of 7Li atoms. At moderate disorder strengths (V_D), we observe inhibited transport and damping of dipole excitations, while in time-of-flight images, random but reproducible interference patterns are observed. In-situ images reveal that the appearance of interference is correlated with density modulation, without complete fragmentation. At higher V_D, the interference contrast diminishes as the BEC fragments into multiple pieces with little phase coherence.Comment: 4 pages, 5 figures, distortions in figures 1 and 4 have been fixed in version 3. This paper has been accepted to PR

Quantum fluctuations of the electroweak sphaleron: Erratum and Addendum

We correct an error in our treatment of the tadpole contribution to the fluctuation determinant of the sphaleron, and also a minor mistake in a previous estimate. Thereby the overall agreement between the two existing exact computations and their consistency with the estimate is improved considerably.Comment: 4 pages, Dortmund preprint DO-TH-93/19E

Supersymmetry of the Nonstationary Schr\"odinger equation and Time-Dependent Exactly Solvable Quantum Models

New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.Comment: Talk at the 8th International Conference "Symmetry Methods in Physics". Dubna, Russia, 28 July - 2 August, 199

More on coupling coefficients for the most degenerate representations of SO(n)

We present explicit closed-form expressions for the general group-theoretical factor appearing in the alpha-topology of a high-temperature expansion of SO(n)-symmetric lattice models. This object, which is closely related to 6j-symbols for the most degenerate representation of SO(n), is discussed in detail.Comment: 9 pages including 1 table, uses IOP macros Update of Introduction and Discussion, References adde

Exactly Solvable Hydrogen-like Potentials and Factorization Method

A set of factorization energies is introduced, giving rise to a generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for the radial hydrogen-like Hamiltonian. An algebraic intertwining technique involving such factorization energies leads to derive $n$-parametric families of potentials in general almost-isospectral to the hydrogen-like radial Hamiltonians. The construction of SUSY partner Hamiltonians with ground state energies greater than the corresponding ground state energy of the initial Hamiltonian is also explicitly performed.Comment: LaTex file, 21 pages, 2 PostScript figures and some references added. To be published in J. Phys. A: Math. Gen. (1998

Quantum mechanical spectral engineering by scaling intertwining

Using the concept of spectral engineering we explore the possibilities of building potentials with prescribed spectra offered by a modified intertwining technique involving operators which are the product of a standard first-order intertwiner and a unitary scaling. In the same context we study the iterations of such transformations finding that the scaling intertwining provides a different and richer mechanism in designing quantum spectra with respect to that given by the standard intertwiningComment: 8 twocolumn pages, 5 figure