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

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

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

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

Construction of classical superintegrable systems with higher order integrals of motion from ladder operators

We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a polynomial Poisson algebra. We consider a one-dimensional system with third order ladders operators and found a family of superintegrable systems with higher order integrals of motion. We obtain also the polynomial algebra generated by these integrals. We calculate numerically the trajectories and show that all bounded trajectories are closed.Comment: 10 pages, 4 figures, to appear in j.math.phys

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

Variation in Student Perceptions of Higher Education Course Quality and Difficulty as a Result of Widespread Implementation of Online Education During the COVID-19 Pandemic

The onset of the COVID-19 global pandemic affected higher education in a myriad of ways. One of the most notable effects however was the rapid and sudden transition of nearly all courses at most institutions to an online environment. And while there are a growing number of courses offered online already, this transition to nearly 100% remote education presented numerous challenges for instructors and students of face-to-face and hybrid style courses. Since student perceptions are closely tied to recruitment and retention, it is important to know if there are differences in student perceptions present in the way different courses are taught. This study extends the work of other authors that have investigated student perceptions by looking specifically at how the COVID-19 pandemic may have changed student views of course difficulty and quality both overall and across discipline or institution categories. Course evaluations from 837 courses from 191 different schools archived on RateMyProfessors.com were used in a general linear model where a statistically significant overall decline of 6% in perceived course difficulty and 4% decline in perceived quality was detected. In addition to calculating this mean decrease, courses were also categorized on the basis of academic discipline (Business, Engineering and Mathematics, Humanities, Natural Sciences, Social Sciences), institution type (2-Year, 4-Year), and whether instructors had previous experience teaching online courses (No, Yes) to determine any variation in differences that may have appeared as a result of more nuanced details in course type or delivery. Most notably, declines in course difficulty were slightly more apparent with instructors that had no previous online teaching experience. No other discipline, institution type, or teaching experience interactions were detected with either difficulty or quality variation. These data suggest that there were very real changes in perceived quality and difficulty but that these changes were largely universal irrespective of discipline, institution type, or prior experience teaching online (with exception of course difficulty)