2,735 research outputs found
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
A variational growth approach to topology optimization
In this contribution we present an overview of our work on a novel approach to topology optimization based on growth processes [1, 2, 3]. A compliance parameter to describe the spatial distribution of mass is introduced. It serves as an internal variable for which an associated evolution equation is derived using Hamilton’s principle. The well-known problem of checkerboarding is faced with energy regularization techniques. Numerical examples are given for demonstration purposes
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
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
Investigation of the potential of topology optimization in additive manufacturing using the example of components subject to bending stress
In this application-oriented work, we examine the performance of topology-optimized structures as compared to the reference I-beam. We make use of the thermodynamic topology optimization based on a linear elastic compliance minimization, i. e. minimization of the elastic strain energy of the whole structure. We investigate, how the optimization of the rather theoretical strain energy influences the efficiency of more practical measurements, i. e. the force-displacement response at the loading points and the maximum tolerable force. For this purpose, starting from a cuboid design space with the boundary conditions of a 3-point and 4-point bending stress, the geometry with constant volume was optimized. The topology-optimized bending beams were subsequently produced by stereolithography and mechanically tested with respect to the previously defined boundary conditions. In order to avoid a falsification of results due to internal sample defects, all samples were previously examined with the aid of computer tomography with regard to the defects in the volume. As a general result, the topology-optimized bending beams can bear a higher load in the experiment, which shows the usefulness of the coupling of additive manufacturing and topology optimization methods without any special constraints or enhancements regarding the manufacturing process within the optimization
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
Extreme tunability of interactions in a Li Bose-Einstein condensate
We use a Feshbach resonance to tune the scattering length a of a
Bose-Einstein condensate of 7Li in the |F = 1, m_F = 1> state. Using the
spatial extent of the trapped condensate we extract a over a range spanning 7
decades from small attractive interactions to extremely strong repulsive
interactions. The shallow zero-crossing in the wing of the Feshbach resonance
enables the determination of a as small as 0.01 Bohr radii. In this regime,
evidence of the weak anisotropic magnetic dipole interaction is obtained by
comparison with different trap geometries
Topological methods for searching barriers and reaction paths
We present a family of algorithms for the fast determination of reaction
paths and barriers in phase space and the computation of the corresponding
rates. The method requires the reaction times be large compared to the
microscopic time, irrespective of the origin - energetic, entropic, cooperative
- of the timescale separation. It lends itself to temperature cycling as in
simulated annealing and to activation-relaxation routines. The dynamics is
ultimately based on supersymmetry methods used years ago to derive Morse
theory. Thus, the formalism automatically incorporates all relevant topological
information.Comment: 4 pages, 4 figures, RevTex
Experimental investigation of the tire wear process using camera-assisted observation assessed by numerical modeling
This paper presents a novel experimental method to study the abrasion mechanism of car tires. It is based on the detection of microscopic movements associated with material damage (cracking) on the rubber tread. This is referred to as degrading layer relaxation. It correlates with the wear rate and, interestingly, the direction of the pattern's movement is opposite to the lateral forces during cornering. To measure and analyze the microscopic movements, a new camera-based method with feature point matching using video stabilization was developed. Besides extensive experimental investigation, the formation and propagation of microcracks are investigated using a simplified numerical model in which a phase field approach coupled with a viscoelastic constitutive behavior is implemented in a finite element framework
- …