Tree decompositions of graphs: Saving memory in dynamic programming

We propose a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems. The introduced “anchor technique” is based on a tree-like set covering problem. We substantiate our findings by experimental results. Our strategy has negligible computational overhead concerning running time but achieves memory savings for nice tree decompositions and path decompositions between 60% and 98%.     

A gauge field governing parallel transport along mixed states

At first, a short account is given of some basic notations and results on parallel transport along mixed states. A new connection form (gauge field) is introduced to give a geometric meaning to the concept of parallelity in the theory of density operators.     

The Calderón Problem with Partial Data for Conductivities with 3/2 Derivatives

We study a chain of four interacting rotors (rotators) connected at both ends to stochastic heat baths at different temperatures. We show that for non-degenerate interaction potentials the system relaxes, at a stretched exponential rate, to a non-equilibrium steady state (NESS). Rotors with high energy tend to decouple from their neighbors due to fast oscillation of the forces. Because of this, the energy of the central two rotors, which interact with the heat baths only through the external rotors, can take a very long time to dissipate. By appropriately averaging the oscillatory forces, we estimate the dissipation rate and construct a Lyapunov function. Compared to the chain of length three (considered previously by C. Poquet and the current authors), the new difficulty with four rotors is the appearance of resonances when both central rotors are fast. We deal with these resonances using the rapid thermalization of the two external rotors.     

CuO particles from ionic liquid/water mixtures: evidence for growth via Cu(OH)2 nanorod assembly and fusion

Tetrabutylammonium hydroxide/water mixtures are efficient reaction media for the fabrication of nanoscale metal oxides and hydroxides. Uniform CuO nanoplates, among others, can be grown on a large scale. This work shows that after 30 s at temperatures above 40 degrees C, CuO formation is already essentially complete. X-ray diffraction and transmission electron microscopy (TEM) show that the resulting plates form via a two-step process, where Cu(OH) 2 rods precipitate first. These rods aggregate and fuse into plates with a width/height ratio of about 1.9. High-resolution TEM and electron diffraction show that the plates are single crystals and exhibit only some defects, which most likely originate from the assembly and fusion of the primary rods.     

Vortex quantum creation and winding number scaling in a quenched spinor Bose gas

Motivated by a recent experiment, we study nonequilibrium quantum phenomena taking place in the quench of a spinor Bose-Einstein condensate through the zero-temperature phase transition separating the polar paramagnetic and planar ferromagnetic phases. We derive the typical spin domain structure (correlations of the effective magnetization) created by the quench arising due to spin-mode quantum fluctuations, and we establish a sample-size scaling law for the creation of spin vortices, which are topological defects in the transverse magnetization.     

Determining a Magnetic Schrödinger Operator from Partial Cauchy Data

In this paper we show, in dimension n ≥ 3, that knowledge of the Cauchy data for the Schrödinger equation in the presence of a magnetic potential, measured on possibly very small subsets of the boundary, determines uniquely the magnetic field and the electric potential. We follow the general strategy of [7] using a richer set of solutions to the Dirichlet problem that has been used in previous works on this problem.     

A Multi-Mechanism Model for Cutting Simulations Combining Visco-plastic Asymmetry and Phase Transformation

We develop a multi-mechanism model for strainrate- and temperature-dependent asymmetric plastic material behavior accompanied by phase transformations, which are important phenomena in steel production processes. To this end the well-known Johnson-Cook model is extended by the concept of weighting functions, and it is combined with a model of tranformation-induced plasticity (TRIP) based on Leblond's approach. The bulk model is formulated within a thermodynamic framework at large strains, and it will be specialized and applied to cutting processes in steel production. In the examples parameters are identified for the material DIN 100Cr6, and we illustrate the characteristic effects of our multimechanism model, such as strain softening due to temperature, rate dependence and temperature dependence as well as the SD-effect. A finite-element simulation illustrates the different mechanisms for a cutting process. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure of glassy polymers. V. Small-angle x-ray scattering from polystyrene

Small-angle x-ray scattering (SAXS) from glassy atactic polystyrene has been measured using a Bonse–Hart system. After correcting for absorption, background, and beam divergence, the scattering has been placed on an absolute basis using a standard silica suspension as a reference.The desmeared absolute intensity decreases strongly with increasing scattering angle over the range between 20 sec and 20 min. At larger angles, the intensity decreases much more slowly with increasing angle and approaches the value expected for density fluctuations frozen-in at the glass transition. The angular variation of intensity is well described by the scattering from heterogeneities of various sizes and concentrations superimposed on the scattering from thermal density fluctuations. These heterogeneities range in radius from 10 to 4000 Å. The present SAXS results on glassy polystyrene seem inconsistent with the presence of nodular features as representative of the bulk polymer.     

Remarks on the relation between quantum and classical entropy as proposed by A. Wehrl

Using an inequality of Lieb one can compute a probability distribution which is less mixed than any (z|ωz)dz, where z labels the points of phase space, w is a density matrix, and (z| the appropriate coherent state.