Systematic Density Expansion of the Lyapunov Exponents for a Two-dimensional Random Lorentz Gas

We study the Lyapunov exponents of a two-dimensional, random Lorentz gas at low density. The positive Lyapunov exponent may be obtained either by a direct analysis of the dynamics, or by the use of kinetic theory methods. To leading orders in the density of scatterers it is of the form $A_{0}\tilde{n}\ln\tilde{n}+B_{0}\tilde{n}$, where $A_{0}$ and $B_{0}$ are known constants and $\tilde{n}$ is the number density of scatterers expressed in dimensionless units. In this paper, we find that through order $(\tilde{n}^{2})$, the positive Lyapunov exponent is of the form $A_{0}\tilde{n}\ln\tilde{n}+B_{0}\tilde{n}+A_{1}\tilde{n}^{2}\ln\tilde{n} +B_{1}\tilde{n}^{2}$. Explicit numerical values of the new constants $A_{1}$ and $B_{1}$ are obtained by means of a systematic analysis. This takes into account, up to $O(\tilde{n}^{2})$, the effects of {\it all\/} possible trajectories in two versions of the model; in one version overlapping scatterer configurations are allowed and in the other they are not.Comment: 12 pages, 9 figures, minor changes in this version, to appear in J. Stat. Phy

Genes involved in carotene synthesis and mating in Blakeslea trispora

Mating of Blakeslea trispora and other molds of the order Mucorales requires the interaction of mycelia of opposite sex, (+) and (-), leading to the development of specialized structures and to an enhanced accumulation of beta-carotene. Industry obtains beta-carotene by co-cultivating appropriate strains of Blakeslea (mated cultures). Gene transcription in single and mated cultures was assayed by cDNA-AFLP, a technique to observe the differential expression of subsets of mRNA fragments. Overexpression in mated cultures is about ten times more frequent than underexpression. We obtained and sequenced fragments of 97 candidate genes that appeared to be overexpressed during mating and confirmed four of them by reverse transcription and real-time PCR. Comparisons with gene sequences from other organisms suggest functions in carotene biosynthesis (4 genes), energy metabolism (8), cell wall synthesis (1), transfer of acetyl groups (1), and regulatory processes (10). Sodium acetate inhibited sexual overexpression in about two-thirds of the candidate genes and acted as a signal with broad effects on the metabolism and the morphology of mated cultures. Our work offers new materials for the study of carotene biosynthesis and its regulation and for the improvement of carotene production with Mucorales

Probing quantum-mechanical level repulsion in disordered systems by means of time-resolved selectively-excited resonance fluorescence

We argue that the time-resolved spectrum of selectively-excited resonance fluorescence at low temperature provides a tool for probing the quantum-mechanical level repulsion in the Lifshits tail of the electronic density of states in a wide variety of disordered materials. The technique, based on detecting the fast growth of a fluorescence peak that is red-shifted relative to the excitation frequency, is demonstrated explicitly by simulations on linear Frenkel exciton chains.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Dark matter as integration constant in Horava-Lifshitz gravity

In the non-relativistic theory of gravitation recently proposed by Horava, the Hamiltonian constraint is not a local equation satisfied at each spatial point but an equation integrated over a whole space. The global Hamiltonian constraint is less restrictive than its local version, and allows a richer set of solutions than in general relativity. We show that a component which behaves like pressureless dust emerges as an "integration constant" of dynamical equations and momentum constraint equations. Consequently, classical solutions to the infrared limit of Horava-Lifshitz gravity can mimic general relativity plus cold dark matter.Comment: 16 pages; (non-)conservation equation for "dark matter" added (v2); note added to comment on some recent preprints (v3); version accepted for publication in PRD (v4

Detection of Keplerian dynamics in a disk around the post-AGB star AC Her

So far, only one rotating disk has been clearly identified and studied in AGB or post-AGB objects (in the Red Rectangle), by means of observations with high spectral and spatial resolution. However, disks are thought to play a key role in the late stellar evolution and are suspected to surround many evolved stars. We aim to extend our knowledge on these structures. We present interferometric observations of CO J=2-1 emission from the nebula surrounding the post-AGB star AC Her, a source belonging to a class of objects that share properties with the Red Rectangle and show hints of Keplerian disks. We clearly detect the Keplerian dynamics of a second disk orbiting an evolved star. Its main properties (size, temperature, central mass) are derived from direct interpretation of the data and model fitting. With this we confirm that there are disks orbiting the stars of this relatively wide class of post-AGB objectsComment: 4 pages, 3 figure

Condition number analysis and preconditioning of the finite cell method

The (Isogeometric) Finite Cell Method - in which a domain is immersed in a structured background mesh - suffers from conditioning problems when cells with small volume fractions occur. In this contribution, we establish a rigorous scaling relation between the condition number of (I)FCM system matrices and the smallest cell volume fraction. Ill-conditioning stems either from basis functions being small on cells with small volume fractions, or from basis functions being nearly linearly dependent on such cells. Based on these two sources of ill-conditioning, an algebraic preconditioning technique is developed, which is referred to as Symmetric Incomplete Permuted Inverse Cholesky (SIPIC). A detailed numerical investigation of the effectivity of the SIPIC preconditioner in improving (I)FCM condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the Poisson problem and for two- and three-dimensional problems in linear elasticity, in which Nitche's method is applied in either the normal or tangential direction. The accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method