Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices

The problem of chaotic scattering in presence of direct processes or prompt responses is mapped via a transformation to the case of scattering in absence of such processes for non-unitary scattering matrices, \tilde S. In the absence of prompt responses, \tilde S is uniformly distributed according to its invariant measure in the space of \tilde S matrices with zero average, < \tilde S > =0. In the presence of direct processes, the distribution of \tilde S is non-uniform and it is characterized by the average (\neq 0). In contrast to the case of unitary matrices S, where the invariant measures of S for chaotic scattering with and without direct processes are related through the well known Poisson kernel, here we show that for non-unitary scattering matrices the invariant measures are related by the Poisson kernel squared. Our results are relevant to situations where flux conservation is not satisfied. For example, transport experiments in chaotic systems, where gains or losses are present, like microwave chaotic cavities or graphs, and acoustic or elastic resonators.Comment: Added two appendices and references. Corrected typo

Classical wave experiments on chaotic scattering

We review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves. Inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems, scattering theory has to be applied for a quantitative interpretation of the measurements. Most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation. In all studied examples a quantitative agreement between experiment and theory is achieved. To this end it is necessary, however, to take absorption and imperfect coupling into account, concepts that were ignored in most previous theoretical investigations. Classical phase space signatures of scattering are being examined in a small number of experiments.Comment: 33 pages, 13 figures; invited review for the Special Issue of J. Phys. A: Math. Gen. on "Trends in Quantum Chaotic Scattering

Differentially expressed genes in the femur cartilage transcriptome clarify the understanding of femoral head separation in chickens.

Locomotor problems are among one of the main concerns in the current poultry industry, causing major economic losses and affecting animal welfare. The most common bone anomalies in the femur are dyschondroplasia, femoral head separation (FHS), and bacterial chondronecrosis with osteomyelitis (BCO), also known as femoral head necrosis (FHN). The present study aimed to identify differentially expressed (DE) genes in the articular cartilage (AC) of normal and FHS-affected broilers by RNA-Seq analysis. In the transcriptome analysis, 12,169 genes were expressed in the femur AC. Of those, 107 genes were DE (FDR < 0.05) between normal and affected chickens, of which 9 were downregulated and 98 were upregulated in the affected broilers. In the gene-set enrichment analysis using the DE genes, 79 biological processes (BP) were identified and were grouped into 12 superclusters. The main BP found were involved in the response to biotic stimulus, gas transport, cellular activation, carbohydrate-derived catabolism, multi-organism regulation, immune system, muscle contraction, multi-organism process, cytolysis, leukocytes and cell adhesion. In this study, the first transcriptome analysis of the broilers femur articular cartilage was performed, and a set of candidate genes (AvBD1, AvBD2, ANK1, EPX, ADA, RHAG) that could trigger changes in the broiler´s femoral growth plate was identified. Moreover, these results could be helpful to better understand FHN in chickens and possibly in humans.Article number: 17965