Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic

We study the statistical distribution of components in the non-perturbative parts of energy eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five models show that deviation of the distribution from the prediction of random matrix theory (RMT) is useful in characterizing the process from nearly-integrable to chaotic, in a way somewhat similar to the nearest-level-spacing distribution. But, the statistics of EFs reveals some more properties, as described below. (i) In the process of approaching quantum chaos, the distribution of components shows a delay feature compared with the nearest-level-spacing distribution in most of the models studied. (ii) In the quantum chaotic regime, the distribution of components always shows small but notable deviation from the prediction of RMT in models possessing classical unterparts, while, the deviation can be almost negligible in models not possessing classical counterparts. (iii) In models whose Hamiltonian matrices possess a clear band structure, tails of EFs show statistical behaviors obviously different from those in the main bodies, while, the difference is smaller for Hamiltonian matrices without a clear band structure.Comment: 10 pages, 10 figure

Correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices

In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation functions with respect to energy. The analytical results are tested in several models by numerical simulations. An application is given for a relation between transition probabilities.Comment: 8 pages, 7 figure

Multiscale modelling of fluid and solute transport in soft tissues and microvessels

This study focuses on the movement of particles and extracellular fluid in soft tissues and microvessels. It analyzes modeling applications in biological and physiological fluids at a range of different length scales: from between a few tens to several hundred nanometers, on the endothelial glycocalyx and its effects on interactions between blood and the vessel wall; to a few micrometers, on movement of blood cells in capillaries and transcapillary exchange; to a few millimetres and centimetres, on extracellular matrix deformation and interstitial fluid movement in soft tissues. Interactions between blood cells and capillary wall are discussed when the sizes of the two are of the same order of magnitude, with the glycocalyx on the endothelial and red cell membranes being considered. Exchange of fluid, solutes, and gases by microvessels are highlighted when capillaries have counter-current arrangements. This anatomical feature exists in a number of tissues and is the key in the renal medulla on the urinary concentrating mechanism. The paper also addresses an important phenomenon on the transport of macromolecules. Concentration polarization of hyaluronan on the synovial lining of joint cavities is presented to demonstrate how the mechanism works in principle and how model predictions agree to experimental observations quantitatively