Calculation of the entropy of binary hard sphere mixtures from pair correlation functions

This is the publisher's version, also available electronically from http://scitation.aip.org/content/aip/journal/jcp/97/3/10.1063/1.463103.We evaluate the entropy of several binary hard sphere fluid mixtures using two approximate expressions that require as input only the pair correlation functions,g αβ(r). An approximation based on the incompressible limit is found to be accurate for medium to high density fluids

Sparse Kneser graphs are Hamiltonian

For integers k≥1 and n≥2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1,…,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k≥3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k≥3 and a≥0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k−6 distinct Hamilton cycles for k≥6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words

Lyapunov instability of fluids composed of rigid diatomic molecules

We study the Lyapunov instability of a two-dimensional fluid composed of rigid diatomic molecules, with two interaction sites each, and interacting with a WCA site-site potential. We compute full spectra of Lyapunov exponents for such a molecular system. These exponents characterize the rate at which neighboring trajectories diverge or converge exponentially in phase space. Quam. These exponents characterize the rate at which neighboring trajectories diverge or converge exponentially in phase space. Qualitative different degrees of freedom -- such as rotation and translation -- affect the Lyapunov spectrum differently. We study this phenomenon by systematically varying the molecular shape and the density. We define and evaluate ``rotation numbers'' measuring the time averaged modulus of the angular velocities for vectors connecting perturbed satellite trajectories with an unperturbed reference trajectory in phase space. For reasons of comparison, various time correlation functions for translation and rotation are computed. The relative dynamics of perturbed trajectories is also studied in certain subspaces of the phase space associated with center-of-mass and orientational molecular motion.Comment: RevTeX 14 pages, 7 PostScript figures. Accepted for publication in Phys. Rev.

Dynamical ensembles in stationary states

We propose as a generalization of an idea of Ruelle to describe turbulent fluid flow a chaotic hypothesis for reversible dissipative many particle systems in nonequilibrium stationary states in general. This implies an extension of the zeroth law of thermodynamics to non equilibrium states and it leads to the identification of a unique distribution \m describing the asymptotic properties of the time evolution of the system for initial data randomly chosen with respect to a uniform distribution on phase space. For conservative systems in thermal equilibrium the chaotic hypothesis implies the ergodic hypothesis. We outline a procedure to obtain the distribution \m: it leads to a new unifying point of view for the phase space behavior of dissipative and conservative systems. The chaotic hypothesis is confirmed in a non trivial, parameter--free, way by a recent computer experiment on the entropy production fluctuations in a shearing fluid far from equilibrium. Similar applications to other models are proposed, in particular to a model for the Kolmogorov--Obuchov theory for turbulent flow.Comment: 31 pages, 3 figures, compile with dvips (otherwise no pictures

Isolation of Exosomes from Blood Plasma: Qualitative and Quantitative Comparison of Ultracentrifugation and Size Exclusion Chromatography Methods

BACKGROUND: Exosomes are emerging targets for biomedical research. However, suitable methods for the isolation of blood plasma-derived exosomes without impurities have not yet been described. AIM: Therefore, we investigated the efficiency and purity of exosomes isolated with potentially suitable methods; differential ultracentrifugation (UC) and size exclusion chromatography (SEC). METHODS AND RESULTS: Exosomes were isolated from rat and human blood plasma by various UC and SEC conditions. Efficiency was investigated at serial UC of the supernatant, while in case of SEC by comparing the content of exosomal markers of various fractions. Purity was assessed based on the presence of albumin. We found that the diameter of the majority of isolated particles fell into the size range of exosomes, however, albumin was also present in the preparations, when 1h UC at 4 degrees C was applied. Furthermore, with this method only a minor fraction of total exosomes could be isolated from blood as deduced from the constant amount of exosomal markers CD63 and TSG101 detected after serial UC of rat blood plasma samples. By using UC for longer time or with shorter sedimentation distance at 4 degrees C, or UC performed at 37 degrees C, exosomal yield increased, but albumin impurity was still observed in the isolates, as assessed by transmission electron microscopy, dynamic light scattering and immunoblotting against CD63, TSG101 and albumin. Efficiency and purity were not different in case of using further diluted samples. By using SEC with different columns, we have found that although a minor fraction of exosomes can be isolated without significant albumin content on Sepharose CL-4B or Sephacryl S-400 columns, but not on Sepharose 2B columns, the majority of exosomes co-eluted with albumin. CONCLUSION: Here we show that it is feasible to isolate exosomes from blood plasma by SEC without significant albumin contamination albeit with low vesicle yield

Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients

The foundations of the chaotic scattering theory for transport and reaction-rate coefficients for classical many-body systems are considered here in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is employed to obtain an expression for the escape-rate for a phase space trajectory to leave a finite open region of phase space for the first time. This expression relates the escape rate to the difference between the sum of the positive Lyapunov exponents and the K-S entropy for the fractal set of trajectories which are trapped forever in the open region. This result is well known for systems of a few degrees of freedom and is here extended to systems of many degrees of freedom. The formalism is applied to smooth hyperbolic systems, to cellular-automata lattice gases, and to hard sphere sytems. In the latter case, the goemetric constructions of Sinai {\it et al} for billiard systems are used to describe the relevant chaotic scattering phenomena. Some applications of this formalism to non-hyperbolic systems are also discussed.Comment: 35 pages, compressed file, follow directions in header for ps file. Figures are available on request from [email protected]

Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem

It is shown that the "chaoticity hypothesis", analogous to Ruelle's principle for turbulence and recently introduced in statistical mechanics, implies the Onsager reciprocity and the fluctuation dissipation theorem in various models for coexisting transport phenomena.Comment: 16 pages, postscrip