Anomalous Dynamic Arrest in a Mixture of Big and Small Particles

We present molecular dynamics simulations on the slow dynamics of a mixture of big and small soft-spheres with a large size disparity. Dynamics are investigated in a broad range of temperature and mixture composition. As a consequence of large size disparity, big and small particles exhibit very different relaxation times. As previously reported for simple models of short-ranged attractive colloids and polymer blends, several anomalous dynamic features are observed: i) sublinear behavior for mean squared displacements, ii) concave-to-convex crossover for density-density correlators, by varying temperature or wavevector, iii) logarithmic decay for specific wavevectors of density-density correlators. These anomalous features are observed over time intervals extending up to four decades, and strongly resemble predictions of the Mode Coupling Theory (MCT) for state points close to higher-order MCT transitions, which originate from the competition between different mechanisms for dynamic arrest. For the big particles we suggest competition between soft-sphere repulsion and depletion effects induced by neighboring small particles. For the small particles we suggest competition between bulk-like dynamics and confinement, respectively induced by neighboring small particles and by the slow matrix of big particles. By increasing the size disparity, a new relaxation scenario arises for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The behavior of the latters resembles features characteristic of type-A MCT transitions, defined by a zero value of the critical non-ergodicity parameter.Comment: Version 2. Added major new result

Application of the density dependent hadron field theory to neutron star matter

The density dependent hadron field (DDRH) theory, previously applied to isospin nuclei and hypernuclei is used to describe $\beta$-stable matter and neutron stars under consideration of the complete baryon octet. The meson-hyperon vertices are derived from Dirac-Brueckner calculations of nuclear matter and extended to hyperons. We examine properties of density dependent interactions derived from the Bonn A and from the Groningen NN potential as well as phenomenological interactions. The consistent treatment of the density dependence introduces rearrangement terms in the expression for the baryon chemical potential. This leads to a more complex condition for the $\beta$-equilibrium compared to standard relativistic mean field (RMF) approaches. We find a strong dependence of the equation of state and the particle distribution on the choice of the vertex density dependence. Results for neutron star masses and radii are presented. We find a good agreement with other models for the maximum mass. Radii are smaller compared to RMF models and indicate a closer agreement with results of non-relativistic Brueckner calculations.Comment: 28 pages, 11 figure

Depletion potential in hard-sphere mixtures: theory and applications

We present a versatile density functional approach (DFT) for calculating the depletion potential in general fluid mixtures. In contrast to brute force DFT, our approach requires only the equilibrium density profile of the small particles {\em before} the big (test) particle is inserted. For a big particle near a planar wall or a cylinder or another fixed big particle the relevant density profiles are functions of a single variable, which avoids the numerical complications inherent in brute force DFT. We implement our approach for additive hard-sphere mixtures. By investigating the depletion potential for high size asymmetries we assess the regime of validity of the well-known Derjaguin approximation for hard-sphere mixtures and argue that this fails. We provide an accurate parametrization of the depletion potential in hard-sphere fluids which should be useful for effective Hamiltonian studies of phase behavior and colloid structure

How the viscous subrange determines inertial range properties in turbulence shell models

We calculate static solutions of the 'GOY' shell model of turbulence and do a linear stability analysis. The asymptotic limit of large Reynolds numbers is analyzed. A phase diagram is presented which shows the range of stability of the static solution. We see an unexpected oscillatory dependence of the stability range upon $\lg \nu$, where $\nu$ is the viscosity. This effect depends upon the discrete structure of the shell model and goes to zero as the separation between the shells is brought to zero. These findings show how viscous effects play a role in determining inertial properties of shell models and give some hints for understanding the effects of viscous dissipation upon real turbulence.Comment: Physica D, in pres

Analyze Large Multidimensional Datasets Using Algebraic Topology

This paper presents an efficient algorithm to extract knowledge from high-dimensionality, high- complexity datasets using algebraic topology, namely simplicial complexes. Based on concept of isomorphism of relations, our method turn a relational table into a geometric object (a simplicial complex is a polyhedron). So, conceptually association rule searching is turned into a geometric traversal problem. By leveraging on the core concepts behind Simplicial Complex, we use a new technique (in computer science) that improves the performance over existing methods and uses far less memory. It was designed and developed with a strong emphasis on scalability, reliability, and extensibility. This paper also investigate the possibility of Hadoop integration and the challenges that come with the framework