Arbitrary Mixture Research Articles

Molecular dynamics simulations of vibrated granular gases.

We present molecular dynamics simulations of monodisperse or bidisperse inelastic granular gases driven by vibrating walls, in two dimensions (without gravity). Because of the energy injection at the boundaries, a situation often met experimentally, density and temperature fields display heterogeneous profiles in the direction perpendicular to the walls. A general equation of state for an arbitrary mixture of fluidized inelastic hard spheres is derived and successfully tested against numerical data. Single-particle velocity distribution functions with non-Gaussian features are also obtained, and the influence of various parameters (inelasticity coefficients, density, etc.) are analyzed. The validity of a recently proposed random restitution coefficient model is assessed through the study of projected collisions onto the direction perpendicular to that of energy injection. For the binary mixture, the nonequipartition of translational kinetic energy is studied and compared both to experimental data and to the case of homogeneous energy injection ("stochastic thermostat"). The rescaled velocity distribution functions are found to be very similar for both species.

Poiseuille, thermal creep and Couette flow: results based on the CES model of the linearized Boltzmann equation

A synthetic-kernel model (CES model) of the linearized Boltzmann equation is used along with an analytical discrete-ordinates method (ADO) to solve three fundamental problems concerning flow of a rarefied gas in a plane channel. More specifically, the problems of Couette flow, Poiseuille flow and thermal-creep flow are solved in terms of the CES model equation for an arbitrary mixture of specular and diffuse reflection at the walls confining the flow, and numerical results for the basic quantities of interest are reported. The comparisons made with results derived from solutions based on computationally intensive methods applied to the linearized Boltzmann equation are used to conclude that the CES model can be employed with confidence to improve the accuracy of results available from simpler approximations such as the BGK model or the S model.

Entanglement cost of bipartite mixed states.

We compute the entanglement cost of several families of bipartite mixed states, including arbitrary mixtures of two Bell states. This is achieved by developing a technique that allows us to ascertain the additivity of the entanglement of formation for any state supported on specific subspaces. As a side result, the proof of the irreversibility in asymptotic local manipulations of entanglement is extended to two-qubit systems.

Prediction of trapping rates in mixtures of partially absorbing spheres

The combined effects of diffusion and reaction in heterogeneous media govern the behavior of a wide variety of physical and biological phenomena, including the consumption of nutrients by cells and the study of magnetic relaxation in tissues. We have considered the so-called “trapping problem,” in which diffusion takes place exterior to a collection of fixed traps while reaction occurs at their surface. A simulation technique for predicting the overall trapping rate for systems of partially absorbing spherical traps based on the first-passage spheres method is presented. Using data obtained by applying this simulation technique, we then consider the problem of mixtures of partially absorbing traps. By hypothesizing a method for reducing a general mixture of traps to a mixture of perfect absorbers and perfect reflectors (i.e., reducing the dimensionality of the space of variables), we are able to accurately predict the effective surface rate constant and the trapping rate for an arbitrary mixture of partially absorbing traps. Remarkably, we find that a single, nearly universal curve allows accurate predictions to be made over a wide range of trap volume fractions and even for different trap distributions.

Pole topology of the structure functions of continuous systems.

We develop a theory of the pole topology of the Laplace transform of the structure functions of continuous N component systems based on the Wiener-Hopf technique. We classify systems according to the spectrum of the NxN matrix Q(t), with elements Q(ij)(t)=delta(ij)-2pi square root [rho(i)rho(j)]integrale(-tr)q(ij)(r)dr, associated with their factor functions q(ij)(r). For the simplest nontrivial class of systems--namely, that with only two eigenvalues of Q(t) different from one--a full and explicit analysis of the pole topology is possible. We illustrate the theory with exactly solvable examples, such as the Percus-Yevick equation for arbitrary mixtures of hard spheres (HS) and polydisperse HS and the mean spherical model for binary mixtures of adhesive spheres.

Does the plasma composition affect the long-term evolution of relativistic jets?

We study the influence of the matter content of extragalactic jets on their morphology, dynamics and emission properties. For this purpose we consider jets of extremely different compositions, including pure leptonic and baryonic plasmas. Our work is based on two-dimensional relativistic hydrodynamic simulations of the long-term evolution of powerful extragalactic jets propagating into a homogeneous environment. The equation of state used in the simulations accounts for an arbitrary mixture of electrons, protons and electron-positron pairs. Using the hydrodynamic models, we have also computed synthetic radio maps and the thermal bremsstrahlung X-ray emission from their cavities. Although there is a difference of about three orders of magnitude in the temperatures of the cavities inflated by the simulated jets, we find that both the morphology and the dynamic behaviour are almost independent of the assumed composition of the jets. Their evolution proceeds in two distinct epochs. During the first one, multidimensional effects are unimportant and the jets propagate ballistically. The second epoch starts when the first larger vortices are produced near the jet head, causing the beam cross-section to increase and the jet to decelerate. The evolution of the cocoon and cavity is in agreement with a simple theoretical model. The beam velocities are relativistic (Γ≃4) at kiloparsec scales, supporting the idea that the X-ray emission of several extragalactic jets may be due to relativistically boosted CMB photons. The radio emission of all models is dominated by the contribution of the hotspots. All models exhibit a depression in the X-rays surface brightness of the cavity interior, in agreement with recent observations.

COSMO-RS: a novel view to physiological solvation and partition questions.

Both, dielectric continuum solvation models as well as surface or group based methods using polarity and lipophilicity parameters have been proven to be useful tools for the analysis of solvation and partition questions. For the first time, COSMO-RS provides an integrated theory, which combines the aspects of continuum solvation and surface interactions, and which ends up with chemical potentials of molecules in almost arbitrary solvents and mixtures. Due to its sound theoretical basis, COSMO-RS does not only provide a new quantitative access to solvation and partition properties in well defined solvents, but it also opens a novel view and gives a better understanding of the general problem of solvation. Finally, this allows for a generalisation of COSMO-RS to sophisticated physiological partition problems involving as complex phases as blood, brain, or cell membranes. The use of COSMO-RS for drug discovery and design is demonstrated by applications to blood-brain partition coefficients, and water solubility.

Voltage Stability Analysis of Muscat Power System During Summer Weather Conditions

A systematic and general formulation of a Propagation Simulation Program (PSP) is developed for the coherent field of microwave and millimeter wave carrier signals traversing intermediate layered precipitation media taking into account the random behavior of particle size, orientation, shape and concentration distributions. Based on a rigorous solution of the volumetric multiple-scattering integral equations, the formalism offers the capability of treating the potential transmission impairments on satellite-earth links and radar remote sensing generated by composite atmospheric layers of precipitation in conjunction with the finite polarization isolation of dual-polarized transmitting and receiving antennas. A multi-layered formulation is employed which encompasses an ensemble of discrete particles comprising an arbitrary mixture of ice crystals, melting snow and raindrops that may exist simultaneously along satellite-earth communication paths.

Electromagnetic Modeling of the Propagation Characteristics of Satellite Communications Through Composite Precipitation Layers, Part II: Results of Computer Simulations

A versatile Propagation Simulation Program (PSP) is developed to assess the degrading effects caused by the concurrent occurrences of an arbitrary mixture of ice plates and needles, melting snow and raindrops which may impede the reliability of dual-polarized satellite communications systems carrying independent channels on a single radio path. Specifically, results are presented for the Cross Polarization Discrimination (XPD) due to ice and rain, differential attenuation, Da, and differential phase shift, Df, due to rain and average specific attenuation, a, and phase shift, f , due to the melting layer at hitherto unconsidered frequencies. The inclusion of an ice-cloud medium is found to possess significant effects on rain-induced XPD even for low ice concentrations, particularly at low fade levels. The relative contribution of the melting layer on rain-induced attenuation is extensively studied for frequencies from 1 to 100 GHz and rain rates below 20 mm/h.

Electromagnetic Modeling of the Propagation Characteristics of Satellite Communications Through Composite Precipitation Layers, Part1: Mathematical Formulation

A systematic and general formulation of a Propagation Simulation Program (PSP) is developed for the coherent field of microwave and millimeter wave carrier signals traversing intermediate layered precipitation media, taking into account the random behavior of particle size, orientation, shape and concentration distributions. Based on a rigorous solution of the volumetric multiple-scattering integral equations, the formalism offers the capability of treating the potential transmission impairments on satellite-earth links and radar remote sensing generated by composite atmospheric layers of precipitation in conjunction with the finite polarization isolation of dual-polarized transmitting and receiving antennas. A multi-layered formulation is employed which encompasses an ensemble of discrete particles comprising an arbitrary mixture of ice crystals, melting snow and raindrops that may exist simultaneously along satellite-earth communication paths.

Bayesian estimator for positron emission tomography imaging using a prior image model with mixed continuity constraints

A novel image prior with mixed continuity constraints is proposed for the Bayesian positron emission tomography image re- construction of human brains. Assume that a human brain can be partitioned into four tissue classes: gray matter, white matter, cere- bral spinal fluid, and partial volume. And each partial volume image voxel consists of an arbitrary mixture among pure tissues. The brain image is then modeled as a piece-wise smooth function through a Gibbs prior with the image intensity of each region governed by the thin-plate energy function. We apply first and second order edge detection techniques to estimate region boundaries, and then cat- egorize these boundaries based on the resulting edge maps. Rather than use the binary processes representing region boundaries such as weak-membrane or weak-plate (WP) models, we adopt a controlled-continuity approach to influence boundary formation. We refer to this model as a modified (WP) model with controlled conti- nuity. We present the results of a computer simulated phantom study in which partial volume effects are explicitly modeled. Results indicate that we obtain superior region of interest quantitation using this approach in comparison to a partial volume correction method that has previously been proposed for quantitation using filtered back-projection image. © 2000 SPIE and IS&T.

PORTFOLIO THEORY FOR "FAT TAILS"

We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonious as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the distribution of wealth variations of a portfolio composed of an arbitrary mixture of assets. This approach makes quantitative and rigorous the well-known fact that minimizing the variance, i.e. the relatively "small" risks, often increases larger risks as measured by higher normalized cumulants and the Value-at-Risk.

M.Dyna Mix – a scalable portable parallel MD simulation package for arbitrary molecular mixtures

A general purpose, scalable parallel molecular dynamics package for simulations of arbitrary mixtures of flexible or rigid molecules is presented. It allows use of most types of conventional molecular-mechanical force fields and contains a variety of auxiliary terms for inter- and intramolecular interactions, including an harmonic bond-stretchings. It can handle both isotropic or ordered systems. Besides an NVE MD ensemble, the simulations can also be carried out in either NVT or NPT ensembles, by employing the Nosé–Hoover thermostats and barostats, respectively. If required, the NPT ensemble can be generated by maintaining anisotropic pressures. The simulation cell can be either cubic, rectangular, hexagonal or a truncated octahedron, with corresponding periodic boundary conditions and minimum images. In all cases, the optimized Ewald method can be used to treat the Coulombic interactions. Double time-step or constrained dynamics schemes are included. An external electric field can be applied across the simulation cell. The whole program is highly modular and is written in standard Fortran 77. It can be compiled to run efficiently both on parallel and sequential computers. The inherent complexity of the studied system does not affect the scalability of the program. The scaling is good with the size of the system and with the number of processors. The portability of the program is good, it runs regularly on several common single- and multiprocessor platforms, both scalar and vector architectures included.

Transport mean free path for magneto-transverse light diffusion: an alternative approach

This paper presents a derivation of the transport mean free path for magneto-transverse light diffusion, ℓ*⊥, in an arbitrary random mixture of Faraday-active and non-Faraday-active Mie scatterers. This derivation is based on the standard radiative transfer equation. The expression of the transport mean free path obtained previously from the Bethe–Salpeter equation, for the case where only Faraday-active scatterers are present, is recovered. This simpler formulation can include the case of homogeneous mixtures of Faraday-active and non-Faraday-active scatterers.

Neutrino mixing scenarios and AGN

Active galactic nuclei (AGN) have been suggested to be sources of very high energy neutrinos. We consider the possibility of using AGN neutrinos to test neutrino mixings. From the atmospheric, solar and laboratory data on neutrino oscillations we derive the flavour composition of the AGN neutrino flux in different neutrino mixing schemes. We show that most of the schemes considered can be distinguished from each other and the existence of a sterile neutrino can be specially tested. AGN neutrinos can also be used to test those four-neutrino scenarios where solar neutrinos oscillate into an arbitrary mixture of ν s and ν τ .

The fault span of crash failures

A crashing network protocol is an asynchronous protocol whose memory does not survive crashes. We show that a crashing network protocol that works over unreliable links can be driven to arbitrary global states, where each node is in a state reached in some (possibly different) execution, and each link has an arbitrary mixture of packets sent in (possibly different) executions. Our theorem considerably generalizes an earlier result, due to Fekete et al., which states that there is no correct crashing Data Link Protocol. For example, we prove that there is no correct crashing protocol for token passing and for many other resource allocation protocols such as k -exclusion, and the drinking and dining philosophers problems. We further characterize the reachable states caused by crash failures using reliable non-FIFO and reliable FIFO links. We show that with reliable non-FIFO links any acyclic subset of nodes and links can be driven to arbitrary states. We show that with reliable FIFO links, only nodes can be driven to arbitrary states. Overall, we show a strict hierarchy in terms of the set of states reachable by crash failures in the three link models.

Adaptive meshing techniques for viscous flow calculations on mixed element unstructured meshes

An adaptive refinement strategy based on hierarchical element subdivision is formulated and implemented for meshes containing arbitrary mixtures of tetrahedra, hexahedra, prisms and pyramids. Special attention is given to keeping memory overheads as low as possible. This procedure is coupled with an algebraic multigrid flow solver which operates on mixed-element meshes. Inviscid flows as well as viscous flows are computed on adaptively refined tetrahedral, hexahedral, and hybrid meshes. The efficiency of the method is demonstrated by generating an adapted hexahedral mesh containing 3 million vertices on a relatively inexpensive workstation.

Speed of convergence for estimators of finite translation mixture distributions

A suitably tapered Fourier transform is used to obtain a simple and explicit construction of estimators for the c.d.f.'s of finite translation mixtures. An a.s. speed of L 1-convergence is derived for these c.d.f.'s which corroborates the lower bound for such rates recently derived in Chen (1995) for arbitrary mixtures. In the translation case the rates are determined by the tail behavior of theFourier transform of the kernel of the given location family, i.e., by the degree of ill-posedness of the mixture problem.

On the blind implementation of the ultimate source separators for arbitrary noisy mixtures

Since the beginning of the 1980s the blind second-order (SO) and higher-order (HO) narrow-band (NB) methods of source separation have received a great interest. However, despite this fact, the situations of practical interest for which these blind methods may blindly implement the ultimate ones, such as the spatial matched filter (SMF) or the weighted least square (WLS) source separators, are not still identified for general noisy situations, which may limit the use of these blind methods in operational contexts. Assuming instantaneously mixed NB sources, the purpose of this paper is to enlighten the previous important problem through the analysis of the SO correlation and the FO cross-cumulants at the outputs of the SMF and the WLS separators for arbitrary noisy mixtures of sources.

Diffusion in lattice Lorentz gases with a percolation threshold.

A mean-field approximation for the diffusion coefficient in lattice Lorentz gases with an arbitrary mixture of pointlike stochastic scatterers in the low-density limit is proposed. In this approximation, the diffusion coefficient is directly related to the first return probability of the moving particle in the corresponding Cayley tree through an effective ring operator. A renormalization scheme for the approximate determination of the first return probability is constructed. The predictions of this mean-field theory and those of the repeated ring approximation (RRA) are compared with computer simulation results for models in which a fraction x(B) of the scatterers are deterministic backscatterers, so that the diffusion coefficient vanishes beyond a certain percolation threshold x(c)(B). The approximation proposed in this paper is seen to be in good agreement with the simulation results, in contrast to the RRA, which already fails to give the correct percolation threshold.