maximum likelihood extracting unbiased information from complex networks the choice of free parameters in network models is subjective since it depends on what topological properties are being monitored however we show that the maximum likelihood ml principle indicates a unique statistically rigorous parameter choice associated with a well defined topological feature we then find that if the ml condition is incompatible with the built in parameter choice network models turn out to be intrinsically ill defined or biased to overcome this problem we construct a class of safely unbiased models we also propose an extension of these results that leads to the fascinating possibility to extract only from topological data the hidden variables underlying network organization making them no longer hidden we test our method on world trade web data where we recover the empirical gross domestic product using only topological information

a gas kinetic scheme for the baer nunziato two phase flow model numerical methods for the baer nunziato bn two phase flow model have attracted much attention in recent years in this paper we present a new gas kinetic scheme for the bn two phase flow model containing non conservative terms in the framework of finite volume method in the view of microscopic aspect a generalized bhatnagar gross krook bgk model which matches with the bn model is constructed based on the integral solution of the generalized bgk model we construct the distribution functions at the cell interface then numerical fluxes can be obtained by taking moments of the distribution functions and non conservative terms are explicitly introduced into the construction of numerical fluxes in this method not only the complex iterative process of exact solutions is avoided but also the non conservative terms included in the equation can be handled well

nonlinear resonance in systems of conservation laws the riemann problem for a general inhomogeneous system of conservation laws is solved in a neighborhood of a state at which one of the nonlinear waves in the problem takes on a zero speed the inhomogeneity is modeled by a linearly degenerate field the solution of the riemann problem determines the nature of wave interactions and thus the riemann problem serves as a canonical form for nonlinear systems of conservation laws generic conditions on the fluxes are stated and it is proved that under these conditions the solution of the riemann problem exists is unique and has a fixed structure this demonstrates that in the above sense resonant inhomogeneous systems generically have the same canonical form the wave curves for these systems are only lipschitz continuous in a neighborhood of the states where the wave speeds coincide and so in contrast to strictly hyperbolic systems the implicit function theorem cannot be applied directly to obtain existence and uniqueness here we show that existence

fractional kinetic equations and universal decoupling of a memory function in mesoscale region it is proved that kinetic equations containing non integer integrals and derivatives appear in the result of reduction of a set of micromotions to some averaged collective motion in the mesoscale region in other words it means that after a proper statistical average the microscopic dynamics is converted into a collective motion in the mesoscopic regime a fractal medium containing weakly and strongly correlated relaxation units has been considered it is shown that in most cases the original of the memory function recovers the riemann liouville integral for a strongly correlated fractal medium a generalization of the riemann liouville integral is obtained for the fractal branched processes one can derive the stretched exponential law of relaxation that is widely used for description of relaxation phenomena in disordered media it is shown that the generalized stretched exponential function describes the averaged collective motion in the fractal branched complex systems it is confirmed that the generalized stretched exponential law can be definitely applicable for description of a set of spontaneous evoked postsynaptic signals in the living matter the application of these fractional kinetic equations for the description of the dielectric relaxation phenomena is also discussed these kinetic equations and their generalizations can be applicable for the description of different relaxation or diffusion processes in the intermediate mesoscale region

time fractional telegraph equations and telegraph processes with brownian time we study the fundamental solutions to time fractional telegraph equations of order 2 we are able to obtain the fourier transform of the solutions for any and to give a representation of their inverse in terms of stable densities for the special case 1 2 we can show that the fundamental solution is the distribution of a telegraph process with brownian time in a special case this becomes the density of the iterated brownian motion which is therefore the fundamental solution to a fractional diffusion equation of order 1 2 with respect to time

numerical investigation of a modified family of centered schemes applied to multiphase equations with nonconservative sources systems of hyperbolic partial differential equations are frequently used to model the flow of multiphase mixtures these equations often contain sources referred to as nozzling terms that cannot be posed in divergence form and have proven to be particularly challenging in the development of finite volume methods upwind schemes have recently shown promise in properly resolving the steady wave solution of the associated multiphase riemann problem however these methods require a full characteristic decomposition of the system eigenstructure which may be either unavailable or computationally expensive central schemes such as the kurganov tadmor kt family of methods require minimal characteristic information which makes them easily applicable to systems with an arbitrary number of phases however the proper implementation of nozzling terms in these schemes has been mathematically ambiguous the primary objectives of this work are twofold first an extension of the kt family of schemes is proposed that formally accounts for the nonconservative nozzling sources this modification results in a semidiscrete form that retains the simplicity of its predecessor and introduces little additional computational expense second this modified method is applied to multiple but equivalent forms of the multiphase equations to perform a numerical study by solving several one dimensional test problems both ideal and mie gruneisen equations of state are used with the results compared to an analytical solution this study demonstrates that the magnitudes of the resulting numerical errors are sensitive to the form of the equations considered and suggests an optimal form to minimize these errors finally a separate modification of the wave propagation speeds used in the kt family is also suggested that can reduce the extent of numerical diffusion in multiphase flows

a conservative approximation to compressible two phase flow models in the stiff mechanical relaxation limit in this article we present and analyze a conservative approximation to reduced one pressure one velocity models for compressible two phase flows that contain non conservative products this approximation is valid when certain material properties of the two phases are considerably different from each other although it cannot be applied to arbitrary mixtures it is applicable to many heterogeneous mixtures of technological interest herein we derive the rankine hugoniot relations and riemann invariants for the homogeneous part of the proposed model and develop an exact riemann solver for it further we investigate the structure of the steady two phase detonation waves with inert or reactive solid particles admitted by the proposed model comparisons with the corresponding gaseous detonations are also made moreover we derive a lower limit for the propagation speed of steady two phase detonations in the case of reactive particles at the limiting case of very dilute mixtures this minimum speed tends to the chapman jouguet velocity of gaseous detonations finally we report on numerical simulations of the transmission of a purely gaseous detonation to heterogeneous mixtures containing inert or reactive solid particles the effect of the solid particles on the structure of the resulting two phase detonation is discussed in detail

statistical spectrum of the non markovity parameter for simple model systems the spectra of the non markovity parameter for three model systems are found an ideal gas weakly non ideal gas and a medium in hydrodynamic limits it is shown that the non markovian effects play the dominant role in all three above mentioned cases the effects of molecular memory are connected with the statistical appearance of intermolecular interactions in statistical systems

a godunov type method for the shallow water equations with discontinuous topography in the resonant regime abstract we investigate the riemann problem for the shallow water equations with variable and possibly discontinuous topography and provide a complete description of the properties of its solutions existence uniqueness in the non resonant regime multiple solutions in the resonant regime this analysis leads us to a numerical algorithm that provides one with a riemann solver next we introduce a godunov type scheme based on this riemann solver which is well balanced and of quasi conservative form finally we present numerical experiments which demonstrate the convergence of the proposed scheme even in the resonance regime except in the limiting situation when riemann data precisely belong to the resonance hypersurface

constructing optimal transition matrix for markov chain monte carlo abstract the notion of asymptotic variance has been used as a means for gauging the performance of markov chain monte carlo mcmc methods for an effective mcmc simulation it is imperative to first construct a markov model with minimal asymptotic variance the construction of such a stochastic matrix with prescribed stationary distribution as well as optimal asymptotic variance amounts to an interesting variationally constrained inverse eigenvector problem cast against a specially defined oblique coordinate system the worst case analysis of the asymptotic variance can be formulated as a problem of minimizing the logarithmic 2 norm of a restricted resolvent matrix over a convex and compact monoid based on this framework this paper proposes employing global optimization techniques as a general instrument for numerical construction of optimal transition matrices numerical experiments manifest the complexity of the underlying problem first new global solutions different from the conventional structure characterized in the literature are found across the board for reversible problems second local solutions with high frequencies of occurrence appear widespread for nonreversible problems in all the approach via the global optimization techniques is a feasible and practical means for numerical construction of the optimal markov chain

a positive and entropy satisfying finite volume scheme for the baer nunziato model we present a relaxation scheme for approximating the entropy dissipating weak solutions of the baer nunziato two phase flow model this relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in 16 for the isentropic baer nunziato model and consequently inherits its main properties to our knowledge this is the only existing scheme for which the approximated phase fractions phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable cfl condition for ideal gas and stiffened gas equations of state real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme it is also the only scheme for which a discrete entropy inequality is proven under a cfl condition derived from the natural sub characteristic condition associated with the relaxation approximation this last property which ensures the non linear stability of the numerical method is satisfied for any admissible equation of state we provide a numerical study for the convergence of the approximate solutions towards some exact riemann solutions the numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the baer nunziato model namely schwendeman wahle kapila s godunov type scheme 39 and tokareva toro s hllc scheme 44 the relaxation scheme also shows a higher precision and a lower computational cost for comparable accuracy than a standard numerical scheme used in the nuclear industry namely rusanov s scheme finally we assess the good behavior of the scheme when approximating vanishing phase solutions

fluctuation noise spectroscopy and a universal fitting function of amplitudes of random sequences abstract a universal fitting function has been recognized that makes use of the eigen coordinates method physica a 285 2000 547 to accurately describe the distribution of ordered amplitudes within random sequences taken from a diversity of sources it is shown that sequences with a discrete structure can be described in terms of specific distributions of relative frequencies with respect to the number of quantum levels an investigation of these quantum distributions leads to an increase in both sensitivity and selectivity when attempting the statistical detection of various predominant factors of the hidden signals the physical meaning of this new function is discussed and a proposal is made as the basis of a new fluctuation noise spectroscopy in which the recognized function can be used for the detection of small signals and or the forerunners of strong signals that are hidden within the random sequences analyzed

log periodic oscillations for biased diffusion on random lattice abstract random walks with a fixed bias direction on randomly diluted cubic lattices far above the percolation threshold exhibit log periodic oscillations in the effective exponent versus time a scaling argument accounts for the numerical results in the limit of large biases and small dilution and shows the importance of the interplay of these two ingredients in the generation of the log periodicity these results show that log periodicity is the dominant effect compared to previous predictions of and reports on anomalous diffusion

the normalized laplacian spectrum of subdivisions of a graph determining and analyzing the spectra of graphs is an important and exciting research topic in mathematics science and theoretical computer science the eigenvalues of the normalized laplacian of a graph provide information on its structural properties and also on some relevant dynamical aspects in particular those related to random walks in this paper we give the spectra of the normalized laplacian of iterated subdivisions of simple connected graphs as an example of application of these results we find the exact values of their multiplicative degree kirchhoff index kemeny s constant and number of spanning trees

hllc type riemann solver for the baer nunziato equations of compressible two phase flow we first construct an approximate riemann solver of the hllc type for the baer nunziato equations of compressible two phase flow for the subsonic wave configuration the solver is fully nonlinear it is also complete that is it contains all the characteristic fields present in the exact solution of the riemann problem in particular stationary contact waves are resolved exactly we then implement and test a new upwind variant of the path conservative approach such schemes are suitable for solving numerically nonconservative systems finally we use locally the new hllc solver for the baer nunziato equations in the framework of finite volume discontinuous galerkin finite element and path conservative schemes we systematically assess the solver on a series of carefully chosen test problems

fractional dynamics and mds visualization of earthquake phenomena this paper analyses earthquake data in the perspective of dynamical systems and fractional calculus fc this new standpoint uses multidimensional scaling mds as a powerful clustering and visualization tool fc extends the concepts of integrals and derivatives to non integer and complex orders mds is a technique that produces spatial or geometric representations of complex objects such that those objects that are perceived to be similar in some sense are placed on the mds maps forming clusters in this study over three million seismic occurrences covering the period from january 1 1904 up to march 14 2012 are analysed the events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups according to the flinn engdahl f e seismic regions of earth several correlation indices are proposed to quantify the similarities among regions mds maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events which may not be perceived on traditional geographic maps therefore mds constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes

covariance structure behind breaking of ensemble equivalence in random graphs for a random graph subject to a topological constraint the microcanonical ensemble requires the constraint to be met by every realisation of the graph hard constraint while the canonical ensemble requires the constraint to be met only on average soft constraint it is known that breaking of ensemble equivalence may occur when the size of the graph tends to infinity signalled by a non zero specific relative entropy of the two ensembles in this paper we analyse a formula for the relative entropy of generic discrete random structures recently put forward by squartini and garlaschelli we consider the case of a random graph with a given degree sequence configuration model and show that in the dense regime this formula correctly predicts that the specific relative entropy is determined by the scaling of the determinant of the matrix of canonical covariances of the constraints the formula also correctly predicts that an extra correction term is required in the sparse regime and in the ultra dense regime we further show that the different expressions correspond to the degrees in the canonical ensemble being asymptotically gaussian in the dense regime and asymptotically poisson in the sparse regime the latter confirms what we found in earlier work and the dual degrees in the canonical ensemble being asymptotically poisson in the ultra dense regime in general we show that the degrees follow a multivariate version of the poisson binomial distribution in the canonical ensemble

on the solution to the riemann problem for the compressible duct flow the quasi one dimensional euler equations in a duct of variable cross section form probably one of the simplest nonconservative systems we consider the riemann problem for it and discuss its properties in particular for some initial conditions the solution to the riemann problem appears to be nonunique in order to rule out the nonphysical solutions we provide two dimensional computations of the euler equations in a duct of corresponding geometry and compare them with the one dimensional 1d results then the physically relevant 1d solutions satisfy a kind of entropy rate admissibility criterion

the riemann problem for the baer nunziato two phase flow model we consider the riemann problem for the two phase flow model proposed by baer and nunziato int j multiphase flows 12 1986 861 it describes the flame spread and the deflagration to detonation transition ddt in gaspermeable reactive granular materials the model is given by a non strictly hyperbolic non conservative system of partial differential equations we investigate the structure of the riemann problem and construct the exact solution for it we establish that the solution across one wave is not unique and propose to use the evolutionarity criterion to single out the admissible solution due to special structure of the riemann problem for the baer nunziato model we are able to introduce a notion of a weak solution for it finally we propose a number of test cases based on the exact solution to the riemann problem for the baer nunziato model

numerical simulation of a compressible two layer model a first attempt with an implicit explicit splitting scheme this work is devoted to the numerical simulation of the compressible two layer model developed in 16 the latter is an hyperbolic two fluid two pressure model dedicated to gas liquid flows in pipes especially stratified air water flows using explicit schemes one obtains a cfl condition based on the celerity of fast acoustic waves which typically brings large numerical diffusivity for the slow material waves and small time steps in order to overcome these drawbacks the proposed scheme involves an operator splitting and an implicit explicit time discretization thus the full system is split into two hyperbolic subsystems the first one deals with the transport equation on the liquid height using an explicit scheme and upwind fluxes the second one deals with the averaged mass and momentum conservation equations of both phases using an implicit scheme which handles the propagation of acoustic waves at last the positivity of heights and densities is ensured under a cfl condition which involves material velocities numerical experiments are performed using acoustic as well as material time steps adding the rusanov scheme for comparison the best accuracy is obtained with the proposed scheme used with acoustic time steps when used with material time steps efficiency on the slow waves and stability are obtained regarding analytical solutions of the convective part

log periodic corrections to the cole cole expression in dielectric relaxation abstract a model of the self similar process of relaxation is given and a method of derivation of the kinetic equations for the total polarization based on the ideas of fractional kinetics is suggested the derived kinetic equations contain integro differential operators having non integer order they lead to the cole cole expression for the complex dielectric permittivity it is shown rigorously that the power law exponent in the cole cole expression coincides with the dimension of the mixed space temporal fractal ensemble if the discrete scale invariance for the temporal space structure of the dielectric medium considered becomes important then the expression for the complex dielectric permittivity contains log periodic corrections oscillations and hence it generalizes the conventional cole cole expression the corrections obtained in this model suggest another way of interpretation and analysis of dielectric spectra for different complex materials

mathematical and numerical modeling of two phase compressible flows with micro inertia a new model with full coupling between micro and macroscale motion is developed for compressible multiphase mixtures the equations of motion and the coupling microstructural equation an analogue of the rayleigh lamb equation are obtained by using the hamilton principle of stationary action in the particular case of bubbly fluids the resulting model contains eight partial differential equations one dimensional case and is unconditionally hyperbolic the equations are solved numerically by an adapted godunov method the model and methods are validated for two very different test problems the first one consists of a wave propagating in a liquid containing a small quantity of gas bubbles computed oscillating shock waves fit perfectly the experimental data then the one dimensional multiphase model is used as a reduction tool for the multidimensional interaction of a shock wave with a large bubble good agreement is again obtained

statistical mechanics of nonlinear hydrodynamic fluctuations abstract the paper studies nonlinear hydrodynamic fluctuations by the methods of nonequilibrium statistical mechanics the generalized fokker planck equation for the distribution function of coarse grained densities of conserved quantities is derived from the liouville equation and then is investigated by using the gradient expansions in the flux correlation matrix we have obtained the functional differential fokker planck equation describing the nonlinear hydrodynamic fluctuations in spatially nonuniform systems to second order in gradients of coarse grained fluctuating fields an outline of the derivation of fokker planck equations containing the burnett terms is also given the explicit coordinate representation for the hydrodynamic fokker planck equation is discussed in the case of one component simple fluid the general scheme of a change of coarse grained functional variables is developed for hydrodynamic fokker planck equations the corresponding transformation rules are found for drift terms diffusion coefficients and thermodynamic forces the dynamical equations and stationary conditions for averages of functions functionals of hydrodynamic fields are discussed by using the fokker planck operators acting on such functions the explicit form of these operators are found for various sets of fluctuating fields as an application of the formalism the calculation of the stationary correlation functions is presented for a simple nonequilibrium steady state

correspondence between temporal correlations in time series inverse problems and the spherical model in this paper we employ methods from statistical mechanics to model temporal correlations in time series we put forward a methodology based on the maximum entropy principle to generate ensembles of time series constrained to preserve part of the temporal structure of an empirical time series of interest we show that a constraint on the lag one autocorrelation can be fully handled analytically and corresponds to the well known spherical model of a ferromagnet we then extend such a model to include constraints on more complex temporal correlations by means of perturbation theory showing that this leads to substantial improvements in capturing the lag one autocorrelation in the variance we apply our approach on synthetic data and illustrate how it can be used to formulate expectations on the future values of a data generating process

numerical resolution for a compressible two phase flow model based on the theory of thermodynamically compatible systems this paper is concerned with the numerical solution of the equations governing two phase gas solid mixture in the framework of thermodynamically compatible systems theory the equations constitute a non homogeneous system of nonlinear hyperbolic conservation laws a total variation diminishing tvd slope limiter centre slic numerical scheme based on the splitting approach is presented and applied for the solution of the initial boundary value problem for the equations the model equations and the numerical methods are systematically assessed through a series of numerical test cases strong numerical evidence shows that the model and the methods are accurate robust and conservative the model correctly describes the formations of shocks and rarefactions in two phase gas solid flow

a robust and accurate riemann solver for a compressible two phase flow model in this paper we analyze the riemann problem for the widely used drift flux two phase flow model this analysis introduces the complete information that is attained in the representation of solutions to the riemann problem it turns out that the riemann waves have rarefactions a contact discontinuity and shocks within this respect an exact riemann solver is developed to accurately resolve and represent the complete wave structure of the gas liquid two phase flows to verify the solver a series of test problems selected from the literature are presented including validation against independent numerical simulations where the solution of the riemann problem is fully numerical in this framework the governing equations are discretized by finite volume techniques facilitating the application godunov methods of centred type it is shown that both analytical and numerical results demonstrate the broad applicability and robustness of the new exact riemann solver

fractional diffusion equations and processes with randomly varying time in this paper the solutions u u x t to fractional diffusion equations of order 0 v 2 are analyzed and interpreted as densities of the composition of various types of stochastic processes for the fractional equations of order v 1 2 n n 1 we show that the solutions u 1 2 n correspond to the distribution of the n times iterated brownian motion for these processes the distributions of the maximum and of the sojourn time are explicitly given the case of fractional equations of order v 2 3 n n 1 is also investigated and related to brownian motion and processes with densities expressed in terms of airy functions in the general case we show that u coincides with the distribution of brownian motion with random time or of different processes with a brownian time the interplay between the solutions u and stable distributions is also explored interesting cases involving the bilateral exponential distribution are obtained in the limit

a phase decomposition approach and the riemann problem for a model of two phase flows abstract we present a phase decomposition approach to deal with the generalized rankine hugoniot relations and then the riemann problem for a model of two phase flows by investigating separately the jump relations for equations in conservative form in the solid phase we show that the volume fractions can change only across contact discontinuities then we prove that the generalized rankine hugoniot relations are reduced to the usual form it turns out that shock waves and rarefaction waves remain on one phase only and the contact waves serve as a bridge between the two phases by decomposing riemann solutions into each phase we show that riemann solutions can be constructed for large initial data furthermore the riemann problem admits a unique solution for an appropriate choice of initial data

on the computation of the baer nunziato model using ale formulation with hll and hllc type solvers towards fluid structure interactions computation of compressible two phase flows with the unsteady compressible baer nunziato model in conjunction with the moving grid approach is discussed in this paper both hll and hllc type finite volume methods are presented and implemented in the context of arbitrary lagrangian eulerian formulation in a multidimensional framework the construction of suitable numerical methods is linked to proper approximations of the non conservative terms on moving grids the hll discretization follows global conservation properties such as free stream preservation and uniform pressure and velocity profiles preservation on moving grids the hllc solver initially proposed by tokareva and toro 1 for the baer nunziato model is based on an approximate solution of local riemann problems containing all the characteristic fields present in the exact solution both subsonic and supersonic configurations are considered in the construction of the present hllc solver in addition an adaptive 6 wave hllc scheme is also proposed for computational efficiency the methods are first assessed on a variety of 1 d riemann problems including both fixed and moving grids applications the methods are finally tested on 2 d and 3 d applications 2 d riemann problems a 2 d shock bubble interaction and finally a 3 d fluid structure interaction problem with a good agreement with the experiments

the smallest eigenvalue for reversible markov chains we define a geometric quantity for reversible markov chains and use it to prove lower and upper bounds for the smallest eigenvalue of such chains known bounds are discussed and compared with the new ones

two phase shock tube problems and numerical methods of solution the study involves the flow of compressible gas in a porous bed we are interested in exploring the solution to a shock tube problem that also includes a discontinuous jump in the porosity of the bed the averaging process that is used to derive the governing system of equations introduces terms that prevent the equations taking a standard conservation form the purpose of this work is to explore how the porosity jump effects the solution to the riemann problem and to assess whether standard conservative and nonconservative numerical methods can provide the correct solution to the riemann problem the study illustrates serious shortfalls in the numerical solution to these problems using standard techniques by exploring the exact solution the author suggests how the standard numerical methods can be modified to provide the correct solution to these systems

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

hllc type riemann solver with approximated two phase contact for the computation of the baer nunziato two fluid model abstract the computation of compressible two phase flows with the baer nunziato model is addressed only the convective part of the model that exhibits non conservative products is considered and the source terms of the model that represent the exchange between phases are neglected based on the solver proposed by tokareva toro 1 a new hllc type riemann solver is built the key idea of this new solver lies in an approximation of the two phase contact discontinuity of the model thus the riemann invariants of the wave are approximated in the subsonic case a major consequence of this approximation is that the resulting solver can deal with any equation of state it also allows to bypass the resolution of a non linear equation based on those riemann invariants we assess the solver and compare it with others on 1d riemann problems including grid convergence and efficiency studies the ability of the proposed solver to deal with complex equations of state is also investigated finally the different solvers have been compared on challenging 2d test cases due to the presence of both material interfaces and shock waves a shock bubble interaction and underwater explosions when compared with others the present solver appears to be accurate efficient and robust

the riemann problem and a high resolution godunov method for a model of compressible two phase flow this paper considers the riemann problem and an associated godunov method for a model of compressible two phase flow the model is a reduced form of the well known baer nunziato model that describes the behavior of granular explosives in the analysis presented here we omit source terms representing the exchange of mass momentum and energy between the phases due to compaction drag heat transfer and chemical reaction but retain the non conservative nozzling terms that appear naturally in the model for the riemann problem the effect of the nozzling terms is confined to the contact discontinuity of the solid phase treating the solid contact as a layer of vanishingly small thickness within which the solution is smooth yields jump conditions that connect the states across the contact as well as a prescription that allows the contribution of the nozzling terms to be computed unambiguously an iterative method of solution is described for the riemann problem that determines the wave structure and the intermediate states of the flow for given left and right states a godunov method based on the solution of the riemann problem is constructed it includes non conservative flux contributions derived from an integral of the nozzling terms over a grid cell the godunov method is extended to second order accuracy using a method of slope limiting and an adaptive riemann solver is described and used for computational efficiency numerical results are presented demonstrating the accuracy of the numerical method and in particular the accurate numerical description of the flow in the vicinity of a solid contact where phases couple and nozzling terms are important the numerical method is compared with other methods available in the literature and found to give more accurate results for the problems considered

convergence of the 2 2 godunov method for a general resonant nonlinear balance law we introduce a generalized solution of the riemann problem for a general resonant nonlinear balance law and we prove the convergence of the 2 x 2 godunov numerical method based on these solutions in particular we obtain generic conditions that guarantee a canonical structure for the elementary waves in the solution of the riemann problem and an interesting multiplicity of time asymptotic wave patterns is observed and characterized

a straightforward memory function calculation with the non equilibrium statistical operator method abstract a straightforward function calculation in the non equilibrium statistical operator nso method is suggested as an example the relaxation of a two level system to a thermostat is considered

on the spectrum of the normalized laplacian of iterated triangulations of graphs the eigenvalues of the normalized laplacian of a graph provide information on its topological and structural characteristics and also on some relevant dynamical aspects specifically in relation to random walks in this paper we determine the spectra of the normalized laplacian of iterated triangulations of a generic simple connected graph as an application we also find closed forms for their multiplicative degree kirchhoff index kemeny s constant and number of spanning trees

generalized diffusion equation with fractional derivatives within renyi statistics by using the zubarev nonequilibrium statistical operator method and the liouville equation with fractional derivatives a generalized diffusion equation with fractional derivatives is obtained within the renyi statistics averaging in generalized diffusion coefficient is performed with a power distribution with the renyi parameter q

a robust numerical method for approximating solutions of a model of two phase flows and its properties the objective of the present paper is to extend our earlier works on simpler systems of balance laws in nonconservative form such as the model of fluid flows in a nozzle with variable cross section to a more complicated system consisting of seven equations which has applications in the modeling of deflagration to detonation transition in granular materials first we transform the system into an equivalent one which can be regarded as a composition of three subsystems then depending on the characterization of each subsystem we propose a convenient numerical treatment of the subsystem separately precisely in the first subsystem of the governing equations in the gas phase stationary waves are used to absorb the nonconservative terms into an underlying numerical scheme in the second subsystem of conservation laws of the mixture we can take a suitable scheme for conservation laws for the third subsystem of the compaction dynamics equation the fact that the velocities remain constant across solid contacts suggests us to employ the technique of engquist osher s scheme then we prove that our method possesses some interesting properties it preserves the positivity of the volume fractions in both phases and in the gas phase our scheme is capable of capturing equilibrium states preserves the positivity of the density and satisfies the numerical minimum entropy principle numerical tests show that our scheme can provide reasonable approximations for data the supersonic regions but the results are not satisfactory in the subsonic region however the scheme is numerically stable and robust

runge kutta discontinuous galerkin method for the approximation of baer and nunziato type multiphase models a high order numerical method is developed for the computation of compressible multiphase flows the model we use is based on the baer and nunziato type systems 4 among all the other available models in the literature these systems present the advantage to be able to simulate either interface or mixture problems nevertheless they still raise some issues mainly based on their non conservative feature the numerical method we propose is a discontinuous galerkin type in this work the interior side integrals are computed thanks to 2 robustness and high order of accuracy of the method are proved on classical interface problems but also on suitably derived analytical solutions

recognition of nonextensive statistical distributions by the eigencoordinates method nonextensive statistical distributions suggested by tsallis are studied in the framework of the so called eigencoordinates ecs method which allows to recognize them with high level of authenticity at first the possibilities of the ecs method have been demonstrated on model files to exhibit some peculiarities of this new method then the amplitude distributions of the real noise tracks before and after earthquakes have been analyzed it has been shown that this type of noise is fractal and strongly correlated histograms of the noise amplitudes with high level of reliability are really described by a distribution coming from nonextensive statistics the possibilities and recommendations for the application of the ecs method to identify theoretical curves claimed for the description of experimental data are discussed

the resonant cases and the riemann problem for a model of two phase flows abstract the resonant cases in the riemann problem for a model of two phase flows with resonance are investigated which complete the construction of riemann solutions the model is given by a nonconservative hyperbolic system of balance laws the phase decomposition method is developed to construct solutions in each phase in a relatively separated way but still glued to each other via the contact discontinuities composite wave curves can be built and intersections of wave curves in each phase plane help to determine various configurations of riemann solutions in particular solutions containing multiple waves propagating with the same shock speed are constructed

fractional integral associated to generalized cookie cutter set and its physical interpretation this paper is based on nigmatullin s study when the residual memory set is a generalized cookie cutter set on using various hypotheses it is proved that the fractional exponent of a fractional integral is not uniquely determined by the fractal dimension of the generalized cookie cutter set it is determined by of self similar measure or infinite self similar measure on this generalized cookie cutter set and can run over all positive real numbers

damping characteristics of a fractional oscillator abstract a study of sinusoidally forced oscillations of a fractional oscillator shows that the system exhibits a rich variety of damping characteristics while some aspects of the damping mimic the characteristic features of a damped harmonic oscillator there are others which do not find any parallel in the damped harmonic oscillator system it is clearly demonstrated that the free and forced oscillations of a fractional oscillator are characterized by different damping parameters while both depend on the fractional index the free oscillation damping depends on the natural frequency 0 of the oscillator the forced oscillation damping depends in addition on the driving frequency furthermore there is a different power law tail associated with each of these cases

an exact riemann solver for compressible two phase flow models containing non conservative products in this article we present a new numerical procedure for solving exactly the riemann problem of compressible two phase flow models containing non conservative products these products appear in the expressions for the interactions between the two phases thus in the compressible limit the governing equations are hyperbolic but can not be written as conservation laws i e in divergence form in general the solution to the riemann problem of these models contains six distinct centered waves according to the relative position of these waves in the x t plane the possible solutions can be classified into four principal configurations the riemann solver we propose herein investigates sequentially each of these configurations until an admissible solution is calculated special configurations corresponding to coalescence of waves are also analyzed and included in the solver further we examine the accuracy and robustness of three known methods for the integration of the non conservative products via a series of numerical tests finally the issue of existence and uniqueness of solutions to the riemann problem is discussed

fractional kinetics in kac zwanzig heat bath models we study a variant of the kac zwanzig model of a particle in a heat bath the heat bath consists of n particles which interact with a distinguished particle via springs and have random initial data as n the trajectories of the distinguished particle weakly converge to the solution of a stochastic integro differential equation a generalized langevin equation gle with power law memory kernel and driven by 1 f noise the limiting process exhibits fractional sub diffusive behaviour we further consider the approximation of non markovian processes by higher dimensional markovian processes via the introduction of auxiliary variables and use this method to approximate the limiting gle in contrast we show the inadequacy of a so called fractional fokker planck equation in the present context all results are supported by direct numerical experiments