variance mediated multifractal analysis of group participation in chasing a single dangerous prey abstract complexity of group participation in chasing a single dangerous prey is usually influenced by many factors such as the group size the physiological fitness of predator the hunting tactics and the running speed of prey the group members may take diversified roles and switch their roles in the process of group hunting in this paper we study group participation in lions pride hunting by using a minimal cheating pursuing model formulated in discrete time random walks predator s switching between cheating state and pursuing state is determined by a preset probability transition matrix which is regarded to be a product of the combination of various factors that influence group participation the physiological constraints of lions require that the measurement of complexity of group participation must be built for short time series on the basis of 300 simulated time steps numerical results show that our model reasonably reflects the common expectation that the pride groups tightly in chasing a single slow prey while in chasing a single fast prey it groups loosely we compute the distance between the group center and the center of the concerted pursuing for the quantification of group participation complexity embedded in short time series of these quantities is measured via a new method named variance mediated multifractal analysis this method is based on the partition function which is the weighted sum of probability measures of q th power the short time series is divided into non overlapping windows where the sample variance of each window is used to build the normalized probability measure a strategy one point indent for local past is designed to weigh the probability measures the singularity spectrum exhibits more multifractality in the simulated group participation in chasing a fast prey and far less such in chasing a slow one showing the potential applications of this method in studying short process of group hunting

numerical solutions to compressible flows in a nozzle with variable cross section compressible flows in a nozzle can be modeled by the gas dynamics equations in one dimensional space with source terms it turns out that along stationary waves the entropy is conserved investigating properties of the system leads us to the determination of stationary waves relying on this analysis we construct a numerical scheme which takes into account the use of stationary waves our scheme is shown to be capable of maintaining equilibrium states this demonstrates the efficiency of the new scheme over classical ones which usually give unsatisfactory results when reducing the refinement of the mesh size moreover our scheme converges much faster than the classical ones in most cases

the riemann problem for a nonisentropic fluid in a nozzle with discontinuous cross sectional area we present a full investigation of the riemann problem for a nonisentropic polytropic fluid in a nozzle with piecewise constant cross section first we introduce the concept of elementary waves which turn out to make up riemann solutions second we study a procedure to select admissible stationary waves relying on the monotone criterion by projecting all the wave curves in the p u plane we construct riemann solutions existence of riemann solutions can be obtained for large initial data furthermore we establish the uniqueness of riemann solutions in strictly hyperbolic domains our argument can lead to estimate regions where the riemann problem admits a unique solution

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

a confidence limit for the empirical mode decomposition and hilbert spectral analysis the confidence limit is a standard measure of the accuracy of the result in any statistical analysis most of the confidence limits are derived as follows the data are first divided into subsections and then under the ergodic assumption the temporal mean is substituted for the ensemble mean next the confidence limit is defined as a range of standard deviations from this mean however such a confidence limit is valid only for linear and stationary processes furthermore in order for the ergodic assumption to be valid the subsections have to be statistically independent for non stationary and nonlinear processes such an analysis is no longer valid the confidence limit of the method here termed emd hsa for empirical mode decomposition hilbert spectral analysis is introduced by using various adjustable stopping criteria in the sifting processes of the emd step to generate a sample set of intrinsic mode functions imfs the emd technique acts as a pre processor for hsa on the original data producing a set of components imfs from the original data that equal the original data when added back together each imf represents a scale in the data from smallest to largest the ensemble mean and standard deviation of the imf sample sets obtained with different stopping criteria are calculated and these form a simple random sample set the confidence limit for emd hsa is then defined as a range of standard deviations from the ensemble mean without evoking the ergodic assumption subdivision of the data stream into short sections is unnecessary hence the results and the confidence limit retain the full frequency resolution of the full dataset this new confidence limit can be applied to the analysis of nonlinear and non stationary processes by these new techniques data from length of day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied by providing a confidence limit for this new approach a stable range of stopping criteria for the decomposition or sifting phase emd has been established making the results of the final processing with hsa and the entire emd hsa method more definitive

diophantine definability of infinite discrete nonarchimedean sets and diophantine models over large subrings of number fields we prove that some infinite p adically discrete sets have diophantine definitions in large subrings of number fields first if k is a totally real number field or a totally complex degree 2 extension of a totally real number field then for every prime p of k there exists a set of k primes s of density arbitrarily close to 1 such that there is an infinite p adically discrete set that is diophantine over the ring ok s of s integers in k second if k is a number field over which there exists an elliptic curve of rank 1 then there exists a set of k primes s of density 1 and an infinite diophantine subset of ok s that is v adically discrete for every place v of k third if k is a number field over which there exists an elliptic curve of rank 1 then there exists a set of k primes s of density 1 such that there exists a diophantine model of z over ok s this line of research is motivated by a question of mazur concerning the distribution of rational points on varieties in a nonarchimedean topology and questions concerning extensions of hilbert s tenth problem to subrings of number fields

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

extension of hilbert s tenth problem to some algebraic number fields we extend the solution of hilbert s tenth problem to algebraic number fields having one pair of complex conjugated embeddings the proof is based on the extended method of j denef used for totally real algebraic number fields

comparison of detrending methods for fluctuation analysis abstract we examine several recently suggested methods for the detection of long range correlations in data series based on similar ideas as the well established detrended fluctuation analysis dfa in particular we present a detailed comparison between the regular dfa and two recently suggested methods the centered moving average cma method and a modified detrended fluctuation analysis mdfa we find that cma performs the same as dfa in long data with weak trends and is slightly superior to dfa in short data with weak trends when comparing standard dfa to mdfa we observe that dfa performs slightly better in almost all examples we studied we also discuss how several types of trends affect different types of dfa for weak trends in the data the new methods are comparable with dfa in these respects however if the functional form of the trend in data is not a priori known dfa remains the method of choice only a comparison of dfa results using different detrending polynomials yields full recognition of the trends a comparison with independent methods is recommended for proving long range correlations

a fast and stable well balanced scheme with hydrostatic reconstruction for shallow water flows we consider the saint venant system for shallow water flows with nonflat bottom it is a hyperbolic system of conservation laws that approximately describes various geophysical flows such as rivers coastal areas and oceans when completed with a coriolis term or granular flows when completed with friction numerical approximate solutions to this system may be generated using conservative finite volume methods which are known to properly handle shocks and contact discontinuities however in general these schemes are known to be quite inaccurate for near steady states as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions this difficulty can be overcome by using the so called well balanced schemes we describe a general strategy based on a local hydrostatic reconstruction that allows us to derive a well balanced scheme from any given numerical flux for the homogeneous problem whenever the initial solver satisfies some classical stability properties it yields a simple and fast well balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality

the riemann problem for the one dimensional free surface shallow water equations with a bed step theoretical analysis and numerical simulations in this paper the solution of the riemann problem for the one dimensional free surface shallow water equations over a bed step is analyzed both from a theoretical and a numerical point of view particular attention has been paid to the wave that is generated at the location of the bed discontinuity starting from the classical shallow water equations considering the bed level as an additional variable and adding to the system an equation imposing its time invariance we show that this wave is a contact wave across which one of the riemann invariants namely the energy is not constant this is due to the fact that the relevant problem is nonconservative we demonstrate that in this type of system riemann invariants do not generally hold in contact waves furthermore we show that in this case the equations that link the flow variables across the contact wave are the generalized rankine hugoniot relations and we obtain these for the specific problem from the numerical point of view we present an accurate and efficient solver for the step riemann problem to be used in a finite volume godunov type framework through a two step predictor corrector procedure the solver is able to provide solutions with any desired accuracy the predictor step uses a well balanced generalized roe solver while the corrector step solves the exact nonlinear system of equations that consitutes the problem by means of an iterative procedure that starts from the predictor solution in order to show the effectiveness and the accuracy of the proposed approach we consider several step riemann problems and compare the exact solutions with the numerical results obtained by using a standard roe approach far from the step and the novel two step algorithm for the fluxes over the step achieving good results

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws we develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms the schemes are of equilibrium type hence with uniform bounds on approximate solutions valid in cell entropy inequalities and exact for some equilibrium states convergence is investigated in the framework of kinetic schemes numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms equilibrium type schemes produce accurate results even on test problems for which the standard approach fails for some numerical tests they exhibit exponential type convergence rate in two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 50002 grid points

elliptic curves retaining their rank in finite extensions and hilbert s tenth problem for rings of algebraic numbers using poonen s version of the weak vertical method we produce new examples of large and small rings of algebraic numbers including rings of integers where z and or the ring of integers of a subfield are existentially definable and or where the ring version of mazur s conjecture on the topology of rational points does not hold

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

on hurst exponent estimation under heavy tailed distributions abstract in this paper we show how the sampling properties of the hurst exponent methods of estimation change with the presence of heavy tails we run extensive monte carlo simulations to find out how rescaled range analysis r s multifractal detrended fluctuation analysis m f d f a detrending moving average d m a and generalized hurst exponent approach g h e estimate hurst exponent on independent series with different heavy tails for this purpose we generate independent random series from stable distribution with stability exponent changing from 1 1 heaviest tails to 2 gaussian normal distribution and we estimate the hurst exponent using the different methods r s and g h e prove to be robust to heavy tails in the underlying process g h e provides the lowest variance and bias in comparison to the other methods regardless the presence of heavy tails in data and sample size utilizing this result we apply a novel approach of the intraday time dependent hurst exponent and we estimate the hurst exponent on high frequency data for each trading day separately we obtain hurst exponents for s p500 index for the period beginning with year 1983 and ending by november 2009 and we discuss the surprising result which uncovers how the market s behavior changed over this long period

exact solution of the riemann problem for the shallow water equations with discontinuous bottom geometry in this paper we present the exact solution of the riemann problem for the non linear shallow water equations with a step like bottom the solution has been obtained by solving an enlarged system that includes an additional equation for the bottom geometry and then using the principles of conservation of mass and momentum across the step the resulting solution is unique and satisfies the principle of dissipation of energy across the shock wave we provide examples of possible wave patterns numerical solution of a first order dissipative scheme as well as an implementation of our riemann solver in the second order upwind method are compared with the proposed exact riemann problem solution a practical implementation of the proposed exact riemann solver in the framework of a second order upwind tvd method is also illustrated

detecting and interpreting distortions in hierarchical organization of complex time series hierarchical organization is a cornerstone of complexity and multifractality constitutes its central quantifying concept for model uniform cascades the corresponding singularity spectra are symmetric while those extracted from empirical data are often asymmetric using selected time series representing such diverse phenomena as price changes and intertransaction times in financial markets sentence length variability in narrative texts missouri river discharge and sunspot number variability as examples we show that the resulting singularity spectra appear strongly asymmetric more often left sided but in some cases also right sided we present a unified view on the origin of such effects and indicate that they may be crucially informative for identifying the composition of the time series one particularly intriguing case of this latter kind of asymmetry is detected in the daily reported sunspot number variability this signals that either the commonly used famous wolf formula distorts the real dynamics in expressing the largest sunspot numbers or if not that their dynamics is governed by a somewhat different mechanism

equilibrium schemes for scalar conservation laws with stiff sources we consider a simple model case of stiff source terms in hyperbolic conservation laws namely the case of scalar conservation laws with a zeroth order source with low regularity it is well known that a direct treatment of the source term by finite volume schemes gives unsatisfactory results for both the reduced cfl condition and refined meshes required because of the lack of accuracy on equilibrium states the source term should be taken into account in the upwinding and discretized at the nodes of the grid in order to solve numerically the problem we introduce a so called equilibrium schemes with the properties that i the maximum principle holds true ii discrete entropy inequalities are satisfied iii steady state solutions of the problem are maintained one of the difficulties in studying the convergence is that there are no bv estimates for this problem we therefore introduce a kinetic interpretation of upwinding taking into account the source terms based on the kinetic formulation we give a new convergence proof that only uses property ii in order to ensure desired compactness framework for a family of approximate solutions and that relies on minimal assumptions the computational efficiency of our equilibrium schemes is demonstrated by numerical tests that show that in comparison with an usual upwind scheme the corresponding equilibrium version is far more accurate furthermore numerical computations show that equilibrium schemes enable us to treat efficiently the sources with singularities and oscillating coefficients

modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti persistent processes abstract detrended fluctuation analysis dfa is a simple but very efficient method for investigating the power law long term correlations of non stationary time series in which a detrending step is necessary to obtain the local fluctuations at different timescales we propose to determine the local trends through empirical mode decomposition emd and perform the detrending operation by removing the emd based local trends which gives an emd based dfa method similarly we also propose a modified multifractal dfa algorithm called an emd based mfdfa the performance of the emd based dfa and mfdfa methods is assessed with extensive numerical experiments based on fractional brownian motion and multiplicative cascading process we find that the emd based dfa method performs better than the classic dfa method in the determination of the hurst index when the time series is strongly anticorrelated and the emd based mfdfa method outperforms the traditional mfdfa method when the moment order q of the detrended fluctuations is positive we apply the emd based mfdfa to the 1 min data of shanghai stock exchange composite index and the presence of multifractality is confirmed we also analyze the daily austrian electricity prices and confirm its anti persistence

hilbert s tenth problem and mazur s conjecture for large subrings of mathbb q we give the first examples of infinite sets of primes s such that hilbert s tenth problem over z s 1 has a negative answer in fact we can take s to be a density 1 set of primes we show also that for some such s there is a punctured elliptic curve e over z s 1 such that the topological closure of e z s 1 in e r has infinitely many connected components

diophantine definability over some rings of algebraic numbers with infinite number of primes allowed in the denominator let k be a number field let w be a set of non archimedean primes of k let o k w x k ord p x 0 p w then if k is a totally real non trivial cyclic extension of there exists an infinite set w of finite primes of k such that and the ring of algebraic integers of k have a diophantine definition over o k w thus the diophantine problem of o k w is undecidable

reliable scaling exponent estimation of long range correlated noise in the presence of random spikes abstract detrended fluctuation analysis dfa has been used widely to determine possible long range correlations in data obtained from diverse settings in a recent study z chen p ch ivanov k hu h e stanley effects of nonstationarities on detrended fluctuation analysis phys rev e 65 2002 041107 uncorrelated random spikes superimposed on the long range correlated noise lr noise were found to affect dfa scaling exponent estimates in this brief communication singular value decomposition svd filter is proposed to minimize the effect random spikes superimposed on lr noise thus facilitating reliable estimation of the scaling exponents the effectiveness of the proposed approach is demonstrated on random spikes sampled from normal and uniform distributions

diophantine classes of holomorphy rings of global fields abstract this paper introduces the notions of diophantine generation and diophantine equivalence and explores the resulting diophantine classes of holomorphy rings of number fields and of one variable function fields over finite fields of constants

an hllc type riemann solver and high resolution godunov method for a two phase model of reactive flow with general equations of state abstract a high resolution godunov method is developed for a two phase model of reactive flow the model considers general equations of state of mie gruneisen form and different choices for the reaction rate both relevant for simulations of the dynamical behavior of detonations in pbx type granular explosives the numerical approach employs a riemann solver and various options ranging from an exact solver to an approximate solver of hllc type are described a principal aim of the paper is an assessment of the approximate riemann solvers in terms of the accuracy and efficiency of numerical solutions of the two phase model in particular this study considers the state sensitive behavior in different regimes of the solutions in a reverse impact configuration including compaction run to detonation and the evolution to compaction led and reaction led steady detonations for these regimes the convergence properties of the numerical approach are examined for the different choices of the riemann solver as is the error in the solutions at lower grid resolution finally the computational performance of the time stepping scheme is assessed for the different solvers

a well balanced scheme for the numerical processing of source terms in hyperbolic equations in a variety of physical problems one encounters source terms that are balanced by internal forces and this balance supports multiple steady state solutions that are stable typical of these are gravity driven flows such as those described by the shallow water equations over a nonuniform ocean bottom 1 10 qquad h t hu x 0 text and hu t left hu 2 frac gh 2 2 right x ga x x h 0 many classic numerical schemes cannot maintain these steady solutions or achieve them in the long time limit with an acceptable level of accuracy because they do not preserve the proper balance between the source terms and internal forces we propose here a numerical scheme adapted to a scalar conservation law that preserves this balance and that can it is hoped be extended to more general hyperbolic systems the proof of convergence of this scheme toward the entropy solution is given and some numerical tests are reported

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

on the multifractal effects generated by monofractal signals we study quantitatively the level of false multifractal signal one may encounter while ana lyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis mf dfa the investigated effect appears as a result of finite length of used data series and is additionally amplified by the long term memory the data eventually may contain we pro vide the detailed quantitative description of such apparent multifractal background signal as a threshold in spread of generalized hurst exponent valuesh or a threshold in the width of multifractal spectrum below which multifractal properties of the system are only apparent i e do not exist despite 6 0 orh 6 0 we find this effect quite important for shorter or persistent series and we argue it is linear with respect to autocorrelation exponent its strength decays according to power law with respect to the length of time series the influ ence of basic linear and nonlinear transformations applied to initial data in finite time series with various levels of long memory is also investigated this provides additional set of semi analytical results the obtained formulas are significant in any interdisciplinary application of multifractality including physics financial data analysis or physiology because they allow to separate the true multifractal phenomena from the apparent artificial multifractal effects they should be a helpful tool of the first choice to decide whether we do in particular case with the signal with real multiscaling properties or not

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

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

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

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 godunov type scheme for the isentropic model of a fluid flow in a nozzle with variable cross section we present a godunov type scheme for the isentropic model of a fluid flow in a nozzle with variable cross section the model is of nonconservative form making it hard for standard numerical discretizations of the nonconservative term in particular the error for a standard numerical scheme with a usual discretization of the nonconservative term may become larger as the mesh size gets smaller we first re investigate the riemann problem of the model pointing out several interesting properties of the wave curves and establishing specific existence domain for each type of solutions then we incorporate local riemann solutions to build a godunov type scheme for the model the scheme is constructed in subsonic and supersonic regions where the system is strictly hyperbolic tests show that our scheme can capture standing waves so that it is well balanced furthermore tests also show that our godunov type scheme can give a good accuracy for numerical approximations of exact solutions our godunov type scheme can resolve the difficulty of other existing schemes for similar models of fluid flows with nonconservative terms

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

quantifying origin and character of long range correlations in narrative texts in natural language using short sentences is considered efficient for communication however a text composed exclusively of such sentences looks technical and reads boring a text composed of long ones on the other hand demands significantly more effort for comprehension studying characteristics of the sentence length variability slv in a large corpus of world famous literary texts shows that an appealing and aesthetic optimum appears somewhere in between and involves selfsimilar cascade like alternation of various lengths sentences a related quantitative observation is that the power spectra s f of thus characterized slv universally develop a convincing 1 fs scaling with the average exponent s 1 2 close to what has been identified before in musical compositions or in the brain waves an overwhelming majority of the studied texts simply obeys such fractal attributes but especially spectacular in this respect are hypertext like stream of consciousness novels in addition they appear to develop structures characteristic of irreducibly interwoven sets of fractals called multifractals scaling of s f in the present context implies existence of the long range correlations in texts and appearance of multifractality indicates that they carry even a nonlinear component a distinct role of the full stops in inducing the long range correlations in texts is evidenced by the fact that the above quantitative characteristics on the long range correlations manifest themselves in variation of the full stops recurrence times along texts thus in slv but to a much lesser degree in the recurrence times of the most frequent words in this latter case the nonlinear correlations thus multifractality disappear even completely for all the texts considered treated as one extra word the full stops at the same time appear to obey the zipfian rank frequency distribution however

short note a comment on the computation of non conservative products we are interested in the solution of non conservative hyperbolic systems and consider in particular the so called path conservative schemes see e g 2 3 which rely on the theoretical work in 1 the example of the standard euler equations for a perfect gas is used to illuminate some computational issues and shortcomings of this approach

analysis and approximation of conservation laws with source terms we consider a conservation law of the form cl i ut f u x ax where a cdot is a bounded piecewise smooth source term and f an even convex function we first characterize the solution to the riemann problem through a new lax type formula then we prove that for a cdot fixed the semigroup associated with cl is an l1 contraction and we obtain an existence theorem for weak solutions to cl we conclude by constructing godunov type difference schemes and proving that these schemes are l infty stable and have stable steady solutions similar in structure to those of cl some numerical tests are reported

data driven detrending of nonstationary fractal time series with echo state networks abstract in this paper we propose a novel data driven approach for removing trends detrending from nonstationary fractal and multifractal time series we consider real valued time series relative to measurements of an underlying dynamical system that evolves through time we assume that such a dynamical process is predictable to a certain degree by means of a class of recurrent networks called echo state network esn which are capable to model a generic dynamical process in order to isolate the superimposed multi fractal component of interest we define a data driven filter by leveraging on the esn prediction capability to identify the trend component of a given input time series specifically the estimated trend is removed from the original time series and the residual signal is analyzed with the multifractal detrended fluctuation analysis procedure to verify the correctness of the detrending procedure in order to demonstrate the effectiveness of the proposed technique we consider several synthetic time series consisting of different types of trends and fractal noise components with known characteristics we also process a real world dataset the sunspot time series which is well known for its multifractal features and has recently gained attention in the complex systems field results demonstrate the validity and generality of the proposed detrending method based on esns

on solutions to equilibrium problems for systems of stiffened gases we consider an isolated system of n immiscible fluids each following a stiffened gas equation of state we consider the problem of calculating equilibrium states from the conserved fluid mechanical properties i e the partial densities and internal energies we consider two cases in each case mechanical equilibrium is assumed but the fluids may or may not be in thermal equilibrium for both cases we address the issues of existence uniqueness and physical validity of equilibrium solutions we derive necessary and sufficient conditions for physically valid solutions to exist and prove that such solutions are unique we show that for both cases physically valid solutions can be expressed as the root of a monotonic function in one variable we then formulate efficient algorithms which unconditionally guarantee global and quadratic convergence toward the physically valid solution

wavelet versus detrended fluctuation analysis of multifractal structures we perform a comparative study of applicability of the multifractal detrended fluctuation analysis mfdfa and the wavelet transform modulus maxima wtmm method in proper detecting of monofractal and multifractal character of data we quantify the performance of both methods by using different sorts of artificial signals generated according to a few well known exactly soluble mathematical models monofractal fractional brownian motion bifractal levy flights and different sorts of multifractal binomial cascades our results show that in the majority of situations in which one does not know a priori the fractal properties of a process choosing mfdfa should be recommended in particular wtmm gives biased outcomes for the fractional brownian motion with different values of hurst exponent indicating spurious multifractality in some cases wtmm can also give different results if one applies different wavelets we do not exclude using wtmm in real data analysis but it occurs that while one may apply mfdfa in a more automatic fashion wtmm must be applied with care in the second part of our work we perform an analogous analysis on empirical data coming from the american and from the german stock market for this data both methods detect rich multifractality in terms of broad f alpha but mfdfa suggests that this multifractality is poorer than in the case of wtmm

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

measuring the self similarity exponent in levy stable processes of financial time series abstract geometric method based procedures which will be called gm algorithms herein were introduced in m a sanchez granero j e trinidad segovia j garcia perez some comments on hurst exponent and the long memory processes on capital markets phys a 387 2008 5543 5551 to efficiently calculate the self similarity exponent of a time series in that paper the authors showed empirically that these algorithms based on a geometrical approach are more accurate than the classical algorithms especially with short length time series the authors checked that gm algorithms are good when working with fractional brownian motions moreover in j e trinidad segovia m fernandez martinez m a sanchez granero a note on geometric method based procedures to calculate the hurst exponent phys a 391 2012 2209 2214 a mathematical background for the validity of such procedures to estimate the self similarity index of any random process with stationary and self affine increments was provided in particular they proved theoretically that gm algorithms are also valid to explore long memory in fractional levy stable motions in this paper we prove empirically by monte carlo simulation that gm algorithms are able to calculate accurately the self similarity index in levy stable motions and find empirical evidence that they are more precise than the absolute value exponent denoted by ave onwards and the multifractal detrended fluctuation analysis mf dfa algorithms especially with a short length time series we also compare them with the generalized hurst exponent ghe algorithm and conclude that both gm2 and ghe algorithms are the most accurate to study financial series in addition to that we provide empirical evidence based on the accuracy of gm algorithms to estimate the self similarity index in levy motions that the evolution of the stocks of some international market indices such as u s small cap and nasdaq100 cannot be modelized by means of a brownian motion

constructing a godunov type scheme for the model of a general fluid flow in a nozzle with variable cross section a godunov type scheme for the model of a general fluid flow in a nozzle with variable cross section is presented the model has the form of a nonconservative system of balance laws which poses many challenging questions for study first exact riemann solvers in computing form are described in both subsonic and supersonic regions second the computable exact solutions of local riemann problem are incorporated into a godunov type scheme third the scheme is shown to be well balanced in the sense that it can capture exactly stationary waves finally numerical tests for data belong to both subsonic and supersonic regions are presented these tests show that the scheme has a very fine accuracy especially the scheme can give very good approximations to the exact solutions even in the resonant phenomenon where the solution contains three waves of the same speed

use and misuse of some hurst parameter estimators applied to stationary and non stationary financial time series abstract the detection of long range dependence lrd is an important task in time series analysis lrd is often summarized by the well known hurst parameter or exponent h 0 1 which can be estimated by a number of methods some of these techniques are designed to be applied to signals behaving as a stationary fractional gaussian noise fgn whereas others imply that the analyzed time series behave as a non stationary fractional brownian motion fbm moreover some estimators do not yield the hurst parameter but indexes related to h and ranging outside the unit interval therefore the fgn or fbm nature of the studied time series has to be preliminarily analyzed before applying any estimation method and the relationships between h and the indexes resulting from the analyses have to be taken into account to obtain coherent results since fgn like series represent the increments of fbm like processes and both the signals are characterized by the same h value by definition estimators designed for fgn like series can be applied to fbm like sequences after preventive differentiation and conversely estimators designed for fbm like processes can be applied to fgn like series after preventive integration the signal characterization is particularly important when h is estimated on financial time series because the returns represent the first difference of price time series which are often assumed to behave like self affine sequences the analysis of simulated fgn and fbm time series shows that all the considered methods yield comparable h values when properly applied the reanalysis of several market price time series already studied in the literature points out that a correct application of the estimators supported by a preventive signal classification yields homogeneous h values allowing for a useful cross validation of results reported in different works moreover some conclusions reported in the literature about the anti persistence of some financial series are shown to be incorrect because of the inappropriate application of the estimation methods

on diophantine definability and decidability in some infinite totally real extensions of ℚ let m be a number field and w m a set of its non archimedean primes then let o m wm x m ord t x 0 t w m let p 1 p r be a finite set of prime numbers let f inf be the field generated by all the p j i th roots of unity as j and i 1 r let k inf be the largest totally real subfield of f inf then for any e 0 there exist a number field m k inf and a set w m of non archimedean primes of m such that w m has density greater than 1 e and z has a diophantine definition over the integral closure of o m w m in k inf