algebraic spatial correlations in lattice gas automata violating detailed balance in this paper we discuss the existence of generic long range correlations in spatially homogeneous and stable equilibrium states of closed lattice gas automata whose stochastic collision rules violate the symmetry conditions of detailed balance and in addition satisfy local conservation laws such correlations occur even though the collision rules are strictly local and invariant under all symmetries of the lattice first a phenomenological langevin equation approach is discussed next we present a theoretical analysis on the basis of an approximate microscopic ring kinetic theory this theory is used to calculate the amplitude ofr tails in the spatial correlations and the result is compared with computer simulations

an aerodynamic optimization method based on the inverse problem adjoint equations abstract an adjoint optimization method based on the solution of an inverse flow problem is proposed given a certain performance functional it is necessary to find its extremum with respect to a flow variable distribution on the domain boundary for example pressure the adjoint formulation delivers the functional gradient with respect to such a flow variable distribution and a descent method can be used for optimization the flow constraints are easily imposed in the parameterization of the distributed control and therefore those problems with several strict constraints on the flow solution can be solved very efficiently conversely the geometric constraints are imposed either by additional partial differential equations or by penalization by adequately constraining the geometric solution the classical limitations of the inverse problem design can be overcome several examples pertaining to internal flows are given

detailed balance has a counterpart in non equilibrium steady states when modelling driven steady states of matter it is common practice either to choose transition rates arbitrarily or to assume that the principle of detailed balance remains valid away from equilibrium neither of those practices is theoretically well founded hypothesizing ergodicity constrains the transition rates in driven steady states to respect relations analogous to but different from the equilibrium principle of detailed balance the constraints arise from demanding that the design of any model system contains no information extraneous to the microscopic laws of motion and the macroscopic observables this prevents over description of the non equilibrium reservoir and implies that not all stochastic equations of motion are equally valid the resulting recipe for transition rates has many features in common with equilibrium statistical mechanics

a nonisomorphism theorem for cofree lie coalgebras in the first paragraph of this section we will give a brief overview of this work the remainder of this section contains formal definitions and details omitted from the first paragraph throughout this work all vector spaces linear maps tensor products coalgebras and algebras etc will be taken over a base field k let v be a vector space this paper is concerned with the relation between the cofree lie coalgebra on i and the cofree covered lie coalgebra on v a lie coalgebra will be defined as a coalgebra that satisfies the co anticommutativity and co jacobi lie coidentities this is analogous to the definition of a lie algebra as an algebra that satisfies the anticommutativity and jacobi identities it follows from the poincare birkhoff witt theorem that every lie algebra arises as a subalgebra of an a where a is the lie algebra associated to an associative algebra a a covered lie coalgebra will be defined as the quotient of some c where cis the lie coalgebra associated to an associative coassociative coalgebra c every covered lie coalgebra satisfies the lie coidentities but as was shown by michaelis mill there exist lie coalgebras that do not arise as the quotient of any c thus covered lie coalgebras are a specific type of lie coalgebra this situation for lie coalgebras and covered lie coalgebras is somewhat parallel to the situation for jordan algebras and special jordan algebras we recall that a jordan algebra is an algebra that satisfies the jordan identities and a special jordan algebra is an algebra which arises as a subalgebra of an a a an associative algebra every special jordan algebra is a jordan algebra that is satisfies the identities but there exist jordan algebras which are not special for every vector space v one can construct the cofree lie coalgebra and the cofree covered lie coalgebra on v our main result theorem 1 will show that the canonical injective map from the cofree 431 0021 8693 88 3 00

driven steady states rules for transition rates abstract it is well known that transition rates in a canonical ensemble should respect the principle of detailed balance what are the equivalent constraints that apply in non equilibrium steady states implied by maximization of information entropy the exact theorem for the non equilibrium rates yields a substantial amount of non trivial physics illustrated in some examples including new results for a simple stochastic hopping model some of the implications for shear controlled phase transitions are discussed

sampling rare fluctuations of discrete time markov chains we describe a simple method that can be used to sample the rare fluctuations of discrete time markov chains we focus on the case of markov chains with well defined steady state measures and derive expressions for the large deviation rate functions and upper bounds on such functions for dynamical quantities extensive in the length of the markov chain we illustrate the method using a series of simple examples and use it to study the fluctuations of a lattice based model of active matter that can undergo motility induced phase separation

a general non iterative riemann solver for godunov s method abstract godunov s method is characterized by the use of a riemann problem solution to resolve discontinuities at the interface between cells the major drawback of this method is the difficulty and the high cost of solving the nonlinear riemann problem exactly especially for materials with complex equations of state this paper describes a simplified and noniterative approximate riemann solver which is characterized by only two material dependent parameters for a given material these parameters are the local speed of sound and a parameter which is directly related to the shock density ratio in the limit of strong shocks these parameters are conveniently obtained from a linear fit to the experimental data for the shock hugoniot in various materials the approximate riemann solver retains the essential quadratic nonlinearity which enables it to deal with the whole range of cases from weak sound waves to strong shocks

some facts of life abstract we study the statistics of the time evolution of the game of life we recognize three different time regimes of which the most interesting one is the long time glider regime which has properties typical of a critical state we introduce mean field approximations able to give some insights on the time evolution of the density of the density of living cells extended simulations are reported which deal with the evolution of the density damage spreading and the measurements of a finite size exponent a simple dynamical model explains some aspects of the asymptotic glider regime we study also the dependence of the asymptotic density on the initial density both analytically and numerically

pseudotime method for shape design of euler flows we exploit a novel idea for the optimization of flows governed by the euler equations the algorithm consists of marching on the design hypersurface while improving the distance to the state and costate hypersurfaces we consider the problem of matching the pressure distribution to a desired one subject to the euler equations for both subsonic and supersonic flows we limited our investigation to two dimensional test cases the rate of convergence to the minimum for the cases considered is three to four times slower than that of the analysis problem results are given for ringleb flow and a shockless compression case

an analysis of finite difference and finite volume formulations of conservation laws abstract finite difference and finite volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws a new coordinate free formulation of systems of conservation laws is developed which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system the analysis considers general types of equations potential euler and navier stokes three dimensional unsteady flows with time varying grids are described using a single consistent nomenclature for both formulations grid motion due to a non inertial reference frame as well as flow adaptation is covered in comparing the two formulations it is found useful to distinguish between differences in numerical methods and differences in grid definition the former plays a role for non cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled the differences in grid definition for the two formulations is found to be more important since it affects the manner in which boundary conditions zonal procedures and grid singularities are handled at computational boundaries the proper interpretation of strong and weak conservation law forms for quasi one dimensional and axisymmetric flows is brought out

information theory explanation of the fluctuation theorem maximum entropy production and self organized criticality in non equilibrium stationary states jaynes information theory formalism of statistical mechanics is applied to the stationary states of open non equilibrium systems first it is shown that the probability distribution p of the underlying microscopic phase space trajectories over a time interval of length satisfies p exp 2kb where is the time averaged rate of entropy production of three consequences of this result are then derived 1 the fluctuation theorem which describes the exponentially declining probability of deviations from the second law of thermodynamics as 2 the selection principle of maximum entropy production for non equilibrium stationary states empirical support for which has been found in studies of phenomena as diverse as the earth s climate and crystal growth morphology and 3 the emergence of self organized criticality for flux driven systems in the slowly driven limit the explanation of these results on general information theoretic grounds underlines their relevance to a broad class of stationary non equilibrium systems in turn the accumulating empirical evidence for these results lends support to jaynes formalism as a common predictive framework for equilibrium and non equilibrium statistical mechanics

assessing nonlinear structures in real exchange rates using recurrence plot strategies purchasing power parity ppp is an important theory at the basis of a large number of economic models however the implication derived from the theory that real exchange rates must follow stationary processes is not conclusively supported by empirical studies in a recent paper serletis and gogas appl finance econ 10 2000 615 show evidence of deterministic chaos in several oecd exchange rates as a consequence ppp rejections could be spurious in this work we follow a two stage testing procedure to test for nonlinearities and chaos in real exchange rates using a new set of techniques designed by webber and zbilut j appl physiol 76 1994 965 called recurrence quantification analysis rqa our conclusions differ slightly from serletis and gogas appl finance econ 10 2000 615 but they are also supportive of chaos for some exchange rates

numerical experiments with the osher upwind scheme for the euler equations the osher algorithm for solving the euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations a first order accurate version of the numerical method was derived by osher circa 1980 for the one dimensional non isentropic euler equations in cartesian coordinates in this paper the extension of the scheme to arbitrary two dimensional geometries is explained results are then presented for several example problems in one and two dimensions future work will include extension of the method to second order accuracy and the development of implicit time differencing for the osher algorithm

large deviations of the current for driven periodic diffusions we study the large deviations of the time integrated current for a driven diffusion on the circle often used as a model of nonequilibrium systems we obtain the large deviation functions describing the current fluctuations using a fourier bloch decomposition of the so called tilted generator and we also construct from this decomposition the effective biased auxiliary or driven markov process describing the diffusion as current fluctuations are observed in time this effective process provides a clear physical explanation of the various fluctuation regimes observed it is used here to obtain an upper bound on the current large deviation function which we compare to a recently derived entropic bound and to study the low noise limit of large deviations

quasi conservative lambda formulation the numerical simulation of inviscid transonic flows by means of a modified lambda formulation takes in to account the shock transition from supersonic to subsonic flow conditions thus allowing the coupling of the supersonic region with the shocked subsonic one and as a consequence the upstream movement of the shock the present methodology is applied to one and two dimensional transonic flows although the two dimensional flow calculations involve cartesian coordinates and are limited to the thin airfoil approximation the method can be generalized to arbitrary two and three dimensional flow cases in all of the computed cases the shock is found to have appropriate strength and position for steady flow conditions and to move upstream properly when a change in the downstream pressure warrants it a mono the several numerical methods developed for the jtjlnumerical simulation of transonic inviscid flows the so called lambda formulation recently developed and employed by moretti 1 and zannetti and colasurdo 2 has several very desirable features the time dependent compressible euler equations are recast in terms of compatibility conditions for characteristic riemann variables along characteristic lines and discretized by means of upwind differences which cor rectly take into account the direction of wave propagation in this way a numerical technique is obtained which com bines the coding simplicity of finite differ ence methods with the intrinsic accuracy and physical soundness of the method of characteristi cs since its first appearance the lambda formulation has undergone several improvements in particular various im plicit integration schemes3 5 and relaxation methods6 7 have been developed in order to enhance the efficiency of the lambda methodology by removing the courant friedrichs lewy cfl stability limitation of the explicit schemes previously employed also a significant improvement in ac curacy is achieved by employing a perturbative formula tion8 9 such that only the compressibility effects with respect to a suitable incompressible flow solution need to be computed the lambda formulation has its drawbacks in particular numerical experiments have shown that for one dimensional transonic flows the captured shock cannot move upstream in the supersonic flow region and that this problem persists in some cases for two dimensional transonic flows even if the supersonic bubble is embedded in a subsonic region which would be expected to allow for upstream propagation this drawback is due to the decoupling of the supersonic region from the subsonic one once the shock wave is established recently the flux difference splitting 10 1 3 which uses governing equations in conservation form and splits the fluxes according to the wave nature of the flow has been proposed to solve compressible inviscid flows a comparison of this methodology with the lambda formulation applied to a system of linear hyperbolic equations14 shows that they both lead to identical conclusions but an analysis of the flux difference splitting applied to the one dimensional euler equations demonstrates that it allows a coupling of the supersonic region with the shocked subsonic one by splitting the waves containing a sonic point i e a vertical characteristic in the x t plane such a situation occurs in those mesh intervals where the shock is numerically cap tured on the contrary this basic mechanism is neglected by the classical lambda formulation but it can be taken into ac count in order to obtain a modified lambda formulation characterized by a supersonic region coupled with the shocked subsonic one as done in the present paper the method will be first described for one dimensional flows of a test gas with a specific heat ratio equal to unity the method will then be extended to classical one dimen sional nonisentropic flows and finally to the case of nonhomentropic two dimensional flows within the frame work of thin airfoil theory the validity and usefulness of the modified lambda methodology will be demonstrated by means of a few example calculations

a contribution to the numerical prediction of unsteady flows methods based on flux differe nce splitting are investigated with reference to the prediction of unsteady compressible flows they combine the feature of taking into account the wake like nature of these flows and the capability of correctly capturing shock waves two recently proposed approaches and a third one suggested here are compared for one dimensional flow with particular reference to the means of operating the splitting they are extended to the cases of variable area ducts and a general transformation of the independent variables firstand second order accurate schemes are presented and procedures for the computation at the boundaries are shown finally numerical experiments are reported and discussed

upwind formulations for the euler equations in steady supersonic flows the euler equations that describe the steady supersonic flow can be reformulated in order to emphasize the role of propagating signals from such formulations upwind criteria are derived for the approximation of derivatives by finite differences formulations based on the quasilinear form and the divergence form of the governing equations are considered a numerical procedure based on these formulations is used as a tool for understanding the inviscid physics of the flow about a pointed cone at incidence the generation and development of embedded crossflow shocks and related spiral entropy singularities are investigated

large deviations of the dynamical activity in the east model analysing structure in biased trajectories we consider large deviations of the dynamical activity in the east model we bias this system to larger than average activity and investigate the structure that emerges to best characterize this structure we exploit the fact that there are effective interactions that would reproduce the same behaviour in an equilibrium system we combine numerical results with linear response theory and variational estimates of these effective interactions giving the first insights into such interactions in a many body system across a wide range of biases the system exhibits a hierarchy of responses to the bias remaining quasi equilibrated on short length scales but deviating far from equilibrium on large length scales we discuss the connection between this hierarchy and the hierarchical ageing behaviour of the system

contribution to the optimal shape design of two dimensional internal flows with embedded shocks we explore the praticability of optimal shape design for flows modeled by the euler equations we define a functional whose minimum represents the optimality condition the gradient of the functional with respect to the geometry is calculated with the lagrange multipliers which are determined by solving acostateequation the optimization problem is then examined by comparing the performance of several gradient based optimization algorithms in this formulation the flow field can be computed to an arbitrary order of accuracy finally some results for internal flows with embedded shocks are presented including a case for which the solution to the inverse problem does not belong to the design space

maximum entropy production and the fluctuation theorem recently the author used an information theoretical formulation of non equilibrium statistical mechanics maxent to derive the fluctuation theorem ft concerning the probability of second law violating phase space paths a less rigorous argument leading to the variational principle of maximum entropy production mep was also given here a more rigorous and general mathematical derivation of mep from maxent is presented and the relationship between mep and the ft is thereby clarified specifically it is shown that the ft allows a general orthogonality property of maximum information entropy to be extended to entropy production itself from which mep then follows the new derivation highlights mep and the ft as generic properties of maxent probability distributions involving anti symmetric constraints independently of any physical interpretation physically mep applies to the entropy production of those macroscopic fluxes that are free to vary under the imposed constraints and corresponds to selection of the most probable macroscopic flux configuration in special cases maxent also leads to various upper bound transport principles the relationship between maxent and previous theories of irreversible processes due to onsager prigogine and ziegler is also clarified in the light of these results

large deviations conditioned on large deviations i markov chain and langevin equation we present a systematic analysis of stochastic processes conditioned on an empirical observable q t defined in a time interval 0 t for large t we build our analysis starting with a discrete time markov chain results for a continuous time markov process and langevin dynamics are derived as limiting cases in the large t limit we show how conditioning on a value of q t modifies the dynamics for a langevin dynamics with weak noise and conditioned on q t we introduce large deviation functions and calculate them using either a wkb method or a variational formulation this allows us in particular to calculate the typical trajectory and the fluctuations around this trajectory when conditioned on a certain value of q t for large t

set of boundary conditions for aerodynamic design robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well posed problems a boundary condition should be robust and flexible numerical methodologies for the imposition of boundary conditions are required to formulate well posed problems a boundary condition should be nonreflecting to avoid spurious perturbations that can provocate unsteadiness or instabilities the reflectiveness of various boundary conditions is analyzed in the context of the godunov methods a nonlinear isentropic wave propagation model is used to investigate the reflection mechanism on the flowfield borders and a parameter is defined to give a measure of the boundary reflectiveness a new set of boundary conditions in which 0 that is totally nonreflecting is then proposed the approach has been integrated in an aerodynamic design procedure using a distributed boundary control