conformal invariance and critical dynamics the author discusses the behaviour of dynamic correlation functions under conformal transformations in particular the exact form of the dynamic scaling function at the critical point for an arbitrary isotropic two dimensional model is obtained with either conserved or nonconserved order parameter

critical phenomena at surfaces in a model of nonequilibrium phase transitions critical phenomena at surfaces are studied in a simple two dimensional model of non equilibrium phase transitions belonging to the class of interacting particle systems the mean field renormalization group approach and numerical simulations are used to determine the phase diagram for this system and some of the critical exponents associated with ordinary special extraordinary and surface phase transitions

an improved upwind scheme for the euler equations an implicit upwind scheme of almost second order accuracy is developed for solving the euler equations in a conservative form the scheme uses local eigenvalues to control spatial differencing a continuous transition function is introduced to replace the discontinuity when eigenvalue changes sign the introduction of the continuous transition function eliminates the possibility of capturing an expansion shock at sonic points due to the discontinuity since upwind differencing is naturally dissipative the stability and accuracy of the present algorithm is enhanced numerical results demonstrate that the present scheme is as accurate as the tvd scheme 1 and as efficient as other upwind scheme 2

dynamic correlations in domain growth a 1 n expansion the authors consider the dynamics of the n component ginzburg landau model with nonconserved order parameter model a following a quench from a high temperature equilibrium state to zero temperature the two time correlation function of the order parameter field is found in the 1 n expansion to have the asymptotic scaling form ck t t t d2 t t lambda 2 f k2t k2t for t t with f 0 0 constant the form of the new exponent lambda which is a non trivial function of n and d was given explicitly to o 1 n in a recent letter the purpose of this study is to present a more detailed account of the calculation leading to the o 1 n form for lambda they also examine the role of thermal fluctuations in the ordered phase and the effect of long range initial correlations on the ordering process

a monte carlo study of scaling and universality in 2d directed percolation monte carlo data for the pair correlation function is obtained on five different lattices for the directed percolation problem in two dimensions scaling is tested and found to hold beyond 20 lattice spacings for all models evidence is found to support the universality of the scaling function the values of the exponents gamma v sub and vperpendicular to v sub are extracted from the data the results for all models are summarised by gamma v sub 1 305 or 0 007 and vperpendicular to v sub 0 629 or 0 010 comparison is made with estimates derived by other means

on the identification of quasiprimary scaling operators in local scale invariance the relationship between physical observables defined in lattice models and the associated quasi primary scaling operators of the underlying field theory is revisited in the context of local scale invariance we argue that this relationship is only defined up to a time dependent amplitude and derive the corresponding generalizations of predictions for two time response and correlation functions applications to non equilibrium critical dynamics of several systems with a fully disordered initial state and vanishing initial magnetization including the glauber ising model the frederikson andersen model and the ising spin glass are discussed the critical contact process and the parity conserving non equilibrium kinetic ising model are also considered

upwind relaxation algorithms for the navier stokes equations analyse des erreurs de troncature de la differenciation spatiale et analyse de la stabilite de l algorithme de relaxation calcul pour une serie d ecoulements a l aide de la forme couche mince des equations calcul du decollement de couche limite induit par chocs

on some integral inequalities in n independent variables and their applications abstract using young s technique which is based on a riemann function we unify some inequalities of young and pachpatte in n independent variables we can use these inequalities in the analysis of a class of nonlinear hyperbolic partial integrodifferential equations to study the uniqueness boundedness continuous dependence comparison stability and numerical computations

efficient and robust reynolds stress model computation of three dimensional compressible flows thepurposeofthiswork isthedevelopmentofanefe cientand robustimplicitmethodology fortheintegration of the three dimensional compressible favre reynolds averaged navier stokes equations with near wall reynoldsstressclosure thee vemean e owandseventurbulencetransportequationsarediscretizedinspace ona structured multiblock grid using an o x 3 e nitevolumeupwind biased muscl schemewithvanleere ux vectorsplitting and van albada limiters time integration is based on an implicit dual time stepping procedure with alternating direction implicit subiterations a particular treatment of the approximate jacobians used in the subiterations substantiallydiminishesthecomputing timerequirementsoftheimplicitphase sothatthecomputationaloverhead of the reynolds stress seven equation closure compared to a two equation closure is less than 30 per iteration for steady e ow computations local time steps are used for both the subiterations and the time marching with courant friedrichs lewynumbersof o 10 20 fortheo 1 20 subiterationsneededand o 100 500 forthetime marching the robustness of the method is ensured by appropriate positivity boundedness and reynolds stress realizability constraints the numerical method is illustrated by computing and conducting numerical studies for a high subsonic m 0 7 three dimensional e ow with large separation and for a transonic three dimensional shock wave boundary layer interaction

a numerical method for solving the equations of compressible viscous flow although much progress has already been made in solving problems in aerodynamic design many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely this paper describes one such development a new method for solving these equations has been devised that 1 is second order accurate in space and time 2 is unconditionally stable 3 preserves conservation form 4 requires no block or scalar tridiagonal inversions 5 is simple and straightforward to program estimated 10 modification for the update of many existing programs 6 is more efficient than present methods and 7 should easily adapt to current and future computer architectures computational results for laminar and turbulent flows at reynolds numbers from 3 x 10 exp 5 to 3 x 10 exp 7 and at cfl numbers as high as 10 exp 3 are compared with theory and experiment

schrodinger invariance and strongly anisotropic critical systems the extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated for the special case of an anisotropy or dynamical exponent z 2 the group of local scale transformation considered is the schrodinger group which can be obtained as the nonrelativistic limit of the conformal group the requirement of schrodinger invariance determines the two point function in the bulk and reduces the three point function to a scaling form of a single variable scaling forms are also derived for the two point function close to a free surface which can be either spacelike or timelike these results are reproduced in several exactly solvable statistical systems namely the kinetic ising model with glauber dynamics lattice diffusion lifshitz points in the spherical model and critical dynamics of the spherical model with a nonconserved order parameter for generic values of evidence from higher order lifshitz points in the spherical model and from directed percolation suggests a simple scaling form of the two point function

near wall k e computation of transonic turbomachinery flows with tip clearance acomputational methodforthenumericalintegration ofthefavre reynolds averaged three dimensionalcompressible navier stokes equations in axial turbomachinery using the launder sharma near wall k turbulence closure is developed the mean e ow and turbulence transport equations are discretized using a e nite volume method based on muscl van leere ux vector splitting with van albada limiters and are integrated in time using a fully coupled approximately factored implicit backward euler method the resulting scheme is robust and was found stable for local time steps of courant friedrichs lewy number cfl 20 the computational domain is discretized using a basic h o h grid the tip clearance gap is discretized using a e ne o type grid the radial distribution ofnodeswithin thetip clearancegap is independent of theblade rowo grid and a bufferoverlap grid is used to convey information boundary conditions at periodicity boundaries and at domain interfaces are treated using e ve phantom nodes this procedure ensures stability at high cfl results are presented for the nasa 37 rotor at an operating point near surge computations are compared with measurements both for blade to blade mach number contours and pitchwise distributions and for radial distributions downstream of the blades results are obtained using three grids of 10 6 2 10 6 and 3 10 6 points with 21 31 and 41 radial stations within the tip clearancegap respectively demonstratingthatresultsaregridindependent comparisonwithmeasurementsis satisfactory with theexception of pressureratio overestimation due to unsatisfactory prediction ofe ow separation by the turbulence model

automorphisms and verma modules for generalized schrodinger virasoro algebras abstract let f be a field of characteristic 0 g an additive subgroup of f f satisfying g and 2 g we define a class of infinite dimensional lie algebras which are called generalized schrodinger virasoro algebras and denoted by gsv g in this paper the automorphism group and irreducibility of verma modules for gsv g are completely determined

bellman bihari integral inequalities in several independent variables abstract in this paper we unify certain types of integral inequalities which are established by bellman bihari deo and dhongade

theory of phase ordering kinetics the theory of phase ordering dynamics that is the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken symmetry phase is reviewed with the emphasis on recent developments interest will focus on the scaling regime that develops at long times after the quench how can one determine the growth laws that describe the time dependence of characteristic length scales and what can be said about the form of the associated scaling functions particular attention will be paid to systems described by more complicated order parameters than the simple scalars usually considered for example vector and tensor elds the latter are needed for example to describe phase ordering in nematic liquid crystals on which there have been a number of recent experiments the study of topological defects domain walls vortices strings and monopoles provides a unifying framework for discussing coarsening in these dia erent systems

on two dimensional directed percolation extended series expansions for the mean size and the first and second moments of the pair connectedness for both bond and site percolation on the directed square and triangular lattices have been obtained analysis based on differential approximants allows the critical percolation probabilities and exponents to be estimated and as a result the critical exponents are conjectured to be gamma 41 18 nu perpendicular to 79 72 and nu sub 26 15 scaling then gives beta 199 720 alpha 299 360 and delta 1839 199

a six vertex model as a diffusion problem derivation of correlation functions a cellular automaton which describes diffusion of particles with exclusion in one dimension is shown to be equivalent to a six vertex model on a critical line the arrow arrow correlation function of the six vertex model is calculated exactly on this line using a transfer matrix method

classification of finite irreducible conformal modules over a class of lie conformal algebras of block type abstract we classify finite irreducible conformal modules over a class of infinite lie conformal algebras b p of block type where p is a nonzero complex number in particular we obtain that a finite irreducible conformal module over b p may be a nontrivial extension of a finite conformal module over vir if p 1 where vir is a virasoro conformal subalgebra of b p as a byproduct we also obtain the classification of finite irreducible conformal modules over a series of finite lie conformal algebras b n for n 1

systems of multidimensional volterra integral equations and inequalities on obtient des bornes superieures explicites pour les solutions u x d equations integrales de volterra lineaires ou non lineaires on demontre des theoremes d existence globale

pseudo unsteady difference schemes for discontinuous solutions of steady state one dimensional fluid dynamics problems abstract this paper presents two unsteady difference schemes for one dimensional steady state shock solutions starting from the pseudo unsteady equations the so called explicit upwind scheme is actually an explicit forward time centered space difference scheme with an appropriate artificial viscosity term which depends on the directions of the characteristics this scheme considered as an iterative scheme has good convergence properties and leads to steady state numerical shocks each with at most one point of transition regardless of the position of the shock with respect to the mesh the mesh can be refined locally and computation continued locally to make the profile of the shock sharper to increase the rate of convergence the corresponding implicit scheme is presented results of numerical tests for a shock tube and a convergent divergent nozzle are given

super galilean conformal algebra in ads cft galilean conformal algebra gca is an inonu wigner iw contraction of a conformal algebra while newton hooke string algebra is an iw contraction of an anti de sitter ads algebra which is the isometry of an ads space it is shown that the gca is a boundary realization of the newton hooke string algebra in the bulk ads the string lies along the direction transverse to the boundary and the worldsheet is ads2 the one dimensional conformal symmetry so 2 1 and rotational symmetry so d contained in the gca are realized as the symmetry on the ads2 string worldsheet and rotational symmetry in the space transverse to the ads2 in adsd 2 respectively it follows from this correspondence that 32 supersymmetric gcas can be derived as iw contractions of superconformal algebras psu 2 2 4 osp 8 4 and osp 8 4 we also derive less supersymmetric gcas from su 2 2 2 osp 4 4 osp 2 4 and osp 8 2

more on symmetries of the schrodinger equation besides the usual and well known lie symmetries of the schrodinger equation the authors study higher order symmetry operators and point out their impact on classes of solvable potentials when time independent interactions take place for one dimensional space systems they consider the case of nth order symmetry operators and more particularly the third order context

cellular automata and statistical mechanical models we elaborate on the analogy between the transfer matrix of usual lattice models and the master equation describing the time development of cellular automata transient and stationary properties of probabilistic automata are linked to surface and bulk properties respectively of restricted statistical mechanical systems it is demonstrated that methods of statistical physics can be successfully used to describe the dynamic and the stationary behavior of such automata some exact results are derived including duality transformations exact mappings disorder and linear solutions many examples are worked out in detail to demonstrate how to use statistical physics in order to construct cellular automata with desired properties this approach is considered to be a first step toward the design of fully parallel probabilistic systems whose computational abilities rely on the cooperative behavior of their components

comparison results for multidimensional difference equations on compare les solutions u x de l equation aux differences non lineaire x u u x f x u x avec les solutions x et x des inegalites aux differences non lineaires correspondantes x n x f x x et x n x f x x