transparent acoustic source condition applied to the euler equations it can be concluded from the present calculations that the transparent source model proposed here is useful to numerically simulate an acoustic source in the computational domain that is located far downstream thus it is possible to simulate a complex acoustic problem such as the reflection and transmission of an incident wave

error estimation and adaptation for functional outputs in time dependent flow problems the paper presents an adjoint based approach for determining global error in the time domain that is relevant to functional outputs from unsteady flow simulations the algorithm is derived for the unsteady euler equations that are discretized for second order accuracy in both space and time and takes into account the effect of dynamic meshes in addition to error due to temporal resolution the formulation also takes into account algebraic error arising from partial convergence of the governing equations at each implicit time step the resulting error distributions are then used to drive adaptation of the temporal resolution and the convergence tolerances for the governing equations at each time step the method is demonstrated in the context of both time integrated and instantaneous functionals and the results are compared against traditional adaptation methods

multigrid acceleration of a high resolution computational aeroacoustics scheme a multigrid method is applied to a fourth order accurate spatially and temporally nite difference runge kutta time marching scheme thisisusedto solvethenonlineareulerequationsfortheef cientprediction ofnoise radiation from turbofan engine inlets this noise prediction approach computes a steady state solution rst and thenasourceisturnedonandtheunsteadysolutioniscomputed thishastheadvantageofusingthesamenumerical scheme to evaluate the residuals of the governing equations in both the steady and unsteady calculations which meansthatthesteady statesolutionissmoothand nonumericalerrorscontaminatetheacousticsolution thehigh

shock profiles for the asymmetric simple exclusion process in one dimension the asymmetric simple exclusion process asep on a one dimensional lattice is a system of particles which jump at rates p and 1 p here p 1 2 to adjacent empty sites on their right and left respectively the system is described on suitable macroscopic spatial and temporal scales by the inviscid burgers equation the latter has shock solutions with a discontinuous jump from left density rho to right density rho rho sqrt rho 1 rho rho 1 rho for a special value of the asymmetry given by p 1 p rho 1 rho rho 1 rho the measure is bernoulli with density rho on the left and rho on the right in the weakly asymmetric limit 2p 1 to0 the microscopic width of the shock diverges as 2p 1 1 the stationary measure is then essentially a superposition of bernoulli measures corresponding to a convolution of a density profile described by the viscous burgers equation with a well defined distribution for the location of the second class particle

bethe ansatz solution of zero range process with nonuniform stationary state the eigenfunctions and eigenvalues of the master equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the bethe ansatz weighted with the stationary weights of particle configurations the bethe ansatz applicability requires the rates of hopping of particles out of a site to be the q numbers n q this is a generalization of the rates of hopping of noninteracting particles equal to the occupation number n of a site of departure the noninteracting case can be restored in the limit q ensuremath rightarrow 1 the limiting cases of the model for q 0 ensuremath infty correspond to the totally asymmetric exclusion process and the drop push model respectively we analyze the partition function of the model and apply the bethe ansatz to evaluate the generating function of the total distance traveled by particles at large time in the scaling limit in case of nonzero interaction q ensuremath ne 1 the generating function has the universal scaling form specific for the kardar parizi zhang universality class

random walk of second class particles in product shock measures we consider shock measures in a class of conserving stochastic particle systems on these shock measures have a product structure with a step like density profile and include a second class particle at the shock position we show for the asymmetric simple exclusion process for the exponential bricklayers process and for a generalized zero range process that under certain conditions these shocks and therefore the second class particles perform a simple random walk some previous results including random walks of product shock measures and stationary shock measures seen from a second class particle are direct consequences of our more general theorem multiple shocks can also be handled easily in this framework similar shock structure is also found in a nonconserving model the branching coalescing random walk where the role of the second class particle is played by the rightmost or leftmost particle

doubly periodic solutions of the class i infinitely extended nonlinear schrodinger equation we present doubly periodic solutions of the infinitely extended nonlinear schrodinger equation with an arbitrary number of higher order terms and corresponding free real parameters solutions have one additional free variable parameter that allows one to vary periods along the two axes the presence of infinitely many free parameters provides many possibilities in applying the solutions to nonlinear wave evolution being general this solution admits several particular cases which are also given in this article

duality relations for asymmetric exclusion processes we derive duality relations for a class ofu q su 2 symmetric stochastic processes including among others the asymmetric exclusion process in one dimension like the known duality relations for symmetric hopping processes these relations express certainm point correlation functions inn particle systems n m in terms of sums of correlation functions of the same system but with onlym particles for the totally asymmetric case we obtain exact expressions for some boundary density correlation functions the dynamical exponent for these correlators isz 2 which is different from the dynamical exponent for bulk density correlations which is known to bez 3 2

broadband time domain impedance models the modeling of a set of impedance values given either experimentally or heuristically for implementation as a time domain impedance equivalent boundary condition tdibc is discussed it is shown that impedance as defined by the reflection of plane harmonic waves when extended for broadband time domain applications can correspond to mathematically feasible but physically unacceptable noncausal reflection processes given a set of impedance data on a finite positive and real frequency range it is possible to construct causal time domain models that render efficient implementation of tdibc for broadband reflections however these models defined by measurement of harmonic waves may not be valid for the reflection of impulses for which measurement of transient reflections is warranted

application of a nonlinear computational aeroacoustics code to the gust airfoil problem a time domain solution of the gust airfoil problem is obtained using a high accuracy computational aeroacoustics code to solve the nonlinear euler equations for computational efficiency the equations are cast in chain rule curvilinear form and a structured multiblock solver is used on a distributed memory parallel computer cluster to fully investigate the performance of this solver a test matrix of benchmark problems is computed two airfoil geometries and four gust reduced frequencies these results are compared to benchmark solutions both on the airfoil surface and in the flow domain

design of broadband time domain impedance boundary conditions using the oscillatory diffusive representation of acoustical models a methodology to design broadband time domain impedance boundary conditions tdibcs from the analysis of acoustical models is presented the derived tdibcs are recast exclusively as first order differential equations well suited for high order numerical simulations broadband approximations are yielded from an elementary linear least squares optimization that is for most models independent of the absorbing material geometry this methodology relies on a mathematical technique referred to as the oscillatory diffusive or poles and cuts representation and is applied to a wide range of acoustical models drawn from duct acoustics and outdoor sound propagation which covers perforates semi infinite ground layers as well as cavities filled with a porous medium it is shown that each of these impedance models leads to a different tdibc comparison with existing numerical models such as multi pole or extended helmholtz resonator provides insights into their suitability additionally the broadly applicable fractional polynomial impedance models are analyzed using fractional calculus

statistical inference method for liner impedance eduction with a shear grazing flow this paper presents a statistical inference method for impedance eduction in a flow duct facility the acoustic impedance is recast into a random variable and bayes s theorem is used to obtain the

implicit solution of the unsteady euler equations for high order accurate discontinuous galerkin discretizations efficient solution techniques for high order accurate time dependent problems are investigated for solving the two dimensional non linear euler equations in this work the spatial discretization consists of a high order accurate discontinuous galerkin dg approach implicit time integration techniques are considered exclusively in order to avoid the stability restrictions of explicit methods standard backwards differencing methods bdf1 and bdf2 as well as a second order crank nicholson cn2 and a fourth order implicit runge kutta irk4 scheme are considered in an attempt to balance the spatial and temporal accuracy of the overall approach the implicit system arising at each time step is solved using a p multigrid approach which is shown to produce h independent convergence rates while remaining relatively insensitive to the time step size the crank nicholson methodology although not l stable demonstrates superior performance compared to the bdf2 scheme for the problems chosen in this work however the fourth order accurate implicit runge kutta scheme is found to be the most efficient in terms of computational cost for a given accuracy level as compared to the lower order schemes in spite of the added cost per time step and the benefits of this scheme increase for tighter error tolerances

microscopic shape of shocks in a domain growth model considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities e g the inviscid burgers equation for the simple exclusion process the physical solutions of these partial differential equations develop discontinuities called shocks the microscopic structure of these shocks is of much interest and far from being well understood we introduce a domain growth model in which we find a stationary in time product measure for the model as seen from a defect tracer or second class particle traveling with the shock we also show that under some natural assumptions valid for a wider class of domain growth models no other model has stationary product measure as seen from the moving defect tracer

on the robust flexible and consistent implementation of time domain impedance boundary conditions for compressible flow simulations the accurate simulation of compressible flows requires the appropriate modeling of the reflection of acoustic waves at the boundaries in the present study we discuss time domain impedance boundary conditions tdibc the formulation proposed allows to impose a desired reflection coefficient at the inflow and outflow boundaries our formulation is an extension of the well known navier stokes characteristic boundary conditions the frequency dependent reflections at the boundaries are implemented with a state space model in the time domain we provide a comprehensive discussion on how such state space models can be constructed and interpreted this discussion shows that the state space description allows a robust and flexible implementation it allows to consider complex reflection coefficients and account for non constant cfd time steps in a straight forward manner furthermore we prove analytically and demonstrate numerically that the formulation proposed is consistent i e the formulation ensures that the flow simulation exhibits the reflection coefficient imposed accurately as long as the waves impinging on the boundary are plane and it prohibits drift of the mean flow variables finally the boundary conditions are tested successfully for laminar and turbulent flows

self duality for the two component asymmetric simple exclusion process we study a two component asymmetric simple exclusion process asep that is equivalent to the asep with second class particles we prove self duality with respect to a family of duality functions which are shown to arise from the reversible measures of the process and the symmetry of the generator under the quantum algebra uq x1d524 x1d529 3 we construct all invariant measures in explicit form and discuss some of their properties we also prove a sum rule for the duality functions

euler hydrodynamics of one dimensional attractive particle systems we consider attractive irreducible conservative particle systems on z without necessarily nearest neighbor jumps or explicit invariant measures we prove that for such systems the hydrodynamic limit under euler time scaling exists and is given by the entropy solution to some scalar conservation law with lipschitz continuous flux our approach is a generalization of bahadoran et al stochastic process appl 99 2002 1 30 from which we relax the assumption that the process has explicit invariant measures

discontinuous galerkin methods with plane waves for time harmonic problems a general framework for discontinuous galerkin methods in the frequency domain with numerical flux is presented the main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element the method is formulated for a general system of linear hyperbolic equations and is applied to problems of aeroacoustic propagation by solving the two dimensional linearized euler equations it is found that the method requires only a small number of elements per wavelength to obtain accurate solutions and that it is more efficient than high order drp schemes in addition the conditioning of the method is found to be high but not critical in practice it is shown that the ultra weak variational formulation is in fact a subset of the present discontinuous galerkin method a special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles aeroacoustic problems with non uniform flows are also considered and results are presented for the sound radiated from a two dimensional jet

frequency domain prediction of turbofan noise radiation this paper describes a frequency domain numerical method for predicting noise radiation from ducted fans including acoustic treatment and non uniform background flow effects the method solves the euler equations linearized about a mean flow in the frequency domain a pseudo time derivative term is added to the frequency domain equations so that a time marching technique can be employed to drive the acoustic field to steady state explicitly this approach makes distributed parallel computing more viable for equations of this type and will allow for future use of well known convergence acceleration techniques such as multigrid to obtain the solutions efficiently simulations of the jt15d static test inlet are performed including the effects of liners and the results are compared with experimental data a generic engine geometry is used for demonstrating further the prediction capability of the code calculating the attenuation effects of different liner impedances and liner installation locations on the radiated sound fields

a p multigrid discontinuous galerkin method for the euler equations on unstructured grids a p multigrid p polynomial degree discontinuous galerkin method is presented for the solution of the compressible euler equations on unstructured grids the method operates on a sequence of solution approximations of different polynomial orders a distinct feature of this p multigrid method is to use different time integration schemes on different approximation levels resulting in an accurate fast and low memory method that can be used to accelerate the convergence of the euler equations to a steady state for discontinuous galerkin methods the developed method is used to compute the compressible flows for a variety of test problems on unstructured grids the numerical results obtained strongly indicate the order independent property of this p multigrid method an overall speed up factor more than one order of magnitude for both second and third order solutions of all test cases in comparison with the explicit method is demonstrated

the riemann problem method for solving a perturbed nonlinear schrodinger equation describing pulse propagation in optic fibres we used the riemann problem method with a 3 3 matrix system to find the femtosecond single soliton solution for a perturbed nonlinear schrodinger equation which describes bright ultrashort pulse propagation in properly tailored monomode optical fibres compared with the gel fand levitan marchenko approach the major advantage of the riemann problem method is that it provides the general single soliton solution in a simple and compact form unlike the standard nonlinear schrodinger equation here the single soliton solution exhibits periodic evolution patterns

multiple shocks in bricklayers model in bricklayers model which is a generalization of the misanthrope processes we show that a nontrivial class of product distributions is closed under the time evolution of the process this class also includes measures fitting to shock data of the limiting pde in particular we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting in an attractive way via their jump rates our results are related to those of belitsky and schutz 4 on the simple exclusion process although we do not use quantum formalism as they do the structures we find are described from a fixed position similar ones were found in balazs 2 valak as seen from the random position of the second class particle

a posteriori error bounds and global error control for approximation of ordinary differential equations the author analyzes a finite element method for the integration of initial value problems in ordinary differential equations general and contractive problems are treated and quasi optimal a priori and a posteriori error bounds obtained in each case in particular good results are obtained for a class of stiff dissipative problems these results are used to construct a rigorous and robust theory of global error control the author also derives an asymptotic error estimate that is used in a discussion of the behavior of the error in conclusion the properties of the error control are exhibited in a series of numerical experiments

lie symmetries of a generalised nonlinear schrodinger equation i the symmetry group and its subgroups the symmetry group of the generalised non linear schrodinger equation i psi t delta psi a0 psi a1 mod psi mod 2 psi a2 mod psi mod 4 psi in three space dimensions is shown to be the extended galilei group g 3 for a1a2 not 0 and the galilei similitude group gd 3 including a dilation for a1 oor a2 0 all lie subgroups of g 3 and gd 3 are found they will be used in a subsequent paper to obtain group invariant solutions of the equation

fundamental problems with the model of uniform flow over acoustic linings abstract the walls of ducts containing flow are often acoustically lined in order to reduce sound many simple models of acoustic linings assume the lining to be linear and locally reacting examples considered here include the three parameter mass spring damper helmholtz resonator and enhanced helmholtz resonator models all of these models have been found to have stability issues with uniform mean grazing flow and there has been some confusion over the existence of hydrodynamic instability surface waves over such linings mathematically the standard proven briggs bers stability analysis is not applicable computationally the hydrodynamic modes are routinely ignored in the frequency domain and instabilities filtered out in the time domain this confusion also causes significant problems for mode matching green functions and scattering analyses in this paper it is shown that any situation not capable of being analysed using the briggs bers criterion is illposed and that this is the root cause of the confusion over hydrodynamic instabilities a large class of lining models including all those mentioned above are shown to be illposed with uniform mean flow an explanation is given of the effects of this illposedness in practice and it is argued that illposed models should not be used an alternative stability criterion to briggs bers has been occasionally used in the literature this alternative criterion involving analytic continuation to purely imaginary frequencies was recently christened the crighton leppington stability criterion however this stability criterion is incorrect and several counter examples are given here

discrete adjoint based approach for optimization problems on three dimensional unstructured meshes a comprehensive strategy for developing and implementing discrete adjoint methods for aerodynamic shape optimization problems is presented by linearizing each procedure in the entire optimization problem transposing each linearization and reversing the sequential order of operations the adjoint of the complete optimization problem including flow equations and mesh motion equations is constructed in a modular and verifiable fashion this construction is also shown to produce minimal memory overheads and retain the same convergence characteristics of the original analysis problem in the sensitivity analysis these techniques are implemented in a three dimensional unstructured multigrid navierstokes solver and demonstrated on a transonic drag reduction problem for a wing body configuration

time domain numerical simulation of a flow impedance tube an efficient method has been developed for the application of the surface acoustic impedance condition in time domain solutions of aeroacoustic problems such as the broadband frequency simulation of a flow impedance tube the basis for this method is the standard impedance condition stated in the frequency domain as the particle displacement continuity equation the development of the time domain impedance condition follows the relations among the frequency z and discrete time domains and a rational function representation of the impedance in thez domain the resultant impedance condition consists of finite infinite impulse response type digital filter operations in the time domain which is very suitable to computational aeroacoustics algorithms this paper describes the present approach and discusses the time domain numerical simulations of the nasa langley flow impedance tube with a constant depth ceramic tubular liner both single and broadband frequency simulations are performed excellent agreement is shown with experimental data at various frequencies and flow conditions

a controllable canonical form implementation of time domain impedance boundary conditions for broadband aeroacoustic computation a new method which can be effectively and efficiently applied in the simulations of broadband noise problems is proposed for time domain impedance boundary condition implementations by using the so called controllable canonical form that is well known in linear system usually the impedance boundary condition can be defined in frequency domain as a rational polynomial function with poles in the negative half of the complex plane to guarantee stability otherwise causality might be violated in the corresponding time domain implementation to address this issue various methodologies have been proposed previously that usually lead to complicated polynomials whose numerical implementations are often indirect and intricate the proposed method with a controllable canonical form on the other hand directly transforms the frequency domain transfer function a quotient of rational polynomials to an equivalent state space model which consists of a series of first order ordinary differential equations that can be numerically implemented in a straightforward way the proposed method is demonstrated by using two benchmark problems a two dimensional gaussian pulse propagating in a uniform flow with a lined wall and the test cases from the nasa langley grazing incidence tube experiments good agreements demonstrate the potential of the proposed computational method

lie symmetries of a generalised non linear schrodinger equation ii exact solutions for pt i see ibid vol 21 p 1493 1988 the authors obtain group invariant solutions of the non linear equation i psi t delta psi a0 psi a1 psi mod psi mod 2 a2 psi mod psi mod 4 for which the symmetry group was previously shown to be the extended galilei group for a1a2 not 0 and the extended galilei similitude group for a1 0 or a2 0 they use the symmetry subgroups to reduce the equation to ordinary differential equations which are solved whenever possible with the help of a singularity analysis solutions are obtained in terms of elementary functions jacobi elliptic functions and painleve transcendents

broadband impedance boundary conditions for the simulation of sound propagation in the time domain an accurate and practical surface impedance boundary condition in the time domain has been developed for application to broadband frequency simulation in aeroacoustic problems to show the capability of this method two kinds of numerical simulations are performed and compared with the analytical experimental results one is acoustic wave reflection by a monopole source over an impedance surface and the other is acoustic wave propagation in a duct with a finite impedance wall both single frequency and broadband frequency simulations are performed within the framework of linearized euler equations a high order dispersion relation preserving finite difference method and a low dissipation low dispersion runge kutta method are used for spatial discretization and time integration respectively the results show excellent agreement with the analytical experimental results at various frequencies the method accurately predicts both the amplitude and the phase of acoustic pressure and ensures the well posedness of the broadband time domain impedance boundary condition

efficient implementation of tam and auriault s time domain impedance boundary condition a new and efficient time domain implementation is proposed for the impedance model originally introduced by tam and auriault tam c k w and auriault l time domain impedance boundary conditions for computational aeroacoustics aiaa journal vol 34 no 5 may 1996 pp 917 923 in the frequency domain the pressure can be calculated from the product of the impedance with the normal velocity in the time domain a convolution is needed which may become a costly operation present solutions for this problem involve either a full convolution and storage of a time history of data or a translation of the frequency domain models to time domain formulations involving time derivatives the former approach is very costly in terms of memory and cpu time the latter makes the implementation discretization specific and vulnerable to stability issues a new formulation based on recursive convolution results in an efficient implementation that stores only one accumulator which can be updated at each time step with minimal addition and multiplication it allows for the exact representation of the impedance at a given frequency the formulation is validated by a comparison with the measurement data from the nasa langley grazing flow impedance tube the simulations are performed by introducing a plane wave at a single frequency in the tube and this is done for six frequencies and five different mean flow speeds

critical behaviour in aperiodic systems the author considers layered systems with aperiodically modulated couplings and study the effect of inhomogeneity on the critical behaviour using scaling arguments a relevance irrelevance type criterion is formulated and for relevant inhomogeneities the scaling form of singular quantities is determined the author has performed exact calculations for the surface magnetization of aperiodic quantum ising chains and for a 1 1 dimensional directed polymer in a longitudinal aperiodic environment the results for both systems are in accord with scaling considerations for a marginal aperiodicity the critical exponents are found to be non universal

exact travelling wave solutions for a generalized nonlinear schrodinger equation a wide class of exact travelling wave solutions of a generalized nonlinear schrodinger equation gnls is obtained and analysed in detail this class of solutions incorporates bright and dark solitary waves periodic waves unbounded waves and other solitary waves as asymptotic limits of the periodic or unbounded modes the method of analysis adopted is based on reducing the gnls to an ordinary differential equation and studying the phase plane of the resulting dynamical system application of the obtained results to the problem of propagation of femtosecond duration pulses in nonlinear optical fibres is also discussed

existence of the zero range process and a deposition model with superlinear growth rates we give a construction of the zero range and bricklayers processes in the totally asymmetric attractive case the novelty is that we allow jump rates to grow exponentially earlier constructions have permitted at most linearly growing rates we also show the invariance and extremality of a natural family of i i d product measures indexed by particle density extremality is proved with an approach that is simpler than existing ergodicity proofs

a finite difference frequency domain numerical scheme for the solution of the gust response problem abstract a numerical method is developed for solving subsonic flows with convected three dimensional vortical waves around lifting airfoils the first order method that is presented fully accounts for the distortion effects of the nonuniform mean flow on the convected vorticity the unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the lagrangian coordinates of the mean flow and an irrotational field whose potential satisfies a nonconstant coefficient inhomogeneous convective wave equation using an elliptic coordinate transformation the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the mach number and reduced frequency extensive comparisons are made with known solutions to unsteady vortical flow problems and it is seen that the agreement is in general very good for reduced frequencies ranging from zero to four

high degree efficient symmetrical gaussian quadrature rules for the triangle gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method a brief review of existing quadrature rules for the triangle is given and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed new quadrature rules of degree 12 20 are presented and a short fortran program is included

adjoint sensitivity formulation for discontinuous galerkin discretizations in unsteady inviscid flow problems this paper presents an unsteady discrete adjoint algorithm for high order implicit discontinuous galerkin discretizations in time dependent inviscid flow problems the major function of the adjoint approach is to obtain the sensitivity information in a time dependent functional output which in turn is used to drive an unsteady shape optimization process to deliver a minimum of the objective functional a gradient based optimization strategy is investigated in which the sensitivity derivatives of the objective functional with respect to input variables are formulated in the context of high order discontinuous galerkin discretizations while special emphasis is given to the variations and linearizations of curvilinear boundary elements implicit temporal discretizations consisting of a second order backward euler scheme and a fourth order implicit runge kutta scheme are considered exclusively in this work where the corresponding adjoint problem is required to be solved in a backward time integration manner due to the associated transpose operation two numerical examples for the unsteady shape design techniques are presented to verify the derived sensitivity formulations and to demonstrate the performance of the adjoint approach the first involves an inverse shape optimization case by matching a time dependent target pressure profile for a two dimensional periodic vortical gust impinging on a rae 2822 airfoil and the second considers minimization of the acoustic noise produced by subsonic flow over a naca0012 airfoil with a 0 03c thick blunt trailing edge

from duality to determinants for q tasep and asep we prove duality relations for two interacting particle systems the q deformed totally asymmetric simple exclusion process q tasep and the asymmetric simple exclusion process asep expectations of the duality functionals correspond to certain joint moments of particle locations or integrated currents respectively duality implies that they solve systems of odes these systems are integrable and for particular step and half stationary initial data we use a nested contour integral ansatz to provide explicit formulas for the systems solutions and hence also the moments we form laplace transform like generating functions of these moments and via residue calculus we compute two different types of fredholm determinant formulas for such generating functions for asep the first type of formula is new and readily lends itself to asymptotic analysis as necessary to reprove gue tracy widom distribution fluctuations for asep while the second type of formula is recognizable as closely related to tracy and widom s asep formula comm math phys 279 2008 815 844 j stat phys 132 2008 291 300 comm math phys 290 2009 129 154 j stat phys 140 2010 619 634 for q tasep both formulas coincide with those computed via borodin and corwin s macdonald processes probab theory related fields 2014 158 225 400 both q tasep and asep have limit transitions to the free energy of the continuum directed polymer the logarithm of the solution of the stochastic heat equation or the hopf cole solution to the kardar parisi zhang equation thus q tasep and asep are integrable discretizations of these continuum objects the systems of odes associated to their dualities are deformed discrete quantum delta bose gases and the procedure through which we pass from expectations of their duality functionals to characterizing generating functions is a rigorous version of the replica trick in physics

stabilization of time domain acoustic boundary element method for the interior problem with impedance boundary conditions the time domain boundary element method bem is associated with numerical instability that typically stems from the time marching scheme in this work a formulation of time domain bem is derived to deal with all types of boundary conditions adopting a multi input multi output infinite impulse response structure the fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter which can also invoke a modeling error in the calculation the response at each time step is projected onto the wave vector space of natural radiation modes which can be obtained from the eigensolutions of the single iterative matrix to stabilize the computation unstable oscillatory modes are nullified and the same decay rate is used for two nonoscillatory modes as a test example a transient sound field within a partially lined parallelepiped box is used within which a point source is excited by an octave band impulse in comparison with the results

time domain impedance boundary conditions for computational aeroacoustics it is an accepted practice in aeroacoustics to characterize the properties of an acoustically treated surface by a quantity known as impedance impedance is a complex quantity as such it is designed primarily for frequency domain analysis time domain boundary conditions that are the equivalent of the frequency domain impedance boundary condition are proposed both single frequency and model broadband time domain impedance boundary conditions are provided it is shown that the proposed boundary conditions together with the linearized euler equations form well posed initial boundary value problems unlike ill posed problems they are free from spurious instabilities that would render time marching computational solutions impossible

parallel computation of forward radiated noise of ducted fans with acoustic treatment forward radiated noise of ducted fans is computed numerically on parallel processors solving the three dimensional time dependent euler equations in body conformed coordinates with a fourth order accurate finite difference runge kutta time integration scheme sound attenuation effects of inlet wall acoustic treatment are included in computations employing a time discrete form of the standard impedance condition a distributed computing approach with domain decomposition is used for integrating the equations in parallel using the message passing interface library routines the abilities of the method are demonstrated with hard and soft wall simulations of the jt15d inlet including flow effects

hp adaptive discontinuous galerkin finite element methods for first order hyperbolic problems we consider the a posteriori error analysis of hp discontinuous galerkin finite element approximations to first order hyperbolic problems in particular we discuss the question of error estimation for linear functionals such as the outflow flux and the local average of the solution based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance this involves exploiting both local polynomial degree variation and local mesh subdivision the theoretical results are illustrated by a series of numerical experiments

time domain numerical computation of noise reduction by diffraction and finite impedance of barriers a new time domain numerical method is presented for the estimation of noise reduction by the diffraction and finite impedance of barriers high order finite difference schemes conventionally used for computational aeroacoustics and time domain impedance boundary conditions are utilized for the development of the time domain method compared with other methods this method can be applied more easily to the problems related to nonlinear noise propagation such as impulsive noise and broadband noise linearized euler equations in cartesian co ordinates are considered and solved numerically straight and t shaped barriers with and without surface admittance are calculated in order to assess the accuracy of this time domain method comparison with the results of sysnoise software ver 5 3 are made there are very good agreements between the results of the present time domain numerical method and the boundary element method of the sysnoise software

a finite element propagation model for extracting normal incidence impedance in nonprogressive acoustic wave fields a propagation model method for extracting the normal incidence impedance of an acoustic material installed as a finite length segment in a wall of a duct carrying a nonprogressive wave field is presented the method recasts the determination of the unknown impedance as the minimization of the normalized wall pressure error function a finite element propagation model is combined with a coarse fine grid impedance plane search technique to extract the impedance of the material results are presented for three different materials for which the impedance is known for each material the input data required for the prediction scheme were computed from modal theory and then contaminated by random error the finite element method reproduces the known impedance of each material almost exactly for random errors typical of those found in many measurement environments thus the method developed here provides a means for determining the impedance of materials in a nonprogressive wave environment such as that usually encountered in a commercial aircraft engine and in most laboratory settings

exact shock measures and steady state selection in a driven diffusive system with two conserved densities we study driven 1d lattice gas models with two types of particles and nearest neighbor hopping we find the most general case when there is a shock solution with a product measure which has a density profile of a step function for both densities the position of the shock performs a biased random walk we calculate the microscopic hopping rates of the shock we also construct the hydrodynamic limit of the model and solve the resulting hyperbolic system of conservation laws in case of open boundaries the selected steady state is given in terms of the boundary densities

investigation of straightforward impedance eduction in the presence of shear flow abstract a straightforward impedance eduction method is proposed which combines prony s method with the pridmore brown equation to obtain the impedance of acoustic liners in the presence of shear flow particular attention is paid to the reported inconsistency problems associated with the boundary layer effect in the development of impedance eduction techniques a kind of flow insensitive acoustic liner is considered which is placed in a rectangular flow duct containing predominant grazing incidence mode three slip or no slip flow profiles are examined which are the parabola the one seventh power law and the uniform core flow with linear boundary layer a shear flow fem model is also set up to simulate the duct acoustic field the present impedance eduction method has been tested and validated using both the simulated and the published measured data it is shown that despite of their distinct boundary layers the selected flow profiles lead to essentially the same impedance results and also for the impedance eduction the strict consideration of no slip shear flow is very consistent with the use of the ingard myers boundary condition with the uniform flow assumption over the test conditions although not susceptible to the exact shape of flow profile the impedance eduction critically depends on the determination of the cross sectional average mach number the usual practice of approximately representing the duct flow with the midspan profile results in a slight overestimation of the average mach number in the two dimensional acoustic models and thus can considerably affect the accuracy of the impedance eduction to solve this problem the average flow profile is introduced to account for the actual three dimensional flow non uniformity in the rectangular duct it is further found that the effective mach number corresponding to a slightly modified average flow profile can be used to achieve a considerable collapse of the impedance spectra educed at different mach numbers based on the new evaluation of the influence of boundary layer profile the fem simulation using the straightforwardly educed impedance as the boundary condition can achieve an excellent agreement with the benchmark data for the complex sound pressure in the flow duct

oscillatory solitons of u 1 invariant modified korteweg de vries equations ii asymptotic behavior and constants of motion the hirota equation and the sasa satsuma equation are u 1 invariant integrable generalizations of the modified korteweg de vries equation these two generalizations admit oscillatory solitons which describe harmonically modulated complex solitary waves parameterized by their speed modulation frequency and phase depending on the modulation frequency the speeds of oscillatory waves 1 solitons can be positive negative or zero in contrast to the strictly positive speed of ordinary solitons when the speed is zero an oscillatory wave is a time periodic standing wave oscillatory 2 solitons with non zero wave speeds are shown to describe overtake collisions of a fast wave and a slow wave moving in the same direction or head on collisions of two waves moving in opposite directions when one wave speed is zero oscillatory 2 solitons are shown to describe collisions in which a moving wave overtakes a standing wave an asymptotic analysis using moving coordinates is carried out to show that in all collisions the speeds and modulation frequencies of the individual waves are preserved while the phases and positions undergo a shift such that the center of momentum of the two waves moves at a constant speed the primary constants of motion as well as some other features of the nonlinear interaction of the colliding waves are discussed

energy analysis and discretization of nonlinear impedance boundary conditions for the time domain linearized euler equations time domain impedance boundary conditions tdibcs can be enforced using the impeda nce the admittance or the scattering operator this article demonstrates the computational advantage of the last even for nonlinear tdibcs with the linearized euler equations this is achieved by a systematic semi discrete energy analysis of the weak enforcement of a generic nonlinear tdibc in a discontinuous galerkin finite element method in particular the analysis highlights that the sole definition of a discrete model is not enough to fully define a tdibc to support the analysis an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube then the derivation of time delayed broadband tdibcs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners a high order discretization of the derived time local formulation which consists in composing a set of ordinary differential equations with a transport equation is applied to two flow ducts

treatment of frequency dependent admittance boundary conditions in transient acoustic finite infinite element models the paper addresses the handling of frequency dependent local admittance boundary conditions in acoustic transient finite infinite element models the proposed approach avoids the evaluation of a convolution integral along the related boundary based on a similar technique developed in an aeroacoustic finite difference context the spatially local boundary condition is rewritten in a discrete form that involves normal accelerations and pressure time derivatives at the current time step and few steps before the incorporation of such a discrete in time boundary condition in a finite infinite element context is addressed the infinite element scheme selected for that purpose relies on the conjugated astley leis formulation implementation aspects cover the handling of frequency dependent boundary conditions along both finite and infinite element edges numerical examples waveguide single source in a half space bounded by an impedance plane diffraction by an acoustically treated screen are presented in order to demonstrate the efficiency of the proposed approach

orthogonal stochastic duality functions from lie algebra representations we obtain stochastic duality functions for specific markov processes using representation theory of lie algebras the duality functions come from the kernel of a unitary intertwiner between representations which provides generalized orthogonality relations for the duality functions in particular we consider representations of the heisenberg algebra and mathfrak su 1 1 both cases lead to orthogonal self duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes

oscillatory solitons of u 1 invariant mkdv equations i envelope speed and temporal frequency harmonically modulated complex solitary waves which are a generalized type of envelope soliton herein called oscillatory solitons are studied for the two u 1 invariant integrable generalizations of the modified korteweg de vries equation given by the hirota equation and the sasa satsuma equation a bilinear formulation of these two equations is used to derive the oscillatory 1 soliton and 2 soliton solutions which are then written out in a physical form parameterized in terms of their speed modulation frequency and phase depending on the modulation frequency the speeds of oscillatory waves 1 solitons can be positive negative or zero in contrast to the strictly positive speed of ordinary solitons when the speed is zero an oscillatory wave is a time periodic standing wave properties of the amplitude and phase of oscillatory 1 solitons are derived oscillatory 2 solitons are graphically illustrated to describe collisions between two oscillatory 1 solitons in the case when the speeds are distinct in the special case of equal speeds oscillatory 2 solitons are shown to reduce to harmonically modulated breather waves

frequency dependent fdtd methods using z transforms the frequency dependent finite difference time domain method fd sup 2 td method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent however as researchers search for more elaborate applications the formulation of the fd sup 2 td methods becomes more complex in this work the mathematics of the fd sup 2 td method is developed using z transform theory this has the advantages of presenting a clearer formulation and allowing researchers to draw on the literature of systems analysis and signal processing disciplines

impedance and its time domain extensions the classical concept of impedance as a means to characterize the ree ectivity and absorption of a surface to the incident waves has always been a complex valued quantity akin to plane harmonic waves and the analysis of their ree ections a new look at this classical quantity irrespective of the type of incident waves is presented it points out that a direct operational inversion of impedance into time domain boundary operators will in general lead to an unstable system whereas the inversion of the corresponding ree ection coefe cient will result in stable easily implementable boundary operators for time domain prediction of wave ree ection it reveals the equivalent pulselike causal process of time convoluting the incident wave into the ree ected wave excellent agreement with analytical solutions derived here and from other sources supports the validity of the approach and demonstrates the accuracy of the implementations

an adjoint based method for liner impedance eduction validation and numerical investigation abstract an inverse method for liner acoustic impedance eduction in a duct is presented the determination of adjoint equations allows to make explicit the directional derivatives of the objective function needed by the search algorithm direct and adjoint system of equations are spatially discretized by a discontinuous galerkin scheme the propagation model and the eduction process are successfully validated on nasa benchmark data extracted from literature in a no flow configuration objective functions written in terms of acoustic pressure and acoustic velocity are considered successively special attention is given to the possibilities offered by the method such as multiparameter identification with the study of a non homogeneous liner convergence history of the process is also examined revealing interesting properties for the velocity based objective function compared to the pressure based objective function in further developments the method is planned to be used with acoustic velocity fields obtained by laser doppler velocimetry

q zero range has random walking shocks but no other surprises in the zero range world we check all nearest neighbour 1 dimensional asymmetric zero range processes for random walking product shock measures as demonstrated already for a few cases in the literature we find the totally asymmetric version of the celebrated q zero range process as the only new example besides an already known model of doubly infinite occupation numbers and exponentially increasing jump rates we also examine the interaction of shocks which appears somewhat more involved for q zero range than in the already known cases

prefactored small stencil compact schemes abstract a new type of prefactored compact schemes is presented that obtains high order accuracy while using a very small stencil size these schemes require fewer boundary stencils and offer simpler boundary condition implementation than the existing compact schemes results are shown for linear and nonlinear 1 d benchmark problems and a 2 d linear benchmark problem boundary stencils for both exterior and interior multiblock boundaries are given and boundary condition specification is described and demonstrated

a new efficient algorithm for computational aeroacoustics on parallel processors one of the great challenges in computational physics is the prediction of flow associated noise where the quantities of interest namely the sound waves can be at high frequencies and are usually orders of magnitude smaller in magnitude than the mean quantities in order to numerically resolve such small scales governed by the fluid dynamics equations high resolution schemes are required thus solutions of flow noise problems are computationally intensive an efficient hybrid data parallel computational aeroacoustics algorithm has been developed for the prediction of noise radiation and scattering from three dimensional geometries the algorithm solves the euler navier stokes equations in the interior and nonreflecting boundary conditions on the outer boundaries a moving surface kirchhoff method is coupled to the flow solver for far field predictions the algorithm uses standard time and spatial discretization techniques but utilizes several new optimization strategies that are highly suitable for single zone solutions on data parallel processors one strategy for example enables simultaneous residual evaluations of the interior and far field nonreflecting boundary conditions equations reducing the computational effort spent on them by approximately 60 cpu time savings the algorithms for the flow solver and the kirchhoff method and their coupling are described in this paper and results for some example radiation and scattering problems are presented

adaptive discontinuous galerkin finite element methods for the compressible euler equations in this paper a recently developed approach for the design of adaptive discontinuous galerkin finite element methods is applied to physically relevant problems arising in inviscid compressible fluid flows governed by the euler equations of gas dynamics in particular we employ weighted type i a posteriori bounds to drive adaptive finite element algorithms for the estimation of the error measured in terms of general target functionals of the solution these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated this general approach leads to the design of economical finite element meshes specifically tailored to the computation of the target functional of interest as well as providing reliable and efficient error estimation the superiority of the proposed approach over mesh refinement algorithms which employ standard unweighted type ii error indicators which do not require the solution of an auxiliary problem are illustrated by a series of numerical experiments here we consider transonic flow through a nozzle as well as subsonic and supersonic flows around different airfoil geometries

adjoint based h p adaptive discontinuous galerkin methods for the 2d compressible euler equations in this paper we investigate and present an adaptive discontinuous galerkin algorithm driven by an adjoint based error estimation technique for the inviscid compressible euler equations this approach requires the numerical approximations for the flow i e primal problem and the adjoint i e dual problem which corresponds to a particular simulation objective output of interest the convergence of these two problems is accelerated by an hp multigrid solver which makes use of an element gauss seidel smoother on each level of the multigrid sequence the error estimation of the output functional results in a spatial error distribution which is used to drive an adaptive refinement strategy which may include local mesh subdivision h refinement local modification of discretization orders p enrichment and the combination of both approaches known as hp refinement the selection between h and p refinement in the hp adaptation approach is made based on a smoothness indicator applied to the most recently available flow solution values numerical results for the inviscid compressible flow over an idealized four element airfoil geometry demonstrate that both pure h refinement and pure p enrichment algorithms achieve equivalent error reductions at each adaptation cycle compared to a uniform refinement approach but requiring fewer degrees of freedom the proposed hp adaptive refinement strategy is capable of obtaining exponential error convergence in terms of degrees of freedom and results in significant savings in computational cost a high speed flow test case is used to demonstrate the ability of the hp refinement approach for capturing strong shocks or discontinuities while improving functional accuracy

optical solitons in a monomode fiber we discuss the propagation of optical solitons in a monomode fiber as a model of long distance high bit rate transmission system we give several new results which did not appear in our previous papers on this subject such as 1 a derivation of the perturbed nonlinear schrodinger equation from the maxwell equation 2 on the integrability of the perturbed nonlinear schrodinger equation 3 a discussion of the soliton as a stable fixed point of certain infinite dimensional map generated by a transmission system with periodic excitations

a time domain method for duct acoustics this paper reports the development of a time accurate method for prediction of acoustics in lined ducts the multi dimensional euler equations are dimensionally split into a system of uni directional simple wave equations which are discretized and solved using an implicit compact high order finite difference scheme the split equations are closed and coupled through the concept of impedance at domain boundaries time domain extensions of the impedance boundary condition and their efficient implementation are introduced for broadband and monotone waves the method is benchmarked by the modal solution of a monopole in the lined duct and used to investigate wall interference on the acoustic fields of realistic sources excellent agreement is found in the comparison with classical solutions and the discrepancy found in the comparison with experiment is ascribable to experimental uncertainty