finite element solution of compressible viscous flows using conservative variables abstract a finite element method for solving the compressible navier stokes equations is presented these equations are solved in conservation form and using conservative variables appropriate finite element approximations are discussed when a galerkin variational formulation is used for high speed flows the formulation is stabilized using the stream line upwind petrov galerkin method for which we propose an analytical expression for the matrix a new discontinuity capturing operator is also proposed to accurately solve flow problems exhibiting sharp gradients the non linear systems of equations arising from the discretization are solved using an iterative strategy based on the generalized minimal residual gmres algorithm numerical results for transonic and supersonic flows are presented that demonstrate the effectiveness of the proposed finite element method

schramm loewner evolution theory of the asymptotic behaviors of 2 1 dimensional wolf villain model abstract although extensive analytical and numerical work has focus on investigating the 2 1 dimensional wolf villain wv model some problems concerning its asymptotical behaviors such as the universality class to which it belongs remain controversial the schramm loewner evolution sle theory is an attractive approach to describe the fluctuation phenomena and random processes and has also been applied to the analysis of the stochastic growth of surfaces in this work we applied sle theory to the analysis of the saturated surface to conduct in depth research with a new perspective on the asymptotical behaviors of the 2 1 dimensional wv model on the basis of the analysis of the saturated surface contour lines we determine that the diffusion coefficient calculated for 2 1 dimensional wv model is 2 91 0 01 and that for family model is 2 88 0 01 accordingly we can conclude from the view of sle theory that the 2 1 dimensional wv model similar to the family model also belongs to the edwards wilkinson universality class

a comparative study of different sets of variables for solving compressible and incompressible flows a globally conservative galerkin least squares formulation which attains correct shock structure is developed for any choice of variables only the choice of entropy variables satisfies exactly the discrete clausius duhem inequality without any dissipative mechanisms whereas for the rest of the variables artificial diffusion is required to guarantee entropy production the limit of the formulation is well defined for entropy variables and the primitive variables p u t leading to conservative incompressible formulations the approach is stable for any continuous interpolations both for compressible and incompressible flows a comparative study of different variables is performed indicating that entropy variables and the primitive variables p u t possess the most attributes for practical problem solving

a symmetric formulation for computing transient shallow water flows abstract the shallow water equations fall into the category of symmetric advective diffusive systems with source terms these types of equations can be very effectively solved using stabilized methods such as supg and gls a semi discrete finite element method based on these ingredients is presented for the computation of transient shallow water flows special care has been taken in the design of the operators in order to improve the performance for unsteady calculations the solution is advanced in time via a predictor multi corrector algorithm which includes as special cases the second order trapezoidal rule a first order explicit method and a first order implicit method equivalent to the constant in time element of the space time formulation

on the equal time two point distribution of the one dimensional kpz equation by replica in a recent contribution dotsenko establishes a fredholm determinant formula for the two point distribution of the kardar parisi zhang equation in the long time limit and starting from narrow wedge initial conditions we establish that his expression is identical to the fredholm determinant resulting from the airy2 process

high resolution finite element analysis of shallow water equations in two dimensions abstract we present in this study the taylor galerkin finite element model to stimulate shallow water equations for bore wave propagation in a domain of two dimensions to provide the necessary precision for the prediction of a sharply varying solution profile the generalized taylor galerkin finite element model is constructed through introduction of four parameters this paper also presents the fundamental theory behind the choice of free parameters one set of parameters is theoretically determined to obtain the high order accurate taylor galerkin finite element model the other set of free parameters is determined using the underlying discrete maximum principle to obtain the low order monotonic taylor galerkin finite element model theoretical study reveals that the higher order scheme exhibits dispersive errors near the discontinuity while lower order scheme dissipates the discontinuity a scheme which has a high resolution shock capturing ability as a built in feature is thus needed in the present study notice that lumping of the mass matrix equations is invoked in the low order scheme to allow simulation of the hydraulic problem with discontinuities we check the prediction accuracy against suitable test problems preferably ones for which exact solutions are available based on numerical results it is concluded that the taylor galerkin flux corrected transport tg fct finite element method can render the technique suitable for solving shallow water equations with sharply varying solution profiles

schur dynamics of the schur processes abstract we construct discrete time markov chains that preserve the class of schur processes on partitions and signatures one application is a simple exact sampling algorithm for q volume distributed skew plane partitions with an arbitrary back wall another application is a construction of markov chains on infinite gelfand tsetlin schemes that represent deterministic flows on the space of extreme characters of the infinite dimensional unitary group

fluctuation properties of the tasep with periodic initial configuration we consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process tasep they are expressed as fredholm determinants with a kernel defining a signed determinantal point process we then consider certain periodic initial conditions and determine the kernel in the scaling limit this result has been announced first in a letter by one of us sasamoto in j phys a 38 l549 l556 2005 and here we provide a self contained derivation connections to last passage directed percolation and random matrices are also briefly discussed

supg finite element computation of compressible flows with the entropy and conservation variables formulations abstract supg stabilized finite element formulations of compressible euler equations based on the conservation and entropy variables are investigated and compared the formulation based on the conservation variables consists of the formulation introduced by tezduyar and hughes plus a shock capturing term the formulation based on the entropy variables is the same as the one by hughes franca and mallet which has a shock capturing term built in these formulations are tested on several subsonic transonic and supersonic compressible flow problems it is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables furthermore the solutions obtained using the two formulations are very close and in some cases almost indistinguishable consequently it can be deduced that the relative merits of these two formulations will continue to remain under debate

a simple subgrid scale stabilized method for the advection diffusion reaction equation abstract a subgrid scale method has been developed for the advection diffusion reaction equation with a simple intrinsic time scale parameter the proposed formulation combines very good accuracy and stability in all the physical regimes of the equation that is in the exponential regime for both negative and positive source terms and in the propagation regime numerical examples confirm the robustness and accuracy of the method

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

efficient analysis of antennas mounted on large scale complex platforms using hybrid aim po technique to speed up the conventional method of moments physical optics mom po solution process of antennas mounted on electrically large platforms a novel method hybridizing the adaptive integral method aim with the po is presented to solve a coupled electric field integral equation c efie resulted from the mom po method in the hybrid aim po method both the mom and po regions are enclosed in a cube equipping with an auxiliary regular cartesian grid then the standard aim procedure is employed to efficiently perform matrix vector multiplications mvms relating to the mom and po regions to accurately model radiation problems the mutual interactions between the mom and po regions can be fully handled with a set of newly proposed translation coefficients and a mvm scheme the efficiency of the proposed aim po technique is verified through the fast analysis of typical antennas mounted on electrically large conducting platforms

solving the kpz equation we introduce a new concept of solution to the kpz equation which is shown to extend the classical cole hopf solution this notion provides a factorisation of the cole hopf solution map into a universal measurable map from the probability space into an explicitly described auxiliary metric space composed with a new solution map that has very good continuity properties the advantage of such a formulation is that it essentially provides a pathwise notion of a solution together with a very detailed approximation theory in particular our construction completely bypasses the cole hopf transform thus laying the groundwork for proving that the kpz equation describes the uctuations of systems in the kpz universality class as a corollary of our construction we obtain very detailed new regularity results about the solution as well as its derivative with respect to the initial condition other byproducts of the proof include an explicit approximation to the stationary solution of the kpz equation a well posedness result for the fokker planck equation associated to a particle diusing in a rough space time dependent potential and a new periodic homogenisation result for the heat equation with a space time periodic potential one ingredient in our construction is an example of a non gaussian rough path such that the area process of its natural approximations needs to be renormalised by a diverging term for the approximations to converge

upwind residual discretization of enhanced boussinesq equations for wave propagation over complex bathymetries in this paper we consider the solution of the enhanced boussinesq equations of madsen and sorensen 1992 55 by means of residual based discretizations in particular we investigate the applicability of upwind and stabilized variants of continuous galerkin finite element and residual distribution schemes for the simulation of wave propagation and transformation over complex bathymetries these techniques have been successfully applied to the solution of the nonlinear shallow water equations see e g hauke 1998 39 and ricchiuto and bollermann 2009 61 in a first step toward the construction of a hybrid model coupling the enhanced boussinesq equations with the shallow water equations in breaking regions this paper shows that equal order and even low order second upwind stabilized techniques can be used to model non hydrostatic wave propagation over complex bathymetries this result is supported by theoretical truncation and dispersion error analyses and by thorough numerical validation

fast and accurate wide band analysis of antennas mounted on conducting platform using aim and asymptotic waveform evaluation technique the adaptive integral method aim in conjunction with the asymptotic waveform evaluation awe technique is presented for wide band analysis of antennas in the presence of electrically large conducting platforms in the awe technique the pade approximation solution obtained by matching the coefficients of the taylor series namely moments is utilized to achieve fast frequency sweeping besides the calculation and storage of the high order frequency derivatives of impedance matrices the awe technique requires repeatedly solving the linear system for the moments thus the aim is employed to reduce matrix storage and to accelerate all the matrix vector multiplications in both the linear system for the moments and the iterative solver furthermore a localized self box inclusion sbi preconditioner is used to accelerate the solution procedure of the linear system for the moments finally three numerical examples are given and discussed the input admittance and return loss of the antennas over a given frequency band are obtained by aim and aim awe method respectively the good agreements show that the proposed hybrid technique can greatly reduce the computation time without loss of accuracy

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

the airy1 process is not the limit of the largest eigenvalue in goe matrix diffusion using a systematic approach to evaluate fredholm determinants numerically we provide convincing evidence that the airy1 process arising as a limit law in stochastic surface growth is not the limit law for the evolution of the largest eigenvalue in goe matrix diffusion

handbook of brownian motion facts and formulae i theory i stochastic processes in general ii linear diffusions iii stochastic calculus iv brownian motion v local time as a markov process vi differential systems associated to brownian motion appendix 1 briefly on some diffusions ii tables of distributions of functionals of brownian motion and related processes 1 brownian motion 2 brownian motion with drift 3 reflecting brownian motion 4 bessel process of order 5 bessel process of order 1 2 6 bessel process of order zero 7 ornstein uhlenbeck process 8 radial ornstein uhlenbeck process 9 geometric brownian motion appendix 2 special functions appendix 3 inverse laplace transforms appendix 4 differential equations and their solutions appendix 5 formulae for n fold differentiation

stabilized residual distribution for shallow water simulations we propose a stabilized residual distribution rd scheme for the simulation of shallow water flows the final discretization is obtained combining the stabilized rd approach proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 with the conservative formulation already used in ricchiuto et al j comp phys 222 2007 to simulate shallow water flows the scheme proposed is a nonlinear variant of a lax friedrichs type discretization it is well balanced it actually yields second order of accuracy in smooth areas and it preserves the positivity of the height of the water in presence of dry areas this is made possible by the residual character of the discretization by properly adapting the stabilization operators proposed in abgrall j comp phys 214 2006 and ricchiuto and abgrall iccfd4 springer verlag 2006 and thanks to the positivity preserving character of the underlying lax friedrichs scheme we demonstrate the properties of the discretization proposed on a wide variety of tests

spatial correlations of the 1d kpz surface on a flat substrate we study the spatial correlations of the one dimensional kpz surface for the flat initial condition it is shown that the multi point joint distribution for the height is given by a fredholm determinant with its kernel in the scaling limit explicitly obtained this may also describe the dynamics of the largest eigenvalue in the goe dyson s brownian motion model our analysis is based on a reformulation of the determinantal green s function for the totally asep in terms of a vicious walk problem

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

local behavior and hitting probabilities of the text airy _1 process we obtain a formula for the n dimensional distributions of the text airy 1 process in terms of a fredholm determinant on l 2 mathbb r as opposed to the standard formula which involves extended kernels on l 2 1 dots n times mathbb r the formula is analogous to an earlier formula of prahofer and spohn j stat phys 108 5 6 1071 1106 2002 for the text airy 2 process using this formula we are able to prove that the text airy 1 process is holder continuous with exponent frac 1 2 and that it fluctuates locally like a brownian motion we also explain how the same methods can be used to obtain the analogous results for the text airy 2 process as a consequence of these two results we derive a formula for the continuum statistics of the text airy 1 process analogous to that obtained in corwin et al commun math phys 2011 to appear for the text airy 2 process

fast solution of mixed dielectric conducting scattering problem using volume surface adaptive integral method this paper presents the adaptive integral method utilized to solve scattering problems of mixed dielectric and conducting objects using volume surface integral equation the scattering problem is formulated using volume integral equation and surface integral equation for dielectric material object and conducting object respectively the combined field integral equation is formulated to treat closed conducting surfaces the method of moments is applied to discretize the integral equations the resultant matrix system is solved by an iterative solver where the adaptive integral method is employed to accelerate the matrix vector multiplication the block diagonal preconditioner is implemented to further accelerate the convergence of the present solution numerical results are presented to demonstrate the accuracy and efficiency of the technique

an explicit residual based approach for shallow water flows we describe fully explicit residual based discretizations of the shallow water equations with friction on unstructured grids the schemes are obtained by properly adapting the explicit construction proposed in ricchiuto and abgrall 2010 57 in particular previous work on well balanced integration ricchiuto 2011 56 and preservation of the depth non negativity ricchiuto and bollermann 2009 60 is reformulated in the context of a genuinely explicit time stepping still based on a weighted residual approximation the paper discusses in depth how to achieve in this context an exact preservation of all the simple known steady equilibria and how to obtain a super consistent approximation for smooth non trivial moving equilibria the treatment of the wetting drying interface is also discussed giving formal conditions for the preservation of the non negativity of the depth for a particular case based on a nonlinear variant of a lax friedrichs type scheme the approach is analyzed and tested thoroughly the quality of the numerical results shows the interest in the proposed approach over previously proposed schemes in terms of accuracy and efficiency

brownian gibbs property for airy line ensembles consider a collection of n brownian bridges b i n n to mathbb r b i n b i n 0 1 i n conditioned not to intersect the edge scaling limit of this system is obtained by taking a weak limit as n of the collection of curves scaled so that the point 0 21 2 n is fixed and space is squeezed horizontally by a factor of n 2 3 and vertically by n 1 3 if a parabola is added to each of the curves of this scaling limit an x translation invariant process sometimes called the multi line airy process is obtained we prove the existence of a version of this process which we call the airy line ensemble in which the curves are almost surely everywhere continuous and non intersecting this process naturally arises in the study of growth processes and random matrix ensembles as do related processes with wanderers and outliers we formulate our results to treat these relatives as well note that the law of the finite collection of brownian bridges above has the property called the brownian gibbs property of being invariant under the following action select an index 1 k n and erase b k on a fixed time interval a b n n then replace this erased curve with a new curve on a b according to the law of a brownian bridge between the two existing endpoints a b k a and b b k b conditioned to intersect neither the curve above nor the one below we show that this property is preserved under the edge scaling limit and thus establish that the airy line ensemble has the brownian gibbs property an immediate consequence of the brownian gibbs property is a confirmation of the prediction of m prahofer and h spohn that each line of the airy line ensemble is locally absolutely continuous with respect to brownian motion we also obtain a proof of the long standing conjecture of k johansson that the top line of the airy line ensemble minus a parabola attains its maximum at a unique point this establishes the asymptotic law of the transversal fluctuation of last passage percolation with geometric weights our probabilistic approach complements the perspective of exactly solvable systems which is often taken in studying the multi line airy process and readily yields several other interesting properties of this process

janossy densities of coupled random matrices we explicitly calculate the janossy densities for a special class of finite determinantal random point processes with several types of particles introduced by prahofer and spohn and in the full generality by johansson in connection with the analysis of polynuclear growth models the results of this paper generalize the theorem we proved earlier with borodin about the janossy densities in biorthogonal ensembles in particular our results can be applied to ensembles of random matrices coupled in a chain which provide a very important example of determinantal ensembles we study

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension d 1 2 3 via a monte carlo procedure in the disorder in order to probe with high precision the tails of the ground state energy distribution of disordered spin systems k orner katzgraber and hartmann have recently proposed an importance sampling monte carlo markov chain in the disorder in this paper we combine their monte carlo procedure in the disorder with exact transfer matrix calculations in each sample to measure the negative tail of ground state energy distribution p d e 0 for the directed polymer in a random medium of dimension d 1 2 3 in d 1 we check the validity of the algorithm by a direct comparison with the exact result namely the tracy widom distribution in dimensions d 2 and d 3 we measure the negative tail up to ten standard deviations which correspond to probabilities of order p d e 0 ensuremath sim 10 ensuremath 22 our results are in agreement with zhang s argument stating that the negative tail exponent ensuremath eta d of the asymptotic behavior mathrm ln phantom rule 0 2em 0ex p d e 0 ensuremath sim ensuremath ensuremath mid e 0 ensuremath mid ensuremath eta d as e 0 ensuremath rightarrow ensuremath ensuremath infty is directly related to the fluctuation exponent ensuremath theta d which governs the fluctuations ensuremath delta e 0 l ensuremath sim l ensuremath theta d of the ground state energy e 0 for polymers of length l via the simple formula ensuremath eta d 1 1 ensuremath ensuremath theta d throughout the paper we comment on the similarities and differences with spin glasses

local gaussian fluctuations in the airy and discrete png processes this thesis consists of two parts papers a and b in which some stochastic processes originating from random matrix theory rmt are studied in the first paper we study the fluctuations of the kth largest eigenvalue xk of the gaussian unitary ensemble gue that is let n be the dimension of the matrix and k depend on n in such a way that k and n k both tend to infinity as n the main result is that xk when appropriately rescaled converges in distribution to a gaussian random variable as n furthermore if k1 km are such that k1 ki 1 ki and n km i 1 m 1 tend to infinity as n it is shown that xk1 xkm is multivariate gaussian in the rescaled n limit in the second paper we study the airy process a t and prove that it fluctuates like a brownian motion on a local scale we also prove that the discrete polynuclear growth process png fluctuates like a brownian motion in a scaling limit smaller than the one where one gets the airy process

transversal fluctuations of the asep stochastic six vertex model and hall littlewood gibbsian line ensembles we consider the asep and the stochastic six vertex model started with step initial data after a long time t it is known that the one point height function fluctuations for these systems are of order t1 3 we prove the kpz prediction of t2 3 scaling in space namely we prove tightness and brownian absolute continuity of all subsequential limits as t goes to infinity of the height function with spatial coordinate scaled by t2 3 and fluctuations scaled by t1 3 the starting point for proving these results is a connection discovered recently by borodin bufetov wheeler between the stochastic six vertex height function and the hall littlewood process a certain measure on plane partitions interpreting this process as a line ensemble with a gibbsian resampling invariance we show that the one point tightness of the top curve can be propagated to the tightness of the entire curve

application of conservative residual distribution schemes to the solution of the shallow water equations on unstructured meshes we consider the numerical solution of the shallow water equations on unstructured grids we focus on flows over wet areas the extension to the case of dry bed will be reported elsewhere the shallow water equations fall into the category of systems of conservation laws which can be symmetrized thanks to the existence of a mathematical entropy coinciding in this case with the total energy our aim is to show the application of a particular class of conservative residual distribution rd schemes to the discretization of the shallow water equations and to analyze their discrete accuracy and stability properties we give a review of conservative rd schemes showing relations between different approaches previously published and recall l stability and accuracy criteria characterizing the schemes in particular the accuracy of the rd method in presence of source terms is analyzed and conditions to construct rth order discretizations on irregular triangular grids are proved it is shown that the rd approach gives a natural way of obtaining high order discretizations which moreover preserves exactly the steady lake at rest solution independently on mesh topology nature of the variation of the bottom and polynomial order of interpolation used for the unknowns we also consider more general analytical solutions which are less investigated from the numerical view point on irregular grids linearity preserving rd schemes yield a truly second order approximation we also sketch a strategy to achieve discretizations which preserve exactly some of these solutions numerical results on steady and time dependent problems involving smooth and non smooth variations of the bottom topology show very promising features of the approach

transition between airy1 and airy2 processes and tasep fluctuations we consider the totally asymmetric simple exclusion process a model in the kpz universality class we focus on the fluctuations of particle positions starting with certain deterministic initial conditions for large time t one has regions with constant and linearly decreasing density the fluctuations on these two regions are given by the airy1 and airy2 processes whose one point distributions are the goe and gue tracy widom distributions of random matrix theory in this paper we analyze the transition region between these two regimes and obtain the transition process its one point distribution is a new interpolation between goe and gue edge distributions 2007 wiley periodicals inc

fluctuations of the one dimensional polynuclear growth model in half space we consider the multi point equal time height fluctuations of the one dimensional polynuclear growth model in half space for special values of the nucleation rate at the origin the multi layer version of the model is reduced to a process with a determinantal weight for which the asymptotics can be analyzed in the scaling limit the fluctuations near the origin are shown to be equivalent to those of the largest eigenvalue of the orthogonal symplectic to unitary transition ensemble at soft edge in random matrix theory

aim analysis of electromagnetic scattering by arbitrarily shaped magnetodielectric object a fast solution to the electromagnetic scattering by large scale three dimensional magnetodielectric objects with arbitrary permittivity and permeability is presented the scattering problem is characterized by using coupled field volume integral equation cf vie by considering the total electric and magnetic fields i e the sum of incident fields and the radiated fields by equivalent electric and magnetic volume currents the cf vie can be established in the volume of the scatterers the resultant cf vie is discretized and solved by using the method of moments mom for large scale scattering problems the adaptive integral method aim is then applied in the mom in order to reduce the memory requirement and accelerate the matrix vector multiplication in the iterative solver the conventional aim has been modified to cope with the two sets of equivalent volume currents

endpoint distribution of directed polymers in 1 1 dimensions we give an explicit formula for the joint density of the max and argmax of the airy2 process minus a parabola the argmax has a universal distribution which governs the rescaled endpoint for large time or temperature of directed polymers in 1 1 dimensions

renormalization fixed point of the kpz universality class the one dimensional kardar parisi zhang universality class is believed to describe many types of evolving interfaces which have the same characteristic scaling exponents these exponents lead to a natural renormalization rescaling on the space of such evolving interfaces we introduce and describe the renormalization fixed point of the kardar parisi zhang universality class in terms of a random nonlinear semigroup with stationary independent increments and via a variational formula furthermore we compute a plausible formula the exact transition probabilities using replica bethe ansatz the semigroup is constructed from the airy sheet a four parameter space time field which is the airy 2 process in each of its two spatial coordinates minimizing paths through this field describe the renormalization group fixed point of directed polymers in a random potential at present the results we provide do not have mathematically rigorous proofs and they should at most be considered proposals

asymptotics of tracy widom distributions and the total integral of a painleve ii function the tracy widom distribution functions involve integrals of a painleve ii function starting from positive infinity in this paper we express the tracy widom distribution functions in terms of integrals starting from minus infinity there are two consequences of these new representations the first is the evaluation of the total integral of the hastings mcleod solution of the painleve ii equation the second is the evaluation of the constant term of the asymptotic expansions of the tracy widom distribution functions as the distribution parameter approaches minus infinity for the gue tracy widom distribution function this gives an alternative proof of the recent work of deift its and krasovsky the constant terms for the goe and gse tracy widom distribution functions are new

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

two time distribution function in one dimensional random directed polymers the explicit expression for the two time free energy distribution function in one dimensional random directed polymers is derived in terms of the bethe ansatz replica technique it is shown that such type of the distribution function can be represented in the form of a generalized two dimensional fredholm determinant

discrete polynuclear growth and determinantal processes we consider a discrete polynuclear growth png process and prove a functional limit theorem for its convergence to the airy process this generalizes previous results by prahofer and spohn the result enables us to express the f1 goe tracy widom distribution in terms of the airy process we also show some results and give a conjecture about the transversal fluctuations in a point to line last passage percolation problem furthermore we discuss a rather general class of measures given by products of determinants and show that these measures have determinantal correlation functions

a new finite element formulation for computational fluid dynamics x the compressible euler and navier stokes equations a space time element method is presented for solving the compressible euler and navier stokes equations the proposed formulation includes the variational equation predictor multi corrector algorithms and boundary conditions the variational equation is based on the time discontinuous galerkin method in which the physical entropy variables are employed a least squares operator and a discontinuity capturing operator are added resulting in a high order accurate and unconditionally stable method implicit explicit predictor multi corrector algorithms applicable to steady as well as unsteady problems are presented techniques are developed to enhance their efficiency implementation of boundary conditions is addressed in particular a technique is introduced to satisfy nonlinear essential boundary conditions and a consistent method is presented to calculate boundary fluxes numerical results are presented to demonstrate the performance of the method

maximum relative height of elastic interfaces in random media the distribution of the maximal relative height mrh of self affine one dimensional elastic interfaces in a random potential is studied we analyze the ground state configuration at zero driving force and the critical configuration exactly at the depinning threshold both for the random manifold and random periodic universality classes these configurations are sampled by exact numerical methods and their mrh distributions are compared with those with the same roughness exponent and boundary conditions but produced by independent fourier modes with normally distributed amplitudes using pickands theorem we derive an exact analytical description for the right tail of the latter after properly rescaling the mrh distributions we find that corrections from the gaussian independent modes approximation are in general small as previously found for the average width distribution of depinning configurations in the large size limit all corrections are finite except for the ground state in the random periodic class whose mrh distribution becomes for periodic boundary conditions indistinguishable from the airy distribution we find that the mrh distributions are in general sensitive to changes of boundary conditions

aim analysis of scattering and radiation by arbitrary surface wire configurations the adaptive integral method is utilized to solve electromagnetic scattering and radiation problems of conducting surface wire configurations the method of moments mom is applied to establish the integral equations where triangular type basis functions are used to represent the currents on surfaces and wires attachment mode has been used to model the surface wire junction to ensure the current continuity the resultant matrix system is then solved by an iterative solver where the adaptive integral method aim is employed to reduce memory requirements and to accelerate the matrix vector multiplications numerical results are presented to demonstrate the accuracy and efficiency of the present technique for the arbitrary surface wire configurations

airy kernel with two sets of parameters in directed percolation and random matrix theory we introduce a generalization of the extended airy kernel with two sets of real parameters we show that this kernel arises in the edge scaling limit of correlation kernels of determinantal processes related to a directed percolation model and to an ensemble of random matrices

kpz line ensemble for each t ge 1 we construct an mathbb n indexed ensemble of random continuous curves with three properties 1 the lowest indexed curve is distributed as the time t hopf cole solution to the kardar parisi zhang kpz stochastic partial differential equation with narrow wedge initial data 2 the entire ensemble satisfies a resampling invariance which we call the mathbf h brownian gibbs property with mathbf h x e x 3 increments of the lowest indexed curve when centered by t 24 and scaled down vertically by t 1 3 and horizontally by t 2 3 remain uniformly absolutely continuous i e have tight radon nikodym derivatives with respect to brownian bridges as time t goes to infinity this construction uses as inputs the diffusion that o connell discovered ann probab 40 437 458 2012 in relation to the o connell yor semi discrete brownian polymer the convergence result of moreno flores et al in preparation of the lowest indexed curve of that diffusion to the solution of the kpz equation with narrow wedge initial data and the one point distribution formula proved by amir et al commun pure appl math 64 466 537 2011 for the solution of the kpz equation with narrow wedge initial data we provide four main applications of this construction 1 uniform as t goes to infinity brownian absolute continuity of the time t solution to the kpz equation with narrow wedge initial data even when scaled vertically by t 1 3 and horizontally by t 2 3 2 universality of the t 1 3 one point vertical fluctuation scale for the solution of the kpz equation with general initial data 3 concentration in the t 2 3 scale for the endpoint of the continuum directed random polymer 4 exponential upper and lower tail bounds for the solution at fixed time of the kpz equation with general initial data

density fluctuations for exclusion processes with long jumps we show that the stationary density fluctuations of exclusion processes with long jumps whose rates are of the form c pm y x 1 alpha where c pm depends on the sign of y x are given by a fractional ornstein uhlenbeck process for alpha in 0 frac 3 2 when alpha frac 3 2 we show that the density fluctuations are tight in a suitable topology and that any limit point is an energy solution of the fractional burgers equation previously introduced in gubinelli and jara stoch partial differ equ anal comput 1 2 325 350 2013 in the finite volume setting

weakly asymmetric non simple exclusion process and the kardar parisi zhang equation we analyze a class of non simple exclusion processes and the corresponding growth models by generalizing the discrete cole hopf transformation of gartner stoch process appl 27 233 260 1987 we identify the main non linearity and eliminate it by imposing a gradient type condition for hopping range at most 3 using the generalized transformation we prove the convergence of the exclusion process toward the kardar parisi zhang kpz equation this is the first universality result under the weak asymmetry concerning interacting particle systems while this class of exclusion processes are not explicitly solvable under the weak asymmetry we obtain the exact one point limiting distribution for the step initial condition by using the previous result of amir et al commun pure appl math 64 4 466 537 2011 and our convergence result

probability distribution of the free energy of the continuum directed random polymer in 1 1 dimensions we consider the solution of the stochastic heat equation tz d 1 2 x zz p w with delta function initial condition z t d0 x dixd0 whose logarithm with appropriate normalization is the free energy of the con tinuum directed polymer or the hopf cole solution of the kardar parisi zhang equation with narrow wedge initial conditions we obtain explicit formulas for the one dimensional marginal distributions the crossover distributions which interpolate between a standard gaussian dis tribution small time and the gue tracy widom distribution large time the proof is via a rigorous steepest descent analysis of the tracy widom formula for the asymmetric simple exclusion process with antishock initial data which is shown to converge to the continuum equations in an appropriate weakly asymmetric limit the limit also describes the crossover behavior between the symmetric and asymmetric exclusion processes 2010 wiley periodicals inc

skew selfadjoint form for systems of conservation laws abstract hyperbolic systems of conservation laws augumented with an entropy inequality are studied it is shown that such systems can be written in a quasilinear skew selfadjoint form centered differencing of such a form under the smooth regime ends up with a systematic recipe for constructing quasiconservative schemes where the global entropy conservation is recovered employing the above formulation in bounded regions under the nonsmooth regime as well a local entropy decay estimate is also concluded examples of the shallow water and the full gasdynamics equations are explicitly treated

fourier analysis of semi discrete and space time stabilized methods for the advective diffusive reactive equation i supg abstract in this paper the work initiated in part one and two is extended to the transient subgrid scale gradient subgrid scale sgs gsgs stabilized method temporal accuracy and stability of semi discrete and time discontinuous space time versions of the method are examined for transient advection diffusion reaction problems also for the above methods predictor multi corrector algorithms are analyzed with special emphasis on mass and source lumping which has been shown to enhance both stability and accuracy of explicit stabilized methods it will be shown that the parent supg sgs and sgs gsgs methods perform very similarly and that explicit predictor multi corrector mass source lumping practically retains the accuracy of the parent method while gaining stability

limit processes for tasep with shocks and rarefaction fans we consider the totally asymmetric simple exclusion process tasep with two sided bernoulli initial condition i e with left density and right density we study the associated height function whose discrete gradient is given by the particle occurrences macroscopically one has a deterministic limit shape with a shock or a rarefaction fan depending on the values of we characterize the large time scaling limit of the multipoint fluctuations as a function of the densities and of the different macroscopic regions moreover using a slow decorrelation phenomena the results are extended from fixed time to the whole space time except along the some directions the characteristic solutions of the related burgers equation where the problem is still open

the shifted boundary method for hyperbolic systems embedded domain computations of linear waves and shallow water flows abstract we propose a new computational approach for embedded boundary simulations of hyperbolic systems and in particular the linear wave equations and the nonlinear shallow water equations the proposed approach belongs to the class of surrogate approximate boundary algorithms and is based on the idea of shifting the location where boundary conditions are applied from the true to a surrogate boundary accordingly boundary conditions enforced weakly are appropriately modified to preserve optimal error convergence rates this framework is applied here in the setting of a stabilized finite element method even though other spatial discretization techniques could have been employed accuracy stability and robustness of the proposed method are tested by means of an extensive set of computational experiments for the acoustic wave propagation equations and shallow water equations comparisons with standard weak boundary conditions imposed on body fitted grids which conform to the geometry of the computational domain boundaries are also presented

discrete orthogonal polynomial ensembles and the plancherel measure we consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory these ensembles occur in certain problems in combinatorial probability and can be thought of as probability measures on partitions the meixner ensemble is related to a two dimensional directed growth model and the charlier ensemble is related to the lengths of weakly increasing subsequences in random words the krawtchouk ensemble occurs in connection with zig zag paths in random domino tilings of the aztec diamond and also in a certain simplifled directed flrst passage percolation model we use the charlier ensemble to investigate the asymptotics of weakly increasing subsequences in random words and to prove a conjecture of tracy and widom as a limit of the meixner ensemble or the charlier ensemble we obtain the plancherel measure on partitions and using this we prove a conjecture of baik deift and johansson that under the plancherel measure the distribution of the lengths of the flrst k rows in the partition appropriately scaled converges to the asymptotic joint distribution for the k largest eigenvalues of a random matrix from the gaussian unitary ensemble in this problem a certain discrete kernel which we call the discrete bessel kernel plays an important role

revisiting stabilized finite element methods for the advective diffusive equation we give a brief overview of stabilized finite element methods and illustrate the developments applied to the advection diffusion equation this article presents a concise perspective of the developments emanated from the works started in the 1980s through today 2005 elsevier b v all rights reserved pacs 47 11 j

statistical self similarity of one dimensional growth processes abstract for one dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times we argue that for self similar growth from a single seed the universal distribution is the tracy widom distribution from the theory of random matrices and that for the growth from a flat substrate it is some other only numerically determined distribution in particular for the polynuclear growth model in the droplet geometry the height maps onto the longest increasing subsequence of a random permutation from which the height distribution is identified as the tracy widom distribution

exact solution of the master equation for the asymmetric exclusion process using the bethe ansatz we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one dimensional lattice we derive explicit expressions for the conditional probabilitiesp x1 xn t y1 yn 0 of findingn particles on lattices sitesx1 xn at timet with initial occupationy1 yn at timet 0

stochastic burgers and kpz equations from particle systems we consider two strictly related models a solid on solid interface growth model and the weakly asymmetric exclusion process both on the one dimensional lattice it has been proven that in the diffusive scaling limit the density field of the weakly asymmetric exclusion process evolves according to the burgers equation and the fluctuation field converges to a generalized ornstein uhlenbeck process we analyze instead the density fluctuations beyond the hydrodynamical scale and prove that their limiting distribution solves the non linear burgers equation with a random noise on the density current for the solid on solid model we prove that the fluctuation field of the interface profile if suitably rescaled converges to the kardar parisi zhang equation this provides a microscopic justification of the so called kinetic roughening i e the non gaussian fluctuations in some non equilibrium processes our main tool is the cole hopf transformation and its microscopic version we also develop a mathematical theory for the macroscopic equations

limit process of stationary tasep near the characteristic line the totally asymmetric simple exclusion process tasep on input amssym bbb z with the bernoulli measure as an initial condition 0 1 is stationary it is known that along the characteristic line the current fluctuates at an order of t1 3 the limiting distribution has also been obtained explicitly in this paper we determine the limiting multipoint distribution of the current fluctuations moving away from the characteristics by the order t2 3 the main tool is the analysis of a related directed last percolation model we also discuss the process limit in tandem queues in equilibrium 2010 wiley periodicals inc

adaptive streamline diffusion methods for compressible flow using conservation variables we consider the streamline diffusion finite element method applied to compressible flow using conservation variables we propose some adaptive algorithms and present related numerical results

a determinantal formula for the goe tracy widom distribution investigating the long time asymptotics of the totally asymmetric simple exclusion process sasamoto obtains rather indirectly a formula for the tracy widom distribution for the gaussian orthogonal ensemble we establish that his novel formula indeed agrees with more standard expressions

a unified approach to compressible and incompressible flows abstract we present a finite element formulation for solving the compressible navier stokes equations which accommodates the use of any set of variables if primitive variables p u t or entropy variables are used the incompressible limit is well behaved therefore one formulation can be used to solve both compressible and incompressible flows

stationary states of crystal growth in three dimensions a new markov process describing crystal growth in three dimensions is introduced states of the process are configurations of the crystal surface which has a terrace edge kink structure the states are continuous along edges but discrete across edges in accordance with the very different rates for the two types of captures of particles stationary distributions describing steady crystal growth are found in general to our knowledge these are the first examples of stationary distributions for layered crystal growth in three dimensions the steady growth rate and other quantities are obtained explicitly for two interacting edges for many interacting edges growth behavior is determined a in various asymptotic regimes including thermodynamic limits b via simulations and c using series cluster expansions in the slope of the surface the first three coefficients being computed the theoretical growth rates show a marked dependence on surface dimensions this may contribute to the size dependence and dispersion in the observed growth rate of small crystals

differential equations for dyson processes we call a dyson process any process on ensembles of matrices in which the entries undergo diffusion we are interested in the distribution of the eigenvalues or singular values of such matrices in the original dyson process it was the ensemble of n n hermitian matrices and the eigenvalues describe n curves given sets x1 xm the probability that for each k no curve passes through xk at time k is given by the fredholm determinant of a certain matrix kernel the extended hermite kernel for this reason we call this dyson process the hermite process similarly when the entries of a complex matrix undergo diffusion we call the evolution of its singular values the laguerre process for which there is a corresponding extended laguerre kernel scaling the hermite process at the edge leads to the airy process which was introduced by prahofer and spohn as the limiting stationary process for a polynuclear growth model and in the bulk to the sine process scaling the laguerre process at the edge leads to the bessel process

on the thermodynamics stability and hierarchy of entropy functions in fluid flow symmetric forms of systems of equations describing physical phenomena present exceptional desirable properties such as symmetric coefficient matrices well posedness of the cauchy initial value problem finite wave propagation speeds and a link to nonlinear stability principles therefore they should be used when possible to design better numerical methods in this paper such symmetric forms are reviewed for various models of fluid flow and a hierarchy of generalized entropy functions is presented standard concepts are extended to the diffusive terms

universal distributions for growth processes in 1 1 dimensions and random matrices we develop a scaling theory for kardar parisi zhang growth in one dimension by a detailed study of the polynuclear growth model in particular we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape these distribution functions are computed using the partition function of gaussian random matrices in a cosine potential

asymptotics of plancherel measures for symmetric groups 1 1 plancherel measures given a finite group g by the corresponding plancherel measure we mean the probability measure on the set g of irreducible representations of g which assigns to a representation g the weight dim g for the symmetric group s n the set s n is the set of partitions of the number n which we shall identify with young diagrams with n squares throughout this paper the plancherel measure on partitions arises naturally in representation theoretic combinatorial and probabilistic problems for example the plancherel distribution of the first part of a partition coincides with the distribution of the longest increasing subsequence of a uniformly distributed random permutation 31 we denote the plancherel measure on partitions of n by mn

limiting distributions for a polynuclear growth model with external sources the purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by prahofer and spohn depending on the strength of the sources the limiting distribution functions are either the tracy widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero moreover we obtain transition functions between pairs of the above distribution functions in suitably scaled limits there are also similar results for a discrete totally asymmetric exclusion process