the hybrid method for the pdf equations of turbulent reactive flows consistency conditions and correction algorithms the hybrid method solves the modeled transport equation for the joint pdf of velocity turbulence frequency and compositions for turbulent reactive flows a finitevolume fv method is used to solve the mean conservation equations for mass momentum and energy and the mean equation of state and a particle method is used to solve the modeled pdf equation the method is completely consistent at the level of the governing equations solved by the fv and particle algorithms in this work the conditions to be fulfilled for full consistency at the numerical solution level are examined and the independent consistency conditions are identified then correction algorithms are developed to enforce these independent consistency conditions to achieve full consistency at the numerical solution level in addition a new formulation of the energy equation and the equation of state is developed which is both general and simple the hybrid method is applied to a non premixed piloted jet flame the numerical results show that the correction algorithms are completely successful in achieving consistency the convergence of the method is demonstrated and in particular it is shown that the bias error is dramatically reduced compared to that in previous pdf calculations in addition the results are shown to be in a good agreement with some earlier pdf calculations and also with the available experimental data because of the substantially reduced numerical error for given grid size and number of particles the present hybrid method represents a significant advance in the computational efficiency of particle mesh method for the solution of pdf equations c 2001 academic press

periodic solutions and almost periodic solutions of a neutral multispecies logarithmic population model a neutral multispecies logarithmic population model is proposed in this paper by using the contraction mapping principle and constructing a suitable lyapunov functional a set of easily applicable criteria are established for the existence uniqueness and global attractivity of positive periodic solution positive almost periodic solution of the model

positive periodic solutions for a neutral delay lotka volterra system abstract applying a fixed point theorem of strict set contraction some new criteria are established for the existence of positive periodic solutions for a class of neutral delay lotka volterra systems x i t x i t r i t j 1 n a i j t x j t j 1 n b i j t x j t i j t j 1 n c i j t x j t i j t i 1 2 n compared to known results our main generalization is that delays of the derivatives are not assumed to be constants and our results are more easily verifiable

backward doubly stochastic differential equations and systems of quasilinear spdes we introduce a new class of backward stochastic differential equations which allows us to produce a probabilistic representation of certain quasilinear stochastic partial differential equations thus extending the feynman kac formula for linear spde s

backward doubly stochastic volterra integral equations and their applications abstract in this paper we introduce a new class of equations called backward doubly stochastic volterra integral equations bdsvies for short first the well posedness of bdsvies in the sense of introduced m solutions is established second a comparison theorem of bdsvies is proved as an application of the comparison theorem we derive the existence of solutions of bdsvies with continuous coefficients third a duality principle between linear forward doubly stochastic volterra integral equations fdsvies for short and bdsvies is obtained moreover by virtue of the duality principle a maximum principle of pontryagin type is established for an optimal control problem of fdsvies

numerical implementation of mixing and molecular transport in les pdf studies of turbulent reacting flows probability density function pdf methods in combination with large eddy simulations les are a powerful tool for studying turbulent reacting flow problems and we are interested in the implementation of mixing and molecular transport in les pdf methods the numerical methodology used for solution procedure is the hybrid particle mesh method and a fractional step scheme is used to solve for transport reaction and mixing sequentially mixing is modeled using the interaction by exchange with the mean iem model and the effects of molecular transport are incorporated as a mean drift term in the mixing step this methodology avoids spurious production of scalar variance and also allows direct incorporation of differential diffusion effects in this study various numerical implementations of mixing and molecular transport are presented and evaluated using the method of manufactured solutions mms for 1 accuracy 2 detailed conservation 3 realizability and 4 stability moreover the methodology is shown to be successful in capturing the effects of differential diffusion accurately with the additional property of ensuring realizability of species mass fractions finally and most importantly we describe a new variance reduction technique by way of an implicit smoothing methodology this smoothing scheme is shown to satisfy conservation boundedness and regularity criteria moreover for an appropriate choice of the smoothing length scale significant improvements in accuracy can be achieved for an incremental increase in computational cost also it is shown that with smoothing on a length scale greater than the grid size the bias and statistical errors due to there being a finite number of particles in the lagrangian monte carlo simulations scale as n t o t 1 and n t o t 1 2 respectively where n t o t is the total number of particles in the computational domain whereas without smoothing these errors scale as n p c 1 and n p c 1 2 where n p c is the much smaller number of particles in a computational cell

a particle formulation for treating differential diffusion in filtered density function methods we present a new approach for treating molecular diffusion in filtered density function fdf methods for modeling turbulent reacting flows the diffusion term accounts for molecular transport in physical space and molecular mixing in composition space conventionally the fdf is represented by an ensemble of particles and transport is modeled by a random walk in physical space there are two significant shortcomings in this transport model 1 the resulting composition variance equation contains a spurious production term and 2 because the random walk is governed by a single diffusion coefficient the formulation cannot account for differential diffusion which can have a first order effect in reacting flows in our new approach transport is simply modeled by a mean drift in the particle composition equation the resulting variance equation contains no spurious production term and differential diffusion is treated easily hence the new formulation reduces to a direct numerical simulation dns in the limit of vanishing filter width a desirable property of any large eddy simulation les approach we use the iem model for mixing it is shown that there is a lower bound on the specified mixing rate such that the boundedness of the compositions is ensured we present a numerical method for solving the particle equations which is second order accurate in space and time obeys detailed conservation enforces the realizability and boundedness constraints and is unconditionally stable

super brownian motion as the unique strong solution to an spde a stochastic partial differential equation spde is derived for super brownian motion regarded as a distribution function valued process the strong uniqueness for the solution to this spde is obtained by an extended yamada watanabe argument similar results are also proved for the fleming viot process

positive periodic solution for a neutral delay competitive system in this paper we study the existence of positive periodic solutions for a class of neutral type competitive system with delay applying the continuation theorem of coincidence degree theory a general criteria on the existence of positive periodic solutions are established some the related results are generalized and improved it is shown that the arguments delays have no effect on the existence positive periodic solution of system

weak second order splitting schemes for lagrangian monte carlo particle methods for the composition pdf fdf transport equations we study a class of methods for the numerical solution of the system of stochastic differential equations sdes that arises in the modeling of turbulent combustion specifically in the monte carlo particle method for the solution of the model equations for the composition probability density function pdf and the filtered density function fdf this system consists of an sde for particle position and a random differential equation for particle composition the numerical methods considered advance the solution in time with weak second order accuracy with respect to the time step size the four primary contributions of the paper are i establishing that the coefficients in the particle equations can be frozen at the mid time while preserving second order accuracy ii examining the performance of three existing schemes for integrating the sdes iii developing and evaluating different splitting schemes which treat particle motion reaction and mixing on different sub steps and iv developing the method of manufactured solutions mms to assess the convergence of monte carlo particle methods tests using mms confirm the second order accuracy of the schemes in general the use of frozen coefficients reduces the numerical errors otherwise no significant differences are observed in the performance of the different sde schemes and splitting schemes

on positive periodic solutions of a nonautonomous neutral delay n species competitive system abstract the purpose of this paper is to investigate a general neutral delay n species competitive nonautonomous system different from gaines and mawhin s continuation theorem r e gaines j l mawhin coincidence degree and nonlinear differential equations springer verlag berlin 1977 and abstract continuation theory for k set contraction w petryshyn z yu existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems nonlinear anal 6 1982 943 969 r e gaines j l mawhin lecture notes in mathematics vol 586 springer verlag berlin 1977 a new existence theorem is introduced with the help of the theorem and some techniques a set of sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution as an application we also examine some special cases which have been studied extensively in the literature some known results are improved and generalized

periodic solution of a periodic neutral delay equation abstract sufficient conditions are obtained for the existence of a positive periodic solution of the periodic neutral delay equation t n t a t n j 1 b j t n t j j 1 n c j t t j which arise in a food limited population model

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

a hybrid algorithm for the joint pdf equation of turbulent reactive flows in this paper a new particle finite volume hybrid algorithm for the joint velocityfrequency composition pdf method for turbulent reactive flows is presented this method is a combination of a finite volume scheme and a particle method the finitevolume scheme is used to solve the reynolds averaged navier stokes equations and the particle method to solve the joint pdf transport equation the motivation is to reduce the bias and the statistical error and to have an algorithm which is more efficient than stand alone particle mesh methods therefore in the particle method we use the smoother mean densityh i and favre averaged velocity u fields computed

symmetrical martingale solutions of backward doubly stochastic volterra integral equations abstract this paper aims to study a new class of integral equations called backward doubly stochastic volterra integral equations bdsvies for short the notion of symmetrical martingale solutions sm solutions for short is introduced for bdsvies and the existence and uniqueness theorem for bdsvies in the sense of sm solutions is established

a coupled finite element global random walk approach to advection dominated transport in porous media with random hydraulic conductivity solute transport through heterogeneous porous media considered in environmental and industrial problems is often characterized by high peclet numbers in this paper we develop a new numerical approach to advection dominated transport consisting of coupling an accurate mass conservative mixed finite element method mfem used to solve darcy flows with a particle method stable and free of numerical diffusion for non reactive transport simulations the latter is the efficient global random walk grw algorithm which performs the simultaneous tracking of arbitrarily large collections of particles on regular lattices at computational costs comparable to those of single trajectory simulations using traditional particle tracking pt mfem saturated flow solutions are computed for spatially heterogeneous hydraulic conductivities parameterized as samples of random fields the coupling is achieved by projecting the velocity field from the mfem basis onto the regular grw lattice preliminary results show that mfem grw is tens of times faster than the full mfem flow and transport simulation

backward stochastic differential equations with rough drivers backward stochastic differential equations bsdes in the sense of pardoux peng lecture notes in control and inform sci 176 1992 200 217 provide a non markovian extension to certain classes of nonlinear partial differential equations the nonlinearity is expressed in the so called driver of the bsde our aim is to deal with drivers which have very little regularity in time to this end we establish continuity of bsde solutions with respect to rough path metrics in the sense of lyons rev mat iberoam 14 1998 215 310 and so obtain a notion of bsde with rough driver existence uniqueness and a version of lyons limit theorem in this context are established our main tool aside from rough path analysis is the stability theory for quadratic bsdes due to kobylanski ann probab 28 2000 558 602

maximum principle for backward doubly stochastic control systems with applications we investigate the optimal control problems for backward doubly stochastic control systems as a necessary condition of the optimal control we obtain a stochastic maximum principle we found that the deduced stochastic hamiltonian system exactly corresponds to a type of time symmetric forward backward stochastic differential equations which was first introduced by peng and shi c r math acad sci paris 336 2003 pp 773 778 applying the stochastic maximum principle to doubly stochastic linear quadratic problems we obtain the unique optimal control the existence and uniqueness of the solution is also obtained for a type of generalized forward backward doubly stochastic differential equations derived from the maximum principle under some suitable assumptions in particular the result can be used in backward doubly stochastic linear quadratic optimal control problems an example is given to illustrate the theoretical results

mean field anticipated bsdes driven by fractional brownian motion and related stochastic control problem abstract in this paper we focus on mean field anticipated backward stochastic differential equations mf bsdes for short driven by fractional brownian motion with hurst parameter h 1 2 first the existence and uniqueness of this new type of bsdes are established using two different approaches then a comparison theorem for such bsdes is obtained finally as an application of this type of equations a related stochastic optimal control problem is studied

backward doubly stochastic differential equations with random coefficients and quasilinear stochastic pdes abstract in this paper by virtue of malliavin calculus we establish a relationship between backward doubly stochastic differential equations with random coefficients and quasilinear stochastic pdes and thus extend the well known nonlinear stochastic feynman kac formula of pardoux and peng 13 to non markovian case

optimal control problems of forward backward stochastic volterra integral equations with closed control regions optimal control problems of forward backward stochastic volterra integral equations fbsvies with closed control regions are formulated and studied a new duality principle between the linear backward stochastic volterra integral equations and a class of linear stochastic integral equations with nonadapted solutions is derived which extends and improves the corresponding results in y shi t wang and j yong math control relat fields 5 2015 pp 613 649 j yong probab theory related fields 142 2008 pp 21 77 some first order necessary optimality conditions for optimal controls of fbsvies are established via these duality principles instead of using the spike variation method as one may imagine here we choose to treat the nonconvexity of the control regions by borrowing some tools in set valued analysis and adapting them into our framework in contrast with existing routines to deal with the nonconvexity in stochastic control problems here only one adjoint system and one order di

well posedness and regularity of backward stochastic volterra integral equations backward stochastic volterra integral equations bsvies for short are studied notion of adapted m solution is introduced well posedness of bsvies is established and some regularity results are proved for the adapted m solutions via malliavin calculus a pontryagin type maximum principle is presented for optimal controls of stochastic volterra integral equations

assessment of numerical accuracy of pdf monte carlo methods for turbulent reacting flows this study is to explore the numerical features of a particle mesh algorithm developed for a stand alone joint velocity frequency composition pdf method for turbulent reactive flows numerical experiments are performed on a piloted jet nonpremixed turbulent flame of methane to characterize and quantify various numerical errors in terms of numerical parameters number of particles per cellnpc number of cells m2 and time step t first a stationary solution is obtained and is verified to be independent of the time step t then the total numerical error is identified as statistical error bias and discretization error it is revealed that the statistical error converges as npc 1 2 and the bias as npc 1 the statistical error can be reduced by time averaging or by performing multiple independent simulation e g with a parallelized program finally the scheme is shown to be second order accurate the spatial discretization error converging as m 2 a modified turbulence frequency model based on the turbulence production to dissipation ratio is shown to improve the numerical behavior of the turbulence model these results demonstrate that the particle mesh method is convergent also the optimal numerical parameters minimizing computational cost subject to a specified error tolerance are estimated an error reduction scheme similar to richardson extrapolation is proposed and shown to be quite effective in reducing the deterministic error

existence and uniqueness of positive periodic solutions for a neutral logarithmic population model in this paper by using an abstract continuous theorem of k set contractive operator the criteria is established for the existence global attractivity of positive periodic solution of a neutral delay logarithmic population model with multiple delays the result improve the known ones in s p lu w g ge existence of positive periodic solutions for neutral logarithmic population model with multiple delays j comput appl math 166 2 2004 371 383