anomalous scaling of a passive scalar advected by the synthetic compressible flow abstract the field theoretic renormalization group and operator product expansion are applied to the problem of a passive scalar advected by a gaussian nonsolenoidal velocity field with finite correlation time in the presence of large scale anisotropy the energy spectrum of the velocity in the inertial range has the form e k k1 e and the correlation time at the wave number k scales as k 2 it is shown that depending on the values of the exponents e and the model exhibits various types of inertial range scaling regimes with nontrivial anomalous exponents explicit asymptotic expressions for the structure functions and other correlation functions are obtained they are represented by superpositions of power laws with nonuniversal amplitudes and universal independent of the anisotropy anomalous exponents calculated to the first order in e and in any space dimension these anomalous exponents are determined by the critical dimensions of tensor composite operators built of the scalar gradients and exhibit a kind of hierarchy related to the degree of anisotropy the less is the rank the less is the dimension and consequently the more important is the contribution to the inertial range behavior the leading terms of the even odd structure functions are given by the scalar vector operators the anomalous exponents depend explicitly on the degree of compressibility

first passage percolation network flows and electrical resistances we show that the first passage times of first passage percolation on 2 are such that p 0n n decay geometrically as n where may represent any of the four usual first passage time processes the former estimate requires no moment condition on the time coordinates but there exists a geometrically decaying estimate for the latter quantity if and only if the time coordinate distribution has finite moment generating function near the origin here is the time constant and 0 we study the line to line first passage times and describe applications to the maximum network flow through a randomly capacitated subsection of 2 and to the asymptotic behaviour of the electrical resistance of a subsection of 2 when the edges of the subsection are wires in an electrical network with random resistances in the latter case we show for example that if each edge resistance equals 1 or ohms with probabilities p and 1 p respectively then the effective resistance rn across opposite faces of an n by n box satisfies the following a if p 1 2 then p rn 1 as n b if p 1 2 then there exists p such that p p 1 underset raise0 3em hbox smash scriptscriptstyle leqslant mathop lim inf r n limits n to infty underset raise0 3em hbox smash scriptscriptstyle leqslant mathop lim sup r n limits n to infty underset raise0 3em hbox smash scriptscriptstyle leqslant v p 1

zero beta function for a model of diffusion in potential random field a rigorous perturbative proof is given of both the renormalisability of the field theoretic model of diffusion in potential random field and the triviality of the renormalisation group beta function

on the equilibrium state of random walkers in random environments analytical results we study equilibrium properties of random walkers in one dimensional random environments of finite length l from an exact expression for the quenched average of the free energy we derive analytical results for all cumulants and all renyi entropies of the equilibrium distribution in contrast to the finite variance of a typical non equilibrium distribution in the unbiased situation we find that in equilibrium the disorder averaged variance diverges with the size of the system as

nonlinear programming algorithms using trust regions and augmented lagrangians with nonmonotone penalty parameters the strategy for obtaining global convergence is based on the trust region approach the merit function is a type of augmented lagrangian a new updating scheme is introduced for the penalty parameter by means of which monotone increase is not necessary global convergence results are proved and numerical experiments are presented

a nonmonotone trust region algorithm with nonmonotone penalty parameters for constrained optimization in this paper we present a nonmonotone trust region algorithm with nonmonotone penalty parameters for the solution of optimization problems with nonlinear equality constraints and bound constraints the proposed algorithm combines an sqp approach with a trust region strategy to globalize the process each step is obtained through the computation of a normal step to reduce infeasibility and a tangential step to decrease some merit function the algorithm makes use of an augmented lagrangian function as merit function and allows the value of this merit function and the penalty parameter involved in it to decrease non monotonically the global convergence theory for the proposed algorithm is developed without regularity assumption and shows that any limit point of the sequence generated by the algorithm is a stationary point while at least one limit point under the suitable assumptions is a substationary point and a stationary point if it is feasible some preliminary numerical experiments are also reported

a nonmonotone filter trust region method for nonlinear constrained optimization in this paper we present a nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization similar to bryd omojokun class of algorithms each step is composed of a quasi normal step and a tangential step this new method has more flexibility for the acceptance of the trial step compared to the filter methods and requires less computational costs compared with the monotone methods under reasonable conditions we give the globally convergence properties numerical tests are presented that confirm the efficiency of the approach

on toy ageing we consider the dynamics of a simple one dimensional model and we discuss the phenomenon of ageing i e the strong dependence of the dynamical correlation functions over the waiting time our model is the so called random random walk the toy model of a directed polymer evolving in a random medium

fluctuations of extensive functions of quenched random couplings an extensive quantity is a family of functions v of random parameters indexed by the finite regionsv subsets of d over which v are additive up to corrections satisfying the boundary estimate stated below it is shown that unless the randomness is nonessential in the sense that lim v v has a unique value in the absolute i e not just probabilistic sense the variance of such a quantity grows as the volume ofv of particular interest is the free energy of a system with random couplings for such v bounds are derived also for the generating functione et in a separate application variance bounds are used for an inequality concerning the characteristic exponents of directed polymers in a random environment

large deviations for increasing sequences on the plane we prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among poisson points on the plane the rate function for lower tail deviations is derived from a 1977 result of logan and shepp about young diagrams of random permutations for the upper tail we use a coupling with hammersley s particle process and convex analytic techniques along the way we obtain the rate function for the lower tail of a tagged particle in a totally asymmetric hammersley s process

passive advection of a vector field anisotropy finite correlation time exact solution and logarithmic corrections to ordinary scaling in this work we study the generalization of the problem considered in phys rev e 91 013002 2015 to the case of finite correlation time of the environment velocity field the model describes a vector e g magnetic field passively advected by a strongly anisotropic turbulent flow inertial range asymptotic behavior is studied by means of the field theoretic renormalization group and the operator product expansion the advecting velocity field is gaussian with finite correlation time and preassigned pair correlation function due to the presence of distinguished direction n all the multiloop diagrams in this model vanish so that the results obtained are exact the inertial range behavior of the model is described by two regimes the limits of vanishing or infinite correlation time that correspond to the two nontrivial fixed points of the rg equations their stability depends on the relation between the exponents in the energy spectrum e k 1 and the dispersion law k 2 in contrast to the well known isotropic kraichnan s model where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents here the corrections to ordinary scaling are polynomials of logarithms of the integral turbulence scale l

a robust trust region algorithm with a nonmonotonic penalty parameter scheme for constrained optimization an algorithm for solving the problem of minimizing a nonlinear function subject to equality constraints is introduced this algorithm is a trust region algorithm in computing the trial step a projected hessian technique is used that converts the trust region subproblem to one similar to that for the unconstrained case to force global convergence the augmented lagrangian is employed as a merit function one of the main advantages of this algorithm is the way that the penalty parameter is updated we introduce an updating scheme that allows for the first time to the best of our knowledge the penalty parameter to be decreased whenever it is warranted the behavior of this penalty parameter is studied a convergence theory for this algorithm is presented it is shown that this algorithm is globally convergent and that the globalization strategy will not disrupt fast local convergence the local rate of convergence is also discussed this theory is sufficiently general so that it holds for any algorithm t

semismooth karush kuhn tucker equations and convergence analysis of newton and quasi newton methods for solving these equations there are several forms of systems of nonsmooth equations which are equivalent to the karush kuhn tucker kkt system of a nonlinearly constrained optimization problem nlp if the nlp is twice continuously differentiable and the hessian functions of its objective and constraint functions are locally lipschitzian then these kkt equations are strongly semismooth if furthermore the linear independence condition and the strong second order sufficiency condition are satisfied at a kkt point then the generalized jacobians of these kkt equations are nonsingular at that point and the sequence generated by the generalized newton method converges to this point q quadratically however direct application of quasi newton methods cannot guarantee q superlinear convergence we present a mixed quasi newton method which converges q superlinearly with common symmetrical updating rules under the above conditions for the generalized newton method superlinear convergence of the primal variables and global convergence are also discussed

entropy for translation invariant random cluster measures we study translation invariant random cluster measures with techniques from large deviation theory and convex analysis in particular we prove a large deviation principle with rate function given by a specific entropy and a dobrushinlanfordruelle variational principle that characterizes translation invariant random cluster measures as the solutions of the variational equation for free energy consequences of these theorems include inequalities for edge and cluster densities of translationinvariant random cluster measures 1 introduction the random cluster model was introduced around 1972 by fortuin and kasteleyn 18 as a family of models that contains the bernoulli bond percolation model the ising model and the q state potts models as special cases it has developed into an important and very successful tool for studying the ising and potts models our paper focuses on the properties of the random cluster measures themselves our starting point is grimmett s 23 development of elements of a thermodynamic formalism for this model beginning with a definition of infinite volume random cluster measures in terms of a dlr dobrushinlanfordruelle equation just as for gibbsian systems natural next questions concern the validity of large deviation principles and variational characterizations of infinite volume measures these questions we answer in the present paper and derive some consequences here is a brief overview of the dlr approach of 23 the random cluster measures of interest live on the graph formed by putting edges between nearest neighbor vertices of the d dimensional hypercubic lattice d the edge that connects two vertices x and y that are l 1 distance one apart is

renormalization group operator product expansion and anomalous scaling in models of turbulent advection recent progress on the anomalous scaling in models of turbulent heat and mass transport is reviewed with the emphasis on the approach based on the field theoretic renormalization group rg and operator product expansion ope in that approach the anomalous scaling is established as a consequence of the existence in the corresponding field theoretic models of an infinite number of dangerous composite fields operators with negative critical dimensions which are identified with the anomalous exponents this allows one to calculate the exponents in a systematic perturbation expansion similar to the e expansion in the theory of critical phenomena the rg and ope approach is presented in a self contained way for the example of a passive scalar field temperature concentration of an impurity etc advected by a self similar gaussian velocity ensemble with vanishing correlation time the so called kraichnan s rapid change model where the anomalous exponents are known up to order o e3 effects of anisotropy compressibility and the correlation time of the velocity field are discussed passive advection by non gaussian velocity field governed by the stochastic navier stokes equation and passively advected vector e g magnetic fields are considered

large deviations for the empirical field of a gibbs measure on applique le principe de contraction pour obtenir un principe de grande deviation pour la distribution des distributions empiriques on donne une description detaillee de la fonction de taux resultante

anomalous scaling in the n point functions of a passive scalar a recent analysis of the four point correlation function of the passive scalar advected by a time decorrelated random flow is extended to the n point case it is shown that all stationary state inertial range correlations are dominated by homogeneous zero modes of singular operators describing their evolution we compute analytically the zero modes governing the n point structure functions and the anomalous dimensions corresponding to them to the linear order in the scaling exponent of the two point function of the advecting velocity field the implications of these calculations for the dissipation correlations are discussed textcopyright 1996 the american physical society

a trust region method by active set strategy for general nonlinear optimization the paper explores a trust region active set algorithm for general nonlinear optimization with nonlinear equality and inequality constraints in this algorithm an active set strategy is used together with trust region methods to compute the trial step l 1 penalty functions are employed to obtain the global convergence the global convergence of this algorithm is proved under standard conditions the numerical tests show the efficiency of the proposed algorithm

structure of the three point correlation function of a passive scalar in the presence of a mean gradient the three point correlation function of a passive scalar advected by a random incompressible velocity field in the presence of a mean gradient is investigated by means of phenomenological hopf equations numerical solutions are provided in the case where the velocity is gaussian white in time and with a power law in space v stackrel ensuremath rightarrow r ensuremath v stackrel ensuremath rightarrow 0 2 ensuremath sim r 2 ensuremath ensuremath epsilon and in the model introduced by shraiman and siggia c r acad sci 321 279 1995 anomalous scaling exponents are found in both models the numerics agrees with all the available analytic perturbative results in addition the angular dependence of the correlation function is explicitly determined in the batchelor limit of random advection by a smooth velocity field the exponent is found to remain very close to 1 as found experimentally in this limit the three point correlation function is found to be very well represented away from collinearity by an explicit integral representation

spectral projected gradient method with inexact restoration for minimization with nonconvex constraints this work takes advantage of the spectral projected gradient direction within the inexact restoration framework to address nonlinear optimization problems with nonconvex constraints the proposed strategy includes a convenient handling of the constraints together with nonmonotonic features to speed up convergence the numerical performance is assessed by experiments with hard spheres problems pointing out that the inexact restoration framework provides an adequate environment for the extension of the spectral projected gradient method for general nonlinearly constrained optimization

a recursive quadratic programming algorithm that uses differentiable exact penalty functions in this paper a recursive quadratic programming algorithm for solving equality constrained optimization problems is proposed and studied the line search functions used are approximations to fletcher s differentiable exact penalty function global convergence and local superlinear convergence results are proved and some numerical results are given

anomalous scaling nonlocality and anisotropy in a model of the passively advected vector field a model of the passive vector quantity advected by the gaussian velocity field with the covariance ensuremath propto ensuremath delta t ensuremath t ensuremath mathbf x ensuremath mathbf x ensuremath ensuremath varepsilon is studied the effects of pressure and large scale anisotropy are discussed the inertial range behavior of the pair correlation function is described by an infinite family of scaling exponents which satisfy exact transcendental equations derived explicitly in d dimensions by means of the functional techniques the exponents are organized in a hierarchical order according to their degree of anisotropy with the spectrum unbounded from above and the leading minimal exponent coming from the isotropic sector this picture extends to higher order correlation functions like in the scalar model the second order structure function appears nonanomalous and is described by the simple dimensional exponent s 2 ensuremath propto r 2 ensuremath ensuremath varepsilon for the higher order structure functions s 2n ensuremath propto r n 2 ensuremath ensuremath varepsilon ensuremath delta n the anomalous scaling behavior is established as a consequence of the existence in the corresponding operator product expansions of dangerous composite operators whose negative critical dimensions determine the anomalous exponents ensuremath delta n l0 a close formal resemblance of the model with the stirred navier stokes equation reveals itself in the mixing of relevant operators and is the main motivation of the paper using the renormalization group the anomalous exponents are calculated in the o ensuremath varepsilon approximation in large d dimensions for the even structure functions up to the twelfth order

a sequential quadratic programming method for potentially infeasible mathematical programs abstract the paper describes a modification to the wilson han powell sequential quadratic programming technique that is applicable to potentially infeasible nonlinear programs the method is designed to locate stationary points of a nonlinear program in a generalized sense definition 2 8 these stationary points include the familiar kuhn tucker and fritz john points but also include what we call external and strong external stationary points the external and strong external stationary points are not feasible thus the problem may be infeasible and yet have stationary points loosely speaking an external stationary point is one that satisfies a certain first order necessary optimality condition for being as close to feasibility as possible the proposed technique is similar to those described by j v burke and s p han a modified sequential quadratic programming method manuscript and m sahba j optim theory appl 52 1987 291 309 however it is shown to possess substantially enhanced stability properties the global convergence properties of the method are described along with some continuity results for the quadratic programming subproblems

calculation of the anomalous exponents in the rapid change model of passive scalar advection to order epsilon 3 the field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar advected by the gaussian velocity field with zero mean and correlation function approximately equal to delta t t k d epsilon inertial range anomalous exponents identified with the critical dimensions of various scalar and tensor composite operators constructed of the scalar gradients are calculated within the epsilon expansion to order epsilon 3 three loop approximation including the exponents in anisotropic sectors the main goal of the paper is to give the complete derivation of this third order result and to present and explain in detail the corresponding calculational techniques the character and convergence properties of the epsilon expansion are discussed the improved inverse epsilon expansion is proposed and the comparison with the existing nonperturbative results is given

large deviations and the maximum entropy principle for marked point random fields we establish large deviation principles for the stationary and the individual empirical fields of poisson and certain interacting random fields of marked point particles in d the underlying topologies are induced by a class of not necessarily bounded local functions and thus finer than the usual weak topologies our methods yield further that the limiting behaviour of conditional poisson distributions as well as certain distributions of gibbsian type is governed by the maximum entropy principle we also discuss various applications and examples

anomalous scaling of passive scalar fields advected by the navier stokes velocity ensemble effects of strong compressibility and large scale anisotropy the field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities the density and the tracer fields advected by a random turbulent velocity field the latter is governed by the navier stokes equation for compressible fluid subject to external random force with the covariance t t k 4 d y where d is the dimension of space and y is an arbitrary exponent the original stochastic problems are reformulated as multiplicatively renormalizable field theoretic models the corresponding renormalization group equations possess infrared attractive fixed points it is shown that various correlation functions of the scalar field its powers and gradients demonstrate anomalous scaling behavior in the inertial convective range already for small values of y the corresponding anomalous exponents identified with scaling critical dimensions of certain composite fields operators in the quantum field terminology can be systematically calculated as series in y the practical calculation is performed in the leading one loop approximation including exponents in anisotropic contributions it should be emphasized that in contrast to gaussian ensembles with finite correlation time the model and the perturbation theory presented here are manifestly galilean covariant the validity of the one loop approximation and comparison with gaussian models are briefly discussed

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

anomalous scaling of a passive scalar in the presence of strong anisotropy field theoretic renormalization group and the operator product expansion are applied to a model of a passive scalar quantity straight theta t x advected by the gaussian strongly anisotropic velocity field with the covariance infinity delta t t x x epsilon inertial range anomalous scaling behavior is established and explicit asymptotic expressions for the structure functions s n r identical with are obtained they are represented by superpositions of power laws the corresponding anomalous exponents which depend explicitly on the anisotropy parameters are calculated to the first order in epsilon in any space dimension d in the limit of vanishing anisotropy the exponents are associated with tensor composite operators built of the scalar gradients and exhibit a kind of hierarchy related to the degree of anisotropy the less is the rank the less is the dimension and consequently the more important is the contribution to the inertial range behavior the leading terms of the even odd structure functions are given by the scalar vector operators for the finite anisotropy the exponents cannot be associated with individual operators which are essentially mixed in renormalization but the aforementioned hierarchy survives for all the cases studied the second order structure function s2 is studied in more detail using the renormalization group and zero mode techniques the corresponding exponents and amplitudes are calculated within the perturbation theories in epsilon 1 d and in the anisotropy parameters if the anisotropy of the velocity is strong enough the skewness factor s 3 s 3 2 2 increases going down towards the depth of the inertial range the higher order odd ratios increase even if the anisotropy is weak

on the interpretation of 1 f noise we propose a model of 1 f noise based on a random walk in a random potential numerical support for the model is given and physical applicability discussed

entropy limit theorems and variational principles for disordered lattice systems we study infinite volume limits and gibbs states of disordered lattice systems with bounded and continuous potentials our main tools are a generalization of relative entropy for random reference measures and a large deviation theory for nonstationary independent processes we find that many familiar results of invariant potentials such as large deviation theorems variational principles and equivalence of ensembles continue to hold for disordered models with suitably modified statements

a non wiener random walk in a two dimensional bernoulli environment for a degenerate random walk in a 2d bernoulli environment without local traps computer results show a non wiener behavior for a better exploitation of the memory the analysis is based on the statistics of the first exit time from a square

a line search exact penalty method with bi object strategy for nonlinear constrained optimization the exact penalty methods are very popular because of their ability to handle degenerate problems and inconsistent constraint linearizations this paper presents a line search exact penalty method with bi object strategy lsbo for nonlinear constrained optimization in the algorithm lsbo the penalty parameter is selected at every iteration such that the sufficient progress toward feasibility and optimality is guaranteed along the search direction in contrast with classical exact penalization approaches lsbo method has two goals to determine whether the current iteration is successful or not one is improving the feasibility and the other is reducing the value of the objective function moreover the penalty parameter is only related to the information at the current iterate point the sequence of the penalty parameter is non monotone which does not affect the global convergence in theory and is seen to be advantageous in practice it is shown that the algorithm enjoys favorable global convergence properties under the weaker assumptions numerical experiments illustrate the behavior of the algorithm on various difficult situations penalty factor is only related to the information at the current iterate point the sequence of the penalty parameter is non monotone the search direction is related to the penalty factor the acceptable criterion is not related to the penalty factor method can handle degenerate problems and inconsistent constraint linearizations

rigorous renormalisation group and disordered systems abstract we consider random walks in a non symmetric random environment we report a recent result based on a renormalisation group approach showing that for d 62 2 these walks are diffusive when the disorder is weak

global convergence of slanting filter methods for nonlinear programming in this paper we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates independently of how these iterates are computed we prove that all accumulation points of the sequence generated by the algorithm are feasible computing the new iterates by the inexact restoration method we prove stationarity of all accumulation points of the sequence

superlinearly convergent approximate newton methods for lc 1 optimization problems in the literature the proof of superlinear convergence of approximate newton or sqp methods for solving nonlinear programming problems requires twice smoothness of the objective and constraint functions sometimes the second order derivatives of those functions are required to be lipschitzian in this paper we present approximate newton or sqp methods for solving nonlinear programming problems whose objective and constraint functions have locally lipschitzian derivatives and establishq superlinear convergence of these methods under the assumption that these derivatives are semismooth this assumption is weaker than the second order differentiability the extended linear quadratic programming problem in the fully quadratic case is an example of nonlinear programming problems whose objective functions have semismooth but not smooth derivatives

a penalty free type nonmonotone trust region method for nonlinear constrained optimization in this paper we propose a penalty free type nonmonotone trust region method for solving general nonlinear programming problem the algorithmic framework yields global convergence without using any penalty function we analyze the global convergence of the main algorithm for the degenerate problems and also give the globally convergent results under the linear independence constraint qualification the preliminary numerical tests are reported

on local isotropy of passive scalars in turbulent shear flows an assessment of local isotropy and universality in high reynolds number turbulent flows is presented the emphasis is on the behaviour of passive scalar fields advected by turbulence but a brief review of the relevant facts is given for the turbulent motion itself experiments suggest that local isotropy is not a natural concept for scalars in shear flows except perhaps at such extreme reynolds numbers that are of no practical relevance on earth yet some type of scaling exists even at moderate reynolds numbers the relation between these two observations is a theme of this paper

exact calculation of the anomalous dimension of the diffusion coefficient for a model of a random walk in a random potential renormalisation of a model of classical diffusion in a random potential is analysed it is shown that at two dimensions the one loop expression for the anomalous dimension of the diffusion coefficient is perturbatively exact leading to the coupling dependent value 1 nu 2 g 4 pi of the exponent nu

a conic trust region method for optimization with nonlinear equality and inequality constrains via active set strategy in this paper by means of an active set strategy we present a new trust region method based on conic model for mixed constrained nonlinear programming the global convergence of the trust region method is proved under standard conditions in this paper one approximate method is also considered to solve the trust region subproblem as we can see sufficient decrease of the predicted reduction can be guaranteed by the approximate method the numerical tests show the effectiveness of the algorithm

anomalous scaling regimes of a passive scalar advected by the synthetic velocity field the field theoretic renormalization group rg is applied to the problem of a passive scalar advected by the gaussian self similar velocity field with finite correlation time and in the presence of an imposed linear mean gradient the energy spectrum in the inertial range has the form e k ensuremath propto k 1 ensuremath ensuremath varepsilon and the correlation time at the wave number k scales as k ensuremath 2 ensuremath eta it is shown that depending on the values of the exponents ensuremath varepsilon and ensuremath eta the model in the inertial convective range exhibits various types of scaling regimes associated with the infrared stable fixed points of the rg equations diffusive type regimes for which the advection can be treated within ordinary perturbation theory and three nontrivial convection type regimes for which the correlation functions exhibit anomalous scaling behavior the explicit asymptotic expressions for the structure functions and other correlation functions are obtained the anomalous exponents determined by the scaling dimensions of the scalar gradients are calculated to the first order in ensuremath varepsilon and ensuremath eta in any space dimension for the first nontrivial regime the anomalous exponents are the same as in the rapid change version of the model for the second they are the same as in the model with time independent frozen velocity field in these regimes the anomalous exponents are universal in the sense that they depend only on the exponents entering into the velocity correlator for the last regime the exponents are nonuniversal they can depend also on the amplitudes however the nonuniversality can reveal itself only in the second order of the rg expansion a brief discussion of the passive advection in the non gaussian velocity field governed by the nonlinear stochastic navier stokes equation is also given

global convergence of filter methods for nonlinear programming we present a general filter algorithm that allows a great deal of freedom in the step computation each iteration of the algorithm consists basically in computing a point which is not forbidden by the filter from the current point we prove its global convergence assuming that the step must be efficient in the sense that near a feasible nonstationary point the reduction of the objective function is large we show that this condition is reasonable by presenting two classical ways of performing the step which satisfy it in the first one the step is obtained by the inexact restoration method of martinez and pilotta in the second the step is computed by sequential quadratic programming

anisotropic nonperturbative zero modes for passively advected magnetic fields an analytic assessment of the role of anisotropic corrections to the isotropic anomalous scaling exponents is given for the d dimensional kinematic magnetohydrodynamics problem in the presence of a mean magnetic field the velocity advecting the magnetic field changes very rapidly in time and scales with a positive exponent xi inertial range anisotropic contributions to the scaling exponents zeta j of second order magnetic correlations are associated with zero modes and have been calculated nonperturbatively for d 3 the limit xi 0 yields zeta j j 2 xi 2j 3 j 2 5j 4 2 4j 2 1 where j j or 2 is the order in the legendre polynomial decomposition applied to correlation functions conjectures on the fact that anisotropic components cannot change the isotropic threshold to the dynamo effect are also made

on the maximization of a concave quadratic function with box constraints a new method for maximizing a concave quadratic function with bounds on the variables is introduced the new algorithm combines conjugate gradients with gradient projection techniques as the algorithm of more and toraldo siam j optimization 1 1991 pp 93 113 and other well known methods do a new strategy for the decision of leaving the current face is introduced that makes it possible to obtain finite convergence even for a singular hessian and in the presence of dual degeneracy numerical experiments are presented

a global convergence theory for general trust region based algorithms for equality constrained optimization this work presents a global convergence theory for a broad class of trust region algorithms for the smooth nonlinear programming problem with equality constraints the main result generalizes powell s 1975 result for unconstrained trust region algorithms the trial step is characterized by very mild conditions on its normal and tangential components the normal component need not be computed accurately the theory requires a quasi normal component to satisfy a fraction of cauchy decrease condition on the quadratic model of the linearized constraints the tangential component then must satisfy a fraction of cauchy decrease condition on a quadratic model of the lagrangian function in the translated tangent space of the constraints determined by the quasi normal component estimates of the lagrange multipliers and the hessians are assumed only to be bounded the other main characteristic of this class of algorithms is that the step is evaluated by using the augmented lagrangian as a merit function with the penalty parameter updated using the el alem scheme the properties of the step and the way that the penalty parameter is chosen are sufficient to establish global convergence as an example an algorithm is presented that can be viewed as a generalization of the steihaug toint dogleg algorithm for the unconstrained case it is based on a quadratic programming algorithm that uses a step in a quasi normal direction to the tangent space of the constraints and then takes feasible conjugate reduced gradient steps to solve the reduced quadratic program this algorithm should cope quite well with large problems for which effective preconditioners are known

microcanonical distributions for lattice gases in this article a large deviation principle cf theorem 1 3 for the empirical distribution functional is applied to prove a rather general version of boltzmann s principle cf theorem 3 5 for models with shift invariant finite range potentials the final section contains an application of these considerations to the two dimensional ising model at sub critical temperature

anomalous scaling of a passive vector advected by the navier stokes velocity field using the field theoretic renormalization group and the operator product expansion the model of a passive vector field a weak magnetic field in the framework of the kinematic mhd advected by the velocity field which is governed by the stochastic navier stokes equation with the gaussian random stirring force correlated in time and with the correlator proportional to k4 d 2e is investigated to the first order in e one loop approximation it is shown that the single time correlation functions of the advected vector field have anomalous scaling behavior and the corresponding exponents are calculated in the isotropic case as well as in the case with the presence of large scale anisotropy the hierarchy of the anisotropic critical dimensions is briefly discussed and the persistence of the anisotropy inside the inertial range is demonstrated on the behavior of the skewness and hyperskewness dimensionless ratios of correlation functions as functions of the reynolds number re it is shown that even though the present model of a passive vector field advected by the realistic velocity field is mathematically more complicated than on one hand the corresponding models of a passive vector field advected by synthetic gaussian velocity fields and on the other hand than the corresponding model of a passive scalar quantity advected by the velocity field driven by the stochastic navier stokes equation the final one loop approximate asymptotic scaling behavior of the single time correlation or structure functions of the advected fields of all models are defined by the same anomalous dimensions up to normalization

the nonlinear programming method of wilson han and powell with an augmented lagrangian type line search function the paper represents an outcome of an extensive comparative study of nonlinear optimization algorithms this study indicates that quadratic approximation methods which are characterized by solving a sequence of quadratic subproblems recursively belong to the most efficient and reliable nonlinear programming algorithms available at present the purpose of this paper is to analyse the theoretical convergence properties and to investigate the numerical performance in more detail in part 1 the exactl 1 penalty function of han and powell is replaced by a differentiable augmented lagrange function for the line search computation to the able to prove the global convergence and to show that the steplength one is chosen in the neighbourhood of a solution in part 2 the quadratic subproblem is exchanged by a linear least squares problem to improve the efficiency and to test the dependence of the performance from different solution methods for the quadratic or least squares subproblems

multidimensional random walks in random environments with subclassical limiting behavior in this paper we will describe and analyze a class of multidimensional random walks in random environments which contain the one dimensional nearest neighbor situation as a special case and have the pleasant feature that quite a lot can be said about them our results make rigorous a heuristic argument of marinari et al 1983 and show that in anyd we can have a xn is recurrent and b xn logn 2

turbulent compressible fluid renormalization group analysis scaling regimes and anomalous scaling of advected scalar fields we study a model of fully developed turbulence of a compressible fluid based on the stochastic navier stokes equation by means of the field theoretic renormalization group in this approach scaling properties are related to the fixed points of the renormalization group equations previous analysis of this model near the real world space dimension 3 identified a scaling regime n v antonov et al theor math phys 110 305 1997 tmphah0040 577910 1007 bf02630456 the aim of the present paper is to explore the existence of additional regimes which could not be found using the direct perturbative approach of the previous work and to analyze the crossover between different regimes it seems possible to determine them near the special value of space dimension 4 in the framework of double y and expansion where y is the exponent associated with the random force and 4 d is the deviation from the space dimension 4 our calculations show that there exists an additional fixed point that governs scaling behavior turbulent advection of a passive scalar density field by this velocity ensemble is considered as well we demonstrate that various correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial convective range the corresponding anomalous exponents identified as scaling dimensions of certain composite fields can be systematically calculated as a series in y and all calculations are performed in the leading one loop approximation

three loop calculation of the anomalous dimension of diffusivity for a model of a random walk in a potential random field with long range correlations the three loop contribution to the anomalous dimension of the diffusion coefficient of the model of a random walk in a potential random field with long range correlations is calculated contrary to earlier conjectures the result is not zero for logarithmic growth of the correlations but vanishes only in one and two dimensions in which the one loop contribution yields the exact value of the anomalous dimension

conditions for convergence of trust region algorithms for nonsmooth optimization this paper discusses some properties of trust region algorithms for nonsmooth optimization the problem is expressed as the minimization of a functionh f x whereh is convex andf is a continuously differentiable mapping from to bounds for the second order derivative approximation matrices are discussed it is shown that powel s 7 8 results hold for nonsmooth optimization

an algorithm for the topology optimization of geometrically nonlinear structures summary most papers on topology optimization consider that there is a linear relation between the strains and displacements of the structure implicitly assuming that the displacements of the structure are small however when the external loads applied to the structure are large the displacements also become large so it is necessary to suppose that there is a nonlinear relation between strains and displacements in this case we say that the structure is geometrically nonlinear in practice this means that the linear system that needs to be solved each time the objective function of the problem is evaluated is replaced by an ill conditioned nonlinear system of equations moreover the stiffness matrix and the derivatives of the problem also become harder to compute the objective of this work is to solve topology optimization problems under large displacements through a new optimization algorithm named sequential piecewise linear programming this method relies on the solution of convex piecewise linear programming subproblems that include second order information about the objective function to speed up the algorithm these subproblems are converted into linear programming ones the new algorithm is not only globally convergent to stationary points but our numerical experiments also show that it is efficient and robust copyright 2014 john wiley sons ltd

large deviation principles for euclidean functionals and other nearly additive processes we prove a large deviation principle for a process indexed by cubes of the multidimensional integer lattice or euclidean space under approximate additivity and regularity hypotheses the rate function is the convex dual of the limiting logarithmic moment generating function in some applications the rate function can be expressed in terms of relative entropy the general result applies to processes in euclidean combinatorial optimization statistical mechanics and computational geometry examples include the length of the minimal tour the traveling salesman problem the length of the minimal matching graph the length of the minimal spanning tree the length of the k nearest neighbors graph and the free energy of a short range spin glass model

three loop calculation of the random walk problem an application of dimensional transformation and the uniqueness method the method and details of the calculation of the three loop contribution to the anomalous dimension of the diffusion coefficient of the model of a random walk in a potential random field with long range correlations are presented contrary to earlier conjectures this contribution does not vanish identically a new method of calculation of multi loop feynman graphs with complicated numerator structure is suggested it leads to simpler integrals in a space of higher dimensionality which are computed using the recursion relations of the uniqueness method

a trust region algorithm for equality constrained optimization a trust region algorithm for equality constrained optimization is proposed that employs a differentiable exact penalty function under certain conditions global convergence and local superlinear convergence results are proved

current noise and long time tails in biased disordered random walks we calculate the mean velocity and the velocity correlation function for a random walk with a uniform bias on a disordered chain we find a new long time tail in the velocity correlation function due to the combined effects of the bias and of the disorder in the site variables this long time tail persists to a low frequency cutoff inversely proportional to the square of the bias by associating the velocity correlation function with the spectrum of current fluctuations we calculate the excess low frequency current noise associated with this long time tail the spectrum of current fluctuations goes as i2 n f 1 2 wherei is the dc current n is the number of charge carriers andf is the frequency the possible connection to 1 f noise is discussed the calculation is done by a perturbation expansion in the strength of the disorder but is shown to be exact to all orders for weak enough bias

global and local convergence of a penalty free method for nonlinear programming we present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization in each iteration the infeasibility is controlled by a progressively decreasing upper limit and trial steps are computed by a byrd omojokun type trust region strategy measures of optimality and infeasibility are computed whose relationship serves as a criterion on which the algorithm decides which one to focus on improving as a result the algorithm keeps a balance between the improvements on optimality and feasibility even if no restoration phase which is required by filter methods is used the framework of the algorithm ensures the global convergence without assuming regularity or boundedness on the iterative sequence by using a second order correction strategy marato s effect is avoided and fast local convergence is shown the preliminary numerical results are reported

anomalous scaling of a passive scalar advected by the navier stokes velocity field two loop approximation the field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by a non gaussian velocity field with finite correlation time the velocity is governed by the navier stokes equation subject to an external random stirring force with the correlation function proportional to ensuremath delta t ensuremath t ensuremath k 4 ensuremath d ensuremath 2 ensuremath epsilon it is shown that the scalar field is intermittent already for small ensuremath epsilon its structure functions display anomalous scaling behavior and the corresponding exponents can be systematically calculated as series in ensuremath epsilon the practical calculation is accomplished to order ensuremath epsilon 2 two loop approximation including anisotropic sectors as for the well known kraichnan rapid change model the anomalous scaling results from the existence in the model of composite fields operators with negative scaling dimensions identified with the anomalous exponents thus the mechanism of the origin of anomalous scaling appears similar for the gaussian model with zero correlation time and the non gaussian model with finite correlation time it should be emphasized that in contrast to gaussian velocity ensembles with finite correlation time the model and the perturbation theory discussed here are manifestly galilean covariant the relevance of these results for real passive advection and comparison with the gaussian models and experiments are briefly discussed

renormalization group operator product expansion and anomalous scaling in a model of advected passive scalar field theoretical renormalization group methods are applied to the obukhov kraichnan model of a passive scalar advected by the gaussian velocity field with the covariance mathbf v t mathbf x mathbf v t ensuremath mathbf x ensuremath mathbf v t mathbf x mathbf v t ensuremath mathbf x ensuremath ensuremath propto ensuremath delta t ensuremath t ensuremath mathbf x ensuremath mathbf x ensuremath ensuremath varepsilon inertial range anomalous scaling for the structure functions and various pair correlators is established as a consequence of the existence in the corresponding operator product expansions of certain essential or dangerous composite operators powers of the local dissipation rate whose negative critical dimensions determine anomalous exponents the main technical result is the calculation of the anomalous exponents in the order ensuremath varepsilon 2 of the ensuremath varepsilon expansion generalization of the results obtained to the case of a slow velocity field is also presented

equilibrium distributions for random walkers in random media the authors study the renyi entropies of the probability distribution of a random walker in a random medium of finite total volume in one dimension of space it is shown that they tend for large lattices to constants independent of the lattice size thus the distribution is not multifractal in contrast to a recent claim the authors conjecture that the same is true for any dimension if the random force is derived from a potential in the more interesting general case unconstrained forces they cannot make a definite statement

intermittency and anomalous scaling of passive scalars in any space dimension we establish exact inequalities for the structure function scaling exponents of a passively advected scalar in both the inertial convective and viscous convective ranges these inequalities involve the scaling exponents of the velocity structure functions and in a refined form an intermittency exponent of the convective range scalar flux they are valid for three dimensional navier stokes turbulence and satisfied within errors by present experimental data the inequalities also hold for any synthetic turbulent velocity statistics with a finite correlation in time we show that for time correlation exponents of the velocity smaller than the local turnover exponent the scalar spectral exponent is strictly less than that in kraichnan s phys rev lett 72 1016 1994 phys fluids 11 945 1968 j fluid mech 64 737 1974 62 305 1974 soluble rapid change model with velocity ensuremath delta correlated in time our results include as a special case an exponent inequality derived previously by constantin and procaccia nonlinearity 7 1045 1994 but with a more direct proof the inequalities in their simplest form follow from a kolmogorov type relation for the turbulent passive scalar valid in each space dimension d our improved inequalities are based upon a rigorous version of the refined similarity hypothesis for passive scalars these are compared with the relations implied by fusion rules hypothesized for scalar gradients textcopyright 1996 the american physical society

concentration inequalities for functions of gibbs fields with application to diffraction and random gibbs measures we derive useful general concentration inequalities for functions of gibbs fields in the uniqueness regime we also consider expectations of random gibbs measures that depend on an additional disorder field and prove concentration w r t the disorder field both fields are assumed to be in the uniqueness regime allowing in particular for non independent disorder fields the modification of the bounds compared to the case of an independent field can be expressed in terms of constants that resemble the dobrushin contraction coefficient and are explicitly computable on the basis of these inequalities we obtain bounds on the deviation of a diffraction pattern created by random scatterers located on a general discrete point set in euclidean space restricted to a finite volume here we also allow for thermal dislocations of the scatterers around their equilibrium positions extending recent results for independent scatterers we give a universal upper bound on the probability of a deviation of the random scattering measures applied to an observable from its mean the bound is exponential in the number of scatterers with a rate that involves only the minimal distance between points in the point set

normal and anomalous scaling of the fourth order correlation function of a randomly advected passive scalar for a delta correlated velocity field simultaneous correlation functions of a passive scalar satisfy closed equations we analyze the equation for the four point function to describe a solution completely one has to solve the matching problems at the scale of the source and at the diffusion scale we solve both the matching problems and thus find the dependence of the four point correlation function on the diffusion and pumping scale for large space dimensionality d it is shown that anomalous scaling appears in the first order of 1 d perturbation theory anomalous dimensions are found analytically both for the scalar field and for it s derivatives in particular for the dissipation field

renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow field theoretical renormalization group methods are applied to a simple model of a passive scalar quantity advected by the gaussian non solenoidal compressible velocity field with the covariance propto delta t t x x epsilon convective range anomalous scaling for the structure functions and various pair correlators is established and the corresponding anomalous exponents are calculated to the order epsilon 2 of the epsilon expansion these exponents are non universal as a result of the degeneracy of the rg fixed point in contrast to the case of a purely solenoidal velocity field obukhov kraichnan model the correlation functions in the case at hand exhibit nontrivial dependence on both the ir and uv characteristic scales and the anomalous scaling appears already at the level of the pair correlator the powers of the scalar field without derivatives whose critical dimensions determine the anomalous exponents exhibit multifractal behaviour the exact solution for the pair correlator is obtained it is in agreement with the result obtained within the epsilon expansion the anomalous exponents for passively advected magnetic fields are also presented in the first order of the epsilon expansion