pullback and pushout constructions in c algebra theory abstract a systematic study of pullback and pushout diagrams is conducted in order to understand restricted direct sums and amalgamated free products of c algebras particular emphasis is given to the relations with tensor products both with the minimal and the maximal c tensor norm thus it is shown that pullback and pushout diagrams are stable under tensoring with a fixed algebra and stable under crossed products with a fixed group general tensor products between diagrams are also investigated the relations between the theory of extensions and pullback and pushout diagrams are explored in some detail the crowning result is that if three short exact sequences of c algebras are given with appropriate morphisms between the sequences allowing for pullback or pushout constructions at the levels of ideals algebras and quotients then the three new c algebras will again form a short exact sequence under some mild extra conditions as a generalization of a theorem of t a loring it is shown that each morphism between a pair of c algebras combined with its extension to the stabilized algebras gives rise to a pushout diagram this result has applications to corona extendibility and conditional projectivity finally the pullback and pushout constructions are applied to the class of noncommutative cw complexes defined by s eilers t a loring and g k pedersen j reine angew math 1998 499 101 143 to show that this category is stable under tensor products and under restricted direct sums

intertwining operators and unitary representations i abstract for a linear semisimple lie group with a compact cartan subgroup the authors obtain formulas for the action of intertwining operators on certain subspaces of standard induced representations these formulas provide explicit limitations on the pool of candidates for irreducible unitary representations since the only possible invariant inner product is given by such an intertwining operator

crossed products by endomorphisms of c_0 x algebras abstract in the first part of the paper we develop a theory of crossed products of a c algebra a by an arbitrary not necessarily extendible endomorphism a a we consider relative crossed products c a j where j is an ideal in a and describe up to morita rieffel equivalence all gauge invariant ideals in c a j and give six term exact sequences determining their k theory we also obtain certain criteria implying that all ideals in c a j are gauge invariant and that c a j is purely infinite in the second part we consider a situation where a is a c 0 x algebra and is such that f a f a a a f c 0 x where is an endomorphism of c 0 x pictorially speaking is a mixture of a topological dynamical system x dual to c 0 x and a continuous field of homomorphisms x between the fibers a x x x of the corresponding c bundle for systems described above we establish efficient conditions for the uniqueness property gauge invariance of all ideals and pure infiniteness of c a j we apply these results to the case when x prim a is a hausdorff space in particular if the associated c bundle is trivial we obtain formulas for k groups of all ideals in c a j in this way we constitute a large class of crossed products whose ideal structure and k theory is completely described in terms of x x x x y where y is a closed subset of x

divisibility properties for c algebras we consider three notions of divisibility in the cuntz semigroup of a c algebra and show how they reflect properties of the c algebra we develop methods to construct simple and non simple c algebras with specific divisibility behaviour as a byproduct of our investigations we show that there exists a sequence an of simple unital infinite dimensional c algebras such that the product n 1an has a character

dissipation statistics of a passive scalar in a multidimensional smooth flow we compute analytically the probability distribution function p e of the dissipation field e 2 of a passive scalar advected by a d dimensional random flow in the limit of large peclet and prandtl numbers batchelor kraichnan regime the tail of the distribution is a stretched exponential for e ln p e d2e 1 3

self similar decay in the kraichnan model of a passive scalar we study the two point correlation function of a freely decaying scalar in kraichnan s model of advection by a gaussian random velocity field that is stationary and white noise in time but fractional brownian in space with roughness exponent 0 2 appropriate to the inertial convective range of the scalar we find all self similar solutions by transforming the scaling equation to kummer s equation it is shown that only those scaling solutions with scalar energy decay exponent a d 1 are statistically realizable where d is space dimension and 2 an infinite sequence of invariants jp p 0 1 2 is pointed out where j0 is corrsin s integral invariant but the higher invariants appear to be new we show that at least one of the invariants j0 or j1 must be nonzero possibly infinite for realizable initial data initial datum with a finite nonzero invariant the first being jp converges at long times to a scaling solution p with a d p p 0 1 the latter belongs to an exceptional series of self similar solutions with stretched exponential decay in space however the domain of attraction includes many initial data with power law decay when the initial datum has all invariants zero or infinite and also it exhibits power law decay then the solution converges at long times to a nonexceptional scaling solution with the same power law decay these results support a picture of a two scale decay with breakdown of self similarity for a range of exponents d a d 2 analogous to what has recently been found in the decay of burgers turbulence

towards a theory of classification abstract the well known difficulties arising in a classification which is not set theoretically trivial involving what is sometimes called a non smooth quotient have been overcome in a striking way in the theory of operator algebras by the use of what might be called a classification functor the very existence of which is already a surprise here the notion of such a functor is developed abstractly and a number of examples are considered including those which have arisen for various classes of operator algebras

extensions of cuntz krieger algebras abstract we show that a c algebra looking like a cuntz krieger algebra is a cuntz krieger algebra this implies that in an appropriate sense the class of cuntz krieger algebras is closed under extensions of real rank zero

the connes higson construction is an isomorphism let a be a separable c algebra and b a stable c algebra containing a strictly positive element we show that the group ext 1 2 sa b of unitary equivalence classes of extensions of sa by b modulo the extensions which are asymptotically split coincides with the group of homotopy classes of such extensions this is done by proving that the connes higson construction gives rise to an isomorphism between ext 1 2 sa b and the e theory group e a b of homotopy classes of asymptotic homomorphisms from s2a to b

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

poset block equivalence of integral matrices given square matrices b and b with a poset indexed block structure for which an ij block is zero unless i j when are there invertible matrices u and v with this required zero block structure such that ubv b we give complete invariants for the existence of such an equivalence for matrices over a principal ideal domain r as one application when r is a field we classify such matrices up to similarity by matrices respecting the block structure we also give complete invariants for equivalence under the additional requirement that the diagonal blocks of u and v have determinant 1 the invariants involve an associated diagram the k web of r module homomorphisms the study is motivated by applications to symbolic dynamics and c algebras

unitary representations induced from maximal parabolic subgroups abstract it is known that the problem of classifying the irreducible unitary representations of a linear connected semisimple lie group g comes down to deciding which langlands quotients j man v are infinitesimally unitary here man is any cuspidal parabolic subgroup is any discrete series or nondegenerate limit of discrete series representation of m and v is any complex valued linear functional on the lie algebra of a satisfying certain positivity and symmetry properties the authors determine which langlands quotients are infinitesimally unitary under the conditions that g is simple that dim a 1 and that g is neither split f 4 nor split g 2

indefinite intertwining operators for a wide class of linear connected semisimple lie groups one obtains formulas limiting the langlands parameters of irreducible unitary representations obtained from maximal parabolic subgroups the formulas relate unitarity to the number of roots satisfying certain conditions some evidence is presented that the formulas are sharp the results confirm aspects of conjectures that relate unitary parameters to cohomological induction

non simple purely infinite c algebras the hausdorff case abstract local and global definitions of pure infiniteness for a c algebra a are compared and equivalence between them is obtained if the primitive ideal space of a is hausdorff and of finite dimension if a has real rank zero or if a is approximately divisible sufficient criteria are given for local pure infiniteness of tensor products they yield that exact simple tensorially non prime c algebras are purely infinite if they have no semi finite lower semi continuous trace one obtains that a is isomorphic to a o if a is 1 purely infinite separable stable nuclear and prim a is a hausdorff space not necessarily of finite dimension

continuous fields of kirchberg c algebras abstract in this paper we study the c algebras associated to continuous fields over locally compact metrizable zero dimensional spaces whose fibers are kirchberg c algebras satisfying the uct we show that these algebras are inductive limits of finite direct sums of kirchberg algebras and they are classified up to isomorphism by topological invariants

infinite non simple c algebras absorbing the cuntz algebra o abstract the first named author has given a classification of all separable nuclear c algebras a that absorb the cuntz algebra o we say that a absorbs o if a is isomorphic to a o motivated by this classification we investigate here if one can give an intrinsic characterization of c algebras that absorb o this investigation leads us to three different notions of pure infiniteness of a c algebra all given in terms of local algebraic conditions on the c algebra the strongest of the three properties strongly purely infinite is shown to be equivalent to absorbing o for separable nuclear c algebras that either are stable or have an approximate unit consisting of projections in a previous paper 2000 amer j math 122 637 666 we studied an intermediate and perhaps more natural condition purely infinite that extends a well known property for simple c algebras the weakest condition of the three weakly purely infinite is shown to be equivalent to the absence of quasitraces in an ultrapower of the c algebra the three conditions may be equivalent for all c algebras and we prove this to be the case for c algebras that are either simple of real rank zero or approximately divisible

spectral compact difference hybrid computation of passive scalar in isotropic turbulence an accurate and efficient hybrid numerical method is developed for direct numerical simulation of passive scalar in homogeneous turbulence for the schmidt number 1 and 50 the hybrid method uses the standard fourier spectral method for the incompressible navier stokes equation and the combined compact difference scheme for the passive scalar transport equation accuracy of the method is carefully examined by comparing with the full spectral method regarding the spectra probability density function field structure of the passive scalar and is found to be very satisfactory the computational time for the hybrid method is decreased by 26 for the schmidt number 1 when compared to the full spectral method and by 77 for the schmidt number 50 when the number of grid points for the velocity field is reduced under the scale separation

non gaussian invariant measures for the majda model of decaying turbulent transport the problem of turbulent transport of a scalar field by a random velocity field is considered the scalar field amplitude exhibits rare but very large fluctuations whose typical signature is fatter than gaussian tails for the probability distribution of the scalar the existence of such large fluctuations is related to clustering phenomena of the lagrangian paths within the flow this suggests an approach to turn the large deviation problem for the scalar field into a small deviation or small ball problem for some appropriately defined process measuring the spreading with time of the lagrangian paths here such a methodology is applied to a model proposed by majda consisting of a white in time linear shear flow and some generalizations of it where the velocity field has finite or even infinite correlation time the non gaussian invariant measure for the reduced scalar field is derived and in particular it is shown that the one point distribution of the scalar has stretched exponential tails with a stretching exponent depending on the parameters in the model different universality classes for the scalar behavior are identified which all other parameters being kept fixed display a one to one correspondence with an exponent measuring time persistence effects in the velocity field c 2001 john wiley sons inc

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

instanton filtering for the stochastic burgers equation we address the question of whether one can identify instantons in direct numerical simulations of the stochastically driven burgers equation for this purpose we first solve the instanton equations using the chernykh stepanov method 2001 phys rev e 64 026306 these results are then compared to direct numerical simulations by introducing a filtering technique to extract prescribed rare events from massive data sets of realizations using this approach we can extract the entire time history of the instanton evolution which allows us to identify the different phases predicted by the direct method of chernykh and stepanov with remarkable agreement

particle dispersion in a multidimensional random flow with arbitrary temporal correlations abstract we study the statistics of relative distances r t between fluid particles in a spatially smooth random flow with arbitrary temporal correlations using the space dimensionality d as a large parameter we develop an effective description of lagrangian dispersion we describe the exponential growth of relative distances r 2 t exp 2 t at different values of the ratio between the correlation and turnover times we find the stretching correlation time which determines the dependence of r 1 r 2 on the difference t1 t2 the calculation of the next cumulant of r2 shows that statistics of r2 is nearly gaussian at small times as long as d 1 and becomes log normal at large times when large d approach fails for high order moments the crossover time between the regimes is the stretching correlation time which surprisingly appears to depend on the details of the velocity statistics at t we establish the dispersion of the ln r2 in the log normal statistics

exact results for conditional means of a passive scalar in certain statistically homogeneous flows for a passive scalar t r t randomly advected by a statistically homogeneous flow the probability density function pdf of its fluctuation can in general be expressed in terms of two conditional means 2 t t and t 2 t we find that in some special cases either one of the two conditional means can be obtained explicitly from the equation of motion in the cases when there is no external source and that the normalized fluctuation reaches a steady state or when a steady state results from a negative damping 2 t t t 2 t 2 t the linearity of the conditional mean in these cases follows directly from the fact that the advection equation of a passive scalar is linear on the other hand when the scalar is supported by a homogeneous white in time external source t 2 t t 2

two different rapid decorrelation in time limits for turbulent diffusion a turbulent diffusion model in which the velocity field is gaussian and rapidly decorrelating in time grdt has been widely used recently in an endeavor to understand the emergence of anomalous scaling behavior of physical fields in fluid mechanics from the underlying stochastic partial differential equations the utility of the grdt model is the fact that correlation functions of the passive scalar field solve closed partial differential equations the usual moment closure obstacle is averted we study here the sense in which the grdt model describes turbulent diffusion by a general non gaussian velocity field with nontrivial temporal structure in the limit in which the correlation time of the velocity field is taken to zero when the velocity field is rescaled in a particular manner in this rapid decorrelation limit then a limit theorem of khas minskii indeed shows that the passive scalar statistics are described asymptotically by the grdt model for a broad class of velocity field models we provide however an explicit example of a poisson blob model velocity field which has two different well defined rapid decorrelation in time limits in one the passive scalar correlation functions converge to those of the grdt model and in the other they converge to a distinct nontrivial limit in which the correlation functions do not solve closed pde s we provide both mathematical and heuristic explanations for the differences between these two limits the conclusion is that the grdt model provides a universal description of the rapid decorrelation in time limit of general non gaussian velocity field models only when the velocity field is rescaled in a particular manner during the limit process

persistent stability of a chaotic system abstract we report that trajectories of a one dimensional model for inertial particles in a random velocity field can remain stable for a surprisingly long time despite the fact that the system is chaotic we provide a detailed quantitative description of this effect by developing the large deviation theory for fluctuations of the finite time lyapunov exponent of this system specifically the determination of the entropy function for the distribution reduces to the analysis of a schrodinger equation which is tackled by semi classical methods the system has generic instability properties and we consider the broader implications of our observation of long term stability in chaotic systems

classification of unital extensions of at algebras abstract we prove that the six term exact sequence in k theory together with the elliott invariants of the ideal and quotient is a complete invariant for certain unital extensions of a t algebras up to stable isomorphism we also give some necessary and sufficient conditions for such extensions being a t algebras or quasidiagonal extensions and prove the above invariant with the equivalence class of unit is a complete invariant for unital quasidiagonal extensions of a t algebras up to isomorphism

anomalous scaling for a passive scalar near the batchelor limit a class of phenomenological hopf equations describing mixing of a passive scalar by random flow close to the batchelor limit i e advection by random strain and vorticity is analyzed in the batchelor limit multipoint correlators of the scalar are constructed explicitly by exploiting the sl n r symmetry of the hopf operator hopf equations close to this integrable limit are solved via singular perturbation theory based on matched asymptotic expansions the solution for the three point correlator exhibits anomalous scaling indicating persistence of the small scale anisotropy for the scalar in addition to the exponent the full configuration dependence of the correlator is obtained s1063 651x 98 08703 0 pacs number s 47 27 2i

corrigendum to classifying c algebras with both finite and infinite subquotients j funct anal 265 2013 449 468 abstract as recently pointed out by gabe a fundamental paper by elliott and kucerovsky concerning the absorption theory for c algebras contains an error and as a consequence we must report that lemma 4 5 in 3 is not true as stated in this corrigendum we prove an adjusted statement and explain why the error has no consequences to the main results of 3 in particular it is noted that all the authors claims concerning morita equivalence or stable isomorphism of graph c algebras remain correct as stated

classifying c algebras with both finite and infinite subquotients abstract we give a classification result for a certain class of c algebras a over a finite topological space x in which there exists an open set u of x such that u separates the finite and infinite subquotients of a we apply our results to c algebras arising from graphs

the blackadar handelman theorem for non unital c algebras abstract a well known theorem of blackadar and handelman states that every unital stably finite c algebra has a bounded quasitrace rather strong generalizations of stable finiteness to the non unital case can be obtained by either requiring the multiplier algebra to be stably finite or alternatively requiring it to be at least stably not properly infinite this paper deals with the question whether the blackadar handelman result can be extended to the non unital case with respect to these generalizations of stable finiteness two examples of c algebras are constructed the first one is a non unital stably commutative c algebra a that contradicts the weakest possible generalization of the blackadar handelman theorem the multiplier algebra of a is stably finite while a has no bounded quasitrace the second example is a simple c algebra b with no bounded quasitrace such that the multiplier algebras of all matrix algebras over b are not properly infinite

e theory for c algebras over topological spaces abstract we define e theory for separable c algebras over second countable topological spaces and establish its basic properties this includes an approximation theorem that relates the e theory over a general space to the e theories over finite approximations to this space we obtain effective criteria for determining the invertibility of e theory elements over possibly infinite dimensional spaces furthermore we prove a universal multicoefficient theorem for c algebras over totally disconnected metrisable compact spaces

stochastic least action principle for the incompressible navier stokes equation abstract we formulate a stochastic least action principle for solutions of the incompressible navier stokes equation which formally reduces to hamilton s principle for the incompressible euler solutions in the case of zero viscosity we use this principle to give a new derivation of a stochastic kelvin theorem for the navier stokes equation recently established by constantin and iyer which shows that this stochastic conservation law arises from particle relabelling symmetry of the action we discuss issues of irreversibility energy dissipation and the inviscid limit of navier stokes solutions in the framework of the stochastic variational principle in particular we discuss the connection of the stochastic kelvin theorem with our previous martingale hypothesis for fluid circulations in turbulent solutions of the incompressible euler equations

stability of a σp unital continuous field algebra we study the question of whether stability is preserved under the operation of forming a continuous field algebra this is not necessarily true when the base space is infinite dimensional however it is always true when the base space is an n cube or an n torus and when the continuous field algebra is p unital specifically we prove the following theorem 0 1 let a be a p unital separable maximal full algebra of operator fields with base space either an n cube x 0 1 n or an n torus x tn and fibre algebras ax x x if ax is stable for all x x then a is a stable c algebra we also show that under the same hypotheses the corona factorization property is also preserved under the formation of continuous field algebras theorem 0 2 let a be a p unital separable maximal full algebra of operator fields with base space either an n cube x 0 1 n or an n torus x tn and fibre algebras ax x x if ax has the corona factorization property for all x x then a also has the corona factorization property

instanton for the kraichnan passive scalar problem we consider high order correlation functions of the passive scalar in the kraichnan model using the instanton formalism we find the scaling exponents ensuremath zeta n of the structure functions s n for n ensuremath gg 1 under the additional condition d ensuremath zeta 2 ensuremath gg 1 where d is the dimensionality of space at nl n c where n c d ensuremath zeta 2 2 2 ensuremath ensuremath zeta 2 the exponents are ensuremath zeta n ensuremath zeta 2 4 2n ensuremath n 2 n c while at ng n c they are n independent ensuremath zeta n ensuremath zeta 2 n c 4 we also estimate n dependent factors in s n particularly their behavior at n close to n c

mathcal c _ 0 x algebras stability and strongly self absorbing mathcal c algebras we study permanence properties of the classes of stable and so called mathcal d stable mathcal c algebras respectively more precisely we show that a mathcal c 0 x algebra a is stable if all its fibres are provided that the underlying compact metrizable space x has finite covering dimension or that the cuntz semigroup of a is almost unperforated a condition which is automatically satisfied for mathcal c algebras absorbing the jiang su algebra mathcal z tensorially furthermore we prove that if mathcal d is a k 1 injective strongly self absorbing mathcal c algebra then a absorbs mathcal d tensorially if and only if all its fibres do again provided that x is finite dimensional this latter statement generalizes results of blanchard and kirchberg we also show that the condition on the dimension of x cannot be dropped along the way we obtain a useful characterization of when a mathcal c algebra with weakly unperforated cuntz semigroup is stable which allows us to show that stability passes to extensions of mathcal z absorbing mathcal c algebras

rokhlin dimension for flows we introduce a notion of rokhlin dimension for one parameter automorphism groups of c algebras this generalizes kishimoto s rokhlin property for flows and is analogous to the notion of rokhlin dimension for actions of the integers and other discrete groups introduced by the authors and zacharias in previous papers we show that finite nuclear dimension and absorption of a strongly self absorbing c algebra are preserved under forming crossed products by flows with finite rokhlin dimension and that these crossed products are stable furthermore we show that a flow on a commutative c algebra arising from a free topological flow has finite rokhlin dimension whenever the spectrum is a locally compact metrizable space with finite covering dimension for flows that are both free and minimal this has strong consequences for the associated crossed product c algebras those containing a non zero projection are classified by the elliott invariant for compact manifolds this consists of topological k theory together with the space of invariant probability measures and a natural pairing given by the ruelle sullivan map

inverse cascade and intermittency of passive scalar in one dimensional smooth flow random advection of a lagrangian tracer scalar field ensuremath theta t x by a one dimensional spatially smooth and short correlated in time velocity field is considered scalar fluctuations are maintained by a source concentrated at the integral scale l the statistical properties of both scalar differences and the dissipation field are analytically determined exploiting the dynamical formulation of the model the gaussian statistics known to be present at small scales for incompressible velocity fields emerges here at large scales x ensuremath gg l these scales are shown to be excited by an inverse cascade of ensuremath theta 2 and the probability distribution function pdf of the corresponding scalar differences to approach the gaussian form as larger and larger scales are considered small scale x ensuremath ll l statistics is shown to be strongly non gaussian a collapse of scaling exponents for scalar structure functions takes place moments of order pg 1 all scale linearly independently of the order p smooth scaling x p is found for ensuremath 1lpl1 tails of the scalar difference pdf are exponential while at the center a cusped shape tends to develop when smaller and smaller ratios x l are considered the same tendency is present for the scalar gradient pdf with respect to the inverse of the p eclet number the pumping to diffusion scale ratio the tails of the latter pdf are however much more extended decaying as a stretched exponential of exponent 2 3 smaller than unity this slower decay is physically associated with the strong fluctuations of the dynamical dissipative scale

universal coefficient theorems for the stable ext groups let a be a unital separable nuclear c algebra and let b be a stable c algebra using k theory and kk theory we establish universal coefficient theorems for the stable ext groups of unital extensions of a by b when a and b have certain properties which generalize a result of l brown and m dadarlat for the strong ext groups the class of extensions being studied are also enlarged

a path integration formulation of stochastic lagrangian models of turbulent flow abstract in analogy with the feynman kac path integration formulation of quantum mechanics a general path integration formulation of stochastic lagrangian models of turbulent flow is developed with respect to the equivalence with the usual eulerian and stochastic lagrangian descriptions we then discuss efficient numerical methods for the realisation of the lagrangian solutions via path integration which provide an effective alternative to the simpler monte carlo approach

non hermitian localization and population biology the time evolution of spatial fluctuations in inhomogeneous d dimensional biological systems is analyzed a single species continuous growth model in which the population disperses via diffusion and convection is considered time independent environmental heterogeneities such as a random distribution of nutrients or sunlight are modeled by quenched disorder in the growth rate linearization of this model of population dynamics shows that the fastest growing localized state dominates in a time proportional to a power of the logarithm of the system size using an analogy with a schr odinger equation subject to a constant imaginary vector potential we propose a delocalization transition for the steady state of the nonlinear problem at a critical convection threshold separating localized and extended states in the limit of high convection velocity the linearized growth problem in d dimensions exhibits singular scaling behavior described by a d ensuremath 1 dimensional generalization of the noisy burgers equation with universal singularities in the density of states associated with disorder averaged eigenvalues near the band edge in the complex plane the burgers mapping leads to unusual transverse spreading of convecting delocalized populations

classification of extensions of classifiable c algebras abstract for a certain class of extensions e 0 b e a 0 of c algebras in which b and a belong to classifiable classes of c algebras we show that the functor which sends e to its associated six term exact sequence in k theory and the positive cones of k 0 b and k 0 a is a classification functor we give two independent applications addressing the classification of a class of c algebras arising from substitutional shift spaces on one hand and of graph algebras on the other the former application leads to the answer of a question of carlsen and the first named author concerning the completeness of stabilized matsumoto algebras as an invariant of flow equivalence the latter leads to the first classification result for nonsimple graph c algebras

intermittency in passive scalar decay we consider the decay of a passive scalar in a rough turbulent flow we show that at large times the scalar intensity is statistically equivalent to the product of two independent random variables the first factor is a gaussian variable related to the typical fluctuation at initial conditions the second factor is essentially the probability that in a given realization of the flow tracer particles separate at a very slow rate therefore the large time scalar distribution is always broader than gaussian for any initial condition and large scalar excursions are associated to small relative dispersion events

an algebraic approach to the radius of comparison the radius of comparison is an invariant for unital c algebras which extends the theory of covering dimension to noncommutative spaces we extend its definition to general c algebras and give an algebraic as opposed to functional theoretic reformulation this yields new permanence properties for the radius of comparison which strengthen its analogy with covering dimension for commutative spaces we then give several applications of these results new examples of c algebras with finite radius of comparison are given and the question of when the cuntz classes of finitely generated hilbert modules form a hereditary subset of the cuntz semigroup is addressed most interestingly perhaps we treat the question of when a full hereditary subalgebra b of a stable c algebra a is itself stable giving a characterization in terms of the radius of comparison we also use the radius of comparison to quantify the least n for which a c algebra d without bounded 2 quasitraces or unital quotients has the property that mn d is stable

the corona factorization property and refinement monoids the corona factorization property of a c algebra originally defined to study extensions of c algebras has turned out to say something important about intrinsic struc tural properties of the c algebra we show in this paper that a unital c algebra a of real rank zero has the corona factorization property if and only if its monoid v a of murray von neumann equivalence classes of projections in matrix algebras over a has a certain rather weak comparability property that we call the corona factorization property for monoids we show that a projection in such a c algebra is properly infinite if and only if a multiple of it is properly infinite the latter result is obtained from some more general result we establish about conical refinement monoids we show that the set of order units together with the zero element in a conical refinement monoid is again a refinement monoid under the assumption that the monoid satisfies weak divisibility and if u is an element in a refinement monoid such that nu is properly infinite then u can be written as a sum u s t such that ns and nt are properly infinite

anomalous scaling in anisotropic turbulence abstract we present a short review of the work conducted by our group on the subject of anomalous scaling in anisotropic turbulence the basic idea that unifies all the applications discussed here is that the equations of motion for correlation functions are always linear and invariant to rotations and therefore the solutions foliate into sectors of the symmetry group of all rotations so 3 we have considered models of passive scalar and passive vector advections by a rapidly changing turbulent velocity field kraichnan type models for which we find a discrete spectrum of universal anomalous exponents with a different exponent characterizing the scaling behavior in every sector generically the correlation functions and structure functions appear as sums over all these contributions with nonuniversal amplitudes which are determined by the anisotropic boundary conditions in addition we considered navier stokes turbulence by analyzing simulations and experiments and reached some interesting conclusions regarding the scaling exponents in the anisotropic sectors the theory presented here clarifies questions like the restoration of local isotropy upon decreasing scales we explain when the local isotropy is fully restored and when the lingering effects of the anisotropic forcing appear for arbitrarily small scales

evolution of a scalar gradient s probability density function in a random flow the evolution of the probability density function pdf of the passive scalar gradient is studied in the limit of large peclet and prandtl numbers in d dimensions without diffusion the closed fokker planck equation can be derived and solved analytically leading to a number of conclusions in particular it allows the description of the restoration of the rotational symmetry and enables one to distinguish different regimes of evolution and different intervals of pdf behavior

spontaneous stochasticity and anomalous dissipation for burgers equation we develop a lagrangian approach to conservation law anomalies in weak solutions of inviscid burgers equation motivated by previous work on the kraichnan model of turbulent scalar advection we show that the entropy solutions of burgers possess markov stochastic processes of generalized lagrangian trajectories backward in time for which the burgers velocity is a backward martingale this property is shown to guarantee dissipativity of conservation law anomalies for general convex functions of the velocity the backward stochastic burgers flows with these properties are not unique however we construct infinitely many such stochastic flows both by a geometric construction and by the zero noise limit of the constantin iyer stochastic representation of viscous burgers solutions the latter proof yields the spontaneous stochasticity of lagrangian trajectories backward in time for burgers at unit prandtl number it is conjectured that existence of a backward stochastic flow with the velocity as martingale is an admissibility condition which selects the unique entropy solution for burgers we also study linear transport of passive densities and scalars by inviscid burgers flows we show that shock solutions of burgers exhibit spontaneous stochasticity backward in time for all finite prandtl numbers implying conservation law anomalies for linear transport we discuss the relation of our results for burgers with incompressible navier stokes turbulence especially lagrangian admissibility conditions for euler solutions and the relation between turbulent cascade directions and time asymmetry of lagrangian stochasticity

large fredholm triples abstract we give several equivalent condition for busby extensions of a given algebra to be absorbing considerably improving our earlier results g a elliott d kucerovsky an abstract brown douglas fillmore absorption theorem pacific j math 198 2001 385 409 and establish sufficient conditions for fredholm triples to be absorbing in a suitable sense as an application of one of our criteria we prove a multivariable brown douglas fillmore type theorem

rigorous estimates of the tails of the probability distribution function for the random linear shear model in previous work majda and mclaughlin and majda computed explicit expressions for the 2nth moments of a passive scalar advected by a linear shear flow in the form of an integral over r n in this paper we first compute the asymptotics of these moments for large moment number we are able to use this information about the large n behavior of the moments along with some basic facts about entire functions of finite order to compute the asymptotics of the tails of the probability distribution function we find that the probability distribution has gaussian tails when the energy is concentrated in the largest scales as the initial energy is moved to smaller and smaller scales we find that the tails of the distribution grow longer and the distribution moves smoothly from gaussian through exponential and stretched exponential we also show that the derivatives of the scalar are increasingly intermittent in agreement with experimental observations and relate the exponents of the scalar derivative to the exponents of the scalar

diffusing passive tracers in random incompressible flows statistical topography aspects the paper studies statistical characteristics of the passive tracer concentrations and of its spatial gradient in random incompressible velocity fields from the viewpoint of statistical topography the statistics of interest include mean values probability distributions as well as various functionals characterizing topographic features of tracers the functional approach is used we consider the influence of the mean flow the linear shear flow and the molecular diffusion coefficient on the statistics of the tracer most of our analysis is carried out in the framework of the delta correlated in time approximation and conditions for its applicability are established but we also consider the diffusion approximation scheme for finite correlation radius the latter is applied to a diffusing passive tracer that undergoes sedimentation in a random velocity field

large scale probability density function for scalar field advected by high reynolds number turbulent flow a closed equation for the one point probability density function pdf for a scalar field advected by the three dimensional random velocity field with arbitrary many spatial temporal scales and infrared divergence in the limit of high reynolds number has been derived using the functional derivative technique and renormalization theory together with the assumption that the turbulent velocity is a homogeneous isotropic gaussian random field it has been shown that when the spectral parameters of a random velocity field slightly deviate from their kolmogorov obukhov values the equation for the pdf in the long time large distance limit can be derived exactly and well described by a conventional diffusion theory while the lagrangian scaling function describing the large scale particle displacements in turbulent flow is essentially superdiffusive the scaling procedure in the limit of high reynolds number allows us to completely overcome the well known closure problem associated with diffusion term

the suspension of a graph and associated c algebras abstract given a directed graph e we construct for each real number l a quiver whose vertex space is the topological realisation of e and whose edges are directed paths of length l in the vertex space these quivers are not topological graphs in the sense of katsura nor topological quivers in the sense of muhly and tomforde we prove that when l 1 and e is finite the infinite path space of the associated quiver is homeomorphic to the suspension of the one sided shift of e we call this quiver the suspension of e we associate both a toeplitz algebra and a cuntz krieger algebra to each of the quivers we have constructed and show that when l 1 the cuntz krieger algebra admits a natural faithful representation on the l 2 space of the suspension of the one sided shift of e for graphs e in which sufficiently many vertices both emit and receive at least two edges and for rational values of l we show that the toeplitz algebra and the cuntz krieger algebra of the associated quiver are homotopy equivalent to the toeplitz algebra and cuntz krieger algebra respectively of a graph that can be regarded as encoding the lth higher shift associated to the one sided shift space of e

non simple purely infinite c algebras a c algebra a is defined to be purely infiniteif there are no characters on a a nd if for every pair of positive elements a b in a such that b lies in the closed two sided ideal generated by a there exists a sequence rn in a such that rn arn b this definition agrees with the usual definition by j cuntz when a is simple it is shown that the property of being purely infinite is preserved under extensions morita equivalence inductive limits and it passes to quotients and to hereditary sub c algebras it is shown that a is purely infinite for every c algebra a purely infinite c algebras admit no traces and conversely an approximately divisible exact c algebra is purely infinite if it admits no nonzero trace

scalar flux in a uniform mean scalar gradient in homogeneous isotropic steady turbulence abstract statistics of a passive scalar flux in a uniform mean scalar gradient convected by homogeneous isotropic steady turbulence are numerically studied by using very high resolution direct numerical simulation it is found that the nusselt number increases in proportion to the peclet number and that the one point probability density function of the scalar flux is negatively skewed and exponential and is insensitive to the variation of the peclet number the scalar field is studied by visualization and the ramp cliff structure and the mesa canyon structure are observed along the directions parallel and perpendicular to the mean scalar gradient respectively the probability density function of the scalar flux is theoretically computed and found to be in good agreement with the numerical results a lagrangian statistical theory for the scalar flux is developed which predicts that the scalar transfer flux is given by the time integral of the lagrangian velocity autocorrelation and increases in proportion to the peclet number which is consistent with the results of the direct numerical simulation a physical explanation of the asymmetry of the scalar flux pdf is explored

evolution of the probability measure for the majda model new invariant measures and breathing pdfs in 1993 majda proposed a simple random shear model from which scalar inter mittency was rigorously predicted for the invariant probability measure of passive tracers in this work we present an integral formulation for the tracer measure which leads to a new comprehensive study on its temporal evolution based on monte carlo simulation and direct numerical integration an interesting non monotonic breathing phenomenon is discov ered from these results and carefully defined with a solid example for special initial data to predict such phenomenon the signature of this phenomenon may persist at long time char acterized by the approach of the pdf core to its infinite time invariant value we find that this approach may be strongly dependent on the non dimensional peclet number of which the invariant measure itself is independent further the breathing pdf is recovered as a new invariant measure in a distinguished time scale in the diffusionless limit rigorous as ymptotic analysis is also performed to identify the gaussian core of the invariant measures and the critical rate at which the heavy stretched exponential regime propagates towards the tail as a function of time is calculated

decomposition rank and absorbing extensions of type i algebras abstract we prove the following let a and b be separable c algebras suppose that b is a type i c algebra such that i b has only infinite dimensional irreducible representations and ii b has finite decomposition rank if 0 b c a 0 is a unital homogeneous exact sequence with busby invariant then the extension is absorbing in the case of infinite decomposition rank we provide a counterexample specifically we construct a unital homogeneous split exact sequence of the form 0 c z k c c 0 which is not absorbing in this example z is an infinite dimensional compact second countable topological space this gives a counterexample to the natural infinite dimensional generalization of the result of pimsner popa and voiculescu

on stability ofc algebras letabe a unitalc algebra i e aadmits a countable approximate unit it is proved thatais stable i e ais isomorphic toa k where k is the algebra of compact operators on a separable hilbert space if and only if for each positive elementa aand eache 0 there exists a positive elementb asuch that ab eandx x a xx bfor somexina using this characterization it is proved among other things that the inductive limit of any sequence of unital stablec algebras is stable and that the crossed product of a unital stablec algebra by a discrete group is again stable

universal long time properties of lagrangian statistics in the batchelor regime and their application to the passive scalar problem we consider the transport of dynamically passive quantities in the batchelor regime of a smooth in space velocity field for the case of arbitrary temporal correlations of the velocity we formulate the statistics of relevant characteristics of lagrangian motion this allows us to generalize many results obtained previously for strain ensuremath delta correlated in time thus answering a question about the universality of these results

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

extensions contained in ideals we prove a weyl von neumann type absorption theorem for extensions which are not full and give a condition for constructing infinite repeats contained in an ideal we also clear up some questions associated with the purely large criterion for full extensions to be absorbing

on the classification of nonsimple graph c algebras we prove that a graph c algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six term exact sequence in k theory we prove that a similar classification also holds for a graph c algebra with a largest proper ideal that is an af algebra our results are based on a general method developed by the first named author with restorff and ruiz as a key step in the argument we show how to produce stability for certain full hereditary subalgebras associated to such graph c algebras we further prove that except under trivial circumstances a unique proper nontrivial ideal in a graph c algebra is stable

realizations of af algebras as graph algebras exel laca algebras and ultragraph algebras abstract we give various necessary and sufficient conditions for an af algebra to be isomorphic to a graph c algebra an exel laca algebra and an ultragraph c algebra we also explore consequences of these results in particular we show that all stable af algebras are both graph c algebras and exel laca algebras and that all simple af algebras are either graph c algebras or exel laca algebras in addition we obtain a characterization of af algebras that are isomorphic to the c algebra of a row finite graph with no sinks