some model theory of polish structures we introduce a notion of polish structure and in doing so provide a setting which allows the application of ideas and techniques from model theory descriptive set theory topology and the theory of profinite groups we define a topological notion of independence in polish structures and prove that it has some nice properties using this notion we prove counterparts of some basic results from geometric stability theory in the context of small polish structures then we prove some structural theorems about compact groups regarded as polish structures each small nm stable compact g group is solvable by finite each small compact g group of finite n m rank is nilpotent by finite examples of small polish structures and groups are also given

amenability definable groups and automorphism groups abstract we prove several theorems relating amenability of groups in various categories discrete definable topological automor phism group to model theoretic invariants quotients by connected components lascar galois group g compactness among the main tools which is possibly of independent interest is the adaptation and generalization of theorem 12 of 27 to other settings including amenable topological groups whose topology is generated by a family of subgroups on the side of definable groups we prove that if g is definable in a model m and g is definably amenable then the connected components g m 00 and g m 000 coincide answering positively a question from 22 we also prove some natural counterparts for topological groups using our generalizations of 27 by finding a dictionary relating quotients by connected components and galois groups of categorical theories we conclude that if m is countable and categorical and aut m is amenable as a topological group then t th m is g compact i e the lascar galois group gal l t is compact hausdorff equivalently the natural epimorphism from gal l t to gal k p t is an isomorphism we also take the opportunity to further develop the model theoretic approach to topological dynamics obtaining for example some new invariants for topological groups as well as allowing a uniform approach to the theorems above and the various categories

functionals of brownian motion localization and metric graphs we review several results related to the problem of a quantum particle in a random environment in an introductory part we recall how several functionals of brownian motion arise in the study of electronic transport in weakly disordered metals weak localization two aspects of the physics of the one dimensional strong localization are reviewed some properties of the scattering by a random potential time delay distribution and a study of the spectrum of a random potential on a bounded domain the extreme value statistics of the eigenvalues then we mention several results concerning the diffusion on graphs and more generally the spectral properties of the schrodinger operator on graphs the interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated finally we consider a two dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices we recall the connection between spectral properties of this model and winding functionals of planar brownian motion

statistical mechanics of a single particle in a multiscale random potential parisi landscapes in finite dimensional euclidean spaces we construct an n dimensional gaussian landscape with multiscale translation invariant logarithmic correlations and investigate the statistical mechanics of a single particle in this environment in the limit of high dimension n the free energy of the system and overlap function are calculated exactly using the replica trick and parisi s hierarchical ansatz in the thermodynamic limit we recover the most general version of the derrida s generalized random energy model grem the low temperature behaviour depends essentially on the spectrum of length scales involved in the construction of the landscape if the latter consists of k discrete values the system is characterized by a k step replica symmetry breaking solution we argue that our construction is in fact valid in any finite spatial dimensions n 1 we discuss the implications of our results for the singularity spectrum describing multifractality of the associated boltzmann gibbs measure finally we discuss several generalizations and open problems such as the dynamics in such a landscape and the construction of a generalized multifractal random walk

modelling unilateral frictionless contact using the null space method and cubic b spline interpolation the analysis of unilateral sliding contact in elasticity is equivalent to a minimisation problem subjected to a set of inequality constraints however the presence of boundary discontinuities such as those stemming from the spatial discretisation appears as a major problem to determine the set of active constraints this work introduces a smoothing technique of the master surface resorting to cubic b spline interpolation which is c 1 continuous in contact situations between elastic and rigid bodies and g 1 continuous in elastic elastic contact problems the technique is applied in conjunction with the null space method where the solution is searched in an unconstrained manifold the resulting formulation eases the contact transition along the master surface and recovers the quadratic convergence of the iterative newton raphson process the robustness of the method is demonstrated using 2d and 3d examples

extreme value distributions and renormalization group in the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent identically distributed random variables are studied the vast majority of the literature on the subject deals with affine normalization we argue that more general normalizations are natural from a mathematical and physical point of view and work them out the problem is approached using the language of renormalization group transformations in the space of probability densities the limit distributions are fixed points of the transformation and the study of its differential around them allows a local analysis of the domains of attraction and the computation of finite size corrections

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

extreme value theory for constrained physical systems we investigate extreme value theory for physical systems with a global conservation law which describes renewal processes mass transport models and long range interacting spin models as shown previously a special feature is that the distribution of the extreme value exhibits a nonanalytical point in the middle of the support we expose exact relationships between constrained extreme value theory and well known quantities of the underlying stochastic dynamics all valid beyond the midpoint in general i e even far from the thermodynamic limit for example for renewal processes the distribution of the maximum time between two renewal events is exactly related to the mean number of these events in the thermodynamic limit we show how our theory is suitable to describe typical and rare events which deviate from classical extreme value theory for example for the renewal process we unravel dual scaling of the extreme value distribution pointing out two types of limiting laws a normalizable scaling function for the typical statistics and a non normalized state describing the rare events

extremum statistics in scale free network models we investigate the statistics of the most connected node in scale free networks for a scale free network model with homogeneous nodes we show by means of extensive simulations that the exponential truncation due to the finite size of the network of the degree distribution governs the scaling of the extreme values and that the distribution of maxima follows the gumbel statistics for a scale free network model with heterogeneous nodes we show that scaling no longer holds and that the truncation of the degree distribution no longer controls the maxima distribution

locally finite profinite rings abstract we investigate the structure of locally finite profinite rings we classify jacobson semisimple locally finite profinite rings as products of complete matrix rings of bounded cardinality over finite fields and we prove that the jacobson radical of any locally finite profinite ring is nil of finite nilexponent our results apply to the context of small compact g rings where we also obtain a description of possible actions of g on the underlying ring

fluctuating fronts as correlated extreme value problems an example of gaussian statistics in this paper we view fluctuating fronts made of particles on a one dimensional lattice as an extreme value problem the idea is to denote the configuration for a single front realization at time t by the set of co ordinates k i t identical with k 1 t k 2 t k n t t of the constituent particles where n t is the total number of particles in that realization at time t when k i t are arranged in the ascending order of magnitudes the instantaneous front position can be denoted by the location of the rightmost particle i e by the extremal value k f t max k 1 t k 2 t k n t t due to interparticle interactions k i t at two different times for a single front realization are naturally not independent of each other and thus the probability distribution p k f t based on an ensemble of such front realizations describes extreme value statistics for a set of correlated random variables in view of the fact that exact results for correlated extreme value statistics are rather rare here we show that for a fermionic front model in a reaction diffusion system p k f t is gaussian in a bosonic front model however we observe small deviations from the gaussian

modelling extremal events using gnedenko distributions we address the problem of fitting a gnedenko distribution to a realization of an iid sample thereby deciding upon the heavy light character of the upper tail of the phenomenon under study an illustration based on earthquake magnitude data is supplied

renormalization flow for extreme value statistics of random variables raised to a varying power using a renormalization approach we study the asymptotic limit distribution of the maximum value in a set of independent and identically distributed random variables raised to a power qn that varies monotonically with the sample size n under these conditions a non standard class of max stable limit distributions which mirror the classical ones emerges furthermore a transition mechanism between the classical and the non standard limit distributions is brought to light if qn grows slower than a characteristic function q n the standard limit distributions are recovered while if qn behaves asymptotically as q n non standard limit distributions emerge

effects of nonlocal stress on the determination of shear banding flow we analyze the steady planar shear flow of the modified johnson segalman model which has an added nonlocal term we find that the new term allows for unambiguous selection of the stress at which two phases coexist in contrast to the original model for general differential constitutive models we show the singular nature of stress selection in terms of a saddle connection between fixed points in the equivalent dynamical system the result means that stress selection is unique under most conditions for space nonlocal models finally illustrated by simple models we show that stress selection generally depends on the form of the nonlocal terms weak universality

perturbative expansion for the maximum of fractional brownian motion brownian motion is the only random process which is gaussian stationary and markovian dropping the markovian property i e allowing for memory one obtains a class of processes called fractional brownian motion indexed by the hurst exponent h for h 1 2 brownian motion is recovered we develop a perturbative approach to treat the non locality in time in an expansion in varepsilon h 1 2 this allows us to derive analytic results beyond scaling exponents for various observables related to extreme value statistics the maximum m of the process and the time t text max at which this maximum is reached as well as their joint distribution we test our analytical predictions with extensive numerical simulations for different values of h they show excellent agreement even for h far from 1 2

jamming hysteresis and oscillation in scalar models for shear thickening we investigate shear thickening and jamming within the framework of a family of spatially homogeneous scalar rheological models these are based on the soft glassy rheology model of sollich et al phys rev lett 78 2020 1997 but with an effective temperature x that is a decreasing function of either the global stress ensuremath sigma or the local strain l for appropriate x x ensuremath sigma it is shown that the flow curves include a region of negative slope around which the stress exhibits hysteresis under a cyclically varying imposed strain rate stackrel ifmmode dot else fi ensuremath gamma a subclass of these x ensuremath sigma have flow curves that touch the stackrel ifmmode dot else fi ensuremath gamma 0 axis for a finite range of stresses imposing a stress from this range jams the system in the sense that the strain ensuremath gamma creeps only logarithmically with time t ensuremath gamma t ensuremath sim mathrm ln t these same systems may produce a finite asymptotic yield stress under an imposed strain in a manner that depends on the entire stress history of the sample a phenomenon we refer to as history dependent jamming in contrast when x x l the flow curves are always monotonic but we show that some x l generate an oscillatory strain response for a range of steady imposed stresses similar spontaneous oscillations are observed in a simplified model with fewer degrees of freedom we discuss this result in relation to the temporal instabilities observed in rheological experiments and stick slip behavior found in other contexts and comment on the possible relationship with delay differential equations that are known to produce oscillations and chaos

the impact of surface higher order differentiability in two dimensional contact elements the aim of this work is to propose new contact elements of higher order of differentiability for analysing two dimensional frictionless contact problems several methods were proposed in the literature to solve the problem caused by the lack of continuity resulting from the discretization among them are bezier interpolation hermitian interpolation and splines one of the difficulties in using hermitian interpolation is to verify the partition of unity therefore new elements that satisfy the c 1 and c 2 continuity at the interface are presented in this paper these new contact elements are based on hermitian polynomials for ensuring a higher order of continuity the advantage is that this approach can be easily developed not only for linear elements but also for quadratic elements with higher order of differentiability the performance of different surface representations is assessed through a comparison with a c 0 surface discretization some numerical examples are used for assessing the accuracy and the convergence behaviour

universality classes for extreme value statistics the equilibrium low temperature physics of disordered systems is governed by the statistics of extremely low energy states it is thus relevant to discuss the possible universality classes for extreme value statistics we compare the usual probabilistic classification to the results of the replica approach we show in detail for several problems including the random energy model and the decaying burgers turbulence that one class of independent variables corresponds exactly to the so called one step replica symmetry breaking solution in the replica language we argue that this universality class holds if the correlations are sufficiently weak and propose a conjecture on the level of correlations which leads to different universality classes

synchronization landscapes in small world connected computer networks motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small world networks embedded in one and two dimensions we find that the synchronization landscape corresponding to the progress of the individual processors exhibits kardar parisi zhang like kinetic roughening on regular networks with short range communication links although the processors on average progress at a nonzero rate their spread the width of the synchronization landscape diverges with the number of nodes desynchronized state hindering efficient data management when random communication links are added on top of the one and two dimensional regular networks resulting in a small world network large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system size limit synchronized state in the resulting synchronization scheme the processors make close to uniform progress with a nonzero rate without global intervention we obtain our results by simulating the simulations based on the exact algorithmic rules supported by coarse grained arguments

generalized extreme value statistics and sum of correlated variables we show that generalized extreme value statistics the statistics of the kth largest value among a large set of random variables can be mapped onto a problem of random sums this allows us to identify classes of non identical and generally correlated random variables with a sum distributed according to one of the three k dependent asymptotic distributions of extreme value statistics namely the gumbel frechet and weibull distributions these classes as well as the limit distributions are naturally extended to real values of k thus providing a clear interpretation to the onset of gumbel distributions with non integer index k in the statistics of global observables this is one of the very few known generalizations of the central limit theorem to non independent random variables finally in the context of a simple physical model we relate the index k to the ratio of the correlation length to the system size which remains finite in strongly correlated systems

extremal driving as a mechanism for generating long term memory it is argued that systems whose elements are renewed according to an extremal criterion can generally be expected to exhibit long term memory this is verified for the minimal extremally driven model which is first defined and then solved for all system sizes n 2 and times t 0 yielding exact expressions for the persistence r t 1 t n 1 1 and the two time correlation function c tw t tw 1 1 n n tw n tw t 1 the existence of long term memory is inferred from the scaling of c tw t tw f t tw denoting aging finally we suggest ways of investigating the robustness of this mechanism when competing processes are present

gumbel central limit theorem for max min and min max the max min and min max of matrices arise prevalently in science and engineering however in many real world situations the computation of the max min and min max is challenging as matrices are large and full information about their entries is lacking here we take a statistical physics approach and establish limit laws akin to the central limit theorem for the max min and min max of large random matrices the limit laws intertwine random matrix theory and extreme value theory couple the matrix dimensions geometrically and assert that gumbel statistics emerge irrespective of the matrix entries distribution due to their generality and universality as well as their practicality these results are expected to have a host of applications in the physical sciences and beyond

a modified node to segment algorithm passing the contact patch test summary several investigations have shown that the classical one pass node to segment nts algorithms for the enforcement of contact constraints fail the contact patch test this implies that the algorithms may introduce solution errors at the contacting surfaces and these errors do not necessarily decrease with mesh refinement the previous research has mainly focused on the lagrange multiplier method to exactly enforce the contact geometry conditions the situation is even worse with the penalty method due to its inherent approximation that yields a solution affected by a non zero penetration the aim of this study is to analyze and improve the contact patch test behavior of the one pass nts algorithm used in conjunction with the penalty method for 2d frictionless contact the paper deals with the case of linear elements for this purpose several sequential modifications of the basic formulation have been considered which yield incremental improvements in results of the contact patch test the final proposed formulation is a modified one pass nts algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method in other words this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration copyright q 2009 john wiley sons ltd

airy distribution function from the area under a brownian excursion to the maximal height of fluctuating interfaces the airy distribution function describes the probability distribution of the area under a brownian excursion over a unit interval surprisingly this function has appeared in a number of seemingly unrelated problems mostly in computer science and graph theory in this paper we show that this distribution function also appears in a rather well studied physical system namely the fluctuating interfaces we present an exact solution for the distribution p h m l of the maximal height h m measured with respect to the average spatial height in the steady state of a fluctuating interface in a one dimensional system of size l with both periodic and free boundary conditions for the periodic case we show that p h m l l 1 2f h m l 1 2 for all l 0 where the function f x is the airy distribution function this result is valid for both the edwards wilkinson ew and the kardar parisi zhang interfaces for the free boundary case the same scaling holds p h m l l 1 2f h m l 1 2 but the scaling function f x is different from that of the periodic case we compute this scaling function explicitly for the ew interface and call it the f airy distribution function numerical simulations are in excellent agreement with our analytical results our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables some of these results were announced in a recent letter s n majumdar and a comtet phys rev lett 92 225501 2004

multifractality and freezing phenomena in random energy landscapes an introduction abstract we start our lectures with introducing and discussing the general notion of multifractality spectrum for random measures on lattices and how it can be probed using moments of that measure then we show that the boltzmann gibbs probability distributions generated by logarithmically correlated random potentials provide a simple yet non trivial example of disorder induced multifractal measures the typical values of the multifractality exponents can be extracted from calculating the free energy of the associated statistical mechanics problem to succeed in such a calculation we introduce and discuss in some detail two analytically tractable models for logarithmically correlated potentials the first model uses a special definition of distances between points in space and is based on the idea of multiplicative cascades which originated in theory of turbulent motion it is essentially equivalent to statistical mechanics of directed polymers on disordered trees studied long ago by derrida and spohn 1988 in ref 12 in this way we introduce the notion of the freezing transition which is identified with an abrupt change in the multifractality spectrum second model which allows for explicit analytical evaluation of the free energy is the infinite dimensional version of the problem which can be solved by employing the replica trick in particular the latter version allows one to identify the freezing phenomenon with a mechanism of the replica symmetry breaking rsb and to elucidate its physical meaning the corresponding one step rsb solution turns out to be marginally stable everywhere in the low temperature phase we finish with a short discussion of recent developments and extensions of models with logarithmic correlations in particular in the context of extreme value statistics the first appendix summarizes the standard elementary information about gaussian integrals and related subjects and introduces the notion of the gaussian free field characterized by logarithmic correlations three other appendices provide the detailed exposition of a few technical details underlying the replica analysis of the model discussed in the lectures

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

statistics of extremal intensities for gaussian interfaces the extremal fourier intensities are studied for stationary edwards wilkinson type gaussian interfaces with power law dispersion we calculate the probability distribution of the maximal intensity and find that generically it does not coincide with the distribution of the integrated power spectrum i e roughness of the surface nor does it obey any of the known extreme statistics limit distributions the fisher tippett gumbel limit distribution is however recovered in three cases i in the nondispersive white noise limit ii for high dimensions and iii when only short wavelength modes are kept in the last two cases the limit distribution emerges in nonconventional scenarios

interfaces in a random medium and replica symmetry breaking the authors develop a variational approach for studying interfaces and other manifolds in a disordered quenched medium the method may be applied to problems which range from directed polymers to the interface of an ising model in a random magnetic field they find that replica symmetry is spontaneously broken and the results of the flory approximation are recovered in a simple way corrections to this approximation may be computed in a systematic way

simulations of complex fluids by mixed lattice boltzmann finite difference methods abstract we present the numerical results of simulations of complex fluids under shear flow we employ a mixed approach which combines the lattice boltzmann method for solving the navier stokes equation and a finite difference scheme for the convection diffusion equation the evolution in time of shear banding phenomenon is studied this is allowed by the presented numerical model which takes into account the evolution of local structures and their effect on fluid flow

small profinite structures we propose a model theoretic framework for investigating profinite structures we prove that in many cases small profinite structures interpret infinite groups this corresponds to results of hrushovski and peterzil on interpreting groups in locally modular stable and o minimal structures

a mortar based frictional contact formulation for large deformations using lagrange multipliers abstract in this work a lagrange multiplier method is proposed to solve 2d coulomb frictional contact problems in the context of large deformations as the proposed formulation is based on the mortar method the constraints are imposed in a weak integral sense along the contact surface in order to compute the contact integrals we use a numerical integration based on the definition of the kinematical variables gap slip and their variations at the quadrature points the linearization of non linear equations virtual work and contact constraints is developed in order to apply a newton s method the examples show that the numerical integration still preserves the optimal rate of convergence of the finite element solution

cn continuous modelling of smooth contact surfaces using nurbs and application to 2d problems this paper presents a strategy for the finite element implementation of cn continuous contact surfaces for deformable bodies undergoing finite deformations whereby n represents an arbitrary level of continuity the proposed novel approach avoids the non physical oscillations of contact forces which are induced by the traditional enforcement of kinematic contact constraints via faceted surfaces discretizing the interacting boundaries in particular for certain problems the level of continuity may influence the rate of convergence significantly within a non linear solution scheme a hierarchical tree data structure is proposed for an efficient search algorithm to find the neighbour elements on adaptively refined meshes which are involved in the smoothing process of a particular finite element the same data structure is used for the automatic detection of the contact surfaces of a body three representative numerical examples demonstrate the increased rate of convergence the ability to trace the actual surface more accurately and the prevention of pressure jumps of the proposed method copyright 2003 john wiley sons ltd

density of near extreme events we provide a quantitative analysis of the phenomenon of crowding of near extreme events by computing exactly the density of states dos near the maximum of a set of independent and identically distributed random variables we show that the mean dos converges to three different limiting forms depending on whether the tail of the distribution of the random variables decays slower than pure exponential faster than pure exponential or as a pure exponential function we argue that some of these results would remain valid even for certain correlated cases and verify it for power law correlated stationary gaussian sequences satisfactory agreement is found between the near maximum crowding in the summer temperature reconstruction data of western siberia and the theoretical prediction

central limit theorem for a class of globally correlated random variables the standard central limit theorem with a gaussian attractor for the sum of independent random variables may lose its validity in the presence of strong correlations between the added random contributions here we study this problem for similar interchangeable globally correlated random variables under these conditions a hierarchical set of equations is derived for the conditional transition probabilities this result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables depending on the correlation mechanisms and statistics of the single variables the corresponding sums are characterized by distinct probability densities for a class of urn models it is also possible to characterize their domain of attraction which as in the standard case is parametrized by the probability density of each random variable symmetric and asymmetric q gaussian attractors q 1 arise in a particular two state case of these urn models

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

distribution of the time at which n vicious walkers reach their maximal height we study the extreme statistics of n nonintersecting brownian motions vicious walkers over a unit time interval in one dimension using path integral techniques we compute exactly the joint distribution of the maximum m and of the time m at which this maximum is reached we focus in particular on nonintersecting brownian bridges watermelons without wall and nonintersecting brownian excursions watermelons with a wall we discuss in detail the relationships between such vicious walkers models in watermelon configurations and stochastic growth models in curved geometry on the one hand and the directed polymer in a disordered medium dprm with one free end point on the other hand we also check our results using numerical simulations of dyson s brownian motion and confront them with numerical simulations of the polynuclear growth model png and of a model of dprm on a discrete lattice some of the results presented here were announced in a recent letter j rambeau and g schehr europhys lett 91 60006 2010

on the modelling of smooth contact surfaces using cubic splines in this paper a new strategy for the smooth representation of 2d contact surfaces is developed and implemented the contact surfaces are modelled using cubic splines which interpolate the nite element nodes these splines provide a unique surface normal vector and do not require prior knowledge of surface tangents and normals c continuous cubic splines are suitable for representing rigid contact surfaces while c continuous overhauser splines are shown to be most suitable for representing exible contact surfaces a consistent linearization of the kinematic contact constraints based on the spline interpolation is derived the new spline based contact surface interpolation scheme does not in uence the element calculations consequently it can be easily implemented in standard fe codes several numerical examples are used to illustrate the advantages of the proposed smooth representation of contact surfaces the results show a signi cant improvement in accuracy compared to traditional piecewise element based surface interpolation the predicted contact stresses are also less sensitive to the mismatch in the meshes of the di erent contacting bodies this property is useful for problems where the contact area is unknown a priori and when there is signi cant tangential slip copyright 2001 john wiley sons ltd

aging in two dimensional bouchaud s model let e x be a collection of i i d exponential random variables symmetric bouchaud s model on 2 is a markov chain x t whose transition rates are given by w xy exp e x if x y are neighbours in 2 we study the behaviour of two correlation functions x t w t x t w and x t x t w t t w t w t we prove the sub aging behaviour of these functions when 1

a branching random walk seen from the tip we show that all the time dependent statistical properties of the rightmost points of a branching brownian motion can be extracted from the traveling wave solutions of the fisher kpp equation the distribution of all the distances between the rightmost points has a long time limit which can be understood as the delay of the fisher kpp traveling waves when the initial condition is modified the limiting measure exhibits the surprising property of superposability the statistical properties of the distances between the rightmost points of the union of two realizations of the branching brownian motion shifted by arbitrary amounts are the same as those of a single realization we discuss the extension of our results to more general branching random walks

a segment to segment mortar contact method for quadratic elements and large deformations abstract this paper describes a new extension of mortar based segment to segment algorithms for large deformation contact analysis permitting their use when quadratic interpolations are used in the underlying finite element method the work builds upon results previously described by puso and laursen m a puso t a laursen a mortar segment to segment contact method for large deformation solid mechanics comput methods appl mech engrg 193 2004 601 629 m a puso t a laursen a mortar segment to segment frictional contact method for large deformations comput methods appl mech engrg 193 2004 601 629 where methods were developed for quasistatic and implicit dynamic analysis in the context of linear element interpolations here we see that many algorithmic ideas from the linear case can be adopted for use with quadratic elements along with different alternative interpolations of the mortar contact multipliers the result is a class of methods appropriate for use for either mesh tying true large sliding simulation frictionless or frictional and readily admits mixing of element types several numerical examples are given to demonstrate the effectiveness of the approach

order statistics of 1 fα signals order statistics of periodic gaussian noise with 1 f power spectrum is investigated using simulations and phenomenological arguments we find three scaling regimes for the average gap d k x k x k 1 between the kth and k 1 st largest values of the signal the result d k k 1 known for independent identically distributed variables remains valid for 0 5 the spectra of average ordered values e k x 1 x k k is also examined the exponent is derived from the gap scaling as well as by relating e k to the density of near extreme states known results for the density of near extreme states combined with scaling suggest that 2 1 2 4 3 2 and 2 are exact values we also show that parallels can be drawn between e k and the quantum mechanical spectra of a particle in power law potentials

three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs a three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs is presented in the finite deformation regime within a setting where the nurbs discretization of the contact surface is inherited directly from the nurbs discretization of the volume the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities the formulation delivers a non negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative lagrange discretizations independent of the discretization order these enable the achievement of improved smoothness in global contact forces and moments through higher order geometrical descriptions it is concluded that the presented mortar based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume

freezing transition of the random bond rna model statistical properties of the pairing weights to characterize the pairing specificity of rna secondary structures as a function of temperature we analyze the statistics of the pairing weights as follows for each base i of the sequence of length n we consider the n 1 pairing weights w i j with the other bases j not equal i of the sequence we numerically compute the probability distributions p1 w of the maximal weight w i max max j w i j the probability distribution pi y 2 of the parameter y2 i summation operator j w i 2 j as well as the average values of the moments y k i summation operator j w i k j we find that there are two important temperatures t c t gap the distribution p1 w vanishes at some value w 0 t 1 and accordingly the moments y k i decay exponentially as w 0 t k in k for t t gap the distributions p1 w and pi y2 present the characteristic derrida flyvbjerg singularities at w 1n and y 2 1 n for n 1 2 in particular there exists a temperature dependent exponent mu t that governs the singularities p1 w approximately 1 w mu t 1 and pi y2 approximately 1 y 2 mu t 1 as well as the power law decay of the moments y k i approximately 1k mu t the exponent mu t grows from the value mu t 0 0 up to mu t gap approximately 2 the study of spatial properties indicates that the critical temperature t c where the large scale roughness exponent changes from the low temperature value zeta approximately 0 67 to the high temperature value zeta approximately 0 5 corresponds to the exponent mu t c 1 for t t c there exists frozen pairs of all sizes whereas for t c t t gap there exists frozen pairs but only up to some characteristic length diverging as xi t approximately 1 t c t nu with nu approximately 2 the similarities and differences with the weight statistics in levy sums and in derrida s random energy model are discussed

microscopic realizations of the trap model monte carlo optimizations of number partitioning and of diophantine approximations are microscopic realizations of trap model dynamics this offers a fresh look at the physics behind this model and points at other situations in which it may apply our results strongly suggest that in any such realization of the trap model the response and correlation functions of smooth observables obey the fluctuation dissipation theorem even in the aging regime our discussion of the number partitioning problem may be relevant for the class of optimization problems whose cost function does not scale linearly with the size and are thus awkward from the statistical mechanic point of view

law of corresponding states for open collaborations we study the relation between number of contributors and product size in wikipedia and github in contrast to traditional production this is strongly probabilistic but is characterized by two quantitative nonlinear laws a power law bound to product size for increasing number of contributors and the universal collapse of rescaled distributions a variant of the random energy model shows that both laws are due to the heterogeneity of contributors and displays an intriguing finite size scaling property with no equivalent in standard systems the analysis uncovers the right intensive densities enabling the comparison of projects with different numbers of contributors on equal grounds we use this property to expose the detrimental effects of conflicting interactions in wikipedia

numerical study of the two replica overlap of the 3d edwards anderson ising spin glass abstract we present results of recent high statistics monte carlo simulations of the edwards anderson ising spin glass model in three dimensions the study is based on a non boltzmann sampling technique the multi self overlap algorithm which is specifically tailored for sampling rare event states we thus concentrate on those properties which are difficult to obtain with standard canonical boltzmann sampling such as the free energy barriers f b q in the probability densities p j q of the parisi overlap parameter q and the behavior of the tails of the disorder averaged density p q p j q av our results for the tails disagree with mean field predictions and support extreme order statistics over many orders of magnitude

phase separation in random cluster models i uniform upper bounds on local deviation this is the first in a series of three papers that addresses the behaviour of the droplet that results in the percolating phase from conditioning the planar fortuin kasteleyn random cluster model on the presence of an open dual circuit 0 encircling the origin and enclosing an area of at least or exactly n2 by the fortuin kasteleyn representation the model is a close relative of the droplet formed by conditioning the potts model on an excess of spins of a given type we consider local deviation of the droplet boundary measured in a radial sense by the maximum local roughness mlr 0 this being the maximum distance from a point in the circuit 0 to the boundary of the circuit s convex hull and in a longitudinal sense by what we term maximum facet length mlf 0 namely the length of the longest line segment of which the polygon is formed the principal conclusion of the series of papers is the following uniform control on local deviation that there are constants 0 c c such that the conditional probability that the normalized quantity n 1 3 log n 2 3mlr lies in the interval c c tends to 1 in the high n limit and that the same statement holds for n 2 3 log n 1 3 mlf in this way we confirm the anticipated n1 3 scaling of maximum local roughness and provide a sharp logarithmic power law correction this local deviation behaviour occurs by means of locally gaussian effects constrained globally by curvature and we believe that it arises in many radially defined stochastic interface models including growth models belonging to the kardar parisi zhang universality class

smooth c1 interpolations for two dimensional frictional contact problems finite deformation contact problems are associated with large sliding in the contact area thus in the discrete problem a slave node can slide over several master segments standard contact formulations of surfaces discretized by low order finite elements leads to sudden changes in the surface normal field this can cause loss of convergence properties in the solution procedure and furthermore may initiate jumps in the velocity field in dynamic solutions furthermore non smooth contact discretizations can lead to incorrect results in special cases where a good approximation of the contacting surfaces is needed in this paper a smooth contact discretization is developed which circumvents most of the aformentioned problems a smooth deformed surface with no slope discontinuities between segments is obtained by a c1 continuous interpolation of the master surface different forms of discretizations are possible among these are bezier hermitian or other types of spline interpolations in this paper we compare two formulations which can be used to obtain smooth normal and tangent fields for frictional contact of deformable bodies the formulation is developed for two dimensional applications and includes finite deformation behaviour examples show the performance of the new discretization technique for contact copyright 2001 john wiley sons ltd

orbits of the pseudocircle the following theorem is proved theorem the pseudocircle has uncountably many orbits under the action of its homeomorphism group each orbit is the union of uncountably many composants a pseudocircle is a circularly chainable hereditarily indecomposable separating plane continuum r h bing 1 constructed a pseudocircle in 1951 and asked two questions are any two pseudocircles homeomorphic is a pseudocircle homogeneous in 1968 l fearnley 6 proved that the answer to the first question is yes and fearnley 5 and j t rogers jr 14 independently proved that the answer to the second question is no since the advent of the effros theorem several elegant proofs of the nonhomogeneity of the pseudocircle have appeared 7 10 and 13 in 1968 after seeing the proof that the pseudocircle is not homogeneous f b jones asked the second author how many orbits the pseudocircle had under the action of its homeomorphism group but the matter was not pursued further recently however the question has arisen again and wayne lewis 3 has asked if the pseudocircle has uncountably many orbits the purpose of this paper is to prove the following theorem which gives an affirmative answer to this question theorem the pseudocircle has uncountably many orbits under the action of its homeomorphism group each of these orbits is the union of uncountably many composants an interesting sidelight of the proof is the construction of two homeomorphic sets one being an open set of the pseudocircle and the other being an open set of the pseudoarc during the proof we construct an uncountable abelian subgroup of the homeomorphism group of the pseudocircle the homeomorphism constructed by handel 8 might be an element of this group each orbit of the pseudocircle is a borel set 4 lewis has announced that no orbit can be a g6 in the course of our argument we prove this but we do not determine further restrictions on the type of the borel set for the orbit question what classes of borel sets occur as the orbits of the pseudocircle in particular are each two orbits of the same class received by the editors may 1 1984 and in revised form august 13 1985 1980 mathematics subject classification primary 54f20 54f50

extreme statistics for time series distribution of the maximum relative to the initial value the extreme statistics of time signals is studied when the maximum is measured from the initial value in the case of independent identically distributed iid variables we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn then we turn to correlated periodic gaussian signals with a 1 f ensuremath alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height mathrm mrh mathrm i the exact mathrm mrh mathrm i distribution is derived for ensuremath alpha 0 iid variables ensuremath alpha 2 random walk ensuremath alpha 4 random acceleration and ensuremath alpha ensuremath infty single sinusoidal mode for other intermediate values of ensuremath alpha the distribution is determined from simulations we find that the mathrm mrh mathrm i distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all ensuremath alpha the two main distinguishing features of the mathrm mrh mathrm i distribution are the much larger weight for small relative heights and the divergence at zero height for ensuremath alpha g3 we also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some nonperiodic boundary conditions finally we show that for signals arising from time translationally invariant distributions the density of near extreme states is the same as the mathrm mrh mathrm i distribution this is used in developing a scaling theory for the threshold singularities of the two distributions

wealth condensation in a simple model of economy abstract we introduce a simple model of economy where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading in such a way that the fundamental symmetry of the economy under an arbitrary change of monetary units is insured we investigate a mean field limit of this equation and show that the distribution of wealth is of the pareto power law type the pareto behaviour of the tails of this distribution appears to be robust for finite range models as shown using both a mapping to the random directed polymer problem as well as numerical simulations in this context a phase transition between an economy dominated by a few individuals and a situation where the wealth is more evenly spread out is found an interesting outcome is that the distribution of wealth tends to be very broadly distributed when exchanges are limited either in amplitude or topologically favouring exchanges and less surprisingly increasing taxes seems to be an efficient way to reduce inequalities

dynamical behavior of a complex fluid near an out of equilibrium transition approaching simple rheological chaos we report here an extensive study of sustained oscillations of the viscosity of a complex fluid near an out of equilibrium transition using well defined protocols we perform rheological measurements of the onion texture near a layering transition in a couette flow this complex fluid exhibits sustained oscillations of the viscosity on a large time scale 500 s at controlled stress these oscillations are directly correlated to an oscillating microstructural change of the texture of the fluid we observe a great diversity of dynamical behavior and show that there is a coupling with spatial effects in the inverted delta v direction this is in agreement with a careful analysis of the temporal series of the viscosity with the dynamical system theory this analysis indicates that the observed dynamical responses do not strictly correspond to three dimensional chaotic states probably because some spatiotemporal effects are present and are likely to play an important role

products of finite abelian groups as profinite groups abstract we investigate products of finite abelian groups of bounded exponent as profinite structures in the sense of newelski in such groups we describe orbits under the action of the standard structural group of automorphisms then we conclude that such groups are small m normal and m stable let x be a product of countably many finite abelian groups we also investigate the influence of modifications of the standard structural group of x on its smallness m normality and m stability

maximal and minimal height distributions of fluctuating interfaces maximal and minimal height distributions mahd mihd of two dimensional interfaces grown with the nonlinear equations of kardar parisi zhang kpz second order and of villain lai das sarma vlds fourth order are shown to be different two universal curves may be mahd or mihd of each class depending on the sign of the relevant nonlinear term which is confirmed by results of several lattice models in the kpz and vlds classes the difference between mahd and midh is connected with the asymmetry of the local height distribution a simple exactly solvable deposition erosion model is introduced to illustrate this feature the average extremal heights scale with the same exponent of the average roughness in contrast to other correlated systems generalized gumbel distributions do not fit those mahd and mihd nor those of edwards wilkinson growth

single big jump principle in physical modeling the big jump principle is a well established mathematical result for sums of independent and identically distributed random variables extracted from a fat tailed distribution it states that the tail of the distribution of the sum is the same as the distribution of the largest summand in practice it means that when in a stochastic process the relevant quantity is a sum of variables the mechanism leading to rare events is peculiar instead of being caused by a set of many small deviations all in the same direction one jump the biggest of the lot provides the main contribution to the rare large fluctuation we reformulate and elevate the big jump principle beyond its current status to allow it to deal with correlations finite cutoffs continuous paths memory and quenched disorder doing so we are able to predict rare events using the extended big jump principle in l evy walks in a model of laser cooling in a scattering process on a heterogeneous structure and in a class of l evy walks with memory we argue that the generalized big jump principle can serve as an excellent guideline for reliable estimates of risk and probabilities of rare events in many complex processes featuring heavy tailed distributions ranging from contamination spreading to active transport in the cell

the behaviour of aging functions in one dimensional bouchaud s trap model let i be a collection of i i d positive random variables with distribution in the domain of attraction of an stable law with 1 the symmetric bouchaud s trap model on is a markov chain x t whose transition rates are given by w xy 2 x 1 if x y are neighbours in we study the behaviour of two correlation functions x t w t x t w and open image in new window it is well known that for any of these correlation functions a time scale t f t w such that aging occurs can be found we study these correlation functions on time scales different from f t w and we describe more precisely the behaviour of a singular diffusion obtained as the scaling limit of bouchaud s trap model

small profinite groups and rings abstract a small profinite ring has an open nil ideal of finite nil exponent we also discuss various conjectures about small profinite rings and give examples illustrating them

anomalous diffusion localization aging and subaging effects in trap models at very low temperature we study in detail the dynamics of the one dimensional symmetric trap model via a real space renormalization procedure which becomes exact in the limit of zero temperature in this limit the diffusion front in each sample consists of two delta peaks which are completely out of equilibrium with each other the statistics of the positions and weights of these delta peaks over the samples allows to obtain explicit results for all observables in the limit t 0 we first compute disorder averages of one time observables such as the diffusion front the thermal width the localization parameters the two particle correlation function and the generating function of thermal cumulants of the position we then study aging and subaging effects our approach reproduces very simply the two different aging exponents and yields explicit forms for scaling functions of the various two time correlations we also extend the real space renormalization group method to include systematic corrections to the previous zero temperature procedure via a series expansion in t we then consider the generalized trap model with parameter alpha in 0 1 and obtain that the large scale effective model at low temperature does not depend on alpha in any dimension so that the only observables sensitive to alpha are those that measure the local persistence such as the probability to remain exactly in the same trap during a time interval finally we extend our approach at a scaling level for the trap model in d 2 and obtain the two relevant time scales for aging properties