large deviations of the lyapunov exponent and localization for the 1d anderson model the proof of anderson localization for the 1d anderson model with arbitrary e g bernoulli disorder originally given by carmona klein martinelli in 1987 is based in part on the multi scale analysis later in the 90s it was realized that for one dimensional models with positive lyapunov exponents some parts of multi scale analysis can be replaced by considerations involving subharmonicity and large deviation estimates for the corresponding cocycle leading to nonperturbative proofs for 1d quasiperiodic models in this paper we present a short proof along these lines for the anderson model to prove dynamical localization we also develop a uniform version of craig simon s bound that works in high generality and may be of independent interest

regularity of the invariant measure and of the density of states in the one dimensional anderson model abstract let h 1 2 v on l2 z where v x x z are i i d r v s with common probability distribution let h t e itvd v let n e be the integrated density of states and let e be the invariant measure at energy e it is proven 1 1 let h be d times differentiable on 0 with bounded derivatives such that h j t 0 as t for j 0 1 d then i n e is a cd function ii if d 3 e is absolutely continuous for all e r and d e dx is of class c d 1 2 1 jointly in e and x 2 2 let h be differentiable on 0 with h j t o e b t for j 0 1 and some b 0 then d e dx is jointly analytic in e and x

high order finite elements for shells in this article the p version finite element method is applied to thin walled structures two different hierarchic element formulations are compared a shell approach as well as a shell like solid formulation both approaches are compared for linear elastic and elastoplastic problems special emphasis is placed on the efficiency as well as on determining the area of application for both formulations

positive lyapunov exponents for schrodinger operators with quasi periodic potentials we present a new simple way to estimate the rate of exponential growth lyapunov exponent of solutions of the finite difference schrodinger equation h e psi n mathop limits def psi n 1 psi n 1 lambda f alpha n theta psi n heref is a non constant real analytic function of period 1 and is irrational for large we prove that the lyapunov exponent is positive for every energye in the spectrum ofh and a e in particular the absolutely continuous spectrum ofh is empty in the continuum we study the quasi periodic operator onl2 r h frac d 2 dx 2 k 2 cos x cos alpha x theta for largek and show that for wide intervals of low energies the lyapunov exponent is positive the main idea which originated from m herman s subharmonic argument 11 is to deform the phase to the complex plane this enables us to avoid small denominator problems by moving them off the axis making estimates much easier to perform we recover the information for real using an elementary extension of jensen s formula subharmonicity

analyticity of the density of states in the anderson model on the bethe lattice let h 1 2 v on l2 b whereb is the bethe lattice andv x xeb are i i d r v s with common probability distribution it is shown that for distributions sufficiently close to the cauchy distribution the density of states e is analytic in a strip about the real axis

pure point spectrum for discrete almost periodic schrodinger operators the finite difference schrodinger operator on m is considered hu j left sum limits v 1 m d v 2 right u j frac 1 varepsilon q j u j u in ell 2 mathbb z m where sum limits v 1 m d v 2 is the difference laplacian inm dimensions for sufficiently small almost periodic potentialsq j are constructed such that the operatorh has only pure point spectrum the method is an inverse spectral procedure which is a modification of the kolmogorov arnol d moser technique

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

finite deformation post buckling analysis involving inelasticity and contact constraints this paper is concerned with the numerical solution of large deflection structural problems involving finite strains subject to contact constraints and unilateral boundary conditions and exhibiting inelastic constitutive response first a three dimensional finite strain beam model is summarized and its numerical implementation in the two dimensional case is discussed next a penalty formulation for the solution of contact problems is presented and the correct expression for consistent tangent matrix is developed finally basic strategies for tracing limit points are reviewed and a modification of the arc length method is proposed the good performance of the procedures discussed is illustrated by means of numerical examples

the jackknife estimate of variance tukey s jackknife estimate of variance for a statistic s x 1 x 2 cdots x n which is a symmetric function of i i d random variables x i is investigated using an anova like decomposition of s it is shown that the jackknife variance estimate tends always to be biased upwards a theorem to this effect being proved for the natural jackknife estimate of operatorname var s x 1 x 2 cdots x n 1 based on x 1 x 2 cdots x n

a lower bound on the lyapunov exponent for the generalized harper s model we obtain a lower bound for the lyapunov exponent of a family of discrete schrodinger operators hu n u n 1 u n 1 2a 1 cos 2 pi theta n alpha u n 2a 2 cos 4 pi theta n alpha u n that incorporates both a 1 and a 2 thus going beyond the herman s bound

harmonic analysis on sl 2 r and smoothness of the density of states in the one dimensional anderson model we consider infinite jacobi matrices with ones off diagonal and independent identically distributed random variables with distributionf v dv on diagonal iff has compact support and lies in some sobolev spacel 1 then we prove that the integrated density of states k e isc ine

on the solvability of closest point projection procedures in contact analysis analysis and solution strategy for surfaces of arbitrary geometry abstract the uniqueness and existence of the closest point projection procedure widely used in contact mechanics are analyzed in the current article first a projection domain for c 2 continuous surfaces is created based on the geometrical properties of surfaces then any point from the projection domain has a unique projection onto the given surface it is shown that in order to construct a continuous projection domain for arbitrary globally c 1 or c 0 continuous surfaces a projection routine should be generalized and also include a projection onto a curved edge and onto corner points criteria of uniqueness and existence of the corresponding projection routine are given and discussed from the geometrical point of view some examples showing the construction of the projection domain as well as the necessity of a generalized projection routine are given

technical note central limit theorems for estimated functions at estimated points the need to estimate a function value from sample data at a point that is itself estimated from the same data set arises in many application settings such applications include value at risk condi

an extension of kotani s theorem to random generalized sturm liouville operators we consider the random operator d m dx d dx q x wherem dx andq x are a stationary ergodic random measure and a random function respectively to this general case we extend kotani s theorem which asserts that the absolutely continuous spectrum is completely determined by the ljapounov indices our framework includes the case of stochastic jacobi matrices treated by simon

on information rates of the fading wyner cellular model via the thouless formula for the strip in this paper we apply the theory of random schrodinger operators to the analysis of multiusers communication channels similar to the wyner model which are characterized by short range intercell interference with h the channel transfer matrix hhf is a narrow band matrix a fact that does not permit the use of classical random matrices theory on the other hand hhf is in many aspects similar to a random schrodinger operator we relate the per cell sum rate capacity of the channel to the integrated density of states of a random schrodinger operator the latter is then related to the top lyapunov exponent of a random sequence of matrices via a version of the thouless formula we also derive several bounds on the limiting per cell sum rate capacity some based on the theory of random schrodinger operators and some derived from information theoretical considerations finally we get explicit results in the high signal to noise ratio snr regime for some particular cases

mortar based frictional contact formulation for higher order interpolations using the moving friction cone abstract finite element discretizations including contact usually apply the standard nts node to segment element thus a coupling with higher order solid elements leads to inconsistencies in the transmission of contact stresses one can circumvent this using the mortar method which includes a weak projection of the contact constraints in this paper we present a penalty formulation based on the mortar concept for two dimensional large deformation frictional contact the discretization of the contact surfaces contains quadratic approximations which can be used within a quadratic approximation of the solid elements to obtain a simple and efficient matrix formulation the moving friction cone algorithm is applied

the rotation number for almost periodic potentials we define and analyze the rotation number for the almost periodic schrodinger operatorl d2 dx2 q x we use the rotation number to discuss i the spectrum ofl ii its relation to the korteweg de vries equation

on the role of frame invariance in structural mechanics models at finite rotations in this work we re examine so called geometrically exact models for structures such as beams shells or solids with independent rotation field with respect to invariance under superposed rigid body motion a special attention is given to clarifying the issues pertaining to the finite element implementation which guarantees that the invariance of the continuum problem is preserved by its discrete approximation several numerical simulations dealing with finite rotations of structural models are presented in order to further illustrate and confirm the given theoretical considerations

transient three dimensional domain decomposition problems frame indifferent mortar constraints and conserving integration the present work deals with transient large deformation domain decomposition problems the tying of dissimilar meshed grids is performed by applying the mortar method in this connection a reformulation of the original linear mortar constraints is proposed which retains frame indifference for arbitrary discretizations of the interface furthermore a specific coordinate augmentation technique is proposed to make possible the design of an energy momentum scheme numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energy momentum scheme for three dimensional problems copyright 2009 john wiley sons ltd

computing densities for markov chains via simulation we introduce a new class of density estimators termed look ahead density estimators for performance measures associated with a markov chain look ahead density estimators are given for both transient and steady state quantities look ahead density estimators converge faster especially in multidimensional problems and empirically give visually superior results relative to more standard estimators such as kernel density estimators several numerical examples that demonstrate the potential applicability of look ahead density estimation are given

performance evaluation of output analysis methods in steady state simulations output analysis methods of steady state simulations have extensively been subject of study to evaluate the performance when estimating the mean however smaller efforts have been placed on performance evaluation of these methods to estimate variance and quantiles in this paper we empirically evaluate the performance of output analysis methods based on multiple replications and batches to estimate mean variance and quantile with the same set of data the evaluation of the performance of the methods is based on the empirical coverage of the true value using confidence intervals the average bias relative error and mean squared error the methods are applied to estimate the average variance and quantiles of waiting time in an m m 1 queue the results show that the methods based on non overlapping batches perform consistently well in all the metrics the performance of the other methods varies depending on the metric and the parameters of the simulation in addition we provide another example of a non geometric ergodic markov chain to show that asymptotically valid confidence intervals for quantiles can be obtained using batches and replications

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

dynamical description of bidimensional linear systems with a measurable 2 sheet abstract the dynamical behaviour of the projective flow induced by a family of bidimensional linear systems with a measurable 2 sheet is studied when the lyapunov exponent vanishes it is shown that the trajectories move from one sheet to the other either whenttends to or this extends and completes some known results on oscillatory dynamics to a more general ergodic situation

singular unbounded random jacobi matrices there have been several recent proofs of one dimensional anderson localization based on positive lyapunov exponent that hold for bounded potentials we provide a lyapunov exponent based proof for unbounded potentials simultaneously treating the singular and unbounded jacobi case by extending the techniques in a recent work by jitomirskaya and zhu there have been several recent proofs of one dimensional anderson localization based on positive lyapunov exponent that hold for bounded potentials we provide a lyapunov exponent based proof for unbounded potentials simultaneously treating the singular and unbounded jacobi case by extending the techniques in a recent work by jitomirskaya and zhu

franco american meeting on the mathematics of random and almost periodic potentials we present the abstracts of papers given at a conference held at the ecole polytechnique in june 1983 on the mathematics of random and almost periodic potentials

consistent development of a beam to beam contact algorithm via the curve to solid beam contact analysis for the nonfrictional case summary beam to beam contact can be dually described depending on the scale as contact between curves or contact between surfaces the surface to surface algorithm requires a computationally expensive continuum description of the beams the curve to curve ctc contact algorithm is generated from the corresponding closest point projection cpp procedure determining a minimal distance between curves and involves less expensive beam finite elements the existence and uniqueness criterion of the cpp procedure formulated already in earlier publications is analyzed in detail especially in the case of multiple solutions for parallel curves it is shown that the ctc contact algorithm cannot be applied for general parallel curves which can be generated in an arbitrary range of angles between the tangent lines a new curve to solid beam contact algorithm is here developed this algorithm requires a special solid beam finite element and is combining the advantages of surface contact together with the flexibility of the application to beam to beam contact further a special case with parallel tangent vectors is considered from the classical hertzian contact problem it is found numerically that the corresponding length of a contact zone is well correlated with the hertz theory a possible application of the developed strategy for wire ropes is analyzed numerically this article is protected by copyright all rights reserved

localization for one dimensional continuum bernoulli anderson models we use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional continuum anderson type models with singular distributions in particular the case of a bernoulli dis tribution is covered the operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms our main tools are the reflection and transmission coefficients for compactly supported single site perturbations of a periodic background which we use to verify the necessary hypotheses of multi scale analysis we show that non reflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs

singular continuous spectrum under rank one perturbations and localization for random hamiltonians we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic for a in terms of the spectral measure d a we give necessary and sufficient conditions for a p to have empty singular continuous spectrum or to have only point spectrum for a e we apply these results to questions of localization in the one and multi dimensional anderson models

simulation output analysis using standardized time series the method of standardized time series sts was proposed by schruben as an approach for constructing asymptotic confidence intervals for the steady state mean from a single simulation run the sts method cancels out the variance constant while other methods attempt to consistently estimate the variance constant our goal in this paper is to generalize the sts method and to study some of its basic properties starting from a functional central limit theorem fclt for the sample mean of the simulated process a class of mappings of c 0 1 to is identified each of which leads to a sts confidence interval one of these mappings leads to the batch means method a lower bound is obtained for the expected length of the asymptotic as the run size becomes large sts confidence intervals this lower bound is not attained but can be approached arbitrarily closely by sts confidence intervals methods that consistently estimate the variance constant do realize this lower bound the variance of the length of a sts confidence interval is of larger order in the run length than is that for the regenerative method

low energy properties of the random displacement model abstract we study low energy properties of the random displacement model a random schrodinger operator describing an electron in a randomly deformed lattice all periodic displacement configurations which minimize the bottom of the spectrum are characterized while this configuration is essentially unique for dimension greater than one there are infinitely many different minimizing configurations in the one dimensional case the latter leads to unusual low energy asymptotics for the integrated density of states of the one dimensional random displacement model for symmetric bernoulli distributed displacements it has a 1 log 2 singularity at the bottom of the spectrum in particular it is not holder continuous

kotani theory for one dimensional stochastic jacobi matrices we consider families of operators h on l2 given by h u n u n 1 u n 1 v n u n wherev is a stationary bounded ergodic sequence we prove analogs of kotani s results including that for a e ac h is the essential closure of the set ofe where e the lyaponov index vanishes and the result that ifv is non deterministic then ac is empty

limit periodic schrodinger operators in the regime of positive lyapunov exponents abstract we investigate the spectral properties of discrete one dimensional schrodinger operators whose potentials are generated by continuous sampling along the orbits of a minimal translation of a cantor group we show that for given cantor group and minimal translation there is a dense set of continuous sampling functions such that the spectrum of the associated operators has zero hausdorff dimension and all spectral measures are purely singular continuous the associated lyapunov exponent is a continuous strictly positive function of the energy it is possible to include a coupling constant in the model and these results then hold for every non zero value of the coupling constant

log holder continuity of the integrated density of states for stochastic jacobi matrices we consider the integrated density of states k e of a general operator on l2 v of the formh h0 v where h 0 u n sum limits left i right 1 u n i and vu n v n u n wherev is a general bounded ergodic stationary process on v we show that k e k e c log e e 1 when e e 1 2 the key is a thouless formula for the strip

anderson localization for the almost mathieu equation ii point spectrum for lambda 2 we prove that for any 2 and a e the pure point spectrum of the almost mathieu operator h n n 1 n 1 cos 2 n n contains the essential closure hat sigma of the spectrum corresponding eigenfunctions decay exponentially the singular continuous component if it exists is concentrated on a set of zero measure which is nowhere dense in hat sigma

regular spacings of complex eigenvalues in the one dimensional non hermitian anderson model we prove that in dimension one the non real eigenvalues of the non hermitian anderson nha model with a selfaveraging potential are regularly spaced the class of selfaveraging potentials which we introduce in this paper is very wide and in particular includes stationary potentials with probability one as well as all quasi periodic potentials it should be emphasized that our approach here is much simpler than the one we used before it allows us a to investigate the above mentioned spacings b to establish certain properties of the integrated density of states of the hermitian anderson models with selfaveraging potentials and c to obtain as a by product much simpler proofs of our previous results concerned with non real eigenvalues of the nha model

rotation number associated with difference equations satisfied by polynomials orthogonal on the unit circle abstract the techniques of topological dynamics and differential dynamical systems are used to study polynomials orthogonal with respect to a measure supported on the unit circle it is assumed that the reflection coefficients associated with these polynomials form a stationary stochastic ergodic process in particular the techniques mentioned above are used to prove a gap labelling result

on finite element implementation of geometrically nonlinear reissner s beam theory three dimensional curved beam elements abstract finite element implementation of the three dimensional finite strain beam theory of reissner is considered in this work in contrast with some earlier works on the subject discussed here are the beam elements whose reference axes are arbitrary space curved lines we have shown that an improved representation of curved reference geometry significantly increases the accuracy of the results however it also makes the choice of non locking finite element interpolations somewhat more delicate a hierarchical displacement interpolation proposed here is proved to be capable of eliminating both shear and membrane locking phenomena a very satisfying non locking performance is demonstrated for a set of problems in nonlinear elasto statics

a batch means methodology for estimation of a nonlinear function of a steady state mean we study the estimation of steady state performance measures from an d valued stochastic process y y t t 0 representing the output of a simulation in many applications we may be interested in the estimation of a steady state performance measure that cannot be expressed as a steady state mean r e g the variance of the steady state distribution the ratio of steady state means and steady state conditional expectations these examples are particular cases of a more general problem the estimation of a nonlinear function f r of r we propose a batch means based methodology that allows us to use jackknifing to reduce the bias of the point estimator asymptotically valid confidence intervals for f r are obtained by combining three different point estimators classical batch means and jackknife with two different variability estimators classical and jackknife the performances of the point estimators are discussed by considering asymptotic expansions for their biases and mean squared error

stochastic schrodinger operators and jacobi matrices on the strip we discuss stochastic schrodinger operators and jacobi matrices with wave functions taking values in l so there are 2l lyaponov exponents 1 l 0 l 1 2l 1 our results include the fact that if 1 0 on a set positive measure thenv is deterministic and one that says that e exactly 2j s are zero is the essential support of the a c spectrum of multiplicity 2j

analytic quasi perodic cocycles with singularities and the lyapunov exponent of extended harper s model we show how to extend and with what limitations avila s global theory of analytic sl 2 c cocycles to families of cocycles with singularities this allows us to develop a strategy to determine the lyapunov exponent for the extended harper s model for all values of parameters and all irrational frequencies in particular this includes the self dual regime for which even heuristic results did not previously exist in physics literature the extension of avila s global theory is also shown to imply continuous behavior of the le on the space of analytic m 2 mathbb c cocycles this includes rational approximation of the frequency which so far has not been available

brownian survival and lifshitz tail in perturbed lattice disorder abstract we consider the annealed asymptotics for the survival probability of brownian motion among randomly distributed traps the configuration of the traps is given by independent displacements of the lattice points we determine the long time asymptotics of the logarithm of the survival probability up to a multiplicative constant as applications we show the lifshitz tail effect of the density of states of the associated random schrodinger operator and derive a quantitative estimate for the strength of intermittency in the parabolic anderson problem

metal insulator transition for the almost mathieu operator we prove that for diophantine and almost every the almost mathieu operator h n n 1 ni 1 cos 2 n n exhibits localization for 2 and purely absolutely continuous spectrum for 2

ergodic properties and rotation number for linear hamiltonian systems abstract this paper is concerned with the dynamical behavior of the solutions of a class of linear hamiltonian systems including those to which kotani s theory applies we first present a symplectic l 2 perron transformation which takes these systems into skew symmetric form this allows us to study the average of the trajectories and the fourier coefficients of the solutions in addition from the construction of two invariant complex lagrange planes the differentiability of the rotation number is analyzed

on some aspects for contact with rigid surfaces surface to rigid surface and curves to rigid surface algorithms abstract special algorithms allowing a simplified description of contact between deformable body and rigid surfaces are developed based on the geometrically exact covariant description of contact a special attention is given to various geometric combinations where the contact can be represented as a contact between surfaces and b contact between a curve and a surface for contact between surfaces leading to the segment to analytical surface stas approach two algorithms can be distinguished based on the selection of a coordinate system for the closest point projection cpp procedure a rigid surface is a slave surface and b rigid surface is a master surface a special combination of both contact kinematics for the surface to surface and for the curve to curve approaches is employed for the contact between a curve and a surface leading to the curve to rigid surface ctrs approach the last algorithm is verified with the well known euler formula for the rope cylinder interaction as well as with a new derived generalization into a 3d spiral rope on a cylinder the developed algorithms can be straightforwardly implemented within an iso geometric approach as well as within the conventional finite elements where rigid surfaces are given by cad patches any type of elements can be employed for the contacting deformable surface curve because the algorithms are formulated in a covariant form

minimizing the ground state energy of an electron in a randomly deformed lattice we provide a characterization of the spectral minimum for a random schrodinger operator of the form h delta sum i in mathbb z d q x i omega i in l 2 mathbb r d where the single site potential q is reflection symmetric compactly supported in the unit cube centered at 0 and the displacement parameters i are restricted so that adjacent single site potentials do not overlap in particular we show that a minimizing configuration of the displacements is given by a periodic pattern of densest possible 2 d clusters of single site 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

critical coupling constants and eigenvalue asymptotics of perturbed periodic sturm liouville operators perturbations of asymptotic decay c r 2 arise in the partial wave analysis of rotationally symmetric partial differential operators we show that for each end point 0 of the spectral bands of a perturbed periodic sturm liouville operator there is a critical coupling constant c crit such that eigenvalues in the spectral gap accumulate at 0 if and only if c c crit 1 the oscillation theoretic method used in the proof also yields the asymptotic distribution of the eigenvalues near 0

bounded solutions and absolute continuity of sturm liouville operators this work is a contribution to the theory of the absolutely continuous spectrum of one dimensional schriidinger operators i e sturm liouville operators generated by differential expressions of the form ru u qu in proofs of absolute continuity for such operators and also for the closely related dirac systems always asymptotic properties of solutions of zu lu for real or complex values of 1 have played an important role see for example 18 19 8 4 9 lo in these works and a number of others particular classes of potentials q were treated using properties of solutions in the course of the proof of absolute continuity somewhat more recently the connection between asymptotic properties of solutions and absolute continuity was given a theory i e results of the following form were proved let the solutions of zu lu satisfy some specific asymptotic property for a varying in some subset of r no or almost no a priori assumptions on q then operators generated by z are absolutely continuous in this set a first result of this type was given by carmona 3 who proved that local uniform boundedness of solutions together with their derivatives in some open a set implies pure absolute continuity in this set here we will mostly rely on the concept of non or racy of solutions which was shown by gilbert and pearson 7 12 61 to be a powerful tool in the investigation of the continuous spectrum of sturm liouville operators in section 2 we give some consequences of their results whi ch are useful in proofs of absolute continuity these consequences range from non existence of imbedded eigenvalues and the existence of absolutely continuous parts to pure absolute continuity and the existence of transient 210 0022 247x 92 5 00

a supersymmetric transfer matrix and differentiability of the density of states in the one dimensional anderson model let h v on 2 z where v x 9 xez are d r v s with common probability distribution v let h t e itvdv v and let k e be the integrated density of states it is proven i if h is n times differentiable with h j t 0 l t for some 0 7 0 l n then k e is a cn function in particular if v has compact support and h t 0 l h 1 with 0 then k e is c this allows v to be singular continuous ii lfh t 0 e a tl for some 0 then k e is analytic in a strip about the real axis the proof uses the supersymmetric replica trick to rewrite the averaged green s function as a two point function of a one dimensional supersymmetric field theory which is studied by the transfer matrix method

moment asymptotics for the parabolic anderson problem with a perturbed lattice potential abstract the parabolic anderson problem with a random potential obtained by attaching a long tailed potential around a randomly perturbed lattice is studied the moment asymptotics of the total mass of the solution is derived the results show that the total mass of the solution concentrates on a small set in the space of configuration

a mortar finite element method using dual spaces for the lagrange multiplier the mortar finite element method allows the coupling of different discretization schemes and triangulations across subregion boundaries in the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of lagrange multipliers in this paper this lagrange multiplier space is replaced by a dual space without losing the optimality of the method the advantage of this new approach is that the matching condition is much easier to realize in particular all the basis functions of the new method are supported in a few elements the mortar map can be represented by a diagonal matrix in the standard mortar method a linear system of equations must be solved the problem is considered in a positive definite nonconforming variational as well as an equivalent saddle point formulation

consistent mesh tying methods for topologically distinct discretized surfaces in non linear solid mechanics this work presents a new technique for joining dissimilar meshes in non linear finite element analysis with the novel result that the adjoining surfaces do not need to be spatially coincident for patch tests to be passed the work builds in some sense on results previously presented by dohrmann et al international journal for numerical methods in engineering 1991 40 1205 but considerably generalizes upon the results presented there most importantly it is shown that consistency of the tied finite element formulation may be achieved such that implementation of element formulations is not affected through the use of a three field variational principle applied over the contacting region a key conclusion of the work is that although the approach advocated bears some resemblance to mortar element schemes for contact analysis see for example mcdevitt and laursen international journal for numerical methods in engineering 2000 48 1525 a straightforward application of a mortaring scheme is not sufficient to guarantee patch test passage when dissimilar meshing of curved surfaces leads to local open volumes or overlaps between tied surfaces in their reference configurations the proposed algorithm is demonstrated through a number of numerical examples performed within a matrix free non linear equation solving framework published in 2003 by john wiley sons ltd

geometrically exact theory for contact interactions of 1d manifolds algorithmic implementation with various finite element models abstract the intuitive understanding of contact between bodies is based on the geometry of adjoining bodies a more sophisticated approach of an advanced analysis including the application of various numerical methods is to take advantage of the geometry of an analyzed object and describe the problem in the best coordinate system the best coordinate system to describe contact interaction in all its geometrical details is a coordinate system attached to the geometrical features of contacting bodies this leads to a systematical analysis of geometrical situations leading to contact pairs surface to surface line to surface point to surface line to line point to line each contact pair is inherited with a special coordinate system based on its geometrical properties the current contribution is concentrating on contact between 1d manifolds in 3d space this is the majority of edge to edge beam to beam cable to edge etc contact cases the geometrically exact curve to curve contact approach is then systematically combined together with various finite element approaches classical finite elements isogeometric beam finite elements and also with a new developed solid beam approach examples illustrating the diversity of various finite element combinations e g within knot mechanics are shown

on the spectrum of two dimensional schrodinger operators with spherically symmetric radially periodic magnetic fields we investigate the spectrum of the two dimensional schrodinger operator where the magnetic field and the electric potential v are spherically symmetric i e and b is p periodic similarly for v by considering two different gauges we get the following results in case the spectrum contains a semi axis that consists alternately of intervals of absolutely continuous and dense point spectrum in case the essential spectrum is purely dense point spectrum and possibly there are spectral gaps

disordered quantum walks in one lattice dimension we study a spin 12 particle moving on a one dimensional lattice subject to disorder induced by a random space dependent quantum coin the discrete time evolution is given by a family of random unitary quantum walk operators where the shift operation is assumed to be deterministic each coin is an independent identically distributed random variable with values in the group of two dimensional unitary matrices we derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization put differently the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance our findings imply that this effect takes place if the coin is chosen at random from the haar measure or some measure continuous with respect to it but also for a class of discrete probability measures which support consists of two coins one of them being the hadamard coin

inverse tunnelingestimates and applications to the study of spectral statistics ofrandom operators on the real line we present a proof of a minami type estimate for one dimensional random schrodinger operators valid at all energies in the localization regime provided a wegner estimate is known to hold the minami type estimate is then applied to two models to obtain results on their spectral statistics the heuristics underlying our proof of minami type estimates is that close by eigenvalues of a one dimensional schrodinger operator correspond either to eigenfunctions that live far away from each other in space or they come from some tunneling phenomena in the second case one can undo the tunneling and thus construct quasi modes that live far away from each other in space resume nous demontrons une inegalite de type minami pour des operateurs de schrodinger aleatoires uni dimensionnel dans toute la region localisee si une estimee de wegner est connue cette estimee de type de minami est alors appliquee pour obtenir les statistiques spectrales pour deux modeles l heuristique qui guide ce travail est que des valeurs propres proches pour un operateur de schrodinger sur un intervalle sont soient localisees loin l une de l autre soit sont la consequence d un phenomene d effet tunnel dans le second cas on peut en defaisant cet effet tunnel construire des quasi modes qui sont localises loin l un de l autre 0 introduction consider the following two random operators on the real line the anderson model 0 1 h d2 dx2 w

uniform positivity and continuity of lyapunov exponents for a class of c 2 quasiperiodic schrodinger cocycles abstract we show that for a class of c 2 quasiperiodic potentials and for any fixed diophantine frequency the lyapunov exponent of the corresponding schrodinger cocycles as a function of energies are uniformly positive and weakly holder continuous as a corollary we obtain that the corresponding integrated density of states is weakly holder continuous as well our approach is of purely dynamical systems which depends on a detailed analysis of asymptotic stable and unstable directions we also apply it to more general sl 2 r cocycles which in turn can be applied to get uniform positivity and continuity of lyapunov exponents around unique nondegenerate extremal points of any smooth potential and to a certain class of c 2 szeg cocycles

one dimensional schrodinger operators with random or deterministic potentials new spectral types abstract we prove sufficient conditions involving only potential asymptotic near one of the infinities in order to have purely absolutely continuous components in the spectrum these deterministic results are then applied to random cases and exhibit classes of models for which with probability one one component of the spectrum is purely absolutely continuous and the rest is dense pure point with exponentially decaying eigenfunctions

a mixed formulation of mortar based frictionless contact abstract a class of mortar based frictionless contact formulations is derived based on a classical three field mixed variational framework within a penalty regularization complemented by uzawa augmentations discrete mortar constraints are naturally induced by the variational setting major aspects of earlier mortar approaches are obtained through constrained lumped or unconstrained recovery procedures for the mixed kinematic and kinetic mortar quantities from their projected counterparts two and three dimensional examples at the infinitesimal and finite deformation regimes highlight the local and global quality of the contact interactions

localization for anderson models on metric and discrete tree graphs we establish spectral and dynamical localization for several anderson models on metric and discrete radial trees the localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional energies all results are proved under the minimal hypothesis on the type of disorder the random variables generating the trees assume at least two distinct values this level of generality in particular allows us to treat radial trees with disordered geometry as well as schrodinger operators with bernoulli type singular potentials our methods are based on an interplay between graph theoretical properties of radial trees and spectral analysis of the associated random differential and difference operators on the half line

on the choice of finite rotation parameters in this work we discuss some aspects of the three dimensional finite rotations pertinent to the formulation and computational treatment of the geometrically exact structural theories among various possibilities to parameterize the finite rotations special attention is dedicated to a choice featuring an incremental rotation vector some computational aspects pertinent to the implementation of the newton iterative scheme and the newmark time stepping algorithm applied to solving these problems are examined representative numerical simulations are presented in order to illustrate the performance of the proposed formulation

inverse problem for polynomials orthogonal on the unit circle polynomials orthogonal on the unit circle with random recurrence coefficients and finite band spectrum are investigated it is shown that the coefficients are in fact quasi periodic the measures associated with these quasi periodic coefficients are exhibited and necessary and sufficient conditions relating quasi periodicity and spectral measures of this type are given analogs for polynomials orthogonal on subsets of the real line are also presented

spectral extrema and lifshitz tails for non monotonous alloy type models in the present note we determine the ground state energy and study the existence of lifshitz tails near this energy for some non monotonous alloy type models here non monotonous means that the single site potential coming into the alloy random potential changes sign in particular the random operator is not a monotonous function of the random variables