electromagnetic scattering by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate we consider a two dimensional problem of scattering of a time harmonic electromagnetic plane wave by an inhomogeneous conducting or dielectric layer on a perfectly conducting plate the magnetic permeability is assumed to be a fixed positive constant in the media the material properties of the media are characterized completely by an index of refraction which is a bounded measurable function in the layer and a positive constant above the layer corresponding to a homogeneous dielectric medium in this paper we only examine the tm transverse magnetic polarization case a radiation condition is introduced and equivalence with a second kind lippmann schwinger type integral equation is shown with additional assumptions on the index of refraction in the layer uniqueness of solution is proved existence of solution is then established by employing a form of fredholm alternative using a general result on the solvability of integral equations on unbounded domains published earlier by chandler wilde and zhang an approximate analytic solution for the case of a thin inhomogeneous layer is obtained from the integral equation formulation and is used to show that if the index of refraction is appropriately chosen the scattered field can grow with distance from the plate

scattering by stripe grating when bismuth is substituted at certain lattice points of rare earth garnet crystals a material is formed which exhibits an almost ideal magnetic stripe domain structure the structure consists of a one dimensional periodic array of regions of nearly constants magnetization so that the magnitudes of the magnetization vectors in two adjacent regions are the same but their directions are opposite this condition produces the alternating sign magnetic permeability tensors shown in section 1 7 3 when a beam of light is passed through such a film it splits into many diffracted beams all sharing a plane defined by the periodicity direction i e the y component of all the wave vectors is the same see figure 1 1 the angles of the diffracted beam directions relative to the incident beam direction are determined by the periodicity length

algebraic k theory of group rings and the cyclotomic trace map we prove that the farrell jones assembly map for connective alge braic k theory is rationally injective under mild homological niteness condi tions on the group and assuming that a weak version of the leopoldt schneider conjecture holds for cyclotomic elds this generalizes a result of bokstedt hsiang and madsen and leads to a concrete description of a large direct summand of kn z g z q in terms of group homology in many cases the number theoretic conjectures are true so we obtain rational injectivity results about assembly maps in particular for whitehead groups under niteness assumptions on the group only the proof uses the cyclotomic trace map to topological cyclic homology bokstedt hsiang madsen s functor c and new general injectivity results about the assembly maps for topological hochschild homology and c

a posteriori error analysis for the conical diffraction problem abstract maxwell s equations for conical diffraction can be reduced to a system of two helmholtz equations in r 2 coupled via quasi periodic transmission conditions on a set of piecewise smooth interfaces a finite element formulation of the conical diffraction problem is presented in a bounded domain by introducing the nonlocal boundary operators an a posteriori error estimate is established when the truncation of the nonlocal boundary operators takes place as our work in wang et al 2015 a duality argument is applied to overcome the difficulty caused by the fact that the truncated pseudo differential mapping does not converge to the original pseudo differential mapping in its operator norm the a posteriori error estimate consists of two parts finite element discretization error and the truncation error of the nonlocal boundary operators in particular the truncation error is exponentially decaying with respect to the truncation parameter

an adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures we develop a finite element adaptive strategy with error control for the wave scattering by periodic structures the unbounded computational domain is truncated to a bounded one by an extension of the perfectly matched layer pml technique which attenuates both the outgoing and evanescent waves in the pml region pml parameters such as the thickness of the layer and the medium property are determined through sharp a posteriori error estimates numerical experiments are included to illustrate the competitive behavior of the proposed adaptive method

finite gratings at high frequencies in this paper we construct geometric optics solutions to an acoustic scattering problem by a finite periodic dielectric grating placed on the interface between semi infinite dielectric media we rigorously justify that the first order approximation is the solution of the infinite periodic grating the method is extended to maxwell s equations

assouad nagata dimension of connected lie groups we prove that the asymptotic assouad nagata dimension of a connected lie group g equipped with a left invariant riemannian metric coincides with its topological dimension of g c where c is a maximal compact subgroup to prove it we will compute the assouad nagata dimension of connected solvable lie groups and semisimple lie groups as a consequence we show that the asymptotic assouad nagata dimension of a polycyclic group equipped with a word metric is equal to its hirsch length and that some wreath type finitely generated groups can not be quasi isometrically embedded into any cocompact lattice on a connected lie group

thermodynamics based gradient plasticity theories with an application to interface models in the framework of small deformations the so called residual based gradient plasticity theory is reconsidered and improved using the notion of moving geometrically necessary dislocations gnds suitable micromechanics interpretations are heuristically given for the higher order boundary conditions and the long distance particle interactions also a comparison is made between this theory and the analogous virtual work principle vwp based one whereby their respective conceptual and methodological features are pointed out the conditions under which the two theories lead to a same constitutive model are investigated showing that correspondingly a certain indeterminacy exhibited by the vwp based theory disappears a phenomenological interface model is used to better point out differences and analogies of the two theories

limit operators compactness and essential spectra on bounded symmetric domains abstract this paper is a follow up to a recent article about the essential spectrum of toeplitz operators acting on the bergman space over the unit ball as mentioned in the said article some of the arguments can be carried over to the case of bounded symmetric domains and some cannot the aim of this paper is to close the gaps to obtain comparable results for general bounded symmetric domains in particular we show that a toeplitz operator on the bergman space a p is fredholm if and only if all of its limit operators are invertible even more generally we show that this is in fact true for all band dominated operators an algebra that contains the toeplitz algebra moreover we characterize compactness and explain how the berezin transform comes into play in particular we show that a bounded linear operator is compact if and only if it is band dominated and its berezin transform vanishes at the boundary for p 2 band dominated can be replaced by contained in the toeplitz algebra

nonlocal models for damage and fracture comparison of approaches abstract the paper analyzes nonlocal constitutive models used in simulations of damage and fracture processes of quasibrittle materials a number of nonlocal formulations found in the literature are classified according to the type of variable subjected to nonlocal averaging analytical and numerical solutions of a simple one dimensional localization problem are presented it is shown that some of the formulations inevitably lead to residual stresses even at very late stages of the deformation process and consequently they are not capable of modeling complete separation in a widely open macroscopic crack the mechanisms leading to this specific type of stress locking are explained based on a theoretical analysis of the nonlocal constitutive equations it is also pointed out that the nonlocal approach distorts the shape of the stress strain diagram which has to be taken into account when designing an appropriate local softening law

the integral k theoretic novikov conjecture for groups with finite asymptotic dimension the integral assembly map in algebraic k theory is split injective for any geometrically finite discrete group with finite asymptotic dimension

acoustic scattering by mildly rough unbounded surfaces in three dimensions for a nonlocally perturbed half space we consider the scattering of time harmonic acoustic waves a second kind boundary integral equation formulation is proposed for the sound soft case based on a standard ansatz as a combined single and double layer potential but replacing the usual fundamental solution of the helmholtz equation with an appropriate half space green s function due to the unboundedness of the surface the integral operators are noncompact in contrast to the two dimensional case the integral operators are also strongly singular due to the slow decay at infinity of the fundamental solution of the three dimensional helmholtz equation in the case when the surface is sufficiently smooth lyapunov we show that the integral operators are nevertheless bounded as operators on l 2 gamma and on l 2 gamma cap bc gamma and that the operators depend continuously in norm on the wave number and on gamma we further show that for emph mild roughness i e a surface gamma which d

uniqueness of initial boundary value problems in nonlocal elasticity abstract in this study we have dealt with the uniqueness of the solutions of a class of initial boundary value problems in linear isotropic homogeneous nonlocal elasticity the proof of uniqueness is based on the positive definiteness of total strain energy after giving the sufficient conditions under which total strain energy is positive definite it has been shown that the solutions of the initial boundary value problems which are considered in this study are unique existence of the solutions of these problems is an a priori assumption

the cyclotomic trace and the k theoretic analogue of novikov s conjecture abstract a trace construction the cyclotomic trace is given it associates to algebraic k theory of a group ring or better to waldhausen s a theory equivariant stable homotopy classes of the free loop space of its classifying space the cyclotomic trace detects the borel classes in algebraic k theory of the integers it is used to prove for a wide class of groups that the k theory assembly map is rationally injective this is the k theoretic analogue of novikov s conjecture

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

on analyticity of linear waves scattered by a layered medium abstract the scattering of linear waves by periodic structures is a crucial phenomena in many branches of applied physics and engineering in this paper we establish rigorous analytic results necessary for the proper numerical analysis of a class of high order perturbation of surfaces methods for simulating such waves more specifically we prove a theorem on existence and uniqueness of solutions to a system of partial differential equations which model the interaction of linear waves with a multiply layered periodic structure in three dimensions this result provides hypotheses under which a rigorous numerical analysis could be conducted for recent generalizations to the methods of operator expansions field expansions and transformed field expansions

on the dimension growth of groups we prove that the thompson group f has exponential dimension growth we also prove that every solvable finitely generated subgroup of f has polynomial dimension growth while some elementary amenable subgroups of f and some solvable groups of class 3 have dimension growth at least exp n

on banach spaces with kasparov and yu s property h abstract a new geometric property of banach spaces recently introduced by g kasparov and g yu called property h has important applications to the strong novikov conjecture and the coarse novikov conjecture yet is far from being well understood in this paper we investigate various uniformly continuous maps on unit spheres of banach spaces and prove that all separable banach lattices with nontrivial cotype have property h

unique determination of periodic polyhedral structures by scattered electromagnetic fields this work is concerned with the unique determination of a periodic diffraction grating profile in three dimensions by some scattered electromagnetic fields measured above the grating in general it is well known that global uniqueness may not be true when the measurement is only taken for one incident field our goal is to completely characterize the global uniqueness properties when the periodic structure is of polyhedral type corresponding to each incident plane wave we are able to classify all unidentifiable structures into three classes and show that any periodic polyhedral structure can be uniquely determined by one incident field if and only if it belongs to none of the three classes consequently the minimum number of incident waves required for the unique determination of a periodic polyhedral structure can be easily read

a well posed integral equation formulation for three dimensional rough surface scattering we consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft rough surface recently a brakhage werner type integral equation formulation of this problem has been proposed based on an ansatz as a combined single and double layer potential but replacing the usual fundamental solution of the helmholtz equation with an appropriate half space green s function moreover it has been shown in the three dimensional case that thi si ntegral equation is uniquely solvable in the space l 2 g when the scattering surface g does not differ too much from a plane in this paper we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope moreover we construct explicit bounds on the inverse of the associated boundary integral operator as a function of the wave number the parameter coupling the single and double layer potentials and the maximum surface slope these bounds show that the norm of the inverse operator is bounded uniformly in the wave number k f orko0 if the coupling parameter h is chosen proportional to the wave number in the case when g is a plane we show that the choice hzk 2 is nearly optimal in terms of minimizing the condition number

a strain difference based nonlocal elasticity model abstract a two component local nonlocal constitutive model for macroscopically inhomogeneous linear elastic materials but constant internal length is proposed in which the stress is the sum of the local stress and a nonlocal type stress expressed in terms of the strain difference field hence identically vanishing in the case of uniform strain attention is focused upon the particular case of piecewise homogeneous material the proposed model is thermodynamically consistent with a suitable free energy potential it constitutes an improved form of the vermeer and brinkgreve a new effective nonlocal strain measure for softening plasticity in chambon r desrues j vardulakis i eds localization and bifurcation theory for soils and rocks balkema rotterdam 1994 pp 89 100 model and can also be considered derivable from the eringen nonlocal elasticity model through a suitable enhancement technique based on the concept of redistribution of the local stress the concept of equivalent distance is introduced to macroscopically account for the further attenuation effects produced by the inhomogeneity upon the long distance interaction forces with the aid of a piecewise homogeneous bar in tension a portion of which degrades progressively till failure it is shown that under a suitable choice of a material constant the solution procedure exhibits no pathological features numerical instability mesh sensitivity in every degraded bar condition including the limit idealized stress free condition of the failed bar

large riemannian manifolds which are flexible for each k z we construct a uniformly contractible metric on euclidean space which is not mod k hypereuclidean we also construct a pair of uniformly contractible riemannian metrics on r n n 11 so that the resulting manifolds z and z are bounded homotopy equivalent by a homotopy equivalence which is not boundedly close to a homeomorphism we show that for these spaces the c algebra assembly map k lf z k c z from locally finite k homology to the k theory of the bounded propagation algebra is not a monomorphism this shows that an integral version of the coarse novikov conjecture fails for real operator algebras if we allow a single cone like singularity a similar construction yields a counterexample for complex c algebras

benchmarks in nonlocal elasticity defined by eringen s integral model abstract in this paper we present low residual approximate solutions for nonlocal 1d and 2d elasticity problems defined according to eringen s integral model the benchmarks in the 1d cases are defined by prescribing the stress field while the unknown fields are the strains or the displacements for the 2d cases we define problems with equilibrated tractions and evaluate the approximate displacement field meanwhile a fourier series as well as a set of chebyshev polynomials are used as the basis functions for the main unknown fields we increase the number of the approximation functions to decrease the norm of the residuals and repeat the procedure until reasonable accuracy is obtained for the final solution since the procedure is very time consuming in some benchmark problems we present the calculated coefficients and in some other we give some point wise values for further use the results presented in this paper are particularly useful for the validation and convergence studies when numerical methods are to be used for the solution of the nonlocal elasticity problems

scattering by infinite one dimensional rough surfaces we consider the dirichlet boundary value problem for the helmholtz equation in a non locally perturbed half plane this problem models time harmonic electromagnetic scattering by a one dimensional infinite rough perfectly conducting surface the same problem arises in acoustic scattering by a sound soft surface chandler wilde and zhang have suggested a radiation condition for this problem a generalization of the rayleigh expansion condition for diffraction gratings and uniqueness of solution has been established recently an integral equation formulation of the problem has also been proposed and in the special case when the whole boundary is both lyapunov and a small perturbation of a flat boundary the unique solvability of this integral equation has been shown by chandler wilde and ross by operator perturbation arguments in this paper we study the general case with no limit on surface amplitudes or slopes and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers as an important corollary we prove that for a variety of incident fields including the incident plane wave the dirichlet boundary value problem for the scattered field has a unique solution

the finite element method for the mechanically based model of non local continuum summary in this paper the finite element method fem for the mechanically based non local elastic continuum model is proposed in such a model each volume element of the domain is considered mutually interacting with the others beside classical interactions involved by the cauchy stress field by means of central body forces that are monotonically decreasing with their inter distance and proportional to the product of the interacting volume elements the constitutive relations of the long range interactions involve the product of the relative displacement of the centroids of volume elements by a proper distance decaying function which accounts for the decrement of the long range interactions as long as distance increases in this study the elastic problem involving long range central interactions for isotropic elastic continuum will be solved with the aid of the fem the accuracy of the solution obtained with the proposed fem code is compared with other solutions obtained with galerkins approximation as well as with finite difference method moreover a parametric study regarding the effect of the material length scale in the mechanically based model and in the kroner eringen non local elasticity has been investigated for a plane elasticity problem copyright 2011 john wiley sons ltd

a symmetric nonlocal damage theory abstract the paper presents a thermodynamically consistent formulation for nonlocal damage models nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening the main features of the presented formulation are i relations derived by the free energy potential fully complying with nonlocal thermodynamic principles ii nonlocal integral operator which is self adjoint at every point of the solid including zones near to the solid s boundary iii capacity of regularizing the softening ill posed continuum problem restoring a meaningful nonlocal boundary value problem in the present approach the nonlocal integral operator is applied consistently to the damage variable and to its thermodynamic conjugate force i e nonlocality is restricted to internal variables only the present model when associative nonlocal damage flow rules are assumed allows the derivation of the continuum tangent moduli tensor and the consistent tangent stiffness matrix which are symmetric the formulation has been compared with other available nonlocal damage theories finally the theory has been implemented in a finite element program and the numerical results obtained for 1 d and 2 d problems show its capability to reproduce in every circumstance a physical meaningful solution and fully mesh independent results

an adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures an edge element adaptive strategy with error control is developed for wave scattering by biperiodic structures the unbounded computational domain is truncated to a bounded one by a perfectly matched layer pml technique the pml parameters such as the thickness of the layer and the medium properties are determined through sharp a posteriori error estimates numerical experiments are presented to illustrate the competitive behavior of the proposed adaptive method

on homological coherence of discrete groups abstract we explore a weakening of the coherence property of discrete groups studied by f waldhausen the new notion is defined in terms of the coarse geometry of groups and should be as useful for computing their k theory we prove that a group of finite asymptotic dimension is weakly coherent in particular there is a large collection of r modules of finite homological dimension when r is a finite dimensional regular ring this class contains word hyperbolic groups coxeter groups and as we show the cocompact discrete subgroups of connected lie groups

acoustic scattering by an inhomogeneous layer on a rigid plate the problem of scattering of time harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in r 2 is considered the density is assumed to be unity in the media within the layer the sound speed is assumed to be an arbitrary bounded measurable function the problem is modelled by the reduced wave equation with variable wavenumber in the layer and a neumann condition on the plate to formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced a generalization of the rayleigh expansion condition for diffraction gratings with the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate under additional assumptions on the wavenumber in the layer uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established general results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data

on hypersphericity of manifolds with finite asymptotic dimension we prove the following embedding theorems in the coarse geometry theorem a every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into the product of n 1 locally finite trees corollary every metric space x with bounded geometry whose asymptotic dimension does not exceed n admits a large scale uniform embedding into a non positively curved manifold of dimension 2n 2 the corollary is used in the proof of the following theorem b for every uniformly contractible manifold x whose asymptotic dimension is finite the product x x r is integrally hyperspherical for some n theorem b together with a theorem of gromov lawson implies the result previously proven by g yu 1998 which states that an aspherical manifold whose fundamental group has a finite asymptotic dimension cannot carry a metric of positive scalar curvature we also prove that if a uniformly contractible manifold x of bounded geometry is large scale uniformly embeddable into a hilbert space then x is stably integrally hyperspherical

a different approach to eringen s nonlocal integral stress model with applications for beams abstract the nonlocal continuum theory either integral or differential form has been formulated evolved and widely used in our era to explain size effect phenomena in micro and nano structures in the case of euler bernoulli beam theory ebbt the nonlocal integral form produces energy consistent formulas unlike the nonlocal differential form revealing inconsistencies and giving rise to paradoxes in this work our overall research objective mainly focuses on nonlocal integral elasticity analysis of beams by employing a normalized symmetric kernel this kernel corresponds to a finite domain and will be called modified kernel from now on that satisfies all the properties of a probability density function as well as successfully handles the physical inconsistencies of classic types of kernel our concern is to investigate the static response of a beam with various types of loading and boundary conditions bcs by making use the modified kernel and the kernel corresponding to the two phase nonlocal integral tpni model carrying out numerical methods to our problems the deducing results appear more flexible behavior than those of classic local and the common nonlocal differential respectively what is more a comparison is made between the results of the aforementioned kernels to demonstrate the advantages of the modified kernel unlike the common nonlocal differential form the nonlocal integral forms do not give rise to paradoxes moreover it is critical that the tpni model does not raise paradoxes as has been observed in other publications presented in the literature

the coarse geometric novikov conjecture for subspaces of non positively curved manifolds abstract in this paper we prove the coarse geometric novikov conjecture for metric spaces with bounded geometry which admit a coarse embedding into a simply connected complete riemannian manifold of non positive sectional curvature

an adaptive finite element method for the diffraction grating problem with transparent boundary condition the diffraction grating problem is modeled by a boundary value problem governed by a helmholtz equation with transparent boundary conditions an a posteriori error estimate is derived when the truncation of the nonlocal boundary operators takes place to overcome the difficulty caused by the fact that the truncated dirichlet to neumann dtn mapping does not converge to the original dtn mapping in its operator norm a duality argument without assuming more regularity than the weak solution is applied the a posteriori error estimate consists of two parts the finite element discretization error and the truncation error of boundary operators which decays exponentially with respect to the truncation parameter based on the a posteriori error control a finite element adaptive strategy is established for the diffraction grating problem such that the truncation parameter is determined through the truncation error and the mesh elements for local refinements are marked through the finite element discretization

second harmonic generation in nonlinear optical films second harmonic generation an important phenomenon in nonlinear optics is modeled in this work the model is derived from a nonlinear system of maxwell s equations which overcomes the known shortcomings of some commonly used models in the literature existence and uniqueness of solutions are established by a combination of a variational approach and the contraction mapping principle some numerical results are also presented

characteristic classes and distortion of diffeomorphisms let m and n be manifolds of bounded geometry that is the absolute value of their curvatures as well as their covariant derivatives are bounded from above and their injectivity radii are bounded from below a map f m n has bounded d stortion if there is an upper bound on the norm of the derivative d f a bounded distortion diffeomorphism cb d d is assumed to have an inverse which also has bounded distortion similarly homotopies are assumed to have bounded distortion note that this implies that homotopic maps are a finite distance apart we prove the following theorem that describes when characteristic classes of a compact manifold obstruct the existence of bounded distortion diffeomorphisms of universal covers theorem there are compact manifolds a and b with fundamental group r and a map f a b with jcpcb i pca for some rational pontrjagin class p whose universal cover is b d homotopic to a b d diffeomorphism if and only if r is nonamenable

free vibration analysis of functionally graded size dependent nanobeams abstract this paper presents free vibration analysis of functionally graded fg size dependent nanobeams using finite element method the size dependent fg nanobeam is investigated on the basis of the nonlocal continuum model the nonlocal elastic behavior is described by the differential constitutive model of eringen which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators the material properties of fg nanobeams are assumed to vary through the thickness according to a power law the nanobeam is modeled according to euler bernoulli beam theory and its equations of motion are derived using hamilton s principle the finite element method is used to discretize the model and obtain a numerical approximation of the equation of motion the model is validated by comparing the obtained results with benchmark results numerical results are presented to show the significance of the material distribution profile nonlocal effect and boundary conditions on the dynamic characteristics of nanobeams

one dimensional nonlocal and gradient elasticity assessment of high order approximation schemes abstract we investigate the application and performance of high order approximation techniques to one dimensional nonlocal elastic rods governing equations and corresponding discrete forms are derived for the integro differential formulation proposed by eringen and the laplacian based strain gradient formulation developed by aifantis and coworkers accuracy and convergence rate of the numerical solutions obtained with lagrange hermite b spline finite elements and c generalized finite elements are assessed against the corresponding analytical solutions

finite decomposition complexity and the integral novikov conjecture for higher algebraic k theory decomposition complexity for metric spaces was recently introduced by guentner tessera and yu as a natural generalization of asymptotic dimension we prove a vanishing result for the continuously controlled algebraic k theory of bounded geometry metric spaces with finite decomposition complexity this leads to a proof of the integral k theoretic novikov conjecture regarding split injectivity of the k theoretic assembly map for groups with finite decomposition complexity and finite cw models for their classifying spaces by work of guentner tessera and yu this includes all geometrically finite linear groups

nonlocal elasticity and related variational principles abstract the eringen model of nonlocal elasticity is considered and its implications in solid mechanics studied the model is refined by assuming an attenuation function depending on the geodetical distance between material particles such that in the diffusion processes of the nonlocality effects certain obstacles as holes or cracks existing in the domain can be circumvented a suitable thermodynamic framework with nonlocality is also envisaged as a firm basis of the model the nonlocal elasticity boundary value problem for infinitesimal displacements and quasi static loads is addressed and the conditions for the solution uniqueness are established three variational principles nonlocal counterparts of classical ones i e the total potential energy the complementary energy and the mixed hu washizu principles are provided the former is used to derive a nonlocal type fem nl fem in which the symmetric global stiffness matrix reflects the nonlocality features of the problem an alternative standard fem based solution method is also provided which consists in an iterative procedure of the type local prediction nonlocal correction in which the nonlocality is simulated by an imposed like correction strain the potentialities of these analysis methods are pointed out their numerical implementations being the object of an ongoing research work

plane stress problems in nonlocal elasticity finite element solutions with a strain difference based formulation abstract an enhanced computational version of the finite element method in the context of nonlocal strain integral elasticity of eringen type is discussed the theoretical bases of the method are illustrated focusing the attention on numerical and computational aspects as well as on the construction of the nonlocal elements matrices two numerical examples of plane stress nonlocal elasticity are presented to show the potentials and the limits of the promoted approach

nonlocal integral elasticity 2d finite element based solutions abstract a finite element based method theorized in the context of nonlocal integral elasticity and founded on a nonlocal total potential energy principle is numerically implemented for solving 2d nonlocal elastic problems the key idea of the method known as nonlocal finite element method nl fem relies on the assumption that the postulated nonlocal elastic behaviour of the material is captured by a finite element endowed with a set of cross stiffness element s matrices able to interpret the nonlocality effects induced in the element itself by the other elements in the mesh an eringen type nonlocal elastic model is assumed with a constitutive stress strain law of convolutive type which governs the nonlocal material behaviour computational issues as the construction of the nonlocal element and global stiffness matrices are treated in detail few examples are presented and the relevant numerical findings discussed both to verify the reliability of the method and to prove its effectiveness

maxwell s equations in a periodic structure consider a diffraction of a beam of particles in r3 when the dielectric coefficient is a constant cl above a surface s and a constant e2 below a surface s and the magnetic permeability is constant throughout rii s is assumed to be periodic in the xl direction and of the form x1 f1 s x3 f3 s x2 arbitrary we prove that there exists a unique solution to the time harmonic maxwell equations in r 3 having the form of refracted waves for x3 1 and of transmitted waves for x3 1 if and only if there exists a unique solution to a certain system of two coupled fredholm equations thus in particular for all the e s except for a discrete number there exists a unique solution to the maxwell equations introduction in this paper we consider the maxwell equations for time harmonic solutions in the entire space r3 with piecewise constant dielectric coefficient having jump across a periodic surface the magnetic permeability u is assumed to be constant whereas the dielectric coefficient e is given by e 8 above a surface s x3 f xl and e e2 below the surface s e and 82 are different constants if s is a half space x3 0 then the solution eo ho can be computed explicitly we assume in this paper that s is periodic i e f xl l f xl vx1 e r l 0 we wish to find a solution e h such that e eo and h ho are superpositions of transmitted waves 0 1 in x3 a where a maxlfl in 1 7 we assume that f e c2 and we reduce the solution of the maxwell equations to a fredholm system of four integral equations in 8 we reduce it further to a fredholm system of two integral equations thus for all but a discrete sequence of values of the physical parameters there exists a unique solution to the integral equations yielding a solution of the maxwell equations received by the editors january 25 1989 1980 mathematics subject classification 1985 revision primary 78a10 78a45 secondary 35p25 47a40

an etale approach to the novikov conjecture we show that the rational novikov conjecture for a group of finite homological type follows from the mod 2 acyclicity of the higson compactification of an e we then show that for groups of finite asymptotic dimension the higson compactification is mod p acyclic for all p and deduce the integral novikov conjecture for these groups 2007 wiley periodicals inc

on the k theory of groups with finite asymptotic dimension it is proved that the assembly maps in algebraic kand l theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for e the result also applies to certain groups that admit only a finite dimensional model for e in particular it applies to discrete subgroups of virtually connected lie groups

embedding of hyperbolic groups into products of binary trees we show that every gromov hyperbolic group admits a quasi isometric embedding into the product of n 1 binary trees where n dim is the topological dimension of the boundary at infinity of

a notion of geometric complexity and its application to topological rigidity we introduce a geometric invariant called finite decomposition complexity fdc to study topological rigidity of manifolds we prove for instance that if the fundamental group of a compact aspherical manifold m has fdc and if n is homotopy equivalent to m then m n is homeomorphic to n n for n large enough this statement is known as the stable borel conjecture on the other hand we show that the class of fdc groups includes all countable subgroups of gl n k for any field k

isomorphism conjectures in algebraic k theory duff in this paper we are concerned with the four functors y y3 if and which map from the category of topological spaces x to the category diff of q spectra the functor 3 or if maps the space x to the qspectrum of stable topological or smooth pseudoisotopies of x the spaces diff dif 3i x id9 x i 0 are hatcher s deloopings of 970 x yd x cf 29 the functor j maps a path connected space x to the algebraic ktheoretic s2 spectrum for the integral group ring z7r1x the spaces x x i 0 are the gersten wagoner deloopings of z o x cf 27 52 5 x is also defined on a nonpath connected space x to be x1 where xi i e i are the path components of x and ii xi indicates the direct limit of all finite products of the i xi i e i if x is path connected then the functor maps x to the l surgery classifying spaces for oriented surgery problems with fundamental group r i1x identified by their fourfold periodicity k 90 x k 4j x cf 35 39 44 47 in addition if x is not path connected then we set y77 x tiei5 fj xi where xi i e i are the path components of x results obtained by the authors over the past five years cf 15 25 and in particular 19 16 a 1 a 18 together with many earlier results and conjectures which are reviewed in 1 6 1 1 6 6 suggest that for any connected cwcomplex x and for 5 denoting any of the above functors the q spectrum x should be computable in a simple way from the values taken by 9 on covering spaces of x which have very simple fundamental groups in more detail we let 9 x denote the collection of all subgroups h c ir ix which are either finite or virtually infinite cyclic a group h is virtually infinite cyclic if there is a short exact sequence of groups 1 z h f 1 with f equal to a finite group and z equal to the infinite cyclic group for each such group we let xh x denote the covering space projection corresponding to h then the q spectrum 5 x should be computable in a simple way from the q spectra 5 xh h e 9 x the purpose of this paper is to formulate precisely a conjecture along these lines and to verify the conjecture for any x

aperiodic tilings positive scalar curvature and amenability of spaces the object of this paper is to begin a geometric study of noncompact spaces whose local structure has bounded complexity manifolds of this sort arise as leaves of foliations of compact manifolds and as their universal covers we shall introduce a coarse homology theory using chains of bounded complexity and study some of its first properties the most interesting result characterizes when h uf x vanishes as an analogue and strengthening of f0lner s amenability criterion for groups in terms of isoperimetric inequalities see 4 one can view this result as producing a successful infinite ponzi scheme on any nonamenable space each point with only finite resources gives to some of its neighbors some of these resources yet receives more from the remaining neighbors as one can imagine this is useful for eliminating obstructions on noncompact spaces this has a number of applications we present two of them the first produces tilings that are unbalanced on any nonamenable polyhedron unbalanced tilings are automatically aperiodic and this gives many examples of sets of tiles that tile only aperiodically unfortunately imbalance is a particularly unsubtle reason for aperiodicity so that the aperiodic tilings of euclidean space penrose tilings are necessarily not accessible to our method on the other hand most other simply connected noncompact symmetric spaces even have unbalanced tilings using our criterion the second application regards characteristic numbers of manifolds whose universal covers have positive scalar curvature we prove a converse to a theorem of roe we show that for any nonamenable group f one can find a spin manifold with fundamental group f with nonzero a genus whose universal cover has a uniformly positive scalar curvature metric of bounded geometry in the natural strict quasi isometry class

an index theorem on open manifolds ii on decrit et on applique un nouveau theoreme d indice pour des operateurs elliptiques sur certaines varietes non compactes on calcule un indice a valeur reelle pour des operateurs de type dirac sur des varietes non compactes de geometrie bornee

theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage this paper presents the theory and the numerics of an isotropic gradient damage formulation within a thermodynamical background the main motivation is provided by localization computations whereby classical local continuum formulations fail to produce physically meaningful and numerically converging results we propose a formulation in terms of the helmholtz free energy incorporating the gradient of the damage field a dissipation potential and the postulate of maximum dissipation as a result the driving force conjugated to damage evolution is identified as the quasi nonlocal energy release rate which essentially incorporates the divergence of a vectorial damage flux besides the strictly local energy release rate on the numerical side besides balance of linear momentum the algorithmic consistency condition must be solved in weak form thereby the crucial issue is the selection of active constraints which is solved by an active set search algorithm borrowed from convex nonlinear programming in the examples we compare the behavior in local damage with the performance of the gradient formulation

closed form solution for a nonlocal elastic bar in tension a simple mechanical one dimensional problem in the context of nonlocal integral elasticity is solved analytically the nonlocal elastic material behaviour is described by the eringen model whose nonlocality features all reside in the constitutive relation this relation of integral type contains an attenuation function usually assumed symmetric aimed to capture the diffusion process of the nonlocality effects it also exhibits a convolution format the governing equation is a fredholm integral equation of second kind whose analytical treatment even for the usual choice of a symmetric kernel is not easy to develop in the present paper assuming a specific shape for the attenuation function a closed form solution in terms of strains is alternatively obtained by solving a volterra integral equation of second kind the latter can be easily solved with standard techniques at least for the adopted kernel taking also advantage from the symmetry of the solution such a closed form solution is an essential result to validate the effectiveness of numerical procedures aimed to solve more complex mechanical problems in the context of nonlocal elasticity 2002 elsevier science ltd all rights reserved

an asymmetric theory of nonlocal elasticity part 2 continuum field abstract in this paper an asymmetric theory of nonlocal elasticity with nonlocal body couple is developed on the basis of the axiom system in nonlocal continuum field theory the galileo invariance is used for determining the explicit form of the constitutive equations it is shown that both continuum field theory and quasicontinuum theory give the same constitutive equations and field equations for the general theory of nonlocal elasticity finally the relations among nonlocal theory couple stress theory and higher gradient theory are investigated

artificial boundary conditions for axisymmetric eddy current probe problems we study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes for axial fictitious boundaries an exact dirichlet to neumann map is proposed and mathematically analyzed via a non selfadjoint spectral problem under general assumptions we show convergence of the solution to an eddy current problem involving a truncated dirichlet to neumann map to the solution on the entire unbounded axisymmetric domain as the truncation parameter tends to infinity under stronger assumptions on the physical parameters of the eddy current problem convergence rates are shown we further validate our theoretical results through numerical experiments for a realistic physical setting inspired by eddy current probes of nuclear reactor core tubes

nonlocal elasticity defined by eringen s integral model introduction of a boundary layer method abstract in this paper we consider a nonlocal elasticity theory defined by eringen s integral model and introduce for the first time a boundary layer method by presenting the exponential basis functions ebfs for such a class of problems the ebfs playing the role of the fundamental solutions are found so that they satisfy the governing equations on an unbounded domain some insight to the theory is given by showing that the ebfs satisfying the navier equations in the classical elasticity theory also satisfy the governing equations in the nonlocal theory some additional ebfs are particularly obtained for the nonlocal theory in order to use the ebfs on bounded domains the effects of the boundary conditions are taken into account by truncating the kernel attenuation function in the constitutive equations this leads to some residuals in the governing equations which appear near the boundaries a weighted residual approach is employed to minimize the residuals near the boundaries the method presented in this paper has much in common with trefftz methods especially when the influence area of the kernel function is much smaller than the main computational domain several one two dimensional problems are solved to demonstrate the way in which the ebfs can be used through the proposed boundary layer method

the time harmonic maxwell equations in a doubly periodic structure abstract consider the diffraction of a beam of particles in r 3 when the dielectric coefficient is a constant e1 above a surface s and a different constant e2 below s and the magnetic permeability is constant throughout r 3 s is assumed to be a doubly periodic surface say z f x y with f x ml1 y nl2 f x y for integers m n the existence and uniqueness of a solution satisfying a radiation condition at infinity is reduced to a system of fredholm equations thus for all but a discrete set of e s there exists a unique solution

a hurewicz type theorem for asymptotic dimension and applications to geometric group theory we prove an asymptotic analog of the classical hurewicz theorem on mappings that lower dimension this theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension as applications we find upper bound estimates for the asymptotic dimension of nilpotent and polycyclic groups in terms of their hirsch length we are also able to improve the known upper bounds on the asymptotic dimension of fundamental groups of complexes of groups amalgamated free products and the hyperbolization of metric spaces possessing the higson property

numerical analysis of diffraction by periodic structures tm polarization the diffraction of a time harmonic wave in tm polarization by some periodic inhomogeneous material is studied in this paper the diffraction problem is modeled by a generalized helmholtz equation with transparent boundary conditions existence and uniqueness are proved for the model problem uniform error estimates for the finite element approximation of the solution are established error estimates are also obtained when the truncation of the nonlocal boundary operators takes place

an inverse problem for scattering by a doubly periodic structure consider scattering of electromagnetic waves by a doubly periodic structure s x3 f xl x2 with f xl nial x2 n2a2 f xl x2 for integers nl n2 above the structure the medium is assumed to be homogeneous with a constant dielectric coefficient the medium is a perfect conductor below the structure an inverse problem arises and may be described as follows for a given incident plane wave the tangential electric field is measured away from the structure say at x3 b for some large b to what extent can one determine the location of the periodic structure that separates the dielectric medium from the conductor in this paper results on uniqueness and stability are established for the inverse problem a crucial step in our proof is to obtain a lower bound for the first eigenvalue of the following problem in a convex domain q l au in q v u 0 in q n xu 0 on q

finite element approximation of time harmonic waves in periodic structures consider the diffraction of a time harmonic wave incident on a periodic surface of some inhomogeneous material it is shown that the scattering diffraction problem may be modeled by a helmholtz equation with transparent boundary conditions the diffraction problem may be solved by a finite element method in this paper optimal error estimates for the finite element method are established the error estimates are also established when the truncation of the nonlocal transparent boundary operators takes place

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension