on the thermodynamic formalism for the gauss map we study the generalized transfer operator open image in new window of the gauss maptx 1 x mod 1 on the unit interval this operator which for 1 is the familiar perron frobenius operator oft can be defined for re 1 2 as a nuclear operator either on the banach spacea d of holomorphic functions over a certain discd or on the hilbert space open image in new window of functions belonging to some hardy class of functions over the half planeh 1 2 the spectra of open image in new window on the two spaces are identical on the space open image in new window is isomorphic to an integral operator open image in new window with kernel the bessel function mathfrak f 2 beta 1 2 sqrt st and hence to some generalized hankel transform this shows that open image in new window has real spectrum for real 1 2 on the spacea d the operator open image in new window can be analytically continued to the entire plane with simple poles at beta beta k 1 k 2 k 0 1 2 and residue the rank 1 operator mathcal n k f tfrac 1 2 1 k f k 0 from this similar analyticity properties for the fredholm determinant open image in new window of open image in new window and hence also for ruelle s zeta function follow another application is to the function zeta m beta sum limits n 1 infty n beta where n denotes the irrational n n n2 4 1 2 2 m extends to a meromorphic function in the plane with the only poles at 1 both with residue 1

a return mapping algorithm for isotropic elastoplasticity a return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces constructed from all three invariants of the stress tensor based on the first order backward euler difference formula bdf the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter the stresses are recovered afterwards the solution concept is applied to a pressure independent yield function expressed in terms of the second and third invariant of the stress tensor the numerical performance of the method is demonstrated with two examples

solution procedures for j3 plasticity and viscoplasticity abstract a solution strategy for plasticity and viscoplasticity models with isotropic yield surfaces depending upon all the principal invariants of the stress tensor is presented basically it requires the inversion of a fourth order positive definite tensor g both for the solution of the constitutive problem and for the evaluation of the consistent tangent operator it is proved that the assumption of isotropic elastic behaviour and the isotropy of the yield criterion entail an explicit representation formula for g 1 as linear combination of dyadic and square tensor products further an analogous representation formula for the consistent tangent operator is provided by exploiting basic composition rules between dyadic and square tensor products along with rivlin s identities for tensor polynomials all tensor operations required to compute the coefficients of the adopted representation formula for g 1 are carried out in intrinsic form it is thus shown that the relevant computational burden essentially amounts to solving a linear system of order three the performances of the proposed approach are illustrated by means of some numerical examples referred to the argyris failure criterion

ergodic theory for markov fibred systems and parabolic rational maps a paraboiic rational map of the riemann sphere admits a non atomic h conformal measure on its julia set where h the hausdorff dimension of the julia set and satisfies 1 2 h 2 with respect to this measure the rational map is conservative exact and there is an equivalent a finite invariant measure finiteness of the measure is characterised central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one a theory of markov fibred systems is developed and parabolic rational maps are considered within this framework

thermoacoustic tomography for an integro differential wave equation modeling attenuation abstract in this article we study the inverse problem of thermoacoustic tomography tat on a medium with attenuation represented by a time convolution or memory term and whose consideration is motivated by the modeling of ultrasound waves in heterogeneous tissue via fractional derivatives with spatially dependent parameters under the assumption of being able to measure data on the whole boundary we prove uniqueness and stability and propose a convergent reconstruction method for a class of smooth variable sound speeds by a suitable modification of the time reversal technique we obtain a neumann series reconstruction formula

axisymmetric pressure boundary loading for finite deformation analysis using p fem follower loads i e loads which depend on the boundary displacements by definition frequently occur in finite deformation boundary value problems restricting to axisymmetrical applications we provide analytical and numerical solutions for a set of problems in compressible neo hookean materials so to serve as benchmark problems for verifying the accuracy and efficiency of various fe methods for follower load applications thereafter the weak formulation for the follower load in 3 d domain is reduced to an axisymmetrical setting and subsequently consistently linearized in the framework of p fems exploiting the blending function mapping techniques the set of axisymmetric benchmark solutions is compared to numerical experiments in which the results obtained by a p fem code are compared to these obtained by a state of the art commercial h fem code and to the exact results these demonstrate the efficiency and accuracy of p fems when applied to problems in finite deformations with follower loads 2006 elsevier b v all rights reserved

yield criteria for quasibrittle and frictional materials a generalization to surfaces with corners abstract convexity of a yield function or phase transformation function and its relations to convexity of the corresponding yield surface or phase transformation surface is essential to the invention definition and comparison with experiments of new yield or phase transformation criteria this issue was previously addressed only under the hypothesis of smoothness of the surface but yield surfaces with corners for instance the hill tresca or coulomb mohr yield criteria are known to be of fundamental importance in plasticity theory the generalization of a proposition relating convexity of the function and the corresponding surface to nonsmooth yield and phase transformation surfaces is provided in this paper together with the necessary to the proof extension of a theorem on nonsmooth elastic potential functions while the former of these generalizations is crucial for yield and phase transformation functions the latter may find applications for potential energy functions describing phase transforming materials or materials with discontinuous locking in tension or contact of a body with a discrete elastic frictional support

remarks on rate constitutive equations for finite deformation problems computational implications it is explicitly shown that if the spatial elasticity tensor of an elastic material is taken as isotropic for all possible configurations then its coefficients cannot be constants they must depend nontrivially on the jacobian determinant of the deformation gradient moreover the assumption typically made for computational purposes that its coefficients remain constant for all possible configurations is incompatible with elasticity it is further shown that an assumption widely used in the computational literature in the context of finite deformation plasticity namely relating an objective stress rate to the rate of deformation tensor through a fourth rank constant isotropic tensor is also incompatible with elasticity thus furnishing an example of an hypoelastic material which is not elastic

zero temperature limits of gibbs equilibrium states for countable alphabet subshifts of finite type let a be a finitely primitive subshift of finite type on a countable alphabet for appropriate functions f a ir the family of gibbs equilibrium states tf t 1 for the functions tf is shown to be tight any weak accumulation point as t is shown to be a maximizing measure for f

consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part i theoretical formulation abstract a derivation of the projected algorithm for general isotropic three invariant plasticity models under plane stress conditions is presented it is obtained by consistently specializing the 3d formulation to the 2d subspace defined by the plane stress condition closed form intrinsic algorithm linearization and a novel expression of the consistent tangent tensor are provided these are also shown to directly emanate from the analogous quantities pertaining to the fully 3d case a detailed discussion of the proposed implementation along with a representative set of numerical examples is provided in the second part of this paper valoroso n rosati l 2008 consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part ii computational issues international journal of solids and structures 46 92 124

inversion of spherical means and the wave equation in even dimensions we establish inversion formulas of the so called filtered back projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball we also find several formulas to recover initial data of the form f 0 or 0 g for the free space wave equation in even dimensions from the trace of the solution on the boundary of the ball provided that the initial data has support in the ball

universal anisotropic yield criterion based on superquadric functional representation part 1 algorithmic issues and accuracy analysis abstract a robust and efficient stress update algorithm for the anisotropic yield criterion represented in the form of superquadric function introduced by barlat et al is presented it relies on a discrete variational formulation of the lagrangian functional which results from the principle of maximum plastic dissipation numerical solution of the discretized equations of evolution is based on the operator split methodology and the newton raphson method a line search algorithm is implemented to overcome numerical instabilities and to expand the convergence region of the basic newton raphson solution procedure the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discrete kuhn tucker condition numerical testing of the integration algorithm based on iso error maps is provided for several variants of the yield function

recovering functions from the spherical mean transform with limited radii data by expansion into spherical harmonics abstract the aim of the article is to generalize the method presented in 3 theorem 1 by g ambartsoumian r gouia zarrad and m lewis for recovering functions from their spherical mean transform with limited radii data from the two dimensional case to the general n dimensional case the idea behind the method is to expand each function in question into spherical harmonics and then obtain for each term in the expansion an integral equation of volterra s type that can be solved iteratively we show also how this method can be modified for the spherical case of recovering functions from the spherical transform with limited radii data lastly we solve the analogous problem for the case of the funk transform by again using expansion into spherical harmonics and then obtain an abel type integral equation which can be inverted by a method introduced in 14

the p version of the finite element method compared to an adaptive h version for the deformation theory of plasticity a p version of the finite element method is applied to the deformation theory of plasticity and the results are compared to a state of the art adaptive h version it is demonstrated that even for nonlinear elliptic problems the p version is a very efficient discretization strategy

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

consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part ii computational issues abstract the implementation of the projected algorithm and of the consistent tangent tensor for general isotropic three invariant elastoplastic models under plane stress conditions discussed in part i of this paper valoroso n rosati l 2008 consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part i theoretical formulation international journal of solids and structures doi 10 1016 j ijsolstr 2008 08 012 is addressed the connections between the general three dimensional case and the plane stress problem are analyzed in detail and an algorithmic treatment taking full advantage of the isotropic properties of the model is presented in particular intrinsic matrix free expressions are provided for all steps of the stress computation scheme that allow one to carry out the numerical implementation in a way that is completely independent from the matrix representations the numerical performances of the present solution scheme are evaluated through representative numerical examples

high order quasi static finite element computations in space and time with application to finite strain viscoelasticity on the one hand high order quasi static finite elements have been developed on the basis of isogeometric analysis or hierarchical shape functions based on integrated legendre polynomials which display favorable behavior in comparison to linear element formulations if we consider constitutive models of evolutionary type such as elastoplasticity viscoplasticity or viscoelasticity only first order methods are employed to integrate the ordinary differential equations at the gauss point level leading to errors caused by the time integration on the other hand high order time integration methods have been devised to treat the resulting system of differential algebraic equations dae system following the spatial discretization this however is only done using spatial discretizations with linear or quadratic h elements based on lagrange polynomials or related mixed element formulations in this article both approaches are combined using a p version finite element approach on the basis of hierarchical shape functions and the resulting dae system is solved by means of high order one step methods the first step in this treatise is to apply stiffly accurate diagonally implicit runge kutta methods combined with the multilevel newton algorithm since the computational outlay for computing the tangential stiffness matrix is very high in the case of p version finite elements rosenbrock type methods are applied as well which lead to a completely iteration free technique we then compare the two approaches the next step is to investigate three dimensional examples showing the properties on the basis of a constitutive model in finite strain viscoelasticity

an automatic load stepping algorithm with error control summary this paper presents an algorithm for controlling the error in non linear finite element analysis which is caused by the use of finite load steps in contrast to most recent schemes the proposed technique is non iterative and treats the governing load deflection relations as a system of ordinary differential equations this permits the governing equations to be integrated adaptively where the step size is controlled by monitoring the local truncation error the latter is measured by computing the difference between two estimates of the displacement increments for each load step with the initial estimate being found from the first order euler scheme and the improved estimate being found from the second order modified euler scheme if the local truncation error exceeds a specified tolerance then the load step is abandoned and the integration is repeated with a smaller load step whose size is found by local extrapolation local extrapolation is also used to predict the size of the next load step following a successful update in order to control not only the local load path error but also the global load path error the proposed scheme incorporates a correction for the unbalanced forces overall the cost of the automatic error control is modest since it requires only one additional equation solution for each successful load step because the solution scheme is non iterative and founded on successful techniques for integrating systems of ordinary differential equations it is particularly robust to illustrate the ability of the scheme to constrain the load path error to lie near a desired tolerance detailed results are presented for a variety of elastoplastic boundary value problems

remarks on the interpretation of current non linear finite element analyses as differential algebraic equations for the numerical solution of materially non linear problems like in computational plasticity or viscoplasticity the finite element discretization in space is usually coupled with point wise defined evolution equations characterizing the material behaviour the interpretation of such systems as differential algebraic equations dae allows modern day integration algorithms from numerical mathematics to be efficiently applied especially the application of diagonally implicit runge kutta methods dirk together with a multilevel newton method preserves the algorithmic structure of current finite element implementations which are based on the principle of virtual displacements and on backward euler schemes for the local time integration moreover the notion of the consistent tangent operator becomes more obvious in this context the quadratical order of convergence of the multilevel newton algorithm is usually validated by numerical studies however an analytical proof of this second order convergence has already been given by authors in the field of non linear electrical networks we show that this proof can be applied in the current context based on the dae interpretation mentioned above we finally compare the proposed procedure to several well known stress algorithms and show that the inclusion of a step size control based on local error estimations merely requires a small extra time investment copyright 2001 john wiley sons ltd

a mollification approach for inverting the spherical mean radon transform the filtered backprojection algorithm is still one of the most important reconstruction methods in computed tomography it is based on explicit formulas for recovering mollified versions of the original unknown function in this paper we derive such formulas for the spherical mean radon transform with centers restricted to the boundary of a ball in two spatial dimensions we present an efficient implementation strategy that leads to a stable reconstruction algorithm of filtered backprojection type

on the formulation of closest point projection algorithms in elastoplasticity part ii globally convergent schemes this paper presents the formulation of numerical algorithms for the solution of the closest point projection equations that appear in typical implementations of return mapping algorithms in elastoplasticity the main motivation behind this work is to avoid the poor global convergence properties of a straight application of a newton scheme in the solution of these equations the so called newton cppm the mathematical structure behind the closest point projection equations identified in part i of this work delineates clearly different strategies for the successful solution of these equations in particular primal and dual closest point projection algorithms are proposed in non augmented and augmented lagrangian versions for the imposition of the consistency condition the primal algorithms involve a direct solution of the original closest point projection equations whereas the dual schemes involve a two level structure by which the original system of equations is staggered with the imposition of the consistency condition driving alone the iterative process newton schemes in combination with appropriate line search strategies are considered resulting in the desired asymptotically quadratic local rate of convergence and the sought global convergence character of the iterative schemes these properties together with the computational performance of the different schemes are evaluated through representative numerical examples involving different models of finite strain plasticity in particular the avoidance of the large regions of no convergence in the trial state observed in the standard newton cppm is clearly illustrated

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

inversion of circular means and the wave equation on convex planar domains we study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary w of a smooth convex bounded domain w r 2 as a main result we establish back projection type inversion formulas that recover any initial data with support in w modulo an explicitly computed smoothing integral operator k w for circular and elliptical domains the operator k w is shown to vanish identically and hence we establish exact inversion formulas of the back projection type in these cases similar results are obtained for recovering a function from its mean values over circles with centers on w both reconstruction problems are amongst others essential for the hybrid imaging modalities photoacoustic and thermoacoustic tomography

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

sampling conditions for the circular radon transform recovering a function from circular or spherical mean values is the basis of many modern imaging technologies such as photo and thermoacoustic computed tomography or ultrasound reflection tomography recently much progress has been made concerning the problem of recovering a function from its circular mean values its circular radon transform in particular theoretically exact inversion formulas of the back projection type have been discovered using continuously sampled data in practical applications however only a discrete number of circular mean values can be collected in this paper we address this issue in the context of the shannon sampling theory we derive sharp sampling conditions for the number of angular and radial samples such that any essentially b0 bandlimited function can be recovered from a finite number of such circular mean values

large deviations averaging and periodic orbits of dynamical systems the paper deals with large deviation bounds for the proportion of periodic orbits with irregular behavior for expansive dynamical systems with specification in particular we obtain estimates for large deviations from the equidistribution for closed geodesics on negatively curved manifolds we derive also large deviation bounds in the averaging principle when the fast motion is the shift along periodic orbits

the universal back projection formula for spherical means and the wave equation on certain quadric hypersurfaces abstract in many tomographic applications and elsewhere there arises a need to reconstruct a function from the data on the boundary of some domain given either by the spherical means of the function or by the corresponding solution of the free space wave equation in this paper we show that the so called universal back projection formulas provide exact recovery of the unknown function with compact support for data on any quadric hypersurfaces that can be approximated by elliptic hypersurfaces these quadric hypersurfaces include elliptic paraboloid as well as parabolic and elliptic cylinders

the effect of numerical quadrature in the p version of the finite element method we investigate the use of numerical quadrature in the p version of the finite element method we describe a set of minimal conditions that the quadrature rules should satisfy for various types of elements under sufficient assumptions of smoothness we establish optimality of the asymptotic rate of convergence some computational results are presented which illustrate under what conditions overintegration may be useful

a return map algorithm for general isotropic elasto visco plastic materials in principal space we describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto visco plastic models whose yield function incorporates the third stress invariant the developments presented are based upon original results proved in the paper concerning the derivatives of eigenvalues and eigenprojectors of symmetric second order tensors with respect to the tensor itself and upon an original algebra of fourth order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument the analysis initially referred to the small strain case is then extended to a formulation for the large deformation regime for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the lagrangian description of large strain elastoplasticity copyright 2004 john wiley sons ltd

inversion formulas and stability estimates of the wave operator on the hyperplane abstract one of the mathematical problems arising in photoacoustic tomography pat a novel and promising technology in medical imaging is to recover the initial function from the solution of the wave equation on a surface where the detectors of pat are located we define the wave operator as the transform assigning to a given function f the solution of the wave equation on the detector surface where the detectors are located with the initial function f here we study many properties of this wave operator including the inversion formulas and stability estimates assuming that the detector surface is a hyperplane

the mixed complementarity problem arising from non associative plasticity with non smooth yield surfaces abstract an elastic domain with multiple yield surfaces brings about huge troubles to numerical computations due to singularities while non associative plasticity leads further to the open issue of whether constitutive integration is well posed this study reduces the constitutive integration of non associative plasticity with multiple yield surfaces to a mixed complementarity problem represented by micp a special case of finite dimensional variational inequalities by means of the projection contraction algorithm for finite dimensional variational inequalities and the idea of the gauss seidel method a new projection contraction algorithm for micp is designed and denoted by gspc applying the monotonicity of the mapping of the micp gspc is proved convergent theoretically for associative plasticity for non associative plasticity the sufficient condition for gspc to be convergent is also established if the tension part of the mohr coulomb elastic domain is cut off typical examples are designed to illustrate gspc is highly efficient accurate and stable some of which cannot be solved by the conventional return mapping method in all the cases the computational efficiency of gspc is apparently above the mapping return method

uniqueness of minimizer for countable markov shifts and equidistribution of periodic points for a finitely irreducible countable markov shift and a potential with summable variations we provide a condition on the associated pressure function which ensures that bowen s gibbs state the equilibrium state and the minimizer of the level 2 large deviations rate function are all unique and they coincide from this we deduce that the set of periodic points weighted with the potential equidistributes with respect to the gibbs equilibrium state as the periods tend to infinity applications are given to the gauss map and the bowen series map associated with a finitely generated free fuchsian group with parabolic elements

is a curved flight path in sar better than a straight one in the plane we study the transform r gamma f of integrating an unknown function f over circles centered at a given curve gamma this is a simplified model of synthetic aperture radar sar when the radar is not directed but has other applications like thermoacoustic tomography for example we study the problem of recovering the wave front set wf f if the visible singularities of f hit gamma once we show that wf f cannot be recovered i e the artifacts cannot be resolved if gamma partial omega is the boundary of a strictly convex domain omega we show that this is still true on the other hand in the latter case if f is known a priori to have singularities in a compact set then we show that one can recover wf f omega and moreover this can be done in a simple explicit way using backpropagation for the wave equation

multifractal analysis for expanding interval maps with infinitely many branches in this paper we investigate multifractal decompositions based on values of birkhoff averages of functions from a class of symbolically continuous functions this will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches we show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches 1 setting let x d be a metric space and t x x be a piecewise continuous transformation let x r be a real valued function called a potential the birkhoff average of is defined by

anisotropic hierarchic solid finite elements for the simulation of passive active arterial wall models abstract a 3d anisotropic hierarchic solid finite element formulation is provided for the passive and active mechanical response of arteries the artery is modeled as an anisotropic nearly incompressible hyperelastic tube consisting of two layers that correspond to the media and the adventitia these layers are considered as a fiber reinforced material consisting of two collagen fiber families that are symmetrically disposed and helically oriented around the tube s axis the numerical analysis is based on a 3d anisotropic hierarchic solid finite element formulation including the possibility of varying the polynomial degree in all local directions as well as for all displacement components for the purpose of verification analytical solutions are provided for different benchmarks focusing on the aspects of compressible and incompressible 3d stretch plane strain and plane stress pure shear as well as a mono layer anisotropic incompressible circular cylindrical artery of holzapfel gasser ogden material under inflation and extension the resulting solutions including stress and strain distribution through the arterial wall are plotted to point out the passive response and different activation levels in addition the effect of various compressibility levels including nearly incompressibility is studied by numerical examples the robustness and accuracy of the proposed method is demonstrated by comparing the results of different ansatz spaces

an inversion formula for the spherical mean transform with data on an ellipsoid in two and three dimensions abstract in the articles 1 and 2 of d finch m haltmeier s patch and d rakesh inversion formulas were found in any dimension greater than or equal to 2 for recovering a smooth function with compact support in the unit ball from spherical means centered on the unit sphere the aim of this article is to show that the methods used in 1 2 can be modified in order to get similar inversion formulas from spherical means centered on an ellipsoid in two and three dimensional spaces

to local reconstruction from the spherical mean radon transform abstract the article suggests a new approach using the so called consistency method for the inversion of the spherical mean radon transform in 2d with detectors on a line we present a new iterative formula which gives an algorithm to recover an unknown function supported completely on one side of a line l from its spherical means over circles centered on the line l our reconstruction formula has the benefit of being local such an inversion is required in problems of thermo and photo acoustic tomography ultrasound reflection tomography radar imaging and a few other

a monolithic finite element approach using high order schemes in time and space applied to finite strain thermo viscoelasticity this article addresses a thermo mechanically coupled problem of thermo viscoelasticity at finite strains using a monolithic approach the underlying equations are based on the non linear transient heat equation the local equilibrium conditions and the evolution equations of the internal variables the latter describe the hardening behavior of the material if the method of vertical lines is applied its first step namely the spatial discretization yields a system of differential algebraic equations dae system here we employ the p version of the finite element method based on integrated legendre polynomials this can lead to very precise solutions in the spatial domain in order to be accurate in the time domain as well stiffly accurate diagonally implicit runge kutta methods are applied to solve the dae system yielding a coupled system of non linear algebraic equations in this article the system is solved monolithically by employing the multilevel newton algorithm accordingly a high order result is obtained in the space and the time domain the numerical concept is applied to a constitutive model of finite strain thermo viscoelasticity several examples are applied to demonstrate the efficiency and applicability of the numerical scheme it is especially the transient problems that call for time adaptive schemes which are naturally embedded in the concept

on the formulation of closest point projection algorithms in elastoplasticity part i the variational structure we present in this paper the characterization of the variational structure behind the discrete equations defining the closest point projection approximation in elastoplasticity rate independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range the later in the context of isotropic finite strain multiplicative plasticity primal variational principles in terms of the stresses and stress like hardening variables are presented first followed by the formulation of dual principles incorporating explicitly the plastic multiplier augmented lagrangian extensions are also presented allowing a complete regularization of the problem in the constrained rate independent limit the variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in part ii of this work

the spherical radon transform with centers on cylindrical surfaces abstract recovering a function from its spherical radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies including sar ultrasound imaging and photo and thermoacoustic tomography in this paper we study an inversion of the spherical radon transform with centers of integration restricted to cylindrical surfaces of the form r m where is a hypersurface in r n we show that this transform can be decomposed into two lower dimensional spherical radon transforms one with centers on and one with a planar center set in r m 1 together with explicit inversion formulas for the spherical radon transform with a planar center set and existing algorithms for inverting the spherical radon transform with a center set this yields reconstruction procedures for general cylindrical domains in the special case of spherical or elliptical cylinders we obtain novel explicit inversion formulas for three spatial dimensions these inversion formulas can be implemented efficiently by backprojection type algorithms only requiring o n 4 3 floating point operations where n is the total number of unknowns to be recovered we present numerical results demonstrating the efficiency of the derived algorithms

large deviations and the distribution of pre images of rational maps in this article we prove a large deviation result for the pre images of a point in the julia set of a rational mapping of the riemann sphere as a corollary we deduce a convergence result for certain weighted averages of orbital measures generalizing a result of lyubich

on the representation and implicit integration of general isotropic elastoplasticity based on a set of mutually orthogonal unit basis tensors summary a simple and compact representation framework and the corresponding efficient numerical integration algorithm are developed for constitutive equations of isotropic elastoplasticity central to this work is the utilization of a set of mutually orthogonal unit tensor bases and the corresponding invariants the set of bases can be regarded equivalently as a local cylindrical coordinate system in the three dimensional coaxial tensor subspace namely the principal space the base tensors are given in the global coordinate system similar to the principal space approach the proposed method reduces the problem dimension from six to three in contrast to the conventional approach the transformation procedure between the principal space and the general space is avoided and explicit computation of the principal axes is bypassed with the proposed technique the matrices which need to be inverted during iteration take a simple form for the great majority of constitutive equations in use the tangent operator consistent with the proposed algorithm can be decomposed into the direct sum of two linear maps over the coaxial tensor subspace and the subspace orthogonal to it consequently its closed form is derived in an extremely simple manner finally numerical examples demonstrate the high quality performances of the proposed scheme copyright 2014 john wiley sons ltd

a galerkin least squares approach for photoacoustic tomography the development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography in this paper we address this issue for photoacoustic computed tomography in circular geometry we investigate the galerkin least squares method for that purpose for approximating the function to be recovered we use subspaces of translation invariant spaces generated by a single function this includes many systems that have previously been employed in photoacoustic tomography such as generalized kaiser bessel basis functions or the natural pixel basis by exploiting an isometry property of the forward problem we are able to efficiently set up the galerkin equation for a wide class of generating functions and devise efficient algorithms for its solution we establish a convergence analysis and present numerical simulations that demonstrate the efficiency and accuracy of the derived algorithm

higher order meshless schemes applied to the finite element method in elliptic problems abstract this paper presents selected approximation techniques typical for the meshless finite difference method mfdm although applied to the finite element method fem finite elements with standard or hierarchical shape functions are coupled with higher order meshless schemes based upon the correction terms of a simple difference operator those terms consist of higher order derivatives which are evaluated by means of the appropriate formulas composition as well as a numerical solution which corresponds to the primary interpolation order assigned to element shape functions correction terms modify the right hand sides of algebraic fe equations only yielding an iterative procedure therefore neither re generation of the stiffness matrix nor introduction of any additional nodes and or degrees of freedom is required such improved fe mfd solution approach allows for the optimal application of advantages of both methods for instance a high accuracy of the nodal fe solution and a derivatives super convergence phenomenon at arbitrary domain points typical for the meshless fdm existing and proposed higher order techniques applied in the fem are compared with each other in terms of the solution accuracy algorithm efficiency and computational complexity in order to examine the considered algorithms numerical results of several two dimensional benchmark elliptic problems are presented both the accuracy of a solution and the solution s derivatives as well as their convergence rates evaluated on irregular and structured meshes as well as arbitrarily irregular adaptive clouds of nodes are taken into account

deviations of trajectory averages and the defect in pesin s formula for anosov diffeomorphisms a large deviation theorem at the donsker varadhan level three is obtained for the convergence of trajectory averages of anosov diffeomorphisms it is possible to provide an explicit description of the rate function

general invariant representations of the constitutive equations for isotropic nonlinearly elastic materials abstract this paper develops general invariant representations of the constitutive equations for isotropic nonlinearly elastic materials different sets of mutually orthogonal unit tensor bases are constructed from the strain argument tensor by using the representation theorem and corresponding irreducible invariants are defined their relations and geometrical interpretations are established in three dimensional principal space it is shown that the constitutive law linking the stress and strain tensors is revealed to be a simple relationship between two vectors in the principal space relative to two different sets of the basis tensors the constitutive equations are transformed according to the transformation rule of vectors when a potential function is assumed to exist the vector associated with the stress tensor is expressed in terms of its gradient with respect to the vector associated with the strain tensor the hill s stability condition is shown to be that the scalar product of the increment of those two vectors must be positive when potential function exists it becomes to be that the 3 3 constitutive matrix derived from its second order derivative with respect to the vector associated with the strain must be positive definite by decomposing the second order symmetric tensor space into the direct sum of a coaxial tensor subspace and another one orthogonal to it the closed form representations for the fourth order tangent operator and its inversion are derived in an extremely simple way

implicit plane stress algorithm for multilayer j2 plasticity using the prager ziegler translation rule a totally implicit algorithm for plane stress multilayer plasticity is presented the algorithm presents the plane stress version of the 3d plane strain model for multilayer plasticity presented in a previous work as in the 3d plane strain case the model is consistent with the principle of maximum dissipation and it may be considered as an extension of classical j2 plasticity for anisotropic non linear kinematic behaviour preserving masing s rules in order to obtain the asymptotic second order convergence of the newton algorithm the consistent tangent moduli are also given copyright 2003 john wiley sons ltd

structural models based on 3d constitutive laws variational structure and numerical solution abstract in all structural models the section or fiber response is a relation between the strain measures and the stress resultants this relation can only be expressed in a simple analytical form when the material response is linear elastic for other more complex and interesting situations kinematic and kinetic hypotheses need to be invoked and a constrained three dimensional constitutive relation has to be employed at every point of the section in order to implement non linear and dissipative constitutive laws into dimensionally reduced structural models in this article we explain in which sense reduced constitutive models can be expressed as minimization problems helping to formulate the global equilibrium as a single optimization problem casting the problem this way has implications from the mathematical and numerical points of view naturally defining error indicators general purpose solution algorithms for constrained material response with and without optimization character are discussed and provided in an open source library

range descriptions for the spherical mean radon transform abstract the transform considered in the paper averages a function supported in a ball in r n over all spheres centered at the boundary of the ball this radon type transform arises in several contemporary applications e g in thermoacoustic tomography and sonar and radar imaging range descriptions for such transforms are important in all these areas for instance when dealing with incomplete data error correction and other issues four different types of complete range descriptions are provided some of which also suggest inversion procedures necessity of three of these appropriately formulated conditions holds also in general domains while the complete discussion of the case of general domains would require another publication

the p version of the finite element method in incremental elasto plastic analysis summary whereas the higher order versions of the finite element method p and hp versions are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems little has been done to exploit their benefits in elasto plastic structural analysis in this paper we discuss which aspects of incremental elasto plastic finite element analysis are particularly amenable to improvements by the p version these theoretical considerations are supported by several numerical experiments first we study an example for which an analytical solution is available it is demonstrated that the p version performs very well even in cycles of elasto plastic loading and unloading not only as compared with the traditional h version but also with respect to the exact solution finally an example of considerable practical importancethe analysis of a cold working lug is presented which demonstrates how the modelling tools offered by higher order finite element techniques can contribute to an improved approximation of practical problems

a p version finite element approach for two and three dimensional problems of the j2 flow theory with non linear isotropic hardening in this paper an implementation of a two and three dimensional p version approach to the j 2 flow theory with non linear isotropic hardening for small displacements and small strains is presented based on higher order quadrilateral and hexahedral element formulations a newton raphson iteration scheme combined with a radial return algorithm is applied to find approximate solutions for the underlying physically non linear model problem curved boundaries are taken care of with the blending function method allowing an accurate representation of geometry with only a few p elements numerical examples demonstrate that the p version supplies efficient and accurate approximations to this class of physically non linear problems

p fem for finite deformation powder compaction the simulation of powder compaction problems die compaction and cold isostatic pressing is considered herein by an implicit high order p version finite element method in this class of problems use is made of a finite strain viscoplasticity model with evolution equations for internal variables developed for the highly compressible behavior in powder compaction processes the classical approach of implicit finite elements applies the combination of backward euler integration scheme and the multilevel newton algorithm to solve the system of differential algebraic equations resulting from the space discretized weak formulation by means of p version finite elements this approach requires on gauss point level a robust stress algorithm the challenging investigations are the incorporation of the applied highly non linear viscoplasticity model into a p version finite element formulation using follower load applications several axisymmetric numerical examples show the feasibility and good performance of this p version approach

effective discretization of direct reconstruction schemes for photoacoustic imaging in spherical geometries recently kernel methods for the recovery of a function from its spherical means in spherical acquisition geometry have been proposed we present efficient algorithms for these formulas in the two and three dimensional cases our scheme applies fourier techniques for certain convolution type integrals and discretizes physical space on a polar and a spherical grid respectively