decomposition formulas of exponential operators and lie exponentials with some applications to quantum mechanics and statistical physics decomposition formulas of general exponential operators in a banach algebra and in a lie algebra are presented that yield a basis of monte carlo simulation of quantum systems they are applied to study the relaxation and fluctuation from the initially unstable point and to confirm algebraically the scaling theory of transient phenomena a global approximation method of transient phenomena is also formulated on the basis of decomposition formulas it is applied to the laser model as a simple example

sextic formalism in anisotropic elasticity for almost non semisimple matrix n abstract the sextic formalism of stroh for anisotropic elasticity leads to the eigen relation n p in which n is a 6 6 real matrix the orthogonality and closure relations as well as many other relations involving the eigenvalues p and the eigenvectors x are based on the assumption that n is simple or semisimple so that the six eigenvectors span a six dimensional space problems arise when n is non semisimple in fact there are problems even when n is almost non semisimple we present a modified formalism which is valid regardless of whether n is simple almost non semisimple or non semisimple the modified formalism does not apply when n is semisimple

boundary integral equations for recovery of design sensitivities in shape optimization a new formulation for obtaining design sensitivities in shape optimization has been developed the formulation is based on a direct application of the material derivative concept to the appropriate boundary integral equations for displacements and stresses in an elastic solid as a check on accuracy the approach was applied to a uniformly loaded infinite plate containing an elliptical hole in this case the availability of an analytical solution made it possible to calculate errors exactly furthermore a wide range of stress states could be considered simply by varying the aspect ratio of the elliptical hole for convenience the design sensitivities were calculated with respect to changes in the major axis numerical convergence was established by comparing results based on four successive boundary meshes in general the predictions for both displacement and stress sensitivities were remarkably accurate

green s functions of two dimensional anisotropic plates containing an elliptic hole abstract for a two dimensional anisotropic plate the green s function satisfying traction free boundary conditions around an elliptic hole is developed using stroh s formalism a combination of this function and the boundary element method shows that it is the most effective approach for solving hole problems the generality of the present green s function is shown by the broader meaning of the following words two dimensional includes not only in plane but also antiplane problems and the problems where in plane and anti plane deformations couple each other anisotropic which need not have any material symmetry restrictions means that it covers the solutions given in the literature which only deal with orthotropic or monoclinic materials elliptic includes the special case where the minor axis of the ellipse tends to zero i e the case of a griffith crack the accuracy of the numerical method presented is then verified by comparison with exact or accepted solutions of several examples such as an infinite or a finite plate with an elliptic hole or a crack under in plane or anti plane loading the materials used are isotropic orthotropic or laminated composites finally problems where the hole boundary is not traction free are solved such as rigid inclusions and pin loaded holes

nondestructive identification of multiple flaws using xfem and a topologically adapting artificial bee colony algorithm summary we present a novel algorithm based on the extended finite element method xfem and an enhanced artificial bee colony eabc algorithm to detect and quantify multiple flaws in structures the concept is based on recent work that have shown the excellent synergy between xfem used to model the forward problem and a genetic type algorithm to solve an inverse identification problem and converge to the best flaw parameters in this paper an adaptive algorithm that can detect multiple flaws without any knowledge on the number of flaws beforehand is proposed the algorithm is based on the introduction of topological variables into the search space used to adaptively activate deactivate flaws during run time until convergence is reached the identification is based on a limited number of strain sensors assumed to be attached to the structure surface boundaries each flaw is approximated by a circular void with the following three variables center coordinates xc yc and radius rc within the xfem framework in addition the proposed eabc scheme is improved by a guided to best solution updating strategy and a local search ls operator of the nelder mead simplex type that show fast convergence and superior global ls abilities compared with the standard abc or classic genetic algorithms several numerical examples with increasing level of difficulty are studied in order to evaluate the proposed algorithm in particular we consider identification of multiple flaws with unknown a priori information on the number of flaws which makes the inverse problem harder the proximity of flaws flaws having irregular shapes similar to artificial noise and the effect of structured unstructured meshes the results show that the proposed xfem eabc algorithm is able to converge on all test problems and accurately identify flaws hence this methodology is found to be robust and efficient for nondestructive detection and quantification of multiple flaws in structures copyright 2013 john wiley sons ltd

differential invariants for quasi linear and semi linear wave type equations abstract in this paper we consider the class of wave type equations u tt f x t u u xx g x t u u x u t and two special cases of it we derive the equivalence transformations for these equations and using these transformations we obtain differential invariants and invariant equations we employ these invariants or and invariant equations to classify all equations of this general class that can be mapped into a simple linear hyperbolic or into an elliptic equation additional applications are presented

a bem sensitivity formulation for three dimensional active noise control summary in this paper a novel boundary element formulation for sensitivity analysis of local active noise control in a three dimensional field is presented the formulation is based on the helmholtz differential equation and is valid for internal as well as for scattering wave propagation problems the primary noise is attenuated within an enclosure called control volume by adding a control source modelled as an object with a vibrating surface both the optimum position of the control volume and the optimum location orientation of the secondary source are determined by minimisation of a suitable cost function the sensitivities are determined by implicit differentiation a hierarchical adaptive cross approximation approach in conjunction with the generalised minimal residual solver is implemented to accelerate the convergence four numerical examples are presented to demonstrate the accuracy and efficiency of the proposed formulations copyright 2012 john wiley sons ltd

solution of linear partial differential equations by lie algebraic methods a new algorithm is proposed for obtaining explicit solutions of the cauchy problem defined by a certain class of partial differential equations pde of parabolic type the algorithm exploits the algebraic structure of the problem to transform the pde into an ordinary matrix differential equation which is then solved by lie algebraic techniques

a boundary integral equation method for an inverse problem related to crack detection this paper discusses an application of a boundary integral equation method biem to an inverse problem of determining the shape and the location of cracks by boundary measurements suppose that a given body contains an interior crack the shape and the location of which are unknown on the exterior boundary of this body one carries out measurements which are interpreted mathematically as prescribing dirichlet data and measuring the corresponding neumann data or vice versa for a field governed by laplace s equation the inverse problem considered here attempts to determine the geometry of the crack from these experimental data we propose to solve this problem by minimizing the error of a certain boundary integral equation bie the process of this minimization however is shown to require solutions of certain are proposed several 2d and 3d numerical examples are given in order to test the performance of the present method

neural crack identification in steady state elastodynamics an inverse crack identification problem with harmonic excitation in linear elastodynamics is treated here by means of back propagation neural network methods and boundary element techniques the problem concerns the determination of the existence and the characteristics of a hidden crack within an elastic structure by means of measurements of the structural response on the accessible boundary for given external time periodic loadings the direct problem is solved by a boundary element formulation in the frequency domain which leads to a system of linear equations with frequency dependent matrices thus for a given frequency certain similarities with linear elastostatics exist feed forward multilayer neural networks trained by back propagation are used to learn the inverse input output relation of the structural system then the inverse problem is solved by a simple application of the neural network recalling production ability

monopoles and lens space surgeries monopole floer homology is used to prove that real projective three space cannot be obtained from dehn surgery on a nontrivial knot in the three sphere to obtain this result we use a surgery long exact sequence for monopole floer homology together with a nonvanishing theorem which shows that monopole floer homology detects the unknot in addition we apply these techniques to give information about knots which admit lens space surgeries and to exhibit families of three manifolds which do not admit taut foliations

on linearization of hyperbolic equations using differential invariants abstract in this paper we consider the general class of hyperbolic equations u x t f x t u u x u t we use equivalence transformations to derive differential invariants for this class and for two subclasses then we employ these invariants to construct equations that can be linearized via local mappings further applications of the differential invariants are given

solution of inverse problems by boundary integral equations without residual minimization in this paper the solution of some inverse problems for potential fields is tackled the aim is to compute the position and shape of an unknown flaw within a body using some experimental measures as additional data by the linearization of the difference between the boundary integral equation for the actual configuration and the same equation for an assumed configuration an integral equation for the variations is deduced this integral equation is carried to the boundary by a limiting process and a solution procedure is devised to compute an approximation to the actual flaw the solution method proceeds iteratively solving a direct and an inverse problem in every step but no minimization algorithm is involved the performance of the method is shown in several numerical examples

symmetry classification and exact solutions of the kramers equation the complete classification of lie symmetries for the kramers equation is described group invariance under infinitesimal transformations is used to generate a wide class of exact solutions some of the known solutions are obtained as particular cases the general results can also be used to solve some types of moving boundary problems we researched some q conditional symmetry properties of this equation

polygonal holes in anisotropic media abstract based upon the solutions obtained by using stroh s formalism a general and simplified formula for polygonal holes in anisotropic media is provided in this paper the polygon used here is a generalized terminology which covers ellipses polygons and their geometric limits for some special holes such as ellipses circles cracks triangles ovals and squares a further simplified solution is derived the validity of these formulae is then discussed based on the satisfaction of conformal mapping requirement the results show that the solutions are exact for 1 anisotropic media containing elliptic holes or cracks and 2 isotropic media containing general polygonal holes for general anisotropic media with polygonal holes the solutions are well approximated if the critical points of the mapping functions are far away from the holes

lie algebraic solutions of linear fokker planck equations nonstationary solutions of linear fokker planck equations with arbitrary drift and diffusion coefficients are derived using lie algebraic techniques the time evolution operator is given as a product of exponentials of the differential operators appearing in the equations

an experimentally validated damage detection theory in smart structures abstract a method for the non destructive detection and location of damage using parameterized partial differential equations and galerkin approximation techniques is presented damages in a structure cause changes in the physical coefficients of mass density elastic modulus and damping coefficients this paper examines the use of beam like structure with piezoceramic sensors and actuators to perform identification of those physical parameters and hence to detect the damage the method casts the inverse problem as an optimization problem the iterative method is based on enhanced least square error minimization experimental results are presented from tests on cantilevered aluminum beams damaged at different locations and with damage of different dimensions it is demonstrated that the method can sense the presence of damage and locate and characterize the damage to a satisfactory precision

equivalence and symmetries for variable coefficient linear heat type equations i a systematic and unified approach to transformations and symmetries of a class of variable coefficient heat type linear partial differential equations pdes is presented the complete symmetry group classification is re performed in the current context a useful criterion which is necessary and sufficient for being reducible to the standard heat equation by point transformations is established a similar criterion is also valid for the equations to have a four or six dimensional symmetry group nontrivial symmetry groups in this situation the basis elements are listed in terms of coefficients a number of illustrative examples are given in particular some applications from the recent literature are re examined in our new approach multidimensional parabolic pdes of heat and schrodinger type are also considered

a method for the equivalence group and its infinitesimal generators we give an effective method for the systematic determination of the equivalence group for any family of differential equations and for the determination of the infinitesimal generators of this group this is achieved by viewing the equivalence group as a projected subgroup related to the full symmetry group of the equation in which the coefficients specifying the family element in the equation are also considered as dependent variables the method is extended to provide the exact number of fundamental invariants of the equation without any prior calculation of these invariants it is then applied to review a number of results obtained in the recent literature on the subject of invariant functions of differential equations the method is also applied probably for the first time to a case of nonlinear equation

a bem sensitivity and shape identification analysis for acoustic scattering in fluid solid problems in this paper a boundary element formulation for the sensitivity analysis of structures immersed in an inviscide fluid and illuminated by harmonic incident plane waves is presented also presented is the sensitivity analysis coupled with an optimization procedure for analyses of flaw identification problems the formulation developed utilizes the boundary integral equation of the helmholtz equation for the external problem and the cauchy navier equation for the internal elastic problem the sensitivities are obtained by the implicit differentiation technique examples are presented to demonstrate the accuracy of the proposed formulations 1998 john wiley sons ltd

second order differential invariants of a family of diffusion equations an equivalence transformation algebra for a class of nonlinear diffusion equations is found after having obtained the second order differential invariants with respect to we get some results which allow us to linearize a subclass of the equations considered

singular invariant equation for the 1 1 fokker planck equation semi invariants for the linear parabolic equations with two independent variables time variable t and space variable x and one dependent variable u are derived under the transformation of the independent variables by using the infinitesimal method we also obtain the joint invariant equation for the above mentioned equation under equivalence transformation in fact we prove a necessary and sufficient condition for a 1 1 parabolic equation to be reducible via a local equivalence transformation to the one dimensional classical heat equation this result provides practical criteria for reduction finally examples of 1 1 fokker planck equations from applications are given to verify the results obtained

alternating knots with unknotting number one abstract we show that an alternating knot with unknotting number one has an unknotting crossing in any alternating diagram we also prove that an alternating knot has unknotting number one if and only if its branched double cover arises as half integer surgery on a knot in s 3 thus establishing a converse to the montesinos trick along the way we reprove a characterisation of almost alternating diagrams of the unknot originally due to tsukamoto these results are established using the obstruction to unknotting number one developed by greene

nondestructive cavity identification in structures abstract an algorithm for solving an inverse problem in elastostatics is developed in this problem the location and shape of the cavity are unknown instead extra experimental data are provided at several internal points in the structure through an iterative process the unknown boundary is determined by using the boundary element method coupled with nonlinear optimization technique some illustrated numerical examples are presented to demonstrate the method through these examples the effects of the error in the internal displacement data and of the number of measurement points and their locations are examined

a simple direct method to find equivalence transformations of a generalized nonlinear schrodinger equation and a generalized kdv equation a simple direct method is presented to find equivalence transformations of nonlinear mathematical physics equations by using the direct method we obtain the continuous equivalence transformations of a class of nonlinear schroequations with variable coefficients and a family of nonlinear kdv equations with variable coefficients for the nonlinear schrodinger equations with variable coefficients the equivalence transformations obtained by the direct method coincide in nature with those obtained via the infinitesimal lie criterion but our computation is much simpler

the lens space realization problem we determine the lens spaces that arise by integer dehn surgery along a knot in the three sphere specically if surgery along a knot produces a lens space then there exists an equivalent surgery along a berge knot with the same knot floer homology groups this leads to sharp information about the genus of such a knot the arguments rely on tools from floer homology and lattice theory they are primarily combinatorial in nature

locating a crack of arbitrary but known shape by the method of path independent integrals abstract the solution of a crack problem of an arbitrary but known shape inside an infinite plane isotropic elastic medium can be achieved in general by the method of complex singular integral equations and their numerical solution by using the gauss or the lobatto chebyshev methods in a few special cases like straight or circular arc shaped cracks this solution is available in closed form in this paper we will not contribute to the above methods of solution of crack problems but we will propose a method for the determination of the exact position of such a crack inside a closed contour in the elastic medium by gathering and using information along this contour only by experimental techniques and applying the method of complex path independent integrals for the location of the crack this paper constitutes a nontrivial generalization of relevant previous results by the author and it is of quite general applicability in fracture mechanics for nondestructive testing numerical results for the particular case of a straight crack are displayed for the illustration of the efficiency of the method the generalization of the present results to the determination of additional geometric and loading parameters of the crack is also suggested very briefly and related numerical results concerning the length of the crack and the pressure distribution on it in the aforementioned numerical application are also presented

limits on inferring the past here we define and study the properties of retrodictive inference we derive equations relating retrodiction entropy and thermodynamic entropy and as a special case show that under equilibrium conditions the two are identical we demonstrate relations involving the kullback leibler divergence and retrodiction probability and bound the time rate of change of retrodiction entropy as a specific case we invert various langevin processes inferring the initial condition of n particles given their final positions at some later time we evaluate the retrodiction entropy for langevin dynamics exactly for special cases and find that one s ability to infer the initial state of a system can exhibit two possible qualitative behaviors depending on the potential energy landscape either decreasing indefinitely or asymptotically approaching a fixed value we also study how well we can retrodict points that evolve based on the logistic map we find singular changes in the retrodictivity near bifurcations counterintuitively the transition to chaos is accompanied by maximal retrodictability

invariants of two and three dimensional hyperbolic equations abstract we consider linear hyperbolic equations of the form u t t i 1 n u x i x i i 1 n x i x 1 x n t u x i t x 1 x n t u t u x 1 x n t u we derive equivalence transformations which are used to obtain differential invariants for the cases n 2 and n 3 motivated by these results we present the general results for the n dimensional case it appears at least for n 2 that this class of hyperbolic equations admits differential invariants of order one but not of order two we employ the derived invariants to construct interesting mappings between equivalent equations

boundary element iterative techniques for determining the interface boundary between two laplace domains a basic study of impedance plethysmography as an inverse problem the interface boundary between two domains with different conductivity is to be determined from the impedance measured at the domain surface this is an inverse problem two approaches influence coefficient approach and boundary integral approach using a boundary element model are presented to examine the validity of the approaches numerical experiments are carried out for a two dimensional field and the suitability and limitation of the methods for application to impedance plethysmography are discussed

a simple local smoothing scheme in strongly singular boundary integral representation of potential gradient abstract a new approach for computation of potential gradient at and near boundary is introduced a strongly singular boundary integral representation of potential gradient whose integral density is the potential gradient is derived and analysed applying the concept of the osculating circle a local smoothing procedure which computes a continuous approximation of potential gradient from the results of a 2d boundary element method bem analysis using linear elements is proposed and evaluated this approximation is used in the integral representation derived as an integral density which fulfills the continuity requirements numerical experiments demonstrate for quasiuniform meshes an o h 2 accuracy of potential gradient computed by both the local smoothing procedure on smooth parts of the boundary and by the integral representation on smooth boundary parts and near smooth boundary parts for points inside the domain a consequence of the latter result is that no significant increase in the error appears near the boundary boundary layer effect thus being eliminated in this approach

flaw identification using the boundary element method in this paper a new boundary element formulation is presented for the identification of the location and size of internal flaws in two dimensional structures an introduction to inverse analysis is given with special reference to methods of flaw identification along with a brief review of the optimization methods employed both the standard boundary element and the dual boundary element method are presented with the dual boundary element method proposed as the basis for the new formulation the flaw identification method is presented along with the computation of the boundary displacement and traction derivatives and the specialized analytical integration used for cracked boundaries examples are given to demonstrate the accuracy of the sensitivity values and the performance of flaw location

asymptotic imaging of perfectly conducting cracks in this paper we consider cracks with dirichlet boundary conditions we first derive an asymptotic expansion of the boundary perturbations that are due to the presence of a small crack based on this formula we design a noniterative approach for locating a collection of small cracks in order to do so we construct a response matrix from the boundary measurements the location and the length of the crack are estimated respectively from the projection onto the noise space and the first significant singular value of the response matrix indeed the direction of the crack is estimated from the second singular vector we then consider an extended crack with dirichlet boundary conditions we rigorously derive an asymptotic expansion for the boundary perturbations that are due to a shape deformation of the crack to reconstruct an extended crack from many boundary measurements we develop two methods for obtaining a good guess several numerical experiments show how the proposed techniques for imaging small cracks as well as those for obtaining good initial guesses toward reconstructing an extended crack behave

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

dehn surgery on knots in d dehn considered the following method for constructing 3 manifolds remove a solid torus neighborhood n k of some knot x in the 3 sphere s and sew it back differently in particular he showed that taking x to be the trefoil one could obtain infinitely many non simply connected homology spheres o in this way let mx s n k then the different resewings are parametrized by the isotopy class r of the simple closed curve on the torus omk that bounds a meridional disk in the re attached solid torus we denote the resulting closed oriented 3 manifold by mk and say that it is obtained by r dehn surgery on x more generally one can consider the manifolds ml obtained by r dehn surgery on a fc component link l xi u u kk in s where r r it turns out that every closed oriented 3 manifold can be constructed in this way wal lie thus a good understanding of dehn surgery might lead to progress on general questions about the structure of 3 manifolds starting with the case of knots it is natural to extend the context a little and consider the manifolds m r obtained by attaching a solid torus v to an arbitrary compact oriented irreducible every 2 sphere bounds a 3 ball 3 manifold m with dm an incompressible torus where r is the isotopy class slope on dm of the boundary of a meridional disk of v we say that m r is the result of r dehn filling on m an observed feature of this construction is that

symmetry properties of one and two dimensional fokker planck equations the authors study symmetry properties of some fokker planck fp equations in the one dimensional case when symmetry groups turn out to be six parameter ones this allows us to find changes of variables to reduce such fp equations to the one dimensional heat equation they present seven well known fp equations which are reduced to the heat equation they also study the symmetry and obtain some exact solutions of the kramers equation

equivalence transformations and differential invariants of a generalized nonlinear schrodinger equation by using lie s invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear schrodinger equations with variable coefficients we construct the differential invariants of order 1 starting from a special equivalence subalgebra we apply these latter ones to find the most general subclass of variable coefficient nonlinear schrodinger equations which can be mapped by means of an equivalence transformation of to the well known cubic schrodinger equation we also provide the explicit form of the transformation

an algorithm for the solution of inverse laplace problems and its application in flaw identification in materials abstract an algorithm for solving an inverse problem in steady state heat conduction is developed in this problem the location and shape of the inner boundary of a doubly connected domain is unknown instead additional experimental data are provided at several points on the outer boundary through an iterative process the unknown boundary is determined by minimizing a functional convergence properties of the algorithm are examined and the stopping criterion for the iterative process is developed from numerical experiments in a simple case the scheme is shown to perform well for the complex case of an l shaped crack in a square domain

an inverse problem method for crack detection in elastic materials under anti plane strain the problem of crack detection in a two dimensional infinite elastic medium under anti plane strain is studied it is assumed that the medium has an internal closed boundary on which the displacements and stresses are known and the crack begins using cauchy s theorem for integration of analytic functions a simple method capable of determining the parametric equations of each side of the crack using the corresponding displacements as parameters is developed in general the method is valid for functions which tend to infinity like a b ln r o 1 r as r rightarrow infty a and b are constants and for finite and infinite cracks however the existence of rapidly oscillating integrands makes the method vulnerable to rounding error particularly in the far field for infinite cracks and near the crack tip for finite cracks an alternative method for obtaining accurate values of the length and stress intensity factor of a straight finite crack with known inclination is given

symmetry classification and exact solutions of the one dimensional fokker planck equation with arbitrary coefficients of drift and diffusion symmetry properties of the one dimensional fokker planck equations with arbitrary coefficients of drift and diffusion are investigated it is proved that the group symmetry of these equations can be one two four or six parametric and corresponding criteria are obtained the changes of the variables reducing fokker planck equations to the heat equation and schrodinger equation with certain potentials are determined using the substructure of the invariance algebra of the rayleigh process equation we obtain the differential invariants and construct some classes of the exact solutions of this equation

a characterization of the z n z δ lattice and definite nonunimodular intersection forms we prove a generalization of elkies characterization of the bbb z n lattice to nonunimodular definite forms and lattices combined with inequalities of fr o yshov and of ozsv a th and szab o this gives a simple test of whether a rational homology three sphere may bound a definite four manifold as an example we show that small positive surgeries on torus knots do not bound negative definite four manifolds

an identification problem for vibrating cracked beams abstract an identification procedure to determine the crack characteristics location and size of the crack from dynamic measurements is developed and tested this procedure is based on minimization of either the mean square or the max measure of difference between measurement data natural frequencies and mode shapes and the corresponding predictions obtained from the computational model necessary conditions are obtained for both formulations the method is tested for simulated damage in the form of one side or symmetric cracks in a simply supported bernoulli euler beam the sensitivity of the solution of damage identification to the values of parameters that characterize damage is discussed

differential invariants for systems of linear hyperbolic equations in this paper we consider a general class of systems of two linear hyperbolic equations motivated by the existence of the laplace invariants for the single linear hyperbolic equation we adopt the problem of finding differential invariants for the system we derive the equivalence group of transformations for this class of systems the infinitesimal method which makes use of the equivalence group is employed for determining the desired differential invariants we show that there exist four differential invariants and five semi invariants of first order applications of systems that can be transformed by local mappings to simple forms are provided

xfem based crack detection scheme using a genetic algorithm a new computational tool is developed for the accurate detection and identification of cracks in structures to be used in conjunction with non destructive testing of specimens it is based on the solution of an inverse problem based on some measurements typically along part of the boundary of the structure that describe the response of the structure to vibration in a chosen frequency or a combination of frequencies the goal is to estimate whether the structure contains a crack and if so to find the parameters location size orientation and shape of the crack that produces a response closest to the given measurement data in some chosen norm the inverse problem is solved using a genetic algorithm ga the ga optimization process requires the solution of a very large amount of forward problems the latter are solved via the extended finite element method xfem this enables one to employ the same regular mesh for all the forward problems performance of the method is demonstrated via a number of numerical examples involving a cracked flat membrane various computational aspects of the method are discussed including the a priori estimation of the ill posedness of the crack identification problem copyright 2007 john wiley sons ltd

stability of crack fronts under griffith criterion a computational approach using integral equations and domain derivatives of potential energy abstract this paper deals with the numerical study of stability and instantaneous extension of cracks under griffith criterion within the classical linear fracture mechanics framework first and second order domain derivatives of the potential energy w in crack extensions play a central role in the mathematical formulation of such situations the proposed solution strategy called the integral method by reference to the fem based method possesses the following main characteristics i it is based on a symmetric galerkin boundary integral formulations and ii explicit expressions for the domain derivatives of w are established using lagrangian formulas so that the derivations do not increase crack front singularities the numerical solution procedure for the extension velocity problem including all domain derivative evaluations is entirely supported by the boundary element mesh of the current crack configuration numerical differentiation is avoided numerical examples for an isolated crack in a 3 d unbounded elastic body show that in practice an excellent accuracy can be achieved for the energy release rate the second order domain derivatives of w and the prediction of stability or instability of crack growth

absolutely graded floer homologies and intersection forms for four manifolds with boundary abstract in ozsvath and szabo holomorphic triangles and invariants for smooth four manifolds math sg 0110169 2001 we introduced absolute gradings on the three manifold invariants developed in ozsvath and szabo holomorphic disks and topological invariants for closed three manifolds math sg 0101206 ann of math 2001 to appear coupled with the surgery long exact sequences we obtain a number of three and four dimensional applications of this absolute grading including strengthenings of the complexity bounds derived in ozsvath and szabo holomorphic disks and three manifold invariants properties and applications math sg 0105202 ann of math 2001 to appear restrictions on knots whose surgeries give rise to lens spaces and calculations of hf for a variety of three manifolds moreover we show how the structure of hf constrains the exoticness of definite intersection forms for smooth four manifolds which bound a given three manifold in addition to these new applications the techniques also provide alternate proofs of donaldson s diagonalizability theorem and the thom conjecture for cp 2

donaldson s theorem heegaard floer homology and knots with unknotting number one abstract we establish an obstruction to unknotting an alternating knot by a single crossing change the obstruction is lattice theoretic in nature and combines donaldson s diagonalization theorem with an obstruction developed by ozsvath and szabo using heegaard floer homology as an application we enumerate the alternating 3 braid knots with unknotting number one and show that each has an unknotting crossing in its standard alternating diagram

regular article a shape decomposition technique in electrical impedance tomography consider a two dimensional domain containing a medium with unit electrical conductivity and one or more non conducting objects the problem considered here is that of identifying shape and position of the objects on the sole basis of measurements on the external boundary of the domain an iterative technique is presented in which a sequence of solutions of the direct problem is generated by a boundary element method on the basis of assumed positions and shapes of the objects the key new aspect of the approach is that the boundary of each object is represented in terms of fourier coefficients rather than a point wise discretization these fourier coefficients generate the fundamental shapes mentioned in the title in terms of which the object shape is decomposed the iterative procedure consists in the successive updating of the fourier coefficients at every step by means of the levenberg marquardt algorithm it is shown that the fourier decomposition which essentially amounts to a form of image compression enables the algorithm to image the embedded objects with unprecedented accuracy and clarity in a separate paper the method has also been extended to three dimensions with equally good results

damage detection in elastic structures using vibratory residual forces and weighted sensitivity a methodology is presented for detecting structural damage in elastic structures by nondestructiv e means measured modal test data along with a correlated analytical structural model are used to locate potentially damaged regions using residual modal force vectors and to conduct a weighted sensitivity analysis to assess the extent of mass and or stiffness variations where damage is characterized as a stiffness reduction the current approach is unique among other approaches in that it accounts for 1 variations in system mass system stiffness and mass center locations 2 perturbations of both the natural frequencies and modal vectors and 3 statistical confidence factors for the structural parameters and potential experimental instrumentation error moreover this procedure can be used with either full or reduced models a wide variety of numerical examples are presented that show that the current method provides a precise indication of both the location and the extent of structural damage lexible space structures launch vehicles and satellites are susceptible to structural damage over their operating lives from impact operating loads and fatigue undetected and uncorrected damage can lead to structural deterioration of their members and consequently jeopardize the flight safety of the structure thus numerous damage inspection methods and monitoring procedures have been developed examples include x ray ultrasonic testing magnetic resonance coin tap dye penetration and visual inspection these methods can be time consuming and are local assessments often requir ing the exposure of structural elements to the inspector and equipment for detecting damage as a monitoring system for detecting damage of spacecraft in orbit i e space station freedom none of these methods are appropriate an alterna tive approach which formed the basis for our current study is to recognize the fact that modal vibration test data struc tural natural frequencies and mode shapes characterize the state of the structure 1 therefore postflight and in flight e g monitoring data can be used to distinguish whether changes damage have occurred to the structure by comparing these data with a set of baseline data modal testing as a means of inspection has several advantages direct exposure of struc tural elements is not required and at the same time more of the complete structure can be inspected in one modal test by having appropriately placed sensors the consequences of this are a reduction in schedule and cost the use of vibration test data to locate structural damage has been attempted to evaluate the integrity of offshore oil and gas platforms 2 3 composite laminates 4 continuum struc tures 5 8 and recently large space structures 9 11 the early ana lytical and experimental approaches2 3 had limited success as a result of inadequate instrumentation and addressing only fre quency shifts associated with stiffness changes while ignoring changes in the modal vectors the continuum based meth ods5 8 provide valuable insight into the magnitude of fre quency shifts but their usefulness is severely limited to simple structures bars beams plates with unrealistic boundary con

invariants of a family of third order ordinary differential equations we consider a family of third order ordinary differential equations odes with the cubic nonlinearity in second order derivative which is closed with respect to contact transformations using lie s infinitesimal method we construct the basis of differential invariants for this family of equations and the operators of invariant differentiation invariants provide a simple way of finding the equations which may be equivalent to a given nonlinear ode and the transformation connecting two equivalent equations some examples are given to illustrate the results obtained in the paper

direct identification of non uniform beams using static strains abstract a method for identifying the flexural rigidities of a non uniform beam is developed in this paper the finite element method is used to derive the equilibrium equation of the beam the identification problem is then formulated as an optimization program in which the error norm of the equilibrium equation is minimized the proposed method has the following features 1 it uses longitudinal strains as the primary test data 2 the solution is unique and global minimal 3 the method can be applied to a whole beam as well as a part of a beam 4 the method is very stable the identifiability of the inverse problem is studied in depth two numerical examples are presented to demonstrate the proposed method finally a model test is performed to examine the effectiveness of the method in real applications

hole crack identification by static strains from multiple loading modes a method using static strains measured from multiple loading modes for the identification of holes and cracks in linear anisotropic elastic materials is introduced because of the localized effects of holes cracks their existence may not be clearly reflected by a single set of remotely measured boundary strains by the combining of the concept of multiple loading modes with the technique of nonlinear optimization several examples of hole crack identification have been done during the iteration procedure the values of the static strains corresponding to the assumed hole crack geometry and location are obtained by using a recently developed boundary element which is for linear anisotropic elastic materials and has also been extended to piezoelectric materials the identified results show that our method for hole crack identification is stable and accurate for the model problem considered and shows that the method has promise for more complex problems in addition the generality of hole profile the tolerance of measurement error the spacing and arrangement of sensors and the flexibility of multiple loading modes are all discussed in detail