shift and torsion contact problems for arbitrary axisymmetric normal stress distributions abstract in this paper we analyze the contact interaction of axisymmetric particles subject to a subsequent application of a constant normal load and a tangential or rotational force a rigorous solution to the frictional contact problem is given by the known jager theorem that presents a relationship between shear and normal stress distributions provided the latter is an exact solution to a normal contact problem however in the case of strong loading when the normal displacement reaches a value of 5 10 of the spheres diameter exact solutions for the normal problem are absent some model concepts exist instead for instance the rod model describes strong normal loading of spheres as a sort of combination of the hertz problem weak loading of spheres with a compression of a pair of confined cylinder of the same radius as the hertz contact spot here we propose a method that is based on considerations similar to the jager theorem but is appropriate for any model or empirical normal stress distribution the resulting integral representations describe both shearing and torsion of prestressed particles with axisymmetric profiles rolling of particles as well as plasticity and adhesion of the particles material are not considered we also analyze the asymptotic behavior of the integral representations for weak and strong strains the obtained general solutions allow us to use the method of memory diagrams in order to calculate the reaction of the system on arbitrarily varying tangential or rotational actions

brief paper zeros of structured linear systems this paper provides a detailed study of transmission zeros in the context of linear structured systems for such systems the entries of the state space model matrices are supposed to be either fixed zeros or free parameters a directed graph can be associated to such systems and structural properties can be studied i e properties which are valid for almost all values of the parameters we show that there exists two kinds of transmission zeros the parameter dependent ones and the constant ones which can only occur in zero moreover the constant transmission zeros can be directly obtained on the associated graph in terms of particular paths and cycles

a graph theoretical approach to the parameters identifiability characterisation this paper is devoted to the generic parameters identifiability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure necessary and sufficient conditions are expressed in graphical terms which ensure that a given set of unknown parameters characterising the model of the system are structurally identifiable using the available measurements assuming that the inputs and initial conditions are quite informative even if we are not interested in proposing identification schemes these given conditions are necessary and sufficient to the parameter identification whatever the used algorithms to determine numerically the parameters values finally note that the given conditions are quite easy to check because they are based on searching and comparing some specific paths and cycles in a digraph this makes our approach well suited to study large scale systems

bulk stress effects in double contacts of similar elastic materials the effects of a remote applied stress on double contacts of similar elastic materials are examined using a numerical method based on cauchy singular integral equations sie in contrast to single contacts the space of possible shear configurations is very rich in many cases the partial slip problem does not have a contact equivalent an equation based on displacement continuity is derived to relate the stick zone extents for any shear configuration this equation is essential for the solution of general partial slip problems involving two stick zones a shear configuration map that shows the types of partial slip solution that occur for various shear load remote bulk stress combinations is obtained for biquadratic indenters lastly it is shown that it is possible to predict the shear configuration in some cases for double cylindrical indenters

a receding contact plane problem between a functionally graded layer and a homogeneous substrate abstract in this paper we consider the plane problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half space when the two bodies are pressed together the graded layer is modeled as a nonhomogeneous medium with an isotropic stress strain law and over a certain segment of its top surface is subjected to normal tractions while the rest of this surface is free of tractions since the contact between the two bodies is assumed to be frictionless then only compressive normal tractions can be transmitted in the contact area using integral transforms the plane elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact half length the global equilibrium condition of the layer is supplemented to solve the problem the singular integral equation is solved numerically using chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact half length that satisfies the global equilibrium condition the main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact

structural controllability and matrix nets abstract we establish structural controllability results for matrix pairs a b where a a 0 iai b b 0 i bi with the ai bi fixed and the i free scalar parameters the results characterize structural controllability in several ways via tests involving the checking of the rank or the evaluation of the determinant of various constant matrices formed from the ai bi a number of the results used as intermediate results tests for a full rank property of matrix nets i e tests that check if m m0 imi prescribed i variable has full rank for almost all i

identifiability of nonlinear systems with application to hiv aids models in this note we investigate different concepts of nonlinear identifiability in the generic sense we work in the linear algebraic framework necessary and sufficient conditions are found for geometrical identifiability algebraic identifiability and identifiability with known initial conditions relationships between different concepts are characterized constructive procedures are worked out for both generic geometrical and algebraic identifiability of nonlinear systems as an application of the theory developed we study the identifiability properties of a four dimensional model of hiv aids the questions answered in this study include the minimal number of measurement of the variables for a complete determination of all parameters and the best period of time to make such measurements this information will be useful in formulating guidelines for clinical practice

structured systems within the transfer matrix approach application to decoupling abstract we consider a new approach to structured systems within the transfer matrix framework we associate with such a structured system a graph which concentrates both knowledge on structural properties of independent subsystems and on their interconnections the analysis of this associated graph allows to conclude on the decouplability of structured systems

fixed modes in parametrized systems several necessary graph theoretic conditions are presented for a parametrized system nut to have structurally fixed modus under output feedback of some arbitrarily specified pattern the criteria are formulated by the aid of a new graph which represents the couplings inherent in the system as well as the admissible feedback pattern for the special class of structured systems the conditions turn out to be also sufficient

optimization algorithms for the solution of the frictionless normal contact between rough surfaces this paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half plane using the boundary element method bem after recasting the resulting linear complementarity problem lcp as a convex quadratic program qp with nonnegative constraints different optimization algorithms are compared for its solution i a greedy method based on different solvers for the unconstrained linear system conjugate gradient cg gauss seidel cholesky factorization ii a constrained cg algorithm iii the alternating direction method of multipliers admm and iv the non negative least squares nnls algorithm possibly warm started by accelerated gradient projection steps or taking advantage of a loading history the latter method is two orders of magnitude faster than the greedy cg method and one order of magnitude faster than the constrained cg algorithm finally we propose another type of warm start based on a refined criterion for the identification of the initial trial contact domain that can be used in conjunction with all the previous optimization algorithms this method called cascade multi resolution cmr takes advantage of physical considerations regarding the scaling of the contact predictions by changing the surface resolution the method is very efficient and accurate when applied to real or numerically generated rough surfaces provided that their power spectral density function is of power law type as in case of self affine fractal surfaces

frictional contact problem for a rigid cylindrical stamp and an elastic layer resting on a half plane abstract the frictional contact problem for a layer resting on a homogeneous half plane is handled using linear elasticity theory in this study the layer is in contact with a rigid cylindrical stamp that is on the layer and applies a concentrated force in the normal and tangential directions friction between the component couples of layer stamp and layer half plane is taken into account the problem is reduced to a system of singular integral equations in which the contact pressures and the contact areas are the unknowns and it is treated using fourier transforms and the boundary conditions for the problem the system of singular integral equations is solved numerically using the gauss jacobi integration formula with equilibrium and consistency conditions numerical results for the contact pressures and the contact areas are given as a solution for both the frictional and the frictionless cases this work is the first study that investigates the effect of friction on the receding contact problem of a layer and a half plane with two contact areas

filtered backprojection and the exponential radon transform on etudie des conditions sur la mesure qui assurent la validite de 7b r t 7b rf k f e ou e 7b r t k pour une transformee de radon generalisee 7b r et une grande classe de filtres k correspondant a des fonctions delta approchees e

a corrective solution for finding the effects of edge rounding on complete contact between elastically similar bodies part ii near edge asymptotes and the effect of shear abstract this paper is the second part of a new approach to introduce edge rounding into elastic flat punch solutions building on the concept developed in the first paper of using a three quarter plane as an asymptote to the finite punch with rounded edge problem we now move the observation point to the very edge of the contact and introduce asymptotes for the local contact tractions so that shear may be included in the analysis to solve the partial slip problem the edge asymptotes are used to obtain the slip zone size and the normal and tangential contact traction distribution where the rounded edge in contact can be reasonably approximated by a half plane

method of memory diagrams for mechanical frictional contacts subject to arbitrary 2d loading abstract in this paper we present a solution to the contact problem for two elastic bodies with friction loaded by an arbitrarily varying force in 2d the general statement of the problem concerns the following two important challenges on one hand the consideration of an arbitrary contact geometry implies that a multitude of individual arbitrarily shaped contact zones appears which can split and merge as a result of changes in the normal loading on the other hand the existence of friction invokes the presence of a tangential force and consequently of a complicated traction distribution inside each of the contact zones the complexity of these traction distributions results from the fact that generally each contact spot contains stick and slip zones with various boundary conditions defined by the previous tangential contact interaction forces the presence of two classes of boundary conditions makes the problem memory dependent and hysteretic in spite of this by using both conventional and original methods of contact mechanics it is possible to drastically simplify the problem first of all the geometric difficulty residing in the description of arbitrary multiple contacts can be successfully dealt with by applying the reduced friction principle that expresses the tangential solution through the normal loading curve for both normal and tangential forces kept constant the principle is valid for a broad range of geometries and makes it possible to replace an arbitrary contact geometry by an equivalent system of two axisymmetric bodies secondly the hysteretic character of the equivalent axisymmetric problem can be addressed through the method of memory diagrams which replaces the complex traction distribution in the contact zone by a simple internal functional dependency comprising the same memory information following any change of loading the internal memory function evolves in accordance to a definite procedure that is based on the force balance equation written for small increments of the normal and tangential forces in this paper we formulate the method prove its validity and illustrate its numerical implementation with some simulated examples of hysteretic load displacement curves these obtained results might be of use for applications related to solids with cracks and contacts showing acoustical nonlinearity and for any modeling requiring physics based boundary conditions to describe and predict the effect of mechanical contacts with friction

computerized tomography with unknown sources we give a reconstruction method for the attenuation coefficient in a 2d cross section of a 3d object from tomographic data which does not require knowledge of the positions or the intensity of the sources and the sources may even be inside the object such a situation arises in emission computerized tomography the method is based on consistency conditions in the range of the relevant integral transforms the paper contains a detailed description of the algorithm and numerical results for computer generated data

a unified reconstruction framework for both parallel beam and variable focal length fan beam collimators by a cormack type inversion of exponential radon transform a variety of inversions of exponential radon transform has been derived based on the circular harmonic transform in fourier space by several research groups however these inversions cannot be directly applied to deal with the reconstruction for fan beam or variable focal length fan beam collimator geometries in single photon emission computed tomography spect in this paper the authors derived a cormack type inversion of the exponential radon transform by employing the circular harmonic transform directly in the projection space and the image space instead of the fourier space thus a unified reconstruction framework is established for parallel fan and variable focal length fan beam collimator geometries compared to many existing algorithms the presented one greatly mitigates the difficulty of image reconstruction due to the complicated collimator geometry and significantly reduces the computational burden of the special functions such as chebyshev or bessel functions by the well established fast fourier transform fft the authors algorithm is very efficient as demonstrated by several numerical simulations

characteristics of the process zone at sharp notch roots the classical williams solution for the state of stress at the tip of a semi infinite notch is re visited and the two term singular solution re written in a form making the mode mixity and load magnitude explicit this is used to show that for a 270 solid angle the majority of notch problems exhibit a process zone which is entirely or substantially mode i in character which in turn means that the notch strength may practically be governed by a single elastic parameter a method for finding the practical limit on the load and stress intensity ratio where this holds is described

survey generic properties and control of linear structured systems a survey in this survey paper we consider linear structured systems in state space form where a linear system is structured when each entry of its matrices like a b c and d is either a fixed zero or a free parameter the location of the fixed zeros in these matrices constitutes the structure of the system indeed a lot of man made physical systems which admit a linear model are structured a structured system is representative of a class of linear systems in the usual sense it is of interest to investigate properties of structured systems which are true for almost any value of the free parameters therefore also called generic properties interestingly a lot of classical properties of linear systems can be studied in terms of genericity moreover these generic properties can in general be checked by means of directed graphs that can be associated to a structured system in a natural way we review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms by properties we mean here system specific properties like controllability the finite and infinite zero structure and so on as well as solvability issues of certain classical control problems like disturbance rejection input output decoupling and so on in this paper we do not try to be exhaustive but instead by a selection of results we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool we emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only moreover the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well known polynomially bounded combinatorial techniques for larger systems

reconstruction from uniformly attenuated spect projection data using the dbh method an algorithm was developed for the 2 d reconstruction of truncated and nontruncated uniformly attenuated data acquired from single photon emission computed tomography spect the algorithm is able to reconstruct data from half scan 180deg and short scan 180deg fan angle acquisitions for parallel and fan beam geometries respectively as well as data from full scan 360deg acquisitions the algorithm is a derivative backprojection and hilbert transform dbh method which involves the backprojection of differentiated projection data followed by an inversion of the finite weighted hilbert transform the kernel of the inverse weighted hilbert transform is solved numerically using matrix inversion numerical simulations confirm that the dbh method provides accurate reconstructions from half scan and short scan data even when there is truncation however as the attenuation increases finer data sampling is required

accelerated image reconstruction using ordered subsets of projection data the authors define ordered subset processing for standard algorithms such as expectation maximization em for image restoration from projections ordered subsets methods group projection data into an ordered sequence of subsets or blocks an iteration of ordered subsets em is defined as a single pass through all the subsets in each subset using the current estimate to initialize application of em with that data subset this approach is similar in concept to block kaczmarz methods introduced by eggermont et al 1981 for iterative reconstruction simultaneous iterative reconstruction sirt and multiplicative algebraic reconstruction mart techniques are well known special cases ordered subsets em os em provides a restoration imposing a natural positivity condition and with close links to the em algorithm os em is applicable in both single photon spect and positron emission tomography pet in simulation studies in spect the os em algorithm provides an order of magnitude acceleration over em with restoration quality maintained

solving singular integral equations using gaussian quadrature and overdetermined systems abstract for singular integral equations of the cauchy type on an open interval a bounded solution exists only if an additional condition is satisfied in direct methods of solution when the integrals are replaced by quadratures it is not obvious that the resulting discrete system of equations will be consistent it is shown that for gauss chebyshev quadrature the overdetermined system of equations is consistent if and only if the discrete analog of the compatibility condition is satisfied the behavior of solutions to inconsistent systems is examined

solving singular integral equations using gaussian quadrature and overdetermined system abstract gauss chebyshev quadrature and collocation at the zeros of the chebyshev polynomial of the first kind t n x and second kind u n x leads to an overdetermined system of linear algebraic equations the size of the coefficient matrix for the overdetermined system depends on the degrees of chebyshev polynomials used we show that we can get more accurate solution using t 4 n 4 x than other t n x the regularization method using generalized singular value decomposition is described and compared to gauss newton method for solving the overdetermined system of equations computational tests show that gsvd with an appropriate choice of regularization parameter gives better solution in solving singular integral equations

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

the generic number of invariant zeros of a structured linear system in this paper we consider a structured linear system represented by means of a directed graph we present a graph theoretic method to compute the generic number of invariant zeros of the corresponding rosenbrock matrix the method is based on a fundamental decomposition of the directed graph representing the structured system the generic number of invariant zeros is important in generic versions of problems involving controllability and pole placement

the generalized cattaneo partial slip plane contact problem i theory the cattaneo problem is considered for a general plane contact between elastically similar materials i e a monotonically increasing tangential load starting from zero with normal loading held fixed instead of the classical argument on the displacement field in the stick zone of cattaneo solution we attack the problem implicitly from the governing integral equations in the stick zones after discussing and solving the full stick case we move to the more realistic for finite friction case of partial slip we show that upon isolating the effect of full sliding the equalities and inequalities governing the corrective solution for the corrective shearing tractions in the stick zone are exactly the same as those governing the solution of the normal contact problem with a lower load but the same rotation as the actual one this analogy permits us to deduce several general properties and gives a general procedures for solving partial slip cattaneo problems as frictionless normal indentation ones therefore the general solutions for single multiple and periodic contacts is given a comprehensive set of explicit results is given in the part ii of the paper

structural invertibility of transfer functions in this note we study certain properties of a transfer function in terms of the structure of the state space representation a b c specifically the rank of the transfer function and the degree of a decoupled system which can be obtained by applying a left decoupler are characterized in terms of the structure of a b c

discrete mode observability of structured switching descriptor linear systems a graph theoretic approach abstract the main result of the paper consists in necessary and sufficient graphical conditions which ensure the generic discrete mode observability of structured switching descriptor systems the methods used in the previous studies on the observability of switching linear systems on standard form are not applicable to switching descriptor systems so we develop a new approach starting from bipartite representations of these systems and then building a new kind of digraph dedicated to the discrete mode observability study the proposed method assumes only the knowledge of the system s structure and is applicable to a large class of descriptor systems including regular and non regular systems even if they are square or under determined the provided conditions can be implemented by the classical graph theory algorithms

regularization approach for inverting the exponential radon transforms ert in this paper we study the problem of inverting the exponential radon transforms with non exact data a regularization approach is introduced to find approximate solutions of the problem

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

the identification problem for the attenuated x ray transform we study the problem of recovery both the attenuation a and the source f in the attenuated x ray transform in the plane we study the linearization as well it turns out that there is a natural hamiltonian flow that determines which singularities we can recover if the perturbation delta a is supported in a compact set that is non trapping for that flow then the problem is well posed otherwise it may not be and least in the case of radial a f it is not we present uniqueness and non uniqueness results for both the linearized and the non linear problem as well as a h older stability estimate

representation theoretic patterns in three dimensional cryo electron microscopy i the intrinsic reconstitution algorithm in this paper we reveal the formal algebraic structure underlying the intrinsic reconstitution algorithm introduced by singer and shkolnisky in 9 for determining three dimensional macromolecular structures from images obtained by an electron microscope inspecting this algebraic structure we obtain a conceptual explanation for the admissibility correctness of the algorithm and a proof of its numerical stability in addition we explain how the various numerical observations reported in that work follow from basic representation theoretic principles

analysis of linear structured systems using a primal dual algorithm in this paper we give a polynomial algorithm to compute the infinite structure of a structured system a directed graph is associated with such structured systems the infinite zero orders can be computed on the associated graph via the determination of the minimal length of vertex disjoint input output paths this search corresponds to a minimum cost flow determination on an appropriate directed graph the proposed algorithm is based on the primal dual algorithm linked to linear programming this polynomial algorithm is one of the most efficient for this type of problem moreover it allows an iterative determination of the generic infinite structure which is a key tool for solving numerous control problems

on almost invariant subspaces of structural systems and decentralized control graph theoretic conditions are obtained for a structured system to have the property that the supremal l sub p almost invariant controllability subspace is generically the entire state space and that the infimal sup l sub p almost conditional invariant complementary observability subspace is generically the zero subspace the conditions are used to determine stabilizability of structured interconnected systems by means of decentralized feedback control although the obtained graph theoretic conditions are conservative they are considered satisfactory to the extent that the benefits of easy testability involving only binary calculations outweigh the conservativeness in the results

a geometric approach for structured systems application to disturbance decoupling structured systems described by state space models are considered for these systems the entries of the state space model matrices are supposed to be either fixed zeros or free independent parameters for such systems one can study structural properties i e properties that are valid for almost any value of the parameters we revisit the classical geometric theory in the context of structured systems in particular the well known notions of a b invariant and c a invariant subspaces are redefined and analysed in this context we characterize fixed subspaces included or containing these invariant subspaces and show that they play a key role in solving control problems as an application of this geometric approach for structured systems we propose new solutions to the disturbance decoupling problems by state feedback and by output measurement feedback the solvability conditions are easily checked on the associated graph of the system

a unified analysis of exact methods of inverting the 2 d exponential radon transform with implications for noise control in spect exact methods of inverting the two dimensional 2 d exponential radon transform have been proposed by bellini et al 1979 and by inouye et al 1989 both of whom worked in the spatial frequency domain to estimate the 2 d fourier transform of the unattenuated sinogram by hawkins et al 1988 who worked with circularly harmonic bessel transforms and by tretiak and metz 1980 who followed filtering of appropriately modified projections by exponentially weighted backprojection with perfect sampling all four of these methods are exact in the absence of projection data noise but empirical studies have shown that they propagate noise differently and no underlying theoretical relationship among the methods has been evident here an analysis of the 2 d fourier transform of the modified sinogram reveals that all previously proposed linear methods can be interpreted as special cases of a broad class of methods and that each method in the class can be implemented in principle by any one of four distinct techniques moreover the analysis suggests a new member of the class that is predicted to have noise properties better than those of previously proposed members

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

the finite and semi infinite tilted flat but rounded punch the problem of a tilted flat punch having a rounded edge and with a sufficiently large angle of tilt for contact to be lost along the flat face is considered a complete solution to the contact problem within the context of an elastic half plane formulation is derived including the effects of a shearing force either sufficient or insufficient to cause sliding the solution is then modified by making the punch semi infinite in extent so as to render it effective as an asymptote useful in both quantifying fretting damage and in improving the precision of approximate numerical solutions the asymptote is then applied to an example problem

brief paper state and input observability for structured linear systems a graph theoretic approach this paper deals with the state and input observability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure using a particular decomposition of the systems into two subsystems we express in simple graphic terms necessary and sufficient conditions for the generic state and input observability these conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph therefore our approach is suited to study large scale systems

graph theoretic approach to controllability and localizability of decentralized control systems the controllability and the localizability problems are considered under the decentralized information structure using some concepts from graph theory first of all the information structure graph is introduced for a decentralized control system based upon local output controllability matrices between stations when a local output feedback law is applied and some invariant properties of the graph with respect to local output feedback laws are driven then by using these results necessary and sufficient conditions of controllability under decentralized information structure are obtained also obtained are several conditions for localizability of decentralized control systems which is newly introduced in the present paper as an extended concept of a class of disturbance localization and decoupling for centralized systems

determination of an unknown coefficient in a nonlinear heat equation abstract the problem of determining an unknown term k u in the equation k u u t k u u x x is considered in this paper applying tikhonov s regularization approach we develop a procedure to find an approximate stable solution to the unknown coefficient from the overspecified data

new analytical and numerical results for two dimensional contact profiles recently a generalized coulomb law for elastic bodies in contact has been developed by the author which assumes that the tangential traction is the difference of the slip stress of the contact and the stick area whereby each stick area corresponds to a smaller contact area it holds for multiple contact regions also several applications for elastic half planes half spaces thin and thick layers and impact problems have been published for plane contact of equal bodies with friction it provides exact solutions and the interior stress field can be expressed with analytical results in closed form in this article a singular superposition of flat punch solutions is outlined in which the punches are aligned with an edge of the contact area it is shown that this superposition satisfies coulomb s inequalities directly and new results for the muskhelishvili potentials of several profiles are presented it is illustrated how problems of singularity and multi valuedness of complex functions can be solved in closed form and the chebyshev approximation used by earlier authors can be avoided for comparison some previous solutions for symmetric profiles are appended some results for the interior stress field the pressure the frictional traction and the surface displacements are compared with fem solutions of an equivalent problem the small differences between both methods show characteristic features of the fem model and the theoretical assumptions and are shortly explained further this example can be used as benchmark test for fem and bem programs

a receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate abstract in this paper we consider the axisymmetric problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half space when the two bodies are pressed together the graded layer is modeled as a nonhomogeneous medium with an isotropic stress strain law and is subjected over a part of its top surface to normal tractions while the rest of it is free of tractions since the contact between the two bodies is assumed to be frictionless then only compressive normal tractions can be transmitted in the contact area using hankel transform the axisymmetric elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact radius the global equilibrium condition of the layer is supplemented to solve the problem the singular integral equation is solved numerically using orthogonal chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact length that satisfies the global equilibrium condition the main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact

linear elastic contact of the weierstrass profile a contact problem is considered in which an elastic half plane is pressed against a rigid fractally rough surface whose profile is defined by a weierstrass series it is shown that no applied mean pressure is sufficiently large to ensure full contact and indeed there are not even any contact areas of finite dimension the contact area consists of a set of fractal character for all values of the geometric and loading parameters a solution for the partial contact of a sinusoidal surface is used to develop a relation between the contact pressure distribution at scale n 1 and that at scale n recursive numerical integration of this relation yields the contact area as a function of scale an analytical solution to the same problem appropriate at large n is constructed following a technique due to archard this is found to give a very good approximation to the numerical results even at small n except for cases where the dimensionless applied load is large the contact area is found to decrease continuously with n tending to a power law behaviour at large n which corresponds to a limiting fractal dimension of 2 d where d is the fractal dimension of the surface profile however it is not a simple fractal in the sense that it deviates from the power law form at low n at which there is also a dependence on the applied load contact segment lengths become smaller at small scales but an appropriately normalized size distribution tends to a limiting function at large n the authors dedicate this paper to the memory of dr j f archard 1918 1989

a new efficient numerical method for contact mechanics of rough surfaces abstract in this work a numerical method has been developed to investigate the adhesionless contact mechanics between rough surfaces to solve the elastic problem a boundary elements approach is used with self equilibrated square elements the domain of integration is discretized developing an intelligent adaptive mesh and obtaining a considerable memory saving the numerical convergence of the method has been verified by comparing the results with the hertzian solution and by checking the stress probability distribution at the contact interface the methodology has been then utilized to analyse the contact between an elastic flat substrate and a periodic numerically generated self affine fractal rigid surface the fractal surface has been generated by employing spectral methods the results of our investigation supports the findings of some analytical theories persson 2001 and numerical findings yang et al 2006 hyun et al 2004 carbone and bottiglione 2008 campana and muser 2007 in terms of linearity between contact area and load and stress probability distributions

structure at infinity of structured descriptor systems and its applications the generic structure at infinity of the transfer matrix of a descriptor system is investigated under the physically reasonable assumption that the coefficients in the equations are classified into independent physical parameters and dimensionless constants for such a structured descriptor system the generic structure at infinity is characterized in terms of an independent assignment or weighted matroid intersection problem this leads to necessary and sufficient conditions for the generic solvability of the exact matching problem for a singular descriptor system and for the generic solvability of the disturbance decoupling problem for a nonsingular descriptor system the obtained conditions can be checked by efficient matroid theoretic algorithms

simultaneous decoupling and disturbance rejection a structural approach abstract the combined problem of disturbance rejection and decoupling for linear systems is considered new necessary and sufficient conditions are derived for the existence of a state feedback controller that rejects the disturbances and simultaneously decouples the closed loop system these conditions are simple intuitively appealing and are expressed in terms of system structural invariants such as infinite zero orders then we consider the disturbance rejection with simultaneous decoupling problem for structured linear systems necessary and sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

output feedback disturbance decoupling graph interpretation for structured systems abstract in this paper we consider first the output feedback disturbance decoupling problem for linear systems we derive a set of new necessary or sufficient conditions for the solvability of this problem these conditions are expressed in terms of system structural invariants such as infinite zero orders and essential orders then we consider the output feedback disturbance decoupling problem for structured linear systems necessary or sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

hilbert transform based fbp algorithm for fan beam ct full and partial scans this paper presents a new type of filtered backprojection fbp algorithm for fan beam full and partial scans the filtering is shift invariant with respect to the angular variable the backprojection does not include position dependent weights through the hilbert transform and the one dimensional transformation between the fan and parallel beam coordinates the strong symmetry of the filtered projections directly leads to an exact reconstruction for partial data the use of the hilbert transform avoids the approximation introduced by the nonuniform cutoff frequency required in the ramp filter based fbp algorithm variance analysis indicates that the algorithm might lead to a better uniformity of resolution and noise in the reconstructed image numerical simulations are provided to evaluate the algorithm with noise free and noisy projections our simulation results indicate that the algorithm does have better stability over the ramp filter based fbp and circular harmonic reconstruction algorithms this may help improve the image quality for in place computed tomography scanners with single row detectors

incipient sliding of rough surfaces in contact a multiscale numerical analysis in this paper the cattaneo theory of frictional contact is extended to elastic half spaces in contact through rough disordered interfaces the discrete version of the cattaneo theorem is provided and represents the basis of a multiscale numerical contact algorithm mathematical surfaces with imposed roughness as well as experimentally digitised ones are analysed by means of a numerical method the evolution of the contact domain at different resolution is investigated roughness of the interfaces provides lacunarity of the contact domains whose fractal dimension is always smaller than 2 0 when a tangential force is applied the extent of the stick area decreases in the same way as the contact area develops with increasing pressure and the slip area is found to be proportional to the tangential force as predicted by cattaneo theory the evolution of the shear centroid as well as the amount of dissipated energy up to full sliding are provided finally it is shown that at a sufficient level of discretization the distribution of contact pressures is multifractal

the generalized cattaneo partial slip plane contact problem ii examples this second part of the paper uses the method devised in the part i to give explicit solution to several cases of cattaneo s plane contact problem where a monotonically increasing tangential load starting from zero is applied to the bodies in contact with normal loading held fixed the method consists in reducing the partial slip problem to a superposition of frictionless normal contact problems for which several results are available including some recent cases studied by the author therefore a comprehensive set of results is given for single multiple and periodical contacts

an accurate elasto plastic frictional tangential force displacement model for granular flow simulations displacement driven formulation we present in this paper the displacement driven version of a tangential force displacement tfd model that accounts for both elastic and plastic deformations together with interfacial friction occurring in collisions of spherical particles this elasto plastic frictional tfd model with its force driven version presented in l vu quoc l lesburg x zhang an accurate tangential force displacement model for granular flow simulations contacting spheres with plastic deformation force driven formulation journal of computational physics 196 1 2004 298 326 is consistent with the elasto plastic frictional normal force displacement nfd model presented in l vu quoc x zhang an elasto plastic contact force displacement model in the normal direction displacement driven version proceedings of the royal society of london series a 455 1991 4013 4044 both the nfd model and the present tfd model are based on the concept of additive decomposition of the radius of contact area into an elastic part and a plastic part the effect of permanent indentation after impact is represented by a correction to the radius of curvature the effect of material softening due to plastic flow is represented by a correction to the elastic moduli the proposed tfd model is accurate and is validated against nonlinear finite element analyses involving plastic flows in both the loading and unloading conditions the proposed consistent displacement driven elasto plastic nfd and tfd models are designed for implementation in computer codes using the discrete element method dem for granular flow simulations the model is shown to be accurate and is validated against nonlinear elasto plastic finite element analysis

brief paper state and input observability recovering by additional sensor implementation a graph theoretic approach this paper deals with the problem of additional sensor location in order to recover the state and input observability for structured linear systems the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure it allows one to provide the minimal number of the required sensors and either their pertinent location or a necessary and sufficient condition which allows one to check if a sensor location is adequate or not we obtain a sensor placement procedure based on classical and well known graph theory algorithms which have polynomial complexity orders

using green s function molecular dynamics to rationalize the success of asperity models when describing the contact between self affine surfaces we use green s function molecular dynamics to evaluate the effectiveness of asperity models when describing the contact mechanics of elastic solids with self affine surfaces surfaces are created with the help of a fourier filtering algorithm and the interactions between the solids are modeled via hard wall potentials we illustrate how the real area of contact a real is formed by a set of contact clusters two different regimes are identified when the normal force per cluster l c is plotted as a function of its area a c small clusters satisfy a hertzian type law l c approximately a c 32 while large clusters display a linear l c approximately a c behavior it is shown how the area a c where the crossover between the two regimes takes place depends only on the roughness at the smallest length scale if the longitudinal dimension of the surface remains unaltered moreover our results display a distribution of cluster sizes p a c remaining nearly constant for areas smaller than a c while showing power law decay above such a critical value furthermore we found the heights of the contacting atoms to be normally distributed with width inversely proportional to the surface roughness

structurally fixed modes a notion of structurally fixed modes is introduced in the framework of decentralized control systems to identify the modes that cannot be shifted by decentralized feedback regardless of the numerical values of system parameters in this way a qualitative characterization of decentralized fixed modes is provided which is suitable for delineating decentrally stabilizable systems the characterization leads naturally to the notion of fixed modes with respect to arbitrary feedback structure constraints

bounded asymptotic solutions for incomplete contacts in partial slip abstract asymptotic solutions for the contact pressure and shearing tractions present adjacent to the edge of an incomplete contact are derived and for each a dimensional scaling factor akin to a generalised stress intensity factor is defined these two quantities may therefore be used to define the complete local stress state for which purpose the muskhelishvili potentials are derived the application of this technique to a comparison of the hertz cattaneo contact the flat and rounded contact and the tiled punch is described and the extent of the domain of validity of the asymptote found

a frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate abstract this paper investigates the plane problem of a frictional receding contact formed between an elastic functionally graded layer and a homogeneous half space when they are pressed against each other the graded layer is assumed to be an isotropic nonhomogeneous medium with an exponentially varying shear modulus and a constant poisson s ratio a segment of the top surface of the graded layer is subject to both normal and tangential traction while rest of the surface is devoid of traction the entire contact zone thus formed between the layer and the homogeneous medium can transmit both normal and tangential traction it is assumed that the contact region is under sliding contact conditions with the coulomb s law used to relate the tangential traction to the normal component employing fourier integral transforms and applying the necessary boundary conditions the plane elasticity equations are reduced to a singular integral equation in which the unknowns are the contact pressure and the receding contact lengths ensuring mechanical equilibrium is an indispensable requirement warranted by the physics of the problem and therefore the global force and moment equilibrium conditions for the layer are supplemented to solve the problem the gauss chebyshev quadrature collocation method is adopted to convert the singular integral equation to a set of overdetermined algebraic equations this system is solved using a least squares method coupled with a novel iterative procedure to ensure that the force and moment equilibrium conditions are satisfied simultaneously the main objective of this paper is to study the effect of friction coefficient and nonhomogeneity factor on the contact pressure distribution and the size of the contact region

brief paper graph theoretic characterization of fixed modes in frequency domain we examine a characterization of fixed modes in a frequency domain framework based on the graphical representation of systems with multiple poles we present a graph theoretic characterization of the characteristic polynomials of closed loop systems under arbitrary structural constraints based on this characterization fixed modes are characterized using the weight products of 1 factors of the weighted directed graphs associated with closed loop systems it is also shown that the well known characterization of fixed modes in terms of transmission zeros can be derived from the proposed graph theoretic characterization

brief paper observability of switching structured linear systems with unknown input a graph theoretic approach this paper deals with the observability of the discrete mode the internal state and the input of switching structured linear systems with unknown input the proposed method based on a graph theoretic approach assumes only the knowledge of the system s structure we express in graphical terms necessary and sufficient conditions for the generic observability of the discrete mode the continuous internal state and the input of a switching structured linear system these conditions can be implemented by classical graph theory algorithms based on finding particular paths and cycles in a digraph