asymptotic mesh independence of newton s method revisited the paper presents a new affine invariant theory on asymptotic mesh independence of newton s method for discretized nonlinear operator equations compared to earlier attempts the new approach is both much simpler and more intuitive from the algorithmic point of view the theory is exemplified at finite element methods for elliptic pde problems

an objective 3d large deformation finite element formulation for geometrically exact curved kirchhoff rods the objective of this work is the development of a new finite element formulation for beams according to the kirchhoff theory of thin rods which includes the deformation states of axial tension torsion and bending the proposed formulation accounts for large deformations in three dimensional problem settings consisting of slender prismatic beams with arbitrarily curved initial geometries and arbitrary cross section shapes like in geometrically exact reissner theories the derived deformation measures are geometrically exact in the sense that they are consistent with the strong and weak form of the balance equations and the beam geometry for any configuration and for arbitrarily large translations rotations and strains a novel orthogonal interpolation strategy is applied to the triad field representing the cross section orientation in order to fulfill the kirchhoff constraint of vanishing shear strains in a strong sense and to preserve the objectivity of the spatially discretized problem the continuity requirements resulting from the corresponding weak form are fulfilled by a cubic hermite interpolation thus leading to a c1 continuous representation of the beam centerline fundamental properties such as objectivity path independence consistency and accuracy of the developed beam element are verified by means of suitable numerical examples

quantile regression adjusting for dependent censoring from semicompeting risks in this work we study quantile regression when the response is an event time subject to potentially dependent censoring we consider the semi competing risks setting where time to censoring remains observable after the occurrence of the event of interest while such a scenario frequently arises in biomedical studies most of current quantile regression methods for censored data are not applicable because they generally require the censoring time and the event time be independent by imposing rather mild assumptions on the association structure between the time to event response and the censoring time variable we propose quantile regression procedures which allow us to garner a comprehensive view of the covariate effects on the event time outcome as well as to examine the informativeness of censoring an efficient and stable algorithm is provided for implementing the new method we establish the asymptotic properties of the resulting estimators including uniform consistency and weak convergence the theoretical development may serve as a useful template for addressing estimating settings that involve stochastic integrals extensive simulation studies suggest that the proposed method performs well with moderate sample sizes we illustrate the practical utility of our proposals through an application to a bone marrow transplant trial

quasilinear hyperbolic parabolic equations of one dimensional viscoelasticity abstract we study the global existence of solutions of initial boundary value problems for a quasilinear hyperbolic parabolic equation describing the longitudinal motion of a one dimensional viscoelastic rod we treat a variety of nonhomogeneous boundary conditions requiring separate analyses because they lead to distinctive physical effects we employ a constitutive equation giving the stress as a general nonlinear function of the strain and the strain rate all global analyses of this and related problems except that of dafermos j differential equations 1969 71 86 have employed a stress that is merely affine in the strain rate dafermos s assumptions are far more appropriate for shearing motions than for longitudinal motions our constitutive equation satisfies the physically natural requirement that an infinite amount of compressive stress is needed to produce a total compression at any point of the rod this requirement is the source of a severe singularity in the governing partial differential equations which is particularly acute when time dependent dirichlet data are prescribed the further novel yet physically reasonable restrictions we impose on the constitutive function yield estimates that preclude a total compression anywhere at any finite time the resulting estimates are crucial for the global existence theory we obtain

geodesic finite elements on simplicial grids summary we introduce geodesic finite elements as a conforming way to discretize partial differential equations for functions v m where is an open subset of rd and m is a riemannian manifold these geodesic finite elements naturally generalize standard first order finite elements for euclidean spaces they also generalize the geodesic finite elements proposed for d 1 in a previous publication of the author our formulation is equivariant under isometries of m and hence preserves objectivity of continuous problem formulations we concentrate on partial differential equations that can be formulated as minimization problems discretization leads to algebraic minimization problems on product manifolds mn these can be solved efficiently using a riemannian trust region method we propose a monotone multigrid method to solve the constrained inner problems with linear multigrid speed as an example we numerically compute harmonic maps from a domain in r3 to s2 copyright 2012 john wiley sons ltd

l 2 discretization error bounds for maps into riemannian manifolds we study the approximation of functions that map a euclidean domain omega subset mathbb r d into an n dimensional riemannian manifold m g minimizing an elliptic semilinear energy in a function set h subset w 1 2 omega m the approximation is given by a restriction of the energy minimization problem to a family of conforming finite dimensional approximations s h subset h we provide a set of conditions on s h such that we can prove a priori w 1 2 and l 2 approximation error estimates comparable to standard euclidean finite elements this is done in an intrinsic framework independently of embeddings of the manifold or the choice of coordinates

multi parameter bifurcation and asymptotics for the singular lane emden fowler equation with a convection term to the second variable and g is unbounded around the origin the asymptotic behaviour of the solution around the bifurcation point is also established provided g u behaves like u around the origin for some 0 1 our approach relies on finding explicit sub and supersolutions combined with various techniques related to the maximum principle for elliptic equations the analysis we develop in this paper shows the key role played by the convection term u p

a broyden class of quasi newton methods for riemannian optimization this paper develops and analyzes a generalization of the broyden class of quasi newton methods to the problem of minimizing a smooth objective function f on a riemannian manifold a condition on vector transport and retraction that guarantees convergence and facilitates efficient computation is derived experimental evidence is presented demonstrating the value of the extension to the riemannian broyden class through superior performance for some problems compared to existing riemannian bfgs methods in particular those that depend on differentiated retraction

galerkin lie group variational integrators based on unit quaternion interpolation abstract lie group variational integrators of arbitrary order are developed using the galerkin method based on unit quaternion interpolation to our knowledge quaternions have not been used before for this purpose though they allow a very simple and efficient way to perform the interpolation the resulting integrators are symplectic and structure preserving in the sense that certain symmetries in the lagrangian of the mechanical system are carried over to the discrete setting which leads to the preservation of the corresponding momentum maps the integrators furthermore exhibit a very good long time energy behavior i e energy is neither dissipated nor gained artificially at the same time the lie group structure is preserved by carefully defining the variations the interpolation method and by solving the non linear system of equations directly on the manifold rather than constraining it in a surrounding space using lagrange multipliers as a consequence we are able to show that lie group variational integrators based on the special orthogonal group are equivalent to the variational integrators for constrained systems using the discrete null space method employed e g in dmocc discrete mechanics and optimal control of constrained systems we show new numerical results on the convergence rates which are substantially higher than the known theoretical bounds and on the relation between accuracy and computational cost

the ideal pseudo rigid continuum in the literature on pseudo rigid bodies and their applications it is generally assumed that these bodies can undergo only a restricted class of motions without questioning how this restriction is to be strictly enforced in 2004 i proposed in these proceedings that such a restriction may be regarded as a global constraint on a deformable continuum and influenced by ideas of antman marlow from the early 1990s i assumed that the constraint is enforced by a field of reactive stresses and i constructed a mathematical model that idealizes pseudo rigid bodies as globally constrained continua of finite size in a recent article in proceedings of the royal society a the validity of this model was challenged essentially the controversy revolves around the issue of working definitions versus idealized mathematical models of pseudo rigid bodies

radially symmetric motions of nonlinearly viscoelastic bodies under live loads this paper treats radially symmetric motions of nonlinearly viscoelastic circular cylindrical and spherical shells subjected to the live loads of centrifugal force and time dependent hydrostatic pressures the governing equations are exact versions of those for 3 dimensional continuum mechanics so shell does not connote an approximate via some shell theory these motions are governed by quasilinear third order parabolic hyperbolic equations having but one independent spatial variable the principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations the presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis the interaction of geometrically exact formulations the compatible use of general constitutive equations for material response and the presence of live loads show how these factors play crucial roles in the behavior of solutions in particular for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior the analysis using classical methods covers infinite time blowup for cylindrical shells subject to centrifugal forces infinite time blowup for cylindrical shells subject to steady and time dependent hydrostatic pressures finite time blowup for spherical shells subject to steady and time dependent hydrostatic pressures and the preclusion of total compression this paper concludes with a sketch using some modern methods of the existence of regular solutions until the time of blowup

order statistics correlation coefficient as a novel association measurement with applications to biosignal analysis in this paper we propose a novel correlation coefficient based on order statistics and rearrangement inequality the proposed coefficient represents a compromise between the pearson s linear coefficient and the two rank based coefficients namely spearman s rho and kendall s tau theoretical derivations show that our coefficient possesses the same basic properties as the three classical coefficients experimental studies based on four models and six biosignals show that our coefficient performs better than the two rank based coefficients when measuring linear associations whereas it is well able to detect monotone nonlinear associations like the two rank based coefficients extensive statistical analyses also suggest that our new coefficient has superior anti noise robustness small biasedness high sensitivity to changes in association accurate time delay detection ability fast computational speed and robustness under monotone nonlinear transformations

on an inconsistency in the derivation of the equations of elastohydrodynamic lubrication reynolds s lubrication approximation one of the cornerstones of fluid mechanics is constructed on the assumption that the viscosity is independent of the pressure this assumption is reasonable at low pressures and is appropriate for a large class of applications however in an important instance that appeals to the approximation elastohydrodynamic lubrication ehl the liquid lubricant is subjected to extremely high pressures and the assumption that the viscosity is independent of the pressure no longer holds on the contrary pressure dependence of viscosity is severe and the viscosity can increase by several orders of magnitude due to pressure increase nevertheless in the current literature the pressure dependence of viscosity in the derivation of the governing equations for ehl is only recognized a posteriori that is after the reynolds equation has been stated under the assumption of constant viscosity a consistent derivation of the equations of ehl that takes into account the pressure dependence of viscosity right from the outset leads to additional and hitherto neglected terms in the governing equations consequently construction of a single pressure equation analogous to the reynolds equation is no longer possible without additional drastic assumptions in this study we provide a consistent derivation of the equations of motion for ehl and with additional simplifying assumptions derive a modified reynolds equation we then provide a comparison between the solutions to the classical equation of reynolds s and our modified equation the modified equation results in slightly higher pressures but at significantly higher viscosities than the classical reynolds equation

asymptotic analysis of linearly elastic shells iii justification of koiter s shell equations we consider as in part i a family of linearly elastic shells of thickness 2 all having the same middle surfaces r3 where r2 is a bounded and connected open set with a lipschitz continuous boundary and l3 r3 the shells are clamped on a portion of their lateral face whose middle line is 0 where 0 is any portion of withlength 0 0 we make an essential geometrical assumption on the middle surfaces and on the set 0 which states that the space of inextensional displacements begin gathered v f omega eta eta i in h 1 omega times h 1 omega times h 2 omega hfill eta i partial v eta 3 0 on gamma 0 gamma alpha beta eta 0 in omega hfill end gathered where gamma alpha beta are the components of the linearized change is metric tensor ofs contains non zero functions this assumption is satisfied in particular ifs is a portion of cylinder and 0 is contained in a generatrix ofs

combined effects in nonlinear problems arising in the study ofanisotropic continuous media the paper deals with the study of a lane emden fowler equation with dirichlet boundary condition and variable potential functions the analysis developed in this paper combines monotonicity methods with variational arguments

on the global solutions to a class of strongly degenerate parabolic equations abstract we are concerned with degenerate parabolic equations in nondivergence form of the type t u a x u p u g u in 0 where r n n 1 is a smooth bounded domain x dist x 0 p 1 and g is either a nondecreasing function having a sublinear growth or g u u the degenerate character of our problem is also given by the potential a x which may vanish at the boundary under some suitable assumptions on g a and we establish the existence and uniqueness of a classical solution and we determine its asymptotic profile as t if g u u and a satisfies 0 1 s a s d s we also provide a blow up result as approaches the first eigenvalue 1 of the laplace operator

constitutive theory for some constrained elastic crystals abstract some of the observations of a 15 superconductors near cubic tetragonal phase transformations suggest treating them as thermoelastic bodies subject to certain material constraints here we begin to develop a theory of this kind

on thermodynamic active control of shape memory alloy wires we propose a model for the control of high frequency oscillations in shape memory alloy wires we introduce a notion of generalized solution for a generalized control and in this context prove a local exact controllability result effectively corresponding to an approximate controllability result for the nonconvex pseudoelastic material system

homoclinic complexity in the localised buckling of an extensible conducting rod in a uniform magnetic field abstract we study the localised buckling of an extensible conducting rod subjected to end loads and placed in a uniform magnetic field the trivial straight but twisted rod is described by a fixed point of a four dimensional hamiltonian system of equations previously shown to be chaotic localised solutions are given by homoclinic orbits to this fixed point and we explore the spatial complexity of localised rod configurations by means of shooting and parameter continuation methods that exploit the reversibility of the system of equations unlike in localisation studies of non magnetic rods we find that for certain parameter values multiple hamiltonian hopf bifurcations occur where these collide as parameters are varied solutions exhibit delocalisation relocalisation behaviour our results predict buckling instabilities and post buckling behaviour of rods under combined mechanical and magnetic loads which are relevant for electrodynamic space tethers and potentially for conducting nanowires in future electromechanical devices

robust image registration by increment sign correlation abstract a novel and robust statistic as a similarity measure for robust image registration is proposed the statistic is named as increment sign correlation because it is based on the average evaluation of incremental tendency of brightness in adjacent pixels it is formalized to be a binary distribution or a gaussian distribution for a large image size through statistical analysis and modeling by utilizing the proposed statistical model for example we can theoretically determine a reasonable value of threshold for verification of matching this sign correlation can also be proved to expectedly have the constant value 0 5 for any uncorrelated images to a template image and then the property of the constancy can be utilized to analyze the high robustness for occlusion the good performance for the case of saturation or highlight can also be proved through theoretical analysis and fundamental experiments a basic algorithm for image scanning search and registration over a large scene is represented with a technique for a fast version by the branch and bound approach many experimental evidences with real images are provided and discussed

asymptotic properties of order statistics correlation coefficient in the normal cases we have previously proposed a novel order statistics correlation coefficient oscc which possesses some desirable advantages when measuring linear and monotone nonlinear associations between two signals however the understanding of this new coefficient is far from complete a lot of theoretical questions such as the expressions of its distribution and moments remain to be addressed motivated by this unsatisfactory situation in this paper we prove that for samples drawn from bivariate normal populations the distribution of oscc is asymptotically equivalent to that of the pearson s product moment correlation coefficient ppmcc we also reveal its close relationships with the other two coefficients namely gini correlation gc and spearman s rho sr monte carlo simulation results agree with the theoretical findings

self sustained oscillations of nonlinearly viscoelastic layers we study the motion of an incompressible nonlinearly viscoelastic layer subject to a slip stick frictional force applied to one of its faces by a moving belt this system is governed by a third order quasi linear parabolic hyperbolic partial differential equation subject to complicated boundary conditions we use a refined version of the hopf bifurcation theorem to show that this problem admits periodic solutions for the belt speed near critical values with the number of such solutions increasing as the viscosity of the layer decreases to verify the hypotheses of this theorem we must devote considerable effort to the tricky analysis of how the spectrum of the linearized problem depends on the belt speed and material parameters our analysis is complemented with both computations and a proof of the topological fact that the computed disposition of the eigenvalues does not omit any others we complete our study with a perturbation analysis justified by the hopf bifurcation theorem

interpolation in lie groups we consider interpolation in lie groups based on points on the manifold together with tangent vectors at some of these points we construct hermite interpolation polynomials if the points and tangent vectors are produced in the process of integrating an ordinary differential equation in terms of lie algebra actions we use the truncated inverse of the differential of the exponential mapping and the truncated baker campbell hausdorff formula to relatively cheaply construct an interpolation polynomial much effort has lately been put into research on geometric integration i e the process of integrating differential equations in such a way that the configuration space of the true solution is respected by the numerical solution some of these methods may be viewed as generalizations of classical methods and we investigate the construction of intrinsic dense output devices as generalizations of the continuous runge kutta methods

a finite strain quadrilateral shell element based on discrete kirchhoff love constraints this paper improves the 16 degrees of freedom quadrilateral shell element based on pointwise kirchhoff love constraints and introduces a consistent large strain formulation for this element the model is based on classical shell kinematics combined with continuum constitutive laws the resulting element is valid for large rotations and displacements the degrees of freedom are the displacements at the corner nodes and one rotation at each mid side node the formulation is free of enhancements it is almost fully integrated and is found to be immune to locking or unstable modes the patch test is satisfied in addition the formulation is simple and amenable to efficient incorporation in large scale codes as no internal degrees of freedom are employed and the overall calculations are very efficient results are presented for linear and non linear problems copyright 2005 john wiley sons ltd

equilibrium states of an elastic conductor in a magnetic field a paradigm of bifurcation theory in this paper we study the equilibrium states of a nonlinearly elastic conducting wire in a magnetic field the wire is perfectly flexible and is suspended between fixed supports the wire carries an electric current and is subjected to a constant magnetic field whose direction is parallel to the line between the supports we solve this problem exactly and show that the set of solutions gives rise to a paradigmatic bifurcation diagram we then carry out a study of the equations obtained by linearization about the nontrivial solutions in order to gain some insight into the stability of the various solution branches introduction in this paper we study the equilibrium states of a nonlinearly elastic conducting wire in a magnetic field the wire is assumed to be perfectly flexible and is suspended between fixed supports the distance between the supports is assumed to be greater than the natural length of the wire and therefore the wire will always be in tension the magnetic field is assumed to be constant and is directed parallel to the line between the supports we show that this problem can be solved exactly the set of solutions exhibits the classic bifurcation phenomenon the bifurcation parameter is x ib where i is the current in the wire and b the strength of the magnetic field for all values of x 0 there is a trivial solution in which the wire remains straight however at the eigenvalues of the problem obtained by linearizing the equilibrium equation about the trivial solution bifurcation occurs and we obtain branches of nontrivial solutions the situation is quite similar to the classical problem of the buckling of a beam actually in our case the branches of solutions are two dimensional manifolds because the problem is invariant under rotation about the axis of the supports this work was motivated by the discussion in 1 see 4 7 especially figure 29 and the reference quoted therein there are two cases to consider as the wire is elastically homogeneous or not of course it is of interest to study the stability of the equilibria with respect to the hyperbolic equations of motion this is in general a very difficult problem and in the present case it is complicated even further by the multiplicity of equilibria arising from the rotational invariance in the case of the homogeneous wire we can study the operator obtained by linearization about a nontrivial solution we are able to locate received by the editors june 16 1982 1980 mathematics subject classification primary 73c50 secondary 58e07 d1983 american matheniatical society 0002 9947 82 0000 1374 03 50 377 this content downloaded from 157 55 39 180 on mon 25 apr 2016 06 09 45 utc all use subject to http about jstor org terms

scattered manifold valued data approximation we consider the problem of approximating a function f from an euclidean domain to a manifold m by scattered samples f xi i i in mathcal i f i i i where the data sites xi i i in mathcal i i i i are assumed to be locally close but can otherwise be far apart points scattered throughout the domain we introduce a natural approximant based on combining the moving least square method and the karcher mean we prove that the proposed approximant inherits the accuracy order and the smoothness from its linear counterpart the analysis also tells us that the use of karcher s mean dependent on a riemannian metric and the associated exponential map is inessential and one can replace it by a more general notion of center of mass based on a general retraction on the manifold consequently we can substitute the karcher mean by a more computationally efficient mean we illustrate our work with numerical results which confirm our theoretical findings

the parabolic hyperbolic system governing the spatial motion of nonlinearly viscoelastic rods this paper treats initial boundary value problems governing the motion in space of nonlinearly viscoelastic rods of strain rate type it introduces and exploits a set of physically natural constitutive hypotheses to prove that solutions exist for all time and depend continuously on the data the equations are those for a very general properly invariant theory of rods that can suffer flexure torsion extension and shear in this theory the contact forces and couples depend on strains measuring these effects and on the time derivatives of these strains

unique global solvability for initial boundary value problems in one dimensional nonlinear thermoviscoelasticity the balance laws of mass momentum and energy are considered for a broad class of one dimensional nonlinear thermoviscoelastic materials for the initial boundary value problem corresponding to pinned endpoints held at constant temperature we establish existence and uniqueness of temporally global classical solutions for initial data of unrestricted size our approach also applies to all boundary conditions involving pinned or stress free endpoints which are either held at constant temperature or insulated an additional and novel feature of the theory is that solid like and gaseous materials are treated in a unified way

a posteriori modeling error estimation for hierarchic plate models hierarchic plate models are dimensional reductions obtained by semidiscretization of the three dimensional plate problem in the transverse direction and energy projection we derive computable a posteriori estimators for the modeling error thus incurred under the assumption that the resulting two dimensional plate models are solved exactly the estimators are valid for homogeneous monoclinic materials for plates with unsmooth midsurfaces and for a wide class of variational edge conditions computable a posteriori bounds on the effectivity indices are also derived and sufficient conditions for the asymptotic i e as the plate thickness tends to zero and the spectral i e as the order of the plate model tends to infinity exactness of the estimators are given numerical examples are presented

objectivity of strain measures in the geometrically exact three dimensional beam theory and its finite element implementation the paper discusses the issue of discretization of the strainconfiguration relationships in the geometrically exact theory of threedimensional 3d beams which has been at the heart of most recent

a locking free finite element formulation and reduced models for geometrically exact kirchhoff rods in this work we suggest a locking free geometrically exact finite element formulation incorporating the modes of axial tension torsion and bending of thin kirchhoff beams with arbitrary initial curvatures and cross section shapes the proposed formulation has been designed in order to represent general load cases and three dimensional problem settings in the geometrically nonlinear regime of large deformations from this comprehensive theory we not only derive a general beam model but also several reduced formulations which deliver accurate solutions for special problem classes concerning the beam geometry and the external loads the advantages of these reduced models arise for example in terms of simplified finite element formulations less degrees of freedom per element and consequently a higher computational efficiency of the corresponding numerical models a second core topic of this publication is the treatment of membrane locking which is a locking phenomenon predominantly occurring in highly slender curved structures thus exactly in the prime field of application for kirchhoff theories in order to address the membrane locking effect we will propose a new interpolation strategy for the axial strain field and compare this method with common approaches such as assumed natural strains ans or reduced integration the effectiveness of this method as well as the consistency and accuracy of the general finite element formulation and the reduced beam models will be illustrated with selected numerical examples

on the nature of constraints for continua undergoing dissipative processes when dealing with mechanical constraints it is usual in continuum mechanics to enforce ideas that stem from the seminal work of bernoulli and d alembert and require that internal constraints do no

shells with thickness distension abstract a deductive approach to shell theory is presented within which a shell is regarded as a constrained three dimensional continuum with special body structure more precisely admissible deformations are given a restricted form presumed to be consistent with the special shape and partitionability of a shell like body in addition to the standard balance equations of forces and torques an extra balance equation is derived allowing for a description of dilatation or contraction in the thickness dimension as an illustrative application the free oscillations of linearly elastic plates in particular thickness distension waves are studied

the initial value problem for elastodynamics of incompressible bodies we prove short time well posedness of the cauchy problem for incompressible strongly elliptic hyperelastic materials

geodesic finite elements for cosserat rods we introduce geodesic finite elements as a new way to discretize the non linear configuration space of a geometrically exact cosserat rod these geodesic finite elements naturally generalize standard one dimensional finite elements to spaces of functions with values in a riemannian manifold for the special orthogonal group our approach reproduces the interpolation formulas of crisfield and jelenic geodesic finite elements are conforming and lead to objective and path independent problem formulations we introduce geodesic finite elements for general riemannian manifolds discuss the relationship between geodesic finite elements and coefficient vectors and estimate the interpolation error then we use them to find static equilibria of hyperelastic cosserat rods using the riemannian trust region algorithm of absil et al we show numerically that the discretization error depends optimally on the mesh size copyright 2009 john wiley sons ltd

on steady flows of fluids with pressure and shear dependent viscosities there are many technologically important problems such as elastohydrodynamics which involve the flows of a fluid over a wide range of pressures while the density of the fluid remains essentially constant during these flows whereby the fluid can be approximated as being incompressible the viscosity varies significantly by several orders of magnitude it is also possible that the viscosity of such fluids depends on the shear rate here we consider the flows of a class of incompressible fluids with viscosity that depends on the pressure and shear rate we establish the existence of weak solutions for the steady flows of such fluids subjected to homogeneous dirichlet boundary conditions and to specific body forces that are not necessarily assumed to be small a novel aspect of the study is the manner in which we treat the pressure that allows us to establish its compactness as well as that of the velocity gradient the method draws upon the physics of the problem namely that the notion of incompressibility is an idealization that is attained by letting the compressibility of the fluid to tend to zero

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

rapidly detecting disorder in rhythmic biological signals a spectral entropy measure to identify cardiac arrhythmias we consider the use of a running measure of power spectrum disorder to distinguish between the normal sinus rhythm of the heart and two forms of cardiac arrhythmia atrial fibrillation and atrial flutter this spectral entropy measure is motivated by characteristic differences in the power spectra of beat timings during the three rhythms we plot patient data derived from ten beat windows on a disorder map and identify rhythm defining ranges in the level and variance of spectral entropy values employing the spectral entropy within an automatic arrhythmia detection algorithm enables the classification of periods of atrial fibrillation from the time series of patients beats when the algorithm is set to identify abnormal rhythms within 6 s it agrees with 85 7 of the annotations of professional rhythm assessors for a response time of 30 s this becomes 89 5 and with 60 s it is 90 3 the algorithm provides a rapid way to detect atrial fibrillation demonstrating usable response times as low as 6 s measures of disorder in the frequency domain have practical significance in a range of biological signals the techniques described in this paper have potential application for the rapid identification of disorder in other rhythmic signals

finite amplitude elastic waves propagating in compressible solids the paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials including the possibility of dissipation the dissipative term chosen is similar to the classical stress tensor describing a stokesian fluid and is commonly used in nonlinear acoustics the aim of this research is to derive the corresponding general equations of motion valid for any possible form of the strain energy function and to investigate the possibility of obtaining some general and exact solutions to these equations by reducing them to a set of ordinary differential equations then the reductions can lead to some exact closed form solutions for special classes of materials here the examples of the hadamard blatz ko and power law strain energy densities are considered as well as fourth order elasticity the solutions derived are in a time space separable form and may be interpreted as generalized oscillatory shearing motions and generalized sinusoidal standing waves by means of standard methods of dynamical systems theory some peculiar properties of waves propagating in compressible materials are uncovered such as for example the emergence of destabilizing effects these latter features exist for highly nonlinear strain energy functions such as the relatively simple power law strain energy but they cannot exist in the framework of fourth order elasticity

theory and numerics of three dimensional beams with elastoplastic material behaviour a theory of space curved beams with arbitrary cross sections and an associated finite element formulation is presented within the present beam theory the reference point the centroid the centre of shear and the loading point are arbitrary points of the cross section the beam strains are based on a kinematic assumption where torsion warping deformation is included each node of the derived finite element possesses seven degrees of freedom the update of the rotational parameters at the finite element nodes is achieved in an additive way applying the isoparametric concept the kinematic quantities are approximated using lagrangian interpolation functions since the reference curve lies arbitrarily with respect to the centroid the developed element can be used to discretize eccentric stiffener of shells due to the implemented constitutive equations for elastoplastic material behaviour the element can be used to evaluate the load carrying capacity of beam structures copyright 2000 john wiley sons ltd

normal hyperbolicity of center manifolds and saint venant s principle the concept of normal hyperbolicity of center manifolds is generalized to infinite dimensional differential equations in particular to elliptic problems in cylindrical domains it is shown that all solutions u staying close to the center manifold for t l l satisfy an estimate of the form left u t tilde u t right leqslant ce alpha l t where c and are independent of l and is a solution on the center manifold these results are applied to saint venant s principle for the static deformation of nonlinearly elastic prismatic bodies the use of the center manifold permits the effective treatment of the general case of non zero resultant forces and moments acting on each cross section

injectivity and self contact in nonlinear elasticity let be a bounded open connected subset of 3 with a sufficiently smooth boundary the additional condition det dx vol is imposed on the admissible deformations of a hyperelastic body whose reference configuration is we show that the associated minimization problem provides a mathematical model for matter to come into frictionless contact with itself but not interpenetrate we also extend j ball s theorems on existence to this case by establishing the existence of a minimizer of the energy in the space w1 p 3 p 3 that is injective almost everywhere

numerical solution of a bending torsion model for elastic rods aiming at simulating elastic rods we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods after reviewing this model and discussing topological effects of periodic rods we prove convergence of the discretized functionals and stability of a corresponding discrete flow our experiments numerically confirm thresholds e g for michell s instability and indicate a complex energy landscape in particular in the presence of impermeability

global analysis of the flows of fluids with pressure dependent viscosities to describe the flows of fluids over a wide range of pressures it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure that the viscosity depends on the pressure has been verified by numerous careful experiments while the existence of solutions local in time to the equations governing the flows of such fluids are available for small special data and rather unrealistic dependence of the viscosity on the pressure no global existence results are in place our interest here is to establish the existence of weak solutions for spatially periodic three dimensional flows that are global in time for a large class of physically meaningful viscosity pressure relationships

existence and regularity of extremal solutions for a mean curvature equation we study a class of mean curvature equations mu h up where m denotes the mean curvature operator and for p 1 we show that there exists an extremal parameter such that this equation admits a minimal weak solutions for all 0 while no weak solutions exists for weak solutions will be defined as critical points of a suitable functional in the radially symmetric case we then show that minimal weak solutions are classical solutions for all 0 and that another branch of classical solutions exists in a neighborhood of

a new approach in studying one parameter nonlinear eigenvalue problems with constraints abstract the paper presents a new approach for obtaining existence and location of solutions to nonlinear eigenvalue problems depending on a parameter and subject to constraints the location of eigensolutions and subsequent parameters is achieved by means of the graph of the derivative of a function used also to compensate the lack of coercivity the applications concern one parameter families of semilinear elliptic eigenvalue problems with dirichlet boundary conditions for which various qualitative properties of the solution sets are established

geometrically exact thin walled beam including warping formulated on the special euclidean group se 3 abstract based on a formulation on the special euclidean group s e 3 a geometrically exact thin walled beam with an arbitrary open cross section is proposed to deal with the finite deformation and rotation issues the beam strains are based on a kinematic assumption where warping deformation and wagner effects are included such that the nonlinear behavior of a thin walled beam is predicted accurately particular under large torsion to reduce the nonlinearity of rigid motion static and dynamic equations are derived in the s e 3 framework based on the local frame approach as the value of the iteration matrix including the jacobian matrix of inertial and internal forces is invariable under arbitrary rigid motion the number of updates required during the computation process decreases sharply which drastically improves the computational efficiency furthermore the isogeometric analysis iga based on the non uniform rational b splines nurbs basis functions which promotes the integration of computer aided design cad and computer aided engineering cae is adopted to interpolate the displacement rotation and warping fields separately the interpolated strain measures satisfy the objectivity by removing the rigid motion of the reference point to obtain the symmetric jacobian matrix of internal forces the linearization operation is conducted based on the previously converged configuration a lie group s e 3 extension of the generalized time integration method is utilized to solve the equations of motion for thin walled beams finally the proposed formulation is successfully tested and validated in several static and dynamic numerical examples

pseudo rigid continua basic theory and a geometrical derivation of lagrange s equations pseudorigid bodies are regarded here as globally constrained threedimensional homogeneous continua the constraint reaction stresses play a fundamental role in maintaining the homogeneity of the de

nonlinear dynamical theory of the elastica the dynamical behaviour of a slender rod is analyzed here in terms of a generalization of euler s elastica theory the model includes a linear stress strain relation but nonlinear geometric terms properties of the rod may vary along its length and various boundary conditions are considered a rotational inertia term that is neglected in many theories is retained and is essential to the analysis by use of the equivalence of an energy and a sobolev norm and by reformulation of the equations as a semilinear system global existence of solutions is proved for any smooth initial data equilibrium solutions that are stable in the static sense of minimizing the potential energy are then proved to be stable in the dynamic sense due to liapounov

geometrically exact beam finite element formulated on the special euclidean group se 3 abstract this paper describes a dynamic formulation of a straight beam finite element in the setting of the special euclidean group se 3 first the static and dynamic equilibrium equations are derived in this framework from variational principles then a non linear interpolation formula using the exponential map is introduced it is shown that this framework leads to a natural coupling in the interpolation of the position and rotation variables next the discretized internal and inertia forces are developed the semi discrete equations of motion take the form of a second order ordinary differential equation on a lie group which is solved using a lie group time integration scheme it is remarkable that no parameterization of the nodal variables needs to be introduced and that the proposed lie group framework leads to a compact and easy to implement formulation some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed for instance the formulation leads to invariant tangent stiffness and mass matrices under rigid body motions and a locking free element the proposed formulation is successfully tested in several numerical static and dynamic examples

intrinsic representation of tangent vectors and vector transports on matrix manifolds the quasi newton methods on riemannian manifolds proposed thus far do not appear to lend themselves to satisfactory convergence analyses unless they resort to an isometric vector transport this prompts us to propose a computationally tractable isometric vector transport on the stiefel manifold of orthonormal p frames in mathbb r n rn specifically it requires o np 2 o np2 flops which is considerably less expensive than existing alternatives in the frequently encountered case where n gg p n p we then build on this result to also propose computationally tractable isometric vector transports on other manifolds namely the grassmann manifold the fixed rank manifold and the positive semidefinite fixed rank manifold in the process we also propose a convenient way to represent tangent vectors to these manifolds as elements of mathbb r d rd where d is the dimension of the manifold we call this an intrinsic representation as opposed to extrinsic representations as elements of mathbb r w rw where w is the dimension of the embedding space finally we demonstrate the performance of the proposed isometric vector transport in the context of a riemannian quasi newton method applied to minimizing the brockett cost function

quasilinear equations for viscoelasticity of strain rate type we consider the quasilinear m m system of partial differential equations that governs the motion of a viscoelastic material of strain rate type on a bounded domain in mathbb r n the dependence of the stress on both the strain and strain rate is nonlinear and our hypotheses allow for a potential energy which is a nonconvex function of the strain the critical hypothesis is that the dependence of the stress function on the strain rate is uniformly strictly monotone in the sense of minty and browder we prove the existence and uniqueness of weak solutions to a natural initial boundary value problem for a large class of constitutive functions we then treat the question of h2 regularity of solutions and show that while regularity in the initial data is preserved solutions do not in general become more regular than their initial data this generalizes a result for the semilinear case due to rybka

a variational characterization of a hyperelastic rod with hard self contact abstract we consider an elastic rod modeled as a curve in space with an impenetrable surrounding tube of radius subject to a general class of boundary conditions the impossibility of self intersection is then imposed as a family of scalar constraints on the physical separation of nonlocal pairs of points on the rod thus the usual variational formulation of energy minimization is considered in a context of nonconvex nonsmooth optimization we show the existence of minimizers within suitably defined homotopy classes associated with both the centerline and the frame along the rod the principle results are then concerned with derivation of first order necessary conditions for optimality and some consequences of these for the contact forces and for regularity

asymptotic mean and variance of gini correlation for bivariate normal samples this paper derives the asymptotic analytical forms of the mean and variance of the gini correlation gc with respect to samples drawn from bivariate normal populations the asymptotic relative efficiency are of the gini correlation to pearson s product moment correlation coefficient ppmcc is investigated under the normal assumptions to gain further insight into gc we also compare the gini correlation to other two closely related correlation coefficients namely the order statistics correlation coefficient oscc and spearman s rho sr theoretical and simulation results suggest that the performance of gc lies in between those of oscc and sr when estimating the correlation coefficient of the bivariate normal population the newly found theoretical results along with other desirable properties enable gc to be a useful alternative to the existing coefficients especially when one wants to make a trade off between the efficiency and robustness to monotone nonlinearity

mixed models and reduced selective integration displacement models for nonlinear analysis of curved beams simple mixed models are developed for the geometrically nonlinear analysis of deep arches a total lagrangian description of the arch deformation is used and the analytical formulation is based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included the fundamental unknowns consist of the six internal forces and generalized displacements of the arch and the element characteristic arrays are obtained by using hellinger reissner mixed variational principle the polynomial interpolation functions used in approximating the forces are one degree lower than those used for approximating the displacements and the forces are discontinuous at the interelement boundaries the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms is discussed the advantages of mixed models over equivalent displacement models are outlined numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and compare their performance with other mixed models reported in the literature

a justification of nonlinear properly invariant plate theories a single asymptotic derivation of three classical nonlinear plate theories is presented in a setting which preserves the frame invariance properties of three dimensional finite elasticity by a successive scaling of the external loading on the three dimensional body the nonlinear membrane theory the nonlinear inextensional theory and the von karman equations are derived as the leading order terms in the asymptotic expansion of finite elasticity the governing equations of the nonlinear inextensional theory are of particular interest where 1 plane strain kinematics and plane stress constitutive equations are derived simultaneously from the asymptotic analysis 2 the theory can be phrased as a minimization problem over the space of isometric deformations of a surface and 3 the local equilibrium equations are identical to those arising in the one director cosserat shell model furthermore it can be concluded that with a regular single scale asymptotic expansion it is not possible to obtain a system of plate equations in which finite membrane strain and finite bending strain occur simultaneously in the leading order term of an asymptotic analysis

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

constructing reference metrics on multicube representations of arbitrary manifolds reference metrics are used to define the differential structure on multicube representations of manifolds i e they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous this paper introduces a general procedure for constructing reference metrics automatically on multicube representations of manifolds with arbitrary topologies the method is tested here by constructing reference metrics for compact orientable two dimensional manifolds with genera between zero and five these metrics are shown to satisfy the gauss bonnet identity numerically to the level of truncation error which converges toward zero as the numerical resolution is increased these reference metrics can be made smoother and more uniform by evolving them with ricci flow this smoothing procedure is tested on the two dimensional reference metrics constructed here these smoothing evolutions using volume normalized ricci flow with deturck gauge fixing are all shown to produce reference metrics with constant scalar curvatures at the level of numerical truncation error

assessment of long range correlation in time series how to avoid pitfalls due to the ubiquity of time series with long range correlation in many areas of science and engineering analysis and modeling of such data is an important problem while the field seems to be mature three major issues have not been satisfactorily resolved i many methods have been proposed to assess long range correlation in time series under what circumstances do they yield consistent results ii the mathematical theory of long range correlation concerns the behavior of the correlation of the time series for very large times a measured time series is finite however how can we relate the fractal scaling break at a specific time scale to important parameters of the data iii an important technique in assessing long range correlation in a time series is to construct a random walk process from the data under the assumption that the data are like a stationary noise process due to the difficulty in determining whether a time series is stationary or not however one cannot be 100 sure whether the data should be treated as a noise or a random walk process is there any penalty if the data are interpreted as a noise process while in fact they are a random walk process and vice versa in this paper we seek to gain important insights into these issues by examining three model systems the autoregressive process of order 1 on off intermittency and l evy motions and considering an important engineering problem target detection within sea clutter radar returns we also provide a few rules of thumb to safeguard against misinterpretations of long range correlation in a time series and discuss relevance of this study to pattern recognition

equilibrium states of an elastic conducting rod in a magnetic field our principal concern is an analysis of the equilibrium states of a nonlinearly elastic conducting rod in a magnetic field we assume hyperelasticity so the equilibria formally appear as critical points of a potential energy functional on the strains fairly standard methods give existence of a minimum not necessarily unique with e g l2 regularity the assumptions imposed on the functional preclude the use of the usual techniques for justification of the formal necessary conditions for optimality a new general technique is developed to justify these conditions it then follows that minimizers satisfy the equilibrium conditions in the classical sense a feature of this technique is that the variations considered are homotopies so one can consider minimization within a homotopy class in the symmetric case which admits trivial straight and untwisted solutions we show that nontrivial solutions also exist if the field is strong enough

asymptotic behaviour and changes of phase in one dimensional nonlinear viscoelasticity in this paper we study the asymptotic behaviour as t co of solutions u x t to the nonlinear partial differential equation ut m4 a o o 1 1 with initial conditions u 0 q x u x u x o 0 1 3a