inconsistent estimation and asymptotically equal interpolations in model based geostatistics it is shown that in model based geostatistics not all parameters in the matern class can be estimated consistently if data are observed in an increasing density in a fixed domain regardless of the estimation methods used nevertheless one quantity can be estimated consistently by the maximum likelihood method and this quantity is more important to spatial interpolation the results are established by using the properties of equivalence and orthogonality of probability measures some sufficient conditions are provided for both gaussian and non gaussian equivalent measures and necessary conditions are provided for gaussian equivalent measures two simulation studies are presented that show that the fixed domain asymptotic properties can explain some finite sample behavior of both interpolation and estimation when the sample size is moderately large

non linear analysis of nearly saturated porous media theoretical and numerical formulation a formulation for a porous medium saturated with a compressible fluid undergoing large elastic and plastic deformations is presented a consistent thermodynamic formulation is proposed for the two phase mixture problem thus preserving a straightforward and robust numerical scheme a novel feature is the specification of the fluid compressibility in terms of a volumetric logarithmic strain which is energy conjugated to the fluid pressure in the entropy inequality as a result the entropy inequality is used to separate three different mechanisms representing the response effective stress response according to terzaghi in the solid skeleton fluid pressure response to compressibility of the fluid and dissipative darcy flow representing the interaction between the two phases the paper is concluded with a couple of numerical examples that display the predictive capabilities of the proposed formulation in particular we consider results for the kinematically linear theory as compared to the kinematically non linear theory

control of unstable steady states by extended time delayed feedback time delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states we present an application of extended time delay autosynchronization introduced by socolar et al phys rev e 50 3245 1994 to an unstable focus this system represents a generic model of an unstable steady state which can be found for instance in hopf bifurcation in addition to the original controller design we investigate effects of control loop latency and a bandpass filter on the domain of control furthermore we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase we present an analysis of the domain of control and support our results by numerical calculations

stabilization of partitioned solution procedure for pore fluid soil interaction analysis on montre que la solution decalee conventionnelle des problemes d interaction fluide sol dans les pores souffre de restrictions sur la stabilite on presente une forme stabilisee de la procedure de solution decalee de ce probleme on recommande cette procedure pour l implementation des problemes d interaction sol fluide

a fully coupled dynamic model for two phase fluid flow in deformable porous media abstract a fully coupled dynamic model is presented for the analysis of water and air flow in deforming porous media in fully or partially saturated conditions the solid displacements and the pressures of fluids are taken as primary unknowns of the model the finite element method is used for the discrete approximation of the partial differential equations governing the problem the mathematical framework and the numerical implementation of the model are given in detail and the adopted approximations are put into evidence first the model is validated with respect to documented experiments on partially saturated soil behaviour in quasi static condition then the results of a full dynamic analysis are shown and discussed in this paper merits and drawbacks of the proposed model are highlighted

analytical properties and optimization of time delayed feedback control time delayed feedback control is an efficient method for stabilizing unstable periodic orbits of chaotic systems if the equations governing the system dynamics are known the success of the method can be predicted by a linear stability analysis of the desired orbit unfortunately the usual procedures for evaluating the floquet exponents of such systems are rather intricate we show that the main stability properties of the system controlled by time delayed feedback can be simply derived from a leading floquet exponent defining the system behavior under proportional feedback control optimal parameters of the delayed feedback controller can be evaluated without an explicit integration of delay differential equations the method is valid for low dimensional systems whose unstable periodic orbits are originated from a period doubling bifurcation and is demonstrated for the rossler system and the duffing oscillator

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

algorithms for strong coupling procedures abstract this paper considers algorithms for computing the response of a coupled problem with a partitioned approach one important example treated here is fluid structure interaction fsi often procedures or even software exists to solve each sub problem separately and one wants to couple both this setting seems to allow only the so called weak coupling which is not sufficient for some problems the so called strong coupling is often a totally implicit formulation where the system components are evaluated at the same time level this usually requires an iterative procedure the fsi problem is cast as an abstract differential algebraic equation dae for which the coupling procedures are developed with the partitioned approach one simple and frequently used computational procedure is similar to a block gauss seidel iteration it is shown why this approach may experience difficulties and how they may be circumvented with newton like methods still staying in the partitioned framework the functional and software engineering requirements for the simulation interface are described and analysed some simple coupled example problems demonstrate how the proposed procedures work

unconditionally stable staggered solution procedure for soil pore fluid interaction problems this paper presents a simple procedure for modifying the dynamic coupled soil pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used the solution method is simpler than an alternative suggested by park15 and has a direct physical interpretation this stabilized procedure is efficient in numerical time domain analysis of soil pore fluid occurring in earthquake and consolidation problems numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure

stabilized low order finite elements for failure and localization problems in undrained soils and foundations abstract geomaterials in general and soils in particular are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water in the limit of zero compressibility of water and soil grains and zero permeability which correspond to the classical undrained assumption of soil mechanics the functions used to interpolate displacements and pressures must fulfill either the babuska brezzi conditions or the much simpler patch test proposed by zienkiewicz and taylor these requirements exclude the use of elements with equal order interpolation for pressures and displacements for which spurious oscillations may appear the simplest elements with continuous pressures which can be used in 2d are the quadratic triangle and quadrilateral with linear and bilinear pressures respectively the purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures t3p3 and bilinear quadrilaterals q4p4 the proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist

asymptotic theory of generalized information criterion for geostatistical regression model selection information criteria such as akaike s information criterion and bayesian information criterion are often applied in model selection however their asymptotic behaviors for selecting geostatistical regression models have not been well studied particularly under the fixed domain asymptotic framework with more and more data observed in a bounded fixed region in this article we study the generalized information criterion gic for selecting geostatistical regression models under a more general mixed domain asymptotic framework via uniform convergence developments of some statistics we establish the selection consistency and the asymptotic loss efficiency of gic under some regularity conditions regardless of whether the covariance model is correctly or wrongly specified we further provide specific examples with different types of explanatory variables that satisfy the conditions for example in some situations gic is selection consistent even when some spatial covariance parameters cannot be estimated consistently on the other hand gic fails to select the true polynomial order consistently under the fixed domain asymptotic framework moreover the growth rate of the domain and the degree of smoothness of candidate regressors in space are shown to play key roles for model selection

bifurcation analysis of a class of first order nonlinear delay differential equations with reflectional symmetry abstract we consider a general class of first order nonlinear delay differential equations ddes with reflectional symmetry and study completely the bifurcations of the trivial equilibrium under some generic conditions on the taylor coefficients of the dde our analysis reveals a hopf bifurcation curve terminating on a pitchfork bifurcation line at a codimension two takens bogdanov point in parameter space we compute the normal form coefficients of the reduced vector field on the centre manifold in terms of the taylor coefficients of the original dde and in contrast to many previous bifurcation analyses of ddes we also compute the unfolding parameters in terms of these coefficients for application purposes this is important since one can now identify the possible asymptotic dynamics of the dde near the bifurcation points by computing quantities which depend explicitly on the taylor coefficients of the original dde we illustrate these results using simple model systems relevant to the areas of neural networks and atmospheric physics and show that the results agree with numerical simulations

excitable systems with noise and delay with applications to control renewal theory approach we present an approach for the analytical treatment of excitable systems with noise induced dynamics in the presence of time delay an excitable system is modeled as a bistable system with a time delay while another delay enters as a control term taken after pyragas k pyragas phys lett a 170 421 1992 as a difference between the current system state and its state tau time units before this approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term

a consistent u p formulation for porous media with hysteresis this paper presents a continuum formulation based on the theory of porous media for the mechanics of liquid unsaturated porous media the hysteresis of the liquid retention model is carefully modelled including the derivation of the corresponding consistent tangent moduli the quadratic convergence of newton s method for solving the highly nonlinear system with an implicit finite element code is demonstrated a u p formulation is proposed where the time discretisation is carried out prior to the space discretisation in this way the derivation of all consistent moduli is fairly straightforward time integration is approximated with the theta and newmark s methods and hence the fully coupled nonlinear dynamics of porous media is considered it is shown that the liquid retention model requires also the consistent second order derivative for quadratic convergence some predictive simulations are presented illustrating the capabilities of the formulation in particular to the modelling of complex porous media behaviour

1d wave propagation in saturated viscous geomaterials improvement and validation of a fractional step taylor galerkin finite element algorithm abstract this paper tackles the numerical simulation of 1d wave propagation in saturated viscous porous media and especially in soil like geomaterials for this purpose an improved fractional step taylor galerkin algorithm is first formulated and then validated on the basis of a new analytical solution the algorithm based on a stress velocity pressure formulation of the hydro mechanical problem combines an explicit taylor galerkin method with a fractional time stepping while an accurate runge kutta type integrator is introduced to treat the viscosity of the porous skeleton the overall algorithm results in an efficient stabilized scheme allowing for linear equal interpolation of field variables even when the so called undrained incompressible limit is approached the accuracy and stability of the method are verified with reference to a 1d benchmark problem concerning the propagation of p waves along a saturated viscoelastic soil stratum for this problem a frequency domain analytical solution is derived assuming incompressible interstitial fluid and soil grains the assumption of maxwell viscoelastic soil skeleton is analytically convenient to preserve the linearity of the problem while the same rheology of a more realistic elasto viscoplastic non linear behaviour is maintained the performance of the fractional step taylor galerkin algorithm is explored simulating the dynamic response of the stratum to harmonic impulsive and seismic input excitations in particular parametric analyses are performed to confirm the effectiveness of the method in reproducing fully undrained responses as well as in dealing with weakly viscous materials

stabilized mixed finite element formulations for materially nonlinear partially saturated two phase media standard and enhanced bbar or eas low order finite elements applied to the problem of consolidation of two phase nonlinear continua do not satisfy the lbb condition when the same interpolation functions are used for both displacement and pore pressure fields strong spatial pressure oscillations are the main consequence of the lbb condition violation the class of direct stabilized methods widely used in the field of fluid mechanics is a powerful tool to circumvent violation of the aforementioned condition three stabilized formulations designed for the problem of consolidation of fully or partially saturated media are presented galerkin least squares gls with the least squares term construction based on the residuum of the local fluid mass conservation equation the pressure stabilized formulation fpl in which the rate of the pore pressure laplacian residual free in the incompressibility limit is added to the fluid mass conservation equation and finally a stabilized formulation in which the stabilization term is constructed based on the rate of the residuum of the local momentum equation an h convergence study and test problems for the three stabilized schemes are discussed

correlation theory of delayed feedback in stochastic systems below andronov hopf bifurcation here we address the effect of large delay on the statistical characteristics of noise induced oscillations in a nonlinear system below andronov hopf bifurcation in particular we introduce a theory of these oscillations that does not involve the eigenmode expansion and can therefore be used for arbitrary delay time in particular we show that the correlation matrix cm oscillates on two different time scales on the scale of the main period of noise induced oscillations and on the scale close to the delay time at large values of the delay time the cm is shown to decay exponentially only for large values of its argument while for the arguments comparable with the value of the delay the cm remains finite disregarding the delay time the definition of the correlation time of the system with delay is discussed

von neumann stability analysis of biot s general two dimensional theory of consolidation von neumann stability analysis is performed for a galerkin finite element formulation of biot s consolidation equations on two dimensional bilinear elements two dimensionless groups the time factor and void factor are identified and these quantities along with the time integration weighting are used to explore the stability implications for variations in physical property and discretization parameters the results show that the presence and persistence of stable spurious oscillations in the pore pressure are influenced by the ratio of time step size to the square of the space step for fixed time integration weightings and physical property selections in general increasing the time step or decreasing the mesh spacing has a smoothing effect on the discrete solution however special cases exist that violate this generality which can be readily identified through the von neumann approach the analysis also reveals that explicitly dominated schemes are not stable for saturated media and only become possible through a decoupling of the equilibrium and continuity equations in the case of unsaturated media a break down in the von neumann results has been shown to occur due to the influence of boundary conditions on stability 1998 john wiley sons ltd

linear smoothers and additive models we study linear smoothers and their use in building nonparametric regression models in the first part of this paper we examine certain aspects of linear smoothers for scatterplots examples of these are the running mean and running line kernel and cubic spline smoothers the eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother and several other topics such as the number of degrees of freedom of a smoother are discussed in the second part of the paper we describe how linear smoothers can be used to estimate the additive model a powerful nonparametric regression model using the backfitting algorithm we show that backfitting is the gauss seidel iterative method for solving a set of normal equations associated with the additive model we provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers

conversion of stability in systems close to a hopf bifurcation by time delayed coupling we propose a control method with time delayed coupling which makes it possible to convert the stability features of systems close to a hopf bifurcation we consider two delay coupled normal forms for hopf bifurcation and demonstrate the conversion of stability i e an interchange between the sub and supercritical hopf bifurcation the control system provides us with an unified method for stabilizing both the unstable periodic orbit and the unstable steady state and reveals typical effects like amplitude death and phase locking the main method and the results are applicable to a wide class of systems showing hopf bifurcations for example the van der pol oscillator the analytical theory is supported by numerical simulations of two delay coupled van der pol oscillators which show good agreement with the theory

dynamic fundamental solutions for compressible and incompressible modeled poroelastic continua abstract in a two phase material not only each constituent the solid and the fluid may be compressible on the microscopic level but also the skeleton itself possesses a structural compressibility if the compression modulus of a constituent is much larger than the compression modulus of the bulk material this constituent is assumed to be materially incompressible a common example is soil governing equations for such materials are found in the framework of biot s theory either for the unknowns solid displacement and pore pressure or for the unknowns solid displacement and fluid displacement for both formulations fundamental solutions are derived using the method of hormander unlike the u i s p formulation where the incompressible model can be obtained applying a limiting procedure directly to the compressible system of equations a complete new derivation is necessary for the u i s u i f formulation this yields a model of incompressibility different from that of the u i s p formulation which seems to be not suitable for poroelastodynamic problems

a mathematical framework for finite strain elastoplastic consolidation part 1 balance laws variational formulation and linearization a mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented strong and weak forms of the boundary value problem are derived using both the material and spatial descriptions the algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the kirchhoff pore water pressure balance laws are written for the soil water mixture following the motion of the soil matrix alone it is shown that the motion of the fluid phase only affects the jacobian of the solid phase motion and therefore can be characterized completely by the motion of the soil matrix furthermore it is shown from energy balance consideration that the effective or intergranular stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil water mixture finally it is shown that the mathematical model is amenable to consistent linearization and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method

comparison of monolithic and splitting solution schemes for dynamic porous media problems 5 summary proceeding from the governing equations describing a saturated poroelastic material with intrinsically 7 incompressible solid and fluid constituents we compare the monolithic and splitting solution of the different multi field formulations feasible in porous media dynamics because of the inherent solid fluid momentum 9 interactions one is concerned with the class of volumetrically coupled problems involving a potentially strong coupling of the momentum equations and the algebraic incompressibility constraint here the 11 resulting set of differential algebraic equations dae is solved by the finite element method fem following two different strategies 1 an implicit monolithic approach where the equations are first 13 discretized in space using stable mixed finite elements and second in time using stiffly accurate implicit time integrators 2 a semi explicit implicit splitting scheme in the sense of a fractional step method 15 where the dae are first discretized in time split using intermediate variables and then discretized in space using linear equal order approximations for all primary unknowns finally a one and a two dimensional 17 wave propagation example serve to reveal the pros and cons in regard to accuracy and stability of both solution strategies therefore several test cases differing in the used multi field formulation the 19 monolithic time stepping method and the approximation order of the individual unknowns are analyzed for varying degrees of coupling controlled by the permeability parameter in the end we provide a 21 reliable recommendation which of the presented strategies and formulations is the most suitable for which particular dynamic porous media problem copyright q 2009 john wiley sons ltd 23

thermomechanical response of solids at high strains natural approach abstract the paper develops in pursuance of 4 the theoretical framework appertaining to coupled thermomechanical deformations of solids subject to large as well as inelastic deformations the essential feature of the analysis is a consistent natural formulation which encompasses also all thermodynamic aspects on the other hand it must be admitted that current concepts on mechanical constitutive assumptions 5 6 are not sufficiently sophisticated to permit a precise generalisation for the purpose of incorporating thermomechanical effects and delivering a fully compatible theory of the coupled problem uniqueness and bifurcation of the solutions as well as stable postcritical deformation paths are also considered in this account furthermore algorithms for the solution of the nonlinear algebraic equations representing the discretised problem and in particular quasi newton techniques are discussed the paper concludes with a number of applications of technical relevance

beyond the odd number limitation a bifurcation analysis of time delayed feedback control we investigate the normal form of a subcritical hopf bifurcation subjected to time delayed feedback control bifurcation diagrams which cover time dependent states as well are obtained by analytical means the computations show that unstable limit cycles with an odd number of positive floquet exponents can be stabilized by time delayed feedback control contrary to incorrect claims in the literature the model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means

stability analysis of finite difference schemes revisited a study of decoupled solution strategies for coupled multifield problems summary many problems in engineering physics or other disciplines require an integrated treatment of coupled heterogeneous fields the mathematical models of such problems commonly consist of a coupled pde system considerable progress has been made in the development of schemes to solve such systems resulting in a wide spectrum of monolithic and decoupled numerical solution approaches in particular the flexibility offered by the decoupled strategies in choosing appropriate solution methods and adjustable time step sizes has motivated the elaboration of these schemes however the way of decoupling can influence the stability of the resulting solution algorithm and hence urges a comprehensive stability analysis the purpose of this contribution is to elucidate the salient points in the stability analysis of the numerical solution schemes to this end we introduce a general framework for the stability analysis of solution strategies and provide an easy to use procedure to find the necessary stability condition the procedure is tested against decoupled solution strategies for volume and surface coupled problems namely thermoelastodynamics porous media dynamics and fluid and structure structure interaction in this context the influence of explicit and implicit predictors and the sequence of the time integration on the stability condition is carefully examined copyright 2013 john wiley sons ltd

optimal geostatistical model selection in many fields of science predicting variables of interest over a study region based on noisy data observed at some locations is an important problem two popular methods for the problem are kriging and smoothing splines the former assumes that the underlying process is stochastic whereas the latter assumes it is purely deterministic kriging performs better than smoothing splines in some situations but is outperformed by smoothing splines in others however little is known regarding selecting between kriging and smoothing splines in addition how to perform variable selection in a geostatistical model has not been well studied in this article we propose a general methodology for selecting among arbitrary spatial prediction methods based on approximately unbiased estimation of mean squared prediction errors using a data perturbation technique the proposed method accounts for estimation uncertainty in both kriging and smoothing spline predictors and is shown to be optimal in terms of two mean sq

calibrating the degrees of freedom for automatic data smoothing and effective curve checking curve fitting and curve checking based on the local polynomial regression technique are commonly used data analytic methods in statistics this article examines in nonparametric settings both the asymptotic expressions and empirical formulas for degrees of freedom df a notion introduced by hastie and tibshirani of linear smoothers the asymptotic results give useful insights into the nonparametric modeling complexity meanwhile by substituting the exact dfs by the empirical formula an empirical version of the generalized cross validation egcv is obtained an automatic bandwidth selection method based on minimizing egcv is proposed for conducting local smoothing this procedure preserves full benefits of the ordinary and generalized cross validation but offers a substantial reduction in computational burden furthermore the egcv minimizing bandwidth can be extended in a very simple manner to fit multivariate models such as the varying coefficient models applications of calibrating dfs to impo

on global properties of time delayed feedback control weakly nonlinear analysis we address the problem which type of initial state yields successful stabilisation when time delayed feedback control is applied using well known concepts from bifurcation theory we provide a general mechanism that limits the corresponding basins of attraction application of normal form analysis to general delay differential equations proves the universality of our results the empirical criteria which determine the prospective size of the basin are easily accessible and a demonstration in terms of a simple numerical simulation is provided

smoothing spline models with correlated random errors abstract spline smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model their performances depend greatly on the choice of smoothing parameters many methods of selecting smoothing parameters such as generalized maximum likelihood gml generalized cross validation gcv and unbiased risk ubr have been developed under the assumption of independent observations they tend to underestimate smoothing parameters when data are correlated in this article i assume that observations are correlated and that the correlation matrix depends on a parsimonious set of parameters i extend the gml gcv and ubr methods to estimate the smoothing parameters and the correlation parameters simultaneously i also relate a smoothing spline model to three mixed effects models these relationships show that the smoothing spline estimates evaluated at design points are best linear unbiased prediction blup estimates and that the gml estimates of the smoothing parameters an

a new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems abstract in order to accurately model the behaviour of geostructures it is usually not possible to neglect the interaction between the soil skeleton and the pore fluid classical finite element models taking into account this interaction are formulated in terms of the displacement and pore pressure fields and are based on the assumption that the fluid acceleration relative to the soil skeleton is negligible this type of mixed problems is similar to others found in solid and fluid mechanics and might give rise to numerical instabilities unless certain requirements are met there are two classical approaches to this problem the first is usually known as the zienkiewicz taylor patch test for mixed formulations as a consequence of this test the interpolation degree of the displacement field is required to be higher than the corresponding one of the pressure field mathematically speaking this is a necessary condition for stability the second approach mathematically more involved is usually known as the bab ska brezzi inf sup condition and constitutes a sufficient condition for stability however it is possible to obtain stable formulations circumventing the interpolation degree requirement through the so called stabilization techniques these techniques were initially applied in the context of fluid mechanics and later extended to solid mechanics this article presents a new formulation in which stabilization is achieved through an approach based on the simo rifai enhanced strain element

a cucker smale model with noise and delay a generalization of the cucker smale model for collective animal behavior is investigated the model is formulated as a system of delayed stochastic differential equations it incorporates two additional processes which are present in animal decision making but are often neglected in modeling i stochasticity imperfections of individual behavior and ii delayed responses of individuals to signals in their environment sufficient conditions for flocking for the generalized cucker smale model are derived by using a suitable lyapunov functional as a by product a new result regarding the asymptotic behavior of delayed geometric brownian motion is obtained in the second part of the paper results of systematic numerical simulations are presented they not only illustrate the analytical results but hint at a somehow surprising behavior of the system namely that the introduction of an intermediate time delay may facilitate flocking

time delay autosynchronization of the spatiotemporal dynamics in resonant tunneling diodes the double barrier resonant tunneling diode exhibits complex spatiotemporal patterns including low dimensional chaos when operated in an active external circuit we demonstrate how autosynchronization by time delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way we compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom the numerically obtained floquet exponents are explained by analytical results from linear stability analysis

formulation of implicit finite element methods for multiplicative finite deformation plasticity some constitutive and computational aspects of finite deformation plasticity are discussed attention is restricted to multiplicative theories of plasticity in which the deformation gradients are assumed to be decomposable into elastic and plastic terms it is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non symmetric even for associated plastic flow both explicit i e no equilibrium iteration and implicit finite element formulations are considered an assumed strain formulation is used to accommodate the near incompressibility associated with fully developed isochoric plastic flow as an example of explicit integration the rate tangent modulus method is reviewed in some detail an implicit scheme is derived for which the consistent tangents resulting in quadratic convergence of the equilibrium iterations can be written out in closed form for arbitrary material models all the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method

some basic remarks on eigenmode expansions of time delay dynamics abstract we describe in elementary terms how eigenmode expansions can be used to deal with differential difference equations as particular applications we present the full analytical solution of linear stochastic time delay systems and the weakly nonlinear analysis of nonlinear differential difference equations in the limit of large time delay our exposition is essentially based on an explicit analytical expression for the linear spectrum in terms of the lambert w function and on the explicit formula for the eigenfunctions of the adjoint equation

extension of hencky bar net model for vibration analysis of rectangular plates with rectangular cutouts abstract comprising rigid bars and spring systems at the joints and in the cells the hencky bar net model hbm has been shown to be a physical structural representation of the finite difference plate model fdm in this paper the hbm is extended for the vibration analysis of rectangular plates with rectangular cutouts this extension addresses the rotationally elastic and transverse spring stiffnesses for the hbm at the cutout corners after verifying the hbm model by comparing the vibration results with existing solutions for some plate problems the model is used to obtain some new free vibration solutions for plates having various boundary conditions including cracked corners modelled by free small rectangular cutouts

elastoplastic consolidation at finite strain part 2 finite element implementation and numerical examples a mathematical model for finite strain elastoplastic consolidation of fully saturated soil media is implemented into a finite element program the algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the kirchhoff pore water pressure a two field mixed finite element formulation is employed in which the nodal solid displacements and the nodal pore water pressures are coupled via the linear momentum and mass balance equations the constitutive model for the solid phase is represented by modified cam clay theory formulated in the kirchhoff principal stress space and return mapping is carried out in the strain space defined by the invariants of the elastic logarithmic principal stretches the constitutive model for fluid flow is represented by a generalized darcy s law formulated with respect to the current configuration the finite element model is fully amenable to exact linearization numerical examples with and without finite deformation effects are presented to demonstrate the impact of geometric nonlinearity on the predicted responses the paper concludes with an assessment of the performance of the finite element consolidation model with respect to accuracy and numerical stability

partitioned procedures for the transient solution of coupled aroelastic problems part i model problem theory and two dimensional application abstract in order to predict the dynamic response of a flexible structure in a fluid flow the equations of motion of the structure and the fluid must be solved simultaneously in this paper we present several partitioned procedures for time integrating this focus coupled problem and discuss their merits in terms of accuracy stability heterogeneous computing i o transfers subcycling and parallel processing all theoretical results are derived for a one dimensional piston model problem with a compressible flow because the complete three dimensional aeroelastic problem is difficult to analyze mathematically however the insight gained from the analysis of the coupled piston problem and the conclusions drawn from its numerical investigation are confirmed with the numerical simulation of the two dimensional transient aeroelastic response of a flexible panel in a transonic non linear euler flow regime

chaotic attractors of an infinite dimensional dynamical system abstract we study the chaotic attractors of a delay differential equation the dimension of several attractors computed directly from the definition agrees to experimental resolution with the dimension computed from the spectrum of lyapunov exponents according to a conjecture of kaplan and yorke assuming this conjecture to be valid as the delay parameter is varied from computations of the spectrum of lyapunov exponents we observe a roughly linear increase from two to twenty in the dimension while the metric entropy remains roughly constant these results are compared to a linear analysis and the asymptotic behavior of the lyapunov exponents is derived

towards reconciling two asymptotic frameworks in spatial statistics summary two asymptotic frameworks increasing domain asymptotics and infill asymptotics have been advanced for obtaining limiting distributions of maximum likelihood estimators of covariance parameters in gaussian spatial models with or without a nugget effect these limiting distributions are known to be different in some cases it is therefore of interest to know for a given finite sample which framework is more appropriate we consider the possibility of making this choice on the basis of how well the limiting distri butions obtained under each framework approximate their finite sample counterparts we investigate the quality of these approximations both theoretically and empirically showing that for certain consistently estimable parameters of exponential covariograms approximations corresponding to the two frameworks perform about equally well for those parameters that cannot be estimated consistently however the infill asymptotic approximation is preferable

estimating space and space time covariance functions for large data sets a weighted composite likelihood approach in this article we propose two methods for estimating space and space time covariance functions from a gaussian random field based on the composite likelihood idea the first method relies on the maximization of a weighted version of the composite likelihood function while the second one is based on the solution of a weighted composite score equation this last scheme is quite general and could be applied to any kind of composite likelihood an information criterion for model selection based on the first estimation method is also introduced the methods are useful for practitioners looking for a good balance between computational complexity and statistical efficiency the effectiveness of the methods is illustrated through examples simulation experiments and by analyzing a dataset on ozone measurements

analysis of the block gauss seidel solution procedure for a strongly coupled model problem with reference to fluid structure interaction the block gauss seidel procedure is widely used for the resolution of the strong coupling in the computer simulation of fluid structure interaction based on a simple model problem this work presents a detailed analysis of the convergence behaviour of the method in particular the model problem is used to highlight some aspects that arise in the context of the application of the block gauss seidel method to fsi problems thus the effects of the time integration schemes chosen of relaxation techniques of physical constraints and non linearities on the convergence of the iterations are investigated

fdm solutions to linear dynamics of porous media efficiency stability and parallel solution strategy summary this paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation the method is named parallel lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel computations as a result the complexity and the bandwidth of the global matrix are significantly reduced and hence the efficiency is improved the other advantage of the scheme is the fulfilment of the inf sup stability condition the scheme is developed to solve porous media formulations derived from the theory of porous media both the u p and u v p formulations are considered u displacement of solid p pressure of liquid and v velocity of liquid several simulations are performed to demonstrate the capabilities of the method

dynamics of porous media at finite strain we present a finite element model for the analysis of a mechanical phenomenon involving dynamic expulsion of fluids from a fully saturated porous solid matrix in the regime of large deformation momentum and mass conservation laws are written in lagrangian form by a pull back from the current configuration to the reference configuration following the solid matrix motion a complete formulation based on the motion of the solid and fluid phases is first presented then approximations are made with respect to the material time derivative of the relative flow velocity vector to arrive at a so called v p formulation which is subsequently implemented in a finite element model we show how the resulting finite element matrix equations can be consistently linearized using a compressible neo hookean hyperelastic material with a kelvin solid viscous enhancement for the solid matrix as a test function for the nonlinear constitutive model numerical examples are presented demonstrating the significance of large deformation effects on the transient dynamic responses of porous structures as well as the strong convergence profile exhibited by the iterative algorithm

analytical and numerical investigations of the phase locked loop with time delay we derive the normal form for the delay induced hopf bifurcation in the first order phase locked loop with time delay by the multiple scaling method the resulting periodic orbit is confirmed by numerical simulations further detailed numerical investigations demonstrate exemplarily that this system reveals a rich dynamical behavior with phase portraits fourier analysis and lyapunov spectra it is possible to analyze the scaling properties of the control parameter in the period doubling scenario both qualitatively and quantitatively within the numerical accuracy there is evidence that the scaling constant of the time delayed phase locked loop coincides with the feigenbaum constant delta approximately 4 669 in one dimensional discrete systems

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

on measuring and correcting the effects of data mining and model selection abstract in the theory of linear models the concept of degrees of freedom plays an important role this concept is often used for measurement of model complexity for obtaining an unbiased estimate of the error variance and for comparison of different models i have developed a concept of generalized degrees of freedom gdf that is applicable to complex modeling procedures the definition is based on the sum of the sensitivity of each fitted value to perturbation in the corresponding observed value the concept is nonasymptotic in nature and does not require analytic knowledge of the modeling procedures the concept of gdf offers a unified framework under which complex and highly irregular modeling procedures can be analyzed in the same way as classical linear models by using this framework many difficult problems can be solved easily for example one can now measure the number of observations used in a variable selection process different modeling procedures such as a tree based regression and a

exact dynamics of stochastic linear delayed systems application to spatiotemporal coordination of comoving agents delayed dynamics result from finite transmission speeds of a signal in the form of energy mass or information in stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic oscillatory and unstable evolution despite the vast literature quantifying this rich behavior is limited by a lack of explicit analytic studies of high dimensional stochastic delay systems here we fill this gap for systems governed by a linear langevin equation of any number of delays and spatial dimensions with additive gaussian noise by exploiting laplace transforms we are able to derive an exact time dependent analytic solution of the langevin equation by using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables as an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment we propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay we highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and or in their spatial separation we also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay

multiple scale analysis of delayed dynamical systems abstract the model equations of a semiconductor laser with delayed feeback are studied as a prototype of general delayed systems in the case of long delay thermodynamic limit it is shown that its behaviour in the vicinity of the hopf bifurcation can be described by suitable amplitude equations the derivation of the final model follows naturally from the space time representation of the evolution and by the corresponding re formulation of the linear stability problem regions characterized by both direct and inverse hopf bifurcations are found and in particular parameter values are identified for which a chaotic evolution is expected

a space time multiscale method for computing statistical moments in strongly heterogeneous poroelastic media of evolving scales summary a new multiscale procedure is proposed to compute flow in compressible heterogeneous porous media with geology characterized by power law covariance structure at the fine scale the deformable medium is modeled by the partially coupled formulation of poroelasticity with young s modulus and permeability treated as stationary random fields represented by their karhunen loeve decompositions the framework underlying the multiscale procedure is based on mapping these random parameters to an auxiliary domain and constructing a family of equivalent stochastic processes at different length scales characterized by the same ensemble mean and covariance function the poromechanical variables inherit a space time version of the scaling relations of the random input parameters which allows for constructing a set of multiscale solutions of the same governing equations posed at different space and time scales a notable feature of the multiscale method proposed herein is the feasibility of solving both the poroelastic model and the fredholm integral equation for the eigenpairs of the karhunen loeve expansion in an auxiliary domain with much lower computational effort and then derive the long term behavior at a coarser scale from a straightforward rescaling of the auxiliary solution within the framework of the finite element approximation in conjunction with the monte carlo algorithm numerical simulations of fluid withdrawal and injection problems in a heterogeneous poroelastic reservoir are performed to illustrate the potential of the method in drastically reducing the computational burden in the computation of the statistical moments of the poromechanical unknowns in large scale simulations copyright 2012 john wiley sons ltd

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

functional characterization of linear delay langevin equations we present an exact functional characterization of linear delay langevin equations driven by any noise structure defined through its characteristic functional this method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise general properties of the transient dissipative dynamics are analyzed the corresponding interplay with a color gaussian noise is presented as a full application of our functional method we study a model for population growth with non gaussian fluctuations the gompertz model driven by multiplicative white shot noise

implicit dynamic three dimensional finite element analysis of an inelastic biphasic mixture at finite strain part 1 application to a simple geomaterial abstract based on the mixture theory formulation for a fluid saturated inelastic pressure sensitive porous solid subjected to dynamic large strain deformation a 3d finite element implementation with implicit time integration is presented a recently published 2d implementation li et al 2004 cmame v193 p3837 70 is extended to 3d porosity dependent permeability and pressure sensitive inelastic solid skeleton response at finite strain the clausius duhem inequality provides the form of the constitutive equations for the solid and fluid phases as well as the dissipation function a non associative drucker prager cap plasticity model at finite strain is formulated based on a multiplicative decomposition of the deformation gradient and numerically integrated semi implicitly in the intermediate configuration to avoid questions of incremental objectivity the elastic implementation is verified with available 1d analytical and 2d benchmark problems new numerical solutions for 3d large strain dynamic behavior of saturated inelastic porous media are presented the computational efficiency of the implemented formulation in achieving quadratic convergence is illustrated

information transfer between incompatible finite element meshes application to coupled thermo viscoelasticity this article is concerned with information transfer between non matching finite element meshes such a feature is not new in the literature but we focus herein on a geometric approach to transfer solution fields in order to be as application independent as possible moreover the dedicated case concerns the transfer of finite element fields defined at integration points of the meshes and allows iterative exchange of fields in both directions to do so we propose an extension to the mortar technique that fulfills these goals and that does not suffer from a high computational cost the application is the simulation of a strongly coupled thermo viscoelastic problem with phase transition solved with a partitioning technique

variable selection for binary spatial regression penalized quasi likelihood approach we consider the problem of selecting covariates in a spatial regression model when the response is binary penalized likelihood based approach is proved to be effective for both variable selection and estimation simultaneously in the context of a spatially dependent binary variable an uniquely interpretable likelihood is not available rather a quasi likelihood might be more suitable we develop a penalized quasi likelihood with spatial dependence for simultaneous variable selection and parameter estimation along with an efficient computational algorithm the theoretical properties including asymptotic normality and consistency are studied under increasing domain asymptotics framework an extensive simulation study is conducted to validate the methodology real data examples are provided for illustration and applicability although theoretical justification has not been made we also investigate empirical performance of the proposed penalized quasi likelihood approach for spatial count data to explore suitability of this method to a general exponential family of distributions

the signal extraction approach to nonlinear regression and spline smoothing abstract this article shows how to fit a smooth curve polynomial spline to pairs of data values yi xi prior specification of a parametric functional form for the curve is not required the resulting curve can be used to describe the pattern of the data and to predict unknown values of y given x both point and interval estimates are produced the method is easy to use and the computational requirements are modest even for large sample sizes our method is based on maximum likelihood estimation of a signal in noise model of the data we use the kalman filter to evaluate the likelihood function and achieve significant computational advantages over previous approaches to this problem

finite element analysis of poro elastic consolidation in porous media standard and mixed approaches abstract in this paper two different numerical approaches for consolidation in porous media are developed and thoroughly compared galerkin finite element method gfem and least squares mixed finite element methods ls mfem the primary variables of the gfem are fluid pressure and solid displacement fluid fluxes and stresses are derived quantities in the ls mfem method all four unknown functions are primary variables which results in more accurate approximations of fluid fluxes and stresses results of both numerical methods are compared for two examples the first example for which an analytical solution is known is used in order to verify the implementation of the numerical schemes in the second example for a footing problem which was proposed by murad et al m murad v thomee a loula asymptotic behavior of semidiscrete finite element approximations of biot s consolidation problem siam j numer anal 33 1996 1065 1083 a detailed numerical analysis and comparison of both schemes are presented

optimal model assessment selection and combination central to statistical theory and application is statistical modeling which typically involves choosing a single model or combining a number of models of different sizes and from different sources whereas model selection seeks a single best modeling procedure model combination combines the strength of different modeling procedures in this article we look at several key issues and argue that model assessment is the key to model selection and combination most important we introduce a general technique of optimal model assessment based on data perturbation thus yielding optimal selection in particular model selection and combination from a frequentist perspective we advocate model combination over a selected subset of modeling procedures because it controls bias while reducing variability hence yielding better performance in terms of the accuracy of estimation and prediction to realize the potential of model combination we develop methodologies for determining the optimal tuning parameter such

a monolithic approach to fluid structure interaction using space time finite elements abstract the paper presents a simultaneous solution procedure for fluid structure interaction problems the structural motion is described by geometrically nonlinear elastodynamics the fluid is modeled by the incompressible navier stokes equations the space time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure in order to enforce momentum conservation and geometric continuity at the interface a weighted residual formulation of coupling conditions is introduced the discretized model equations for fluid structure and coupling conditions are formulated in a single equation system the nonlinear system and the fluid mesh movement are solved in a single iteration loop two dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology

on the eigenvalue spectrum for time delayed floquet problems abstract a linear homogeneous scalar differential difference equation with harmonic time dependence is investigated the associated eigenvalue problem is solved in terms of a continued fraction expansion for the characteristic equation the dependence of the largest eigenvalue on the system parameters being relevant for stability of periodic states in delay systems is discussed in detail the competition between the two timescales the delay and the external period cause intricate structures the result suggests features to improve control of chaos by time delayed feedback schemes with time dependent control amplitudes

additive model building for spatial regression summary spatial regression is an important predictive tool in many scientific applications and an additive model provides a flexible regression relationship between predictors and a response variable we develop a regularized variable selection technique for building a spatial additive model we find that the methods developed for independent data do not work well for spatially dependent data this motivates us to propose a spatially weighted error norm with a group lasso type of penalty to select additive components in spatial additive models we establish the selection consistency of the approach proposed where the penalty parameter depends on several factors such as the order of approximation of additive components characteristics of the spatial weight and spatial dependence an extensive simulation study provides a vivid picture of the effects of dependent data structure and choice of a spatial weight on selection results as well as the asymptotic behaviour of the estimators as an illustrative example the method is applied to lung cancer mortality data over the period of 2000 2005 obtained from the surveillance epidemiology and end results programme national cancer institute usa

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

maximum likelihood estimation of models for residual covariance in spatial regression we describe the maximum likelihood method for fitting the linear model when residuals are correlated and when the covariance among the residuals is determined by a parametric model containing unknown parameters observations are assumed to be gaussian we give conditions which ensure consistency and asymptotic normality of the estimators our main concern is with the analysis of spatial data and in this context we describe some simulation experiments to assess the small sample behaviour of estimators we also discuss an application of the spectral approximation to the likelihood for processes on a lattice

adaptive model selection most model selection procedures use a fixed penalty penalizing an increase in the size of a model these nonadaptive selection procedures perform well only in one type of situation for instance bayesian information criterion bic with a large penalty performs well for small models and poorly for large models and akaike s information criterion aic does just the opposite this article proposes an adaptive model selection procedure that uses a data adaptive complexity penalty based on a concept of generalized degrees of freedom the proposed procedure combining the benefit of a class of nonadaptive procedures approximates the best performance of this class of procedures across a variety of different situations this class includes many well known procedures such as aic bic mallows s cp and risk inflation criterion ric the proposed procedure is applied to wavelet thresholding in nonparametric regression and variable selection in least squares regression simulation results and an asymptotic

computing unstable manifolds of periodic orbits in delay differential equations we present the first algorithm for computing unstable manifolds of saddle type periodic orbits with one unstable floquet multiplier in systems of autonomous delay differential equations ddes with one fixed delay specifically we grow the one dimensional unstable manifold wu q of an associated saddle fixed point q of a poincare map defined by a suitable poincare section starting close to q along the linear approximation to wu q given by the associated eigenfunction our algorithm grows the manifold as a sequence of points where the distance between points is governed by the curvature of the one dimensional intersection curve wu q of wu q with our algorithm makes it possible to study global bifurcations in ddes we illustrate this with the break up of an invariant torus and a subsequent crisis bifurcation to chaos in a dde model of a semiconductor laser with phase conjugate feedback

space representation of stochastic processes with delay we show that a time series x t evolving by a nonlocal update rule x t f x t ensuremath n x t ensuremath k with two different delays kln can be mapped onto a local process in two dimensions with special time delayed boundary conditions provided that n and k are coprime for certain stochastic update rules exhibiting a nonequilibrium phase transition this mapping implies that the critical behavior does not depend on the short delay k in these cases the autocorrelation function of the time series is related to the critical properties of the corresponding two dimensional model

fokker planck perspective on stochastic delay systems exact solutions and data analysis of biological systems stochastic delay systems with additive noise are examined from the perspective of fokker planck equations for a linear system the exact stationary probability density is derived by means of a delay fokker planck equation we show how to determine the delay equation of the linear system from experimental data and corroborate a fundamental result previously obtained by kuchler and mensch we also propose a method to derive delay equations of nonlinear systems from experimental data to this end the theory of multivariate fokker planck equations is used the applicability of this method is demonstrated for stochastic models describing tracking and pointing movements of humans

formulation and finite element implementation of a multiplicative model of coupled poro plasticity at finite strains under fully saturated conditions in this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro plasticity fully saturated conditions are assumed the model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts together with an additive elastoplastic decomposition of the fluid content the final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation the particular case of an associated drucker prager model in effective stresses is considered as a model example a complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate we describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem finally we present representative numerical simulations to illustrate the features of the proposed models in particular the case of strain localization in globally undrained conditions is studied in the proposed framework