a note on the unification of the akaike information criterion to measure the distance between a robust function evaluated under the true regression model and under a fitted model we propose generalized kullback leibler information using this generalization we have developed three robust model selection criteria aicr aiccr and aiccr that allow the selection of candidate models that not only fit the majority of the data but also take into account non normally distributed errors the aicr and aiccr criteria can unify most existing akaike information criteria three examples of such unification are given simulation studies are presented to illustrate the relative performance of each criterion

dynamics of evolving surfaces with small corner energy regularization to overcome the backward parabolic behavior of geometric evolution laws based on non convex interfacial energies a corner energy regularization is used anisotropic mean curvature flow and surface diffusion are addressed with such a regularization term in one space dimension the resulting problems are fourth respectively sixth order a long wave approximation is performed for both equations resulting in the cahn hilliard equation for the fourth order problem and a higher order cahn hilliard equation for the sixth order problem 2005 elsevier ltd all rights reserved msc 35k55 65m12 65m15 65m60

improved estimators of kullback leibler information for autoregressive model selection in small samples summary a new estimator aici of the kullback leibler information is proposed for gaussian autoregressive time series model selection the expected information is decomposed into two terms the first being estimated without bias the second term is a penalty function which depends only weakly on the model parameters and hence can be tabulated by simulation from a white noise process the estimated information aici is very nearly unbiased when the model is either correct or overfitted it is shown that the penalty term of aic is asymptotically equivalent to that of the aicc criterion of hurvich tsai 1989 for autoregressive models estimated from small samples by burg s method simulation provides strong support for the use of the simpler criterion aicc perhaps using an unbiased version of the first term if the autoregressive models are estimated by maximum likelihood then a if none of the candidate model dimensions exceeds one half the sample size aic provides somewhat better model selections than aicc b if some of the candidate models have large dimension a case considered particularly in engineering applications then aic provides much better model selections in small samples than aicc

wilcoxon type generalized bayesian information criterion we develop a generalized bayesian information criterion for regression model selection the new criterion relaxes the usually strong distributional assumption associated with schwarz s bic by adopting a wilcoxon type dispersion function and appropriately adjusting the penalty term we establish that the wilcoxon type generalized bic preserves the consistency of schwarz s bic without the need to assume a parametric likelihood we also show that it outperforms schwarz s bic with heavier tailed data in the sense that asymptotically it can yield substantially smaller l 2 risk on the other hand when the data are normally distributed both criteria have similar l 2 risk the new criterion function is convex and can be conveniently computed using existing statistical software our proposal provides a flexible yet highly efficient alternative to schwarz s bic at the same time it broadens the scope of wilcoxon inference which has played a fundamental role in classical nonparametric analysis

stress gradient versus strain gradient constitutive models within elasticity abstract a stress gradient elasticity theory is developed which is based on the eringen method to address nonlocal elasticity by means of differential equations by suitable thermodynamics arguments involving the free enthalpy instead of the free internal energy the restrictions on the related constitutive equations are determined which include the well known eringen stress gradient constitutive equations as well as the associated so far uncertain boundary conditions the proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory the associated boundary value problem is shown to admit a unique solution characterized by a hellinger reissner type variational principle the main differences between the eringen stress gradient model and the concomitant aifantis strain gradient model are pointed out a rigorous formulation of the stress gradient euler bernoulli beam is provided the response of this beam model is discussed as for its sensitivity to the stress gradient effects and compared with the analogous strain gradient beam model

motion of a set by the curvature of its boundary abstract the study of a crystal shrinking or growing in a melt gives rise to equations relating the normal velocity of the motion to the curvature of the crystal boundary often these equations are anisotropic indicating the preferred directions of the crystal structure in the isotropic case this equation is called the curve shortening or the mean curvature flow equation and has been studied by differential geometric tools in general there are no classical solutions to these equations in this paper we develop a weak theory for the generalized mean curvature equation using the newly developed theory of viscosity solutions our approach is closely related to that of osher and sethian chen giga and goto and evans and spruck who view the boundary of the crystal as the level set of a solution to a nonlinear parabolic equation although we use their results in an essential way we give an intrinsic definition our main results are the existence of a solution large time asymptotics of this solution and its connection to the level set solution of osher and sethian chen giga and goto and evans and spruck in general there is no uniqueness even for classical solutions but we prove a uniqueness result under restrictive assumptions we also construct a class of explicit solutions which are dilations of wulff crystals

sequential detection with mutual information stopping cost this paper formulates and solves a sequential detection problem that involves the mutual information stochastic observability of a gaussian process observed in noise with missing measurements the main result is that the optimal decision is characterized by a monotone policy on the partially ordered set of positive definite covariance matrices this monotone structure implies that numerically efficient algorithms can be designed to estimate and implement monotone parametrized decision policies the sequential detection problem is motivated by applications in radar scheduling where the aim is to maintain the mutual information of all targets within a specified bound we illustrate the problem formulation and performance of monotone parametrized policies via numerical examples in fly by and persistent surveillance applications involving a ground moving target indicator gmti radar

asymptotic behavior of robust estimators of regression and scale parameters with fixed carriers for the linear regression model y i mathbf x i mathbf beta varepsilon i with fixed mathbf x i s the asymptotic normality of hat mathbf beta hat sigma which minimizes the huber dutter loss function sum sigma rho y i mathbf x i mathbf beta sigma a n sigma is established under rather general conditions

a deconvolution enhancement of the navier stokes αβ model a deconvolution enhancement of the email protected b model for turbulent flow is introduced the energy and energy dissipation rate for the enhanced model are derived it is also shown that the consistency error relative to the navier stokes equations and the microscale of the enhanced model are less than those of the email protected b model the proposed model is used to simulate the taylor green vortex problem and results show a qualitatively improved representation of the mean square vorticity when compared to the email protected b model numerical studies of the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor for three dimensional turbulent flows with re 200 are used to explore the utility of the model a benchmark problem of a two dimensional channel flow over a step for re 600 also indicates that this model can be applied to more general flows than those involving periodic boundary conditions

the postulations a la d alembert and a la cauchy for higher gradient continuum theories are equivalent a review of existing results in order to found continuum mechanics two different postulations have been used the first introduced by lagrange and piola starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients then by using the divergence theorem a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body this method assumes an a priori notion of internal work regards stress tensors as dual of virtual displacements and their gradients deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts the second method conceived by cauchy and based on the celebrated tetrahedron argument starts by postulating the type of contact interactions which can be exerted on the boundary of every suitably regular part of a body then it proceeds by proving the existence of stress tensors from a balance type postulate in this paper we review some relevant literature on the subject discussing how the two postulations can be reconciled in the case of higher gradient theories finally we underline the importance of the concept of contact surface edge and wedge s order forces

a geometric ginzburg landau problem for surfaces embedded in a three dimensional euclidean space consider a functional consisting of two terms a version of the willmore energy and an anisotropic area penalising the first component of the normal vector the latter weighted with the factor 1 epsilon 2 the asymptotic behaviour of such functionals as epsilon tends to 0 is studied in this paper the results include a lower and an upper bound on the minimal energy subject to suitable constraints moreover for embedded spheres a compactness result is obtained under appropriate energy bounds

phase field computations of single needle crystals crystal growth and motion by mean curvature the phase field model for free boundaries consists of a system of parabolic differential equations in which the variables represent a phase or order parameter and temperature respectively the parameters in the equations are related directly to the physical observables including the interfacial width epsilon which we can regard as a free parameter in computation the phase field equations can be used to compute a wide range of sharp interface problems including the classical stefan model its modification to incorporate surface tension and or surface kinetic terms the cahn allen motion by mean curvature the hele shaw model etc also included is anisotropy in the equilibrium and dynamical forms generally considered by materials scientists by adjusting the parameters the computations can be varied continuously from single needle dendritic to faceted crystals the computational method consists of smoothing a sharp interface problem within the scaling of distinguished limits of the phase field e

kernels with prescribed surface tension mobility for threshold dynamics schemes abstract we show how to construct a convolution kernel that has a desired anisotropic surface tension and desired anisotropic mobility to be used in threshold dynamics schemes for simulating weighted motion by mean curvature of interfaces including networks of them in both two and three dimensions moreover we discuss necessary and sufficient conditions for the positivity of the kernel which in the case of two phase flow ensures that the resulting scheme respects a comparison principle and implies convergence to the viscosity solution of the level set formulation of the flow in particular we show in a barrier type statement that the kernel cannot possibly be positive unless both the mobility and the surface tension satisfy necessary conditions in three dimensions and give a complete characterization among other results is a threshold dynamics scheme that is guaranteed to dissipate a non local approximation to the interfacial energy in the fully anisotropic multiphase setting using the new kernel construction

model selection for multivariate regression in small samples we develop a small sample criterion aicc for selecting multivariate regression models this criterion adjusts the akaike information criterion to be an exact unbiased estimator for the expected kullback leibler information a small sample comparison shows that aicc provides better model order choices than other available model selection methods data from an agricultural experiment are analyzed

solving the regularized strongly anisotropic cahn hilliard equation by an adaptive nonlinear multigrid method abstract we present efficient second order accurate and adaptive finite difference methods to solve the regularized strongly anisotropic cahn hilliard equation in 2d and 3d when the surface energy anisotropy is sufficiently strong there are missing orientations in the equilibrium level curves of the diffuse interface solutions corresponding to those missing from the sharp interface wulff shape and the anisotropic cahn hilliard equation becomes ill posed to regularize the equation a higher order derivative term is added to the energy this leads to a sixth order nonlinear parabolic equation for the order parameter an implicit time discretization is used to remove the high order time step stability constraints dynamic block structured cartesian mesh refinement is used to highly resolve narrow interfacial layers a multilevel nonlinear multigrid method is used to solve the nonlinear equations at the implicit time level one of the keys to the success of the method is the treatment of the anisotropic term this term is discretized in conservation form in space and is discretized fully implicitly in time numerical simulations are presented that confirm the accuracy efficiency and stability of the scheme we study the dynamics of interfaces under strong anisotropy and compare near equilibrium diffuse interface solutions to the sharp interface wulff shapes in 2d and 3d we also simulate large scale coarsening of a corrugated surface in 3d evolving by anisotropic surface diffusion we show the emergence of long range order during coarsening and an interesting mechanism of ordered coarsening

a weakly nonlinear energy stable scheme for the strongly anisotropic cahn hilliard equation and its convergence analysis abstract in this paper we propose and analyze a weakly nonlinear energy stable numerical scheme for the strongly anisotropic cahn hilliard model in particular a highly nonlinear and singular anisotropic surface energy makes the pde system very challenging at both the analytical and numerical levels to overcome this well known difficulty we perform a convexity analysis on the anisotropic interfacial energy and a careful estimate reveals that all its second order functional derivatives stay uniformly bounded by a global constant this subtle fact enables one to derive an energy stable numerical scheme moreover a linear approximation becomes available for the surface energy part and a detailed estimate demonstrates the corresponding energy stability its combination with an appropriate treatment for the nonlinear double well potential terms leads to a weakly nonlinear energy stable scheme for the whole system in particular such an energy stability is in terms of the interfacial energy with respect to the original phase variable and no auxiliary variable needs to be introduced this has important implications for example in the case that the method needs to satisfy a maximum principle more importantly with a careful application of the global bound for the second order functional derivatives an optimal rate convergence analysis becomes available for the proposed numerical scheme which is the first such result in this area meanwhile for a cahn hilliard system with a sufficiently large degree of anisotropy a willmore or biharmonic regularization has to be introduced to make the equation well posed for such a physical model all the presented analyses are still available the unique solvability energy stability and convergence estimate can be derived in an appropriate manner in addition the fourier pseudo spectral spatial approximation is applied and all the theoretical results could be extended for the fully discrete scheme finally a few numerical results are presented which confirm the robustness and accuracy of the proposed scheme

a level set approach to anisotropic surface evolution with free adatoms we variationally derive a thermodynamically consistent model for surface evolution under the influence of free adatoms the resulting system of nonlinear partial differential equations couples a diffusion equation on a surface to the evolution of the surface a numerical approach based on a finite element discretization of a level set equation is described for an anisotropic evolution with nonconvex anisotropy functions various simulation examples in two and three dimensions demonstrate the applicability of the method

a new phase field model for strongly anisotropic systems we present a new phase field model for strongly anisotropic crystal and epitaxial growth using regularized anisotropic cahn hilliard type equations such problems arise during the growth and coarsening of thin films when the anisotropic surface energy is sufficiently strong sharp corners form and unregularized anisotropic cahn hilliard equations become ill posed our models contain a high order willmore regularization where the square of the mean curvature is added to the energy to remove the ill posedness the regularized equations are sixth order in space a key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation using the method of matched asymptotic expansions we show the convergence of our phase field model to the general sharp interface model we present two and three dimensional numerical results using an adaptive nonlinear multigrid finite difference method we find excellent agreement between the dynamics of the new phase field model and the sharp interface model the computed equilibrium shapes using the new model also match a recently developed analytical sharp interface theory that describes the rounding of the sharp corners by the willmore regularization

variational theory for nematoacoustics the effect of an ultrasonic wave on the nematic texture has long been known but its interpretation in terms of a coherent dynamical theory has not yet been achieved a proposal for such a theory is made in this paper the diverse theoretical approaches attempted in the past to describe the interaction between sound and nematic molecular orientation are briefly summarized a theory for second grade fluids which provides the appropriate theoretical background for nematoacoustics is also revived an explicit application of the proposed theory to a simple computable case is given which yields predictions that are qualitatively confirmed by a number of experimental results

active classification for pomdps a kalman like state estimator author s zois ds levorato m mitra u abstract 1991 2012 ieee the problem of state tracking with active observation control is considered for a system modeled by a discrete time finite state markov chain observed through conditionally gaussian measurement vectors the measurement model statistics are shaped by the underlying state and an exogenous control input which influence the observations quality exploiting an innovations approach an approximate minimum mean squared error mmse filter is derived to estimate the markov chain system state to optimize the control strategy the associated mean squared error is used as an optimization criterion in a partially observable markov decision process formulation a stochastic dynamic programming algorithm is proposed to solve for the optimal solution to enhance the quality of system state estimates approximate mmse smoothing estimators are also derived finally the performance of the proposed framework is illustrated on the problem of physical activity detection in wireless body sensing networks the power of the proposed framework lies within its ability to accommodate a broad spectrum of active classification applications including sensor management for object classification and tracking estimation of sparse signals and radar scheduling

sparse and robust normal and t portfolios by penalized lq likelihood minimization abstract two important problems arising in traditional asset allocation methods are the sensitivity to estimation error of portfolio weights and the high dimensionality of the set of candidate assets in this paper we address both issues by proposing a new criterion for portfolio selection the new criterion is a two stage description of the available information where the q entropy a generalized measure of information is used to code the uncertainty of the data given the parametric model and the uncertainty related to the model choice the information about the model is coded in terms of a prior distribution that promotes asset weights sparsity our approach carries out model selection and estimation in a single step by selecting a few assets and estimating their portfolio weights simultaneously the resulting portfolios are doubly robust in the sense that they can tolerate deviations from both assumed data model and prior distribution for model parameters empirical results on simulated and real world data support the validity of our approach

a robust version of mallows s c p abstract we present a robust version of mallows s c p for regression models it is defined by rc p w p 2 u p v p where w p i 2 i r 2 i is a weighted residual sum of squares computed from a robust fit of model p 2 is a robust and consistent estimator of 2 in the full model and u p and v p are constants depending on the weight function and the number of parameters in model p good subset models are those with rc p close to v p or smaller than v p when the weights are identically 1 w p becomes the residual sum of squares of a least squares fit and rc p reduces to mallows s c p the robust model selection procedure based on rc p allows us to choose the models that fit the majority of the data by taking into account the presence of outliers and possible departures from the normality assumption on the error distribution together with the classical c p the robust version suggests several models from which we can choose

a numerical method for a second gradient theory of incompressible fluid flow this work concerns the development of a finite element method for discretizing a recent second gradient theory for the flow of incompressible fluids the new theory gives rise to a flow equation involving higher order gradients of the velocity field and introduces an accompanying length scale and boundary conditions finite element methods based on similar equations involving fourth order differential operators typically rely on c 1 continuous basis functions or a mixed approach both of which entail certain implementational difficulties here we examine the adaptation of a relatively inexpensive non conforming method based on c 0 continuous basis functions we first develop the variational form of the method and establish consistency the method weakly enforces continuity of the vorticity traction and hypertraction across interelement boundaries stabilization is achieved via nitsche s method further pressure stabilization scales with the higher order moduli so that the classical formulation is recovered as a particular limit the numerical method is verified for the problem of steady plane poiseuille flow we then provide several numerical examples illustrating the robustness of the method and contrasting the predictions to those provided by classical navier stokes theory

phase field theory of edges in an anisotropic crystal in the presence of sufficiently strong surface energy anisotropy the equilibrium shape of an isothermal crystal may include corners or edges models of edges have to date involved the regularization of the corresponding free boundary problem resulting in equilibrium shapes with smoothed out edges in this paper we take a new approach and consider how a phase field model which provides a diffuse description of an interface can be extended to the consideration of edges by an appropriate regularization of the underlying mathematical model using the method of matched asymptotic expansions we develop an approximate solution which corresponds to a smoothed out edge from which we are able to determine the associated edge energy

a parametric finite element method for fourth order geometric evolution equations we present a finite element approximation of motion by minus the laplacian of curvature and related flows the proposed scheme covers both the closed curve case and the case of curves that are connected via triple junctions on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches it turns out that the new scheme has very good properties with respect to area conservation and the equidistribution of mesh points we state also an extension of our scheme to willmore flow of curves and discuss possible further generalizations

surface evolution of elastically stressed films under deposition by a diffuse interface model we consider the heteroepitaxial growth of thin films by numerical simulations within a diffuse interface model the model is applicable to describe the self organization of nanostructures the influence of strain surface energies and kinetics on the surface evolution is considered a matched asymptotic analysis shows the formal convergence of an anisotropic viscous cahn hilliard model to a general surface evolution equation the system is solved by adaptive finite elements in three dimensions and in special cases compared with sharp interface models

tractions balances and boundary conditions for nonsimple materials with application to liquid flow at small length scales using a nonstandard version of the principle of virtual power we develop general balance equations and boundary conditions for second grade materials our results apply to both solids and fluids as they are independent of constitutive equations as an application of our results we discuss flows of incompressible fluids at small length scales in addition to giving a generalization of the navier stokes equations involving higher order spatial derivatives our theory provides conditions on free and fixed boundaries the free boundary conditions involve the curvature of the free surface among the conditions for a fixed boundary are generalized adherence and slip conditions each of which involves a material length scale we reconsider the classical problem of plane poiseuille flow for generalized adherence and slip conditions

regression and time series model selection in small samples summary a bias correction to the akaike information criterion aic is derived for regression and autoregressive time series models the correction is of particular use when the sample size is small or when the number of fitted parameters is a moderate to large fraction of the sample size the corrected method called aicc is asymptotically efficient if the true model is infinite dimensional furthermore when the true model is of finite dimension aicc is found to provide better model order choices than any other asymptotically efficient method applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed

fast reaction slow diffusion and curve shortening the reaction diffusion problem u 1 varepsilon delta u varepsilon 1 v n u quad u x 0 varepsilon g x quad partial n u 0 text on partial omega for a vector u x t varepsilon is considered in a domain omega in r m an asymptotic solution is constructed for varepsilon small it shows that at each x u tends quickly to a minimum of v u when v has several minima when u tends to a piecewise constant function boundary layer expansions are constructed around the resulting surfaces of discontinuity or fronts each front is found to move along its normal with a constant velocity determined by the discontinuity v in v across it when v 0 the front s normal velocity is varepsilon kappa where kappa is its mean curvature the motion of fronts in this manner is studied for arcs in the plane which are normal to partial omega at their endpoints and for fronts that are closed curves it is shown a front can shrink to a point in

a second strain gradient elasticity theory with second velocity gradient inertia part i constitutive equations and quasi static behavior abstract a multi cell homogenization procedure with four geometrically different groups of cell elements respectively for the bulk the boundary surface the edge lines and the corner points of a body is envisioned which is able not only to extract the effective constitutive properties of a material but also to assess the surface effects produced by the boundary surface on the near bulk material applied to an unbounded material in combination with the thermodynamics energy balance principles this procedure leads to an equivalent continuum constitutively characterized by ordinary double and triple generalized stresses and momenta also applying this procedure to a finite body suitably modelled as a simple material cell system in association with the principle of the virtual power pvp for quasi static actions an equivalent structural system is derived featured by a macro scale pvp having the typical format as for a second strain gradient material model due to the surface effects the latter model does work as a combination of two subsystems i e the bulk material behaving as a cauchy continuum and the boundary surface operating as a membrane like boundary layer each subsystem being in local and global equilibrium by its own further the applied ordinary boundary traction splits into two response dependent parts i e the cauchy traction transmitted to the bulk material and the gurtin murdoch traction acting together with all other boundary tractions upon the boundary layer the role of the boundary layer as a two dimensional manifold enclosing a cauchy continuum is elucidated also with the aid of a discrete model a strain gradient elasticity theory is proposed which includes a minimum total potential energy principle featuring the relevant boundary value problem for quasi static loads and its unique solution a simple application is presented two appendices are included one reports the proof of the global equilibrium of the boundary layer the other is concerned with double and triple stresses the paper is complemented by a companion part ii one on dynamics previous findings by the author polizzotto c 2012 a gradient elasticity theory for second grade materials and higher order inertia int j solids struct 49 2121 2137 are improved and extended

model selection for extended quasi likelihood models in small samples we develop a small sample criterion aicc for the selection of extended quasi likelihood models in contrast to the akaike information criterion aic aicc provides a more nearly unbiased estimator for the expected kullback leibler information consequently it often selects better models than aic in small samples for the logistic regression model monte carlo results show that aicc outperforms aic pregibon s 1979 data analytic methods for generalized linear models ph d thesis university of toronto cp and the cp selection criteria of hosmer et al 1989 biometrics 45 1265 1270 two examples are presented

multiphase thermomechanics with interfacial structure 2 evolution of an isothermal interface paper 1 1988 g 1 of this series began an investigation whose goal is a thermomechanics of two phase continua based on gibbs s notion of a sharp phase interface endowed with thermomechanical structure in that paper a balance law balance of capillary forces was introduced and then applied in conjunction with suitable statements of the first two laws of thermodynamics the chief results are thermodynamic restrictions on constitutive equations exact and approximate free boundary conditions at the interface and a hierarchy of free boundary problems the simplest versions of these problems the mullins sekerka problems are essentially the classical stefan problem with the free boundary condition u 0 for the temperature replaced by the condition u h k where k is the curvature of the free boundary and h 0 is a material constant this dependence on curvature renders the problem difficult and apart from numerical studies involving linearization stability there are almost no supporting theoretical results

a numerical study of the navier stokes αβ model abstract we present a numerical study of the ns model which is a recently proposed multiscale variation of the ns model that attempts to recapture scales lost through over regularization by separately modeling dissipation range scales we develop a similarity theory for the new model which shows that it is better equipped than the ns model to capture smaller scale behavior next we propose and study an unconditionally stable optimally accurate and efficient finite element implementation for the ns model rigorous proofs for stability and convergence are provided finally we present results from two numerical experiments that demonstrate the advantages of the ns model over the ns model

bayesian sequential detection with phase distributed change time and nonlinear penalty a pomdp lattice programming approach we show that the optimal decision policy for several types of bayesian sequential detection problems has a threshold switching curve structure on the space of posterior distributions this is established by using lattice programming and stochastic orders in a partially observed markov decision process pomdp framework a stochastic gradient algorithm is presented to estimate the optimal linear approximation to this threshold curve we illustrate these results by first considering quickest time detection with phase type distributed change time and a variance stopping penalty then it is proved that the threshold switching curve also arises in several other bayesian decision problems such as quickest transient detection exponential delay risk sensitive penalties stopping time problems in social learning and multi agent scheduling in a changing world using blackwell dominance it is shown that for dynamic decision making problems the optimal decision policy is lower bounded by a myopic policy finally it is shown how the achievable cost of the optimal decision policy varies with change time distribution by imposing a partial order on transition matrices

asymptotic solutions for the equilibrium crystal shape with small corner energy regularization dynamic models for facet formation often employ a regularization of the surface energy based on a corner energy term here we consider the effect of this regularization on the equilibrium shape of a solid particle in two dimensions using matched asymptotic expansions we determine the explicit solution for the corner shape in the presence of the regularization our results show that for a class of surface energy anisotropy models the regularized solution approaches the classic sharp corner results as the regularization approaches zero the results validate the use of the regularization in numerical calculations for the equilibrium problem finally a byproduct of the analysis is an exact solution for the equilibrium shape of a semi infinite wedge in the presence of the regularization

variational formulations and extra boundary conditions within stress gradient elasticity theory with extensions to beam and plate models abstract the principle of minimum total potential energy and the primary principle of virtual power for stress gradient elasticity are presented as kinematic type constructs dual of analogous static type principles from the literature polizzotto 2014 polizzotto 2015a the extra gradient induced boundary conditions are formulated as boundary congruence conditions on the microstructure s deformation relative to the continuum which ultimately require that the normal derivative of the stresses must vanish at the boundary surface two forms of the governing pdes for the relevant boundary value problem are presented and their computational aspects are discussed the timoshenko beam and the kirchhoff love plate theories are extended to stress gradient elasticity under the assumption that stress gradient effects do not propagate transversally it is shown that for beam models no extra gradient induced boundary conditions are required whereas for plate models such conditions must be enforced at the contour surface of the plate where the normal derivative of the stress resultants are required to vanish appendix a is devoted to some basic aspects of the mechanics of the microstructure appendix b to a comparison between the present theory and an analogous theory from the literature forest and sab 2012

asymptotic behavior of general m estimates for regression and scale with random carriers let xini y i be a sequence of independent identically distributed random variables where x i r p and y i r and let r p be an unknown vector such that y i x i u i where u i is independent of x i and has distribution function f u where 0 is an unknown parameter this paper deals with a general class of m estimates of regression and scale defined as solutions of the system sum limits i phi text x i r i x i 0 sum limits i chi r i 0 where r y i xi1 with r p r r and r r this class contains estimators of proposed by huber mallows and krasker and welsch the consistency and asymptotic normality of the general m estimators are proved assuming general regularity conditions on and and assuming the joint distribution of x i y i to fulfill the model only approximately

emergent parabolic scaling of nano faceting crystal growth nano faceted crystals answer the call for self assembled physico chemically tailored materials with those arising from a kinetically mediated response to free energy disequilibria thermokinetics holding the greatest promise the dynamics of slightly undercooled crystal melt interfaces possessing strongly anisotropic and curvature dependent surface energy and evolving under attachment detachment limited kinetics offer a model system for the study of thermokinetic effects the fundamental non equilibrium feature of this dynamics is explicated through our discovery of one dimensional convex and concave translating fronts solitons whose constant asymptotic angles provably deviate from the thermodynamically expected wulff angles in direct proportion to the degree of undercooling these thermokinetic solitons induce a novel emergent facet dynamics which is exactly characterized via an original geometric matched asymptotic analysis we thereby discover an emergent parabolic symmetry of its coarsening facet ensembles which naturally implies the universal scaling law l t 1 2 for the growth in time t of the characteristic length l

towards a variational theory of phase transitions involving curvature an anisotropic area functional is often used as a model for the free energy of a crystal surface for models of faceting the anisotropy is typically such that the functional becomes nonconvex and then it may be appropriate to regularize it with an additional term involving curvature when the weight of the curvature term tends to 0 this gives rise to a singular perturbation problem the structure of this problem is comparable to the theory of phase transitions studied first by modica and mortola their ideas are also use ful in this context but they have to be combined with adequate geometric tools in particular a variant of the theory of curvature varifolds intro duced by hutchinson is used in this paper this allows an analysis of the asymptotic behaviour of the energy functionals

a regularized equation for anisotropic motion by curvature for realistic interfacial energies the equations of anisotropic motion by curvature exhibit backward parabolic behavior over portions of their domain thereby inducing phenomena such as the formation of facets and wrinkles in this paper a physically consistent regularized equation that may be used to analyze such phenomena is derived

interface evolution in three dimensions with curvature dependent energy and surface diffusion interface controlled evolution phase transitions epitaxial growth of elastic films when the interfacial energy is a nonconvex function of orientation the anisotropic curvature flow equation becomes backward parabolic to overcome the instability thus generated a regularization of the equation that governs the evolution of the interface is needed in this paper we develop a regularized theory of curvature flow in three dimensions that incorporates surface diffusion and bulk surface interactions the theory is based on a superficial mass balance configurational forces and couples consistent with superficial force and moment balances a mechanical version of the second law that includes via the configurational moments work that accompanies changes in the curvature of the interface a constitutive theory whose main ingredient is a positive definite isotropic quadratic dependence of the interfacial energy on the curvature tensor two special cases are investigated i the interface is a boundary between bulk phases or grains and ii the interface separates an elastic thin film bonded to a rigid substrate from a vapor phase whose sole action is the deposition of atoms on the surface

how to schedule measurements of a noisy markov chain in decision making a decision maker records measurements of a finite state markov chain corrupted by noise the goal is to decide when the markov chain hits a specific target state the decision maker can choose from a finite set of sampling intervals to pick the next time to look at the markov chain the aim is to optimize an objective comprising of false alarm delay cost and cumulative measurement sampling cost taking more frequent measurements yields accurate estimates but incurs a higher measurement cost making an erroneous decision too soon incurs a false alarm penalty waiting too long to declare the target state incurs a delay penalty what is the optimal sequential strategy for the decision maker this paper shows that under reasonable conditions the optimal strategy has the following intuitive structure when the bayesian estimate posterior distribution of the markov chain is away from the target state look less frequently while if the posterior is close to the target state look more frequently bounds are derived for the optimal strategy also the achievable optimal cost of the sequential detector as a function of transition dynamics and observation distribution is analyzed the sensitivity of the optimal achievable cost to parameter and strategy variations is bounded in terms of the kullback divergence also structural results are obtained for joint optimal sampling and measurement control active sensing

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

cauchy tetrahedron argument applied to higher contact interactions second gradient theories are nowadays used in many studies in order to describe in detail some transition layers which may occur in micro structured materials and in which physical properties are sharply varying sometimes higher order theories are also evoked up to now these models have not been based on a construction of stresses similar to the one due to cauchy which has been applied only for simple materials it has been widely recognized that the fundamental assumption by cauchy that the traction depends only on the normal of the dividing surface cannot be maintained for higher gradient theories however this observation did not urge any author to our knowledge to revisit the cauchy construction in order to adapt it to a more general conceptual framework this is what we do in this paper for a continuum of grade n also called n th gradient continuum our construction is very similar to the one due to cauchy based on the tetrahedron argument it does not introduce any argument of a different nature in particular we avoid invoking the principle of virtual work as one should expect the balance assumption and the regularity hypotheses have to be adapted to the new framework and tensorial computations become more complex

motion of level sets by mean curvature i we continue our investigation of the level set technique for describing the generalized evolution of hypersurfaces moving according to their mean curvature the principal assertion of this paper is a kind of reconciliation with the geometric measure theoretic approach pioneered by k brakke we prove that almost every level set of the solution to the mean curvature evolution pde is in fact aunit density varifold moving according to its mean curvature in particular a e level set is endowed with a kind of geometric structure the proof utilizes compensated compactness methods to pass to limits in various geometric expressions

on a theory of nonlocal elasticity of bi helmholtz type and some applications abstract a theory of nonlocal elasticity of bi helmholtz type is studied we employ eringen s model of nonlocal elasticity with bi helmholtz type kernels to study dispersion relations screw and edge dislocations the nonlocal kernels are derived analytically as green functions of partial differential equations of fourth order this continuum model of nonlocal elasticity involves two material length scales which may be derived from atomistics the new nonlocal kernels are nonsingular in one two and three dimensions furthermore the nonlocal elasticity of bi helmholtz type improves the one of helmholtz type by predicting a dispersion relationship with zero group velocity at the end of the first brillouin zone new solutions for the stresses and strain energy of screw and edge dislocations are found

curvature and the evolution of fronts the evolution of a front propagating along its normal vector field with speedf dependent on curvaturek is considered the change in total variation of the propagating front is shown to depend only ondf dk only wherek changes sign analysis of the casef k 1 ek where e is a constant shows that curvature plays a role similar to that of viscosity in burgers equation for e 0 and non convex initial data the curvature blows up corners develop and an entropy condition can be formulated to provide an explicit construction for a weak solution beyond the singularity we then numerically show that the solution as e goes to zero converges to the constructed weak solution numerical methods based on finite difference schemes for marker particles along the front are shown to be unstable in regions where the curvature builds as a remedy we show that front tracking based on volume of fluid techniques can be used together with the entropy condition to provide transition from the classical to weak solution

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

a level set approach to anisotropic flows with curvature regularization modeling and simulation of faceting effects on surfaces are topics of growing importance in modern nanotechnology such effects pose various theoretical and computational challenges since they are caused by non convex surface energies which lead to ill posed evolution equations for the surfaces in order to overcome the ill posedness regularization of the energy by a curvature dependent term has become a standard approach which seems to be related to the actual physics too the use of curvature dependent energies yields higher order partial differential equations for surface variables whose numerical solution is a very challenging task in this paper we investigate the numerical simulation of anisotropic growth with curvature dependent energy by level set methods which yield flexible and robust surface representations we consider the two dominating growth modes namely attachment detachment kinetics and surface diffusion the level set formulations are given in terms of metric gradient flows which are discretized by finite element methods in space and in a semi implicit way as local variational problems in time finally the constructed level set methods are applied to the simulation of faceting of embedded surfaces and thin films

equilibria and dislocations in epitaxial growth abstract an overview of recent analytical developments in epitaxial growth is presented the energy release via the onset of dislocations is addressed regularity of quasistatic equilibria is studied both in the absence and in the presence of dislocations morphological evolution of anisotropic epitaxially strained films is considered under the assumption that the surface evolves by surface diffusion under the influence of a chemical potential

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

a consistent and stabilized continuous discontinuous galerkin method for fourth order incompressible flow problems this paper presents a new consistent and stabilized finite element formulation for fourth order incompressible flow problems the formulation is based on the c 0 interior penalty method the galerkin least square gls scheme which assures that the formulation is weakly coercive for spaces that fail to satisfy the inf sup condition and considers discontinuous pressure interpolations a stability analysis through a lemma establishes that the proposed formulation satisfies the inf sup condition thus confirming the robustness of the method this lemma indicates that at the element level there exists an optimal or quasi optimal gls stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields the geometry of the finite element and the fluid viscosity term numerical experiments are carried out to illustrate the ability of the formulation to deal with arbitrary interpolations for velocity and pressure and to stabilize large pressure gradients

a second strain gradient elasticity theory with second velocity gradient inertia part ii dynamic behavior abstract this paper is the sequel of a companion part i paper devoted to the constitutive equations and to the quasi static behavior of a second strain gradient material model with second velocity gradient inertia in the present part ii paper a multi cell homogenization procedure developed in the part i paper is applied to a nonhomogeneous body modelled as a simple material cell system in conjunction with the principle of virtual work pvw for inertial actions i e momenta and inertia forces which at the macro scale level takes on the typical format as for a second velocity gradient inertia material model the latter macro scale pvw is used to determine the equilibrium equations relating the ordinary double and triple generalized momenta to the inertia forces as a consequence of the surface effects the latter inertia forces include ordinary inertia body forces within the bulk material as well as ordinary and double inertia surface tractions on the boundary layer and ordinary inertia line tractions on the edge line rod they all depend on the acceleration in a nonstandard way but the classical laws are recovered in the case of no higher order inertia the classical linear and angular momentum theorems are extended to the present context of second velocity gradient inertia showing that the extended theorems used in conjunction with the cauchy traction theorem lead to the local force and moment stress symmetry motion equations just like for a classical continuum a gradient elasticity theory is proposed whereby the dynamic evolution problem for assigned initial and boundary conditions is shown to admit a hamilton type variational principle the uniqueness of the solution is also discussed a few simple applications to wave propagation and dispersion problems are presented the paper indicates the correct way to describe the inertia forces in the presence of higher order inertia it extends and improves previous findings by the author polizzotto c 2012 a gradient elasticity theory for second grade materials and higher order inertia int j solids struct 49 2121 2137 overall conclusions are drawn at the end of the paper

a gradient elasticity theory for second grade materials and higher order inertia abstract second grade elastic materials featured by a free energy depending on the strain and the strain gradient and a kinetic energy depending on the velocity and the velocity gradient are addressed an inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics the state variables include the body momentum and the surface momentum related to the velocity in a nonstandard way as well as the concomitant mass accelerations and inertial forces which do intervene into the motion equations and into the force boundary conditions the boundary traction is the sum of two parts i e the cauchy traction and the gurtin murdoch traction whereas the traction boundary condition exhibits the typical format of the equilibrium equation of a material surface as known from the principles of surface mechanics whereby the gurtin murdoch traction incorporating the inertial surface force plays the role of applied surfacial force density the body s boundary surface constitutes a thin boundary layer which is in global equilibrium under all the external forces applied on it a feature that makes it possible to exploit the traction cauchy theorem within second grade materials this means that a second grade material is formed up by two sub systems that is the bulk material operating as a classical cauchy continuum and the thin boundary layer operating as a gurtin murdoch material surface the classical linear and angular momentum theorems are suitably extended for higher order inertia from which the local motion equations and the moment equilibrium equations stress symmetry can be derived for an isotropic material featured by four constants i e the lame constants and two length scale parameters aifantis model the dynamic evolution problem is characterized by a hamilton type variational principle and a solution uniqueness theorem closed form solutions of the wave dispersion analysis problem for beam models are presented and compared with known results from the literature the paper indicates a correct thermodynamically consistent way to take into account higher order inertia effects within continuum mechanics

stochastic observability in network state estimation and control a hidden markov model for the traffic congestion control problem in transmission control protocol tcp networks is developed and the question of observability of this system is posed of specific interest are the dependence of observability on the congestion control law and the interaction between observability ideas and the effectiveness of feedback control analysis proceeds with a survey of observability concepts and an extension of some available definitions for linear and nonlinear stochastic systems the key idea is to link the improvement of state estimator performance to the conditioning on the output data sequence the observability development proceeds from linear deterministic systems to linear gaussian systems nonlinear systems etc with backwards compatibility to deterministic ideas the principal concepts relate to the entropy decrease of scalar functions of the state which in the linear case are describable in terms of covariance matrices a feature of nonlinear systems is that the estimator properties may affect the closed loop control performance results are derived linking stochastic reconstructibility to strict improvement of the optimal closed loop control performance over open loop control for the hidden markov model the entropy provides a means to quantify and thus order simulation results for a simplified tcp network motivated by the link between feedback control and reconstructibility the entropy formulation is also explored as a means to discriminate between different control strategies for improving estimator performance this approach has connections to dual adaptive control ideas where the control has the simultaneous and opposing goals of regulating the system and of exciting the system to prevent estimator divergence

motion of elastic thin films by anisotropic surface diffusion with curvature regularization in this paper we prove short time existence uniqueness and regularity for a surface diffusion evolution equation with curvature regularization in the context of epitaxially strained two dimensional films this is achieved by using the h 1 gradient flow structure of the evolution law via de giorgi s minimizing movements this seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity

coarsening dynamics of the convective cahn hilliard equation abstract we characterize the coarsening dynamics associated with a convective cahn hilliard equation cch in one space dimension first we derive a sharp interface theory through a matched asymptotic analysis two types of phase boundaries kink and anti kink arise due to the presence of convection and their motions are governed to leading order by a nearest neighbors interaction coarsening dynamical system cds theoretical predictions on cds include the characteristic length l m for coarsening exhibits the temporal power law scaling t1 2 provided l m is appropriately small with respect to the peclet length scale l p binary coalescence of phase boundaries is impossible ternary coalescence only occurs through the kink ternary interaction two kinks meet an anti kink resulting in a kink direct numerical simulations performed on both cds and cch confirm each of these predictions a linear stability analysis of cds identifies a pinching mechanism as the dominant instability which in turn leads to kink ternaries we propose a self similar period doubling pinch ansatz as a model for the coarsening process from which an analytical coarsening law for the characteristic length scale l m emerges it predicts both the scaling constant c of the t1 2 regime i e l m ct 1 2 as well as the crossover to logarithmically slow coarsening as l m crosses l p our analytical coarsening law stands in good qualitative agreement with large scale numerical simulations that have been performed on cch