prolongation structures and backlund transformations for the matrix korteweg de vries and the boomeron equation prolongation structures are determined for the matrix korteweg de vries and the boomeron equation by using the integrability condition for a linear system of first order equations symmetries of these prolongation structures are used to derive backlund transformations and to construct solutions for both equations

on estimating standardized risk differences from odds ratios an estimator proposed by greenland and holland 1991 biometrics 47 319 322 for a standardized risk difference parameter is shown to be a maximum likelihood estimator if the consistent estimator of the common odds ratio is appropriately chosen the statistical problem under consideration is reparameterized likelihood equations are derived

an efficient threshold dynamics method for wetting on rough surfaces the threshold dynamics method developed by merriman bence and osher mbo is an efficient method for simulating the motion by mean curvature flow when the interface is away from the solid boundary direct generalization of mbo type methods to the wetting problem with interfaces intersecting the solid boundary is not easy because solving the heat equation in a general domain with a wetting boundary condition is not as efficient as it is with the original mbo method the dynamics of the contact point also follows a different law compared with the dynamics of the interface away from the boundary in this paper we develop an efficient volume preserving threshold dynamics method for simulating wetting on rough surfaces this method is based on minimization of the weighted surface area functional over an extended domain that includes the solid phase the method is simple stable with o n log n complexity per time step and is not sensitive to the inhomogeneity or roughness of the solid boundary

phase transition with the line tension effect we make the connection between the geometric model for capillarity with line tension and the cahn hilliard model of two phase fluids to this aim we consider the energies f eps u eps int o du 2 1 over eps int o w u lambda int bd o v u where u is a scalar density function and w and v are double well potentials we show that the behaviour of f e in the limit e 0 and depends on the limit of e log if this limit is finite and strictly positive then the singular limit of the energies f e leads to a coupled problem of bulk and surface phase transitions and under certain assumptions agrees with the relaxation of the capillary energy with line tension these results were announced in abs1 and abs2

an efficient finite element method for simulation of droplet spreading on a topologically rough surface abstract we study numerically the dynamics of a three dimensional droplet spreading on a rough solid surface using a phase field model consisting of the coupled cahn hilliard and navier stokes equations with a generalized navier boundary condition gnbc an efficient finite element method on unstructured meshes is introduced to cope with the complex geometry of the solid surfaces we extend the gnbc to surfaces with complex geometry by including its weak form along different normal and tangential directions in the finite element formulation the semi implicit time discretization scheme results in a decoupled system for the phase function the velocity and the pressure in addition a mass compensation algorithm is introduced to preserve the mass of the droplet to efficiently solve the decoupled systems we present a highly parallel solution strategy based on domain decomposition techniques we validate the newly developed solution method through extensive numerical experiments particularly for those phenomena that can not be achieved by two dimensional simulations on a surface with circular posts we study how wettability of the rough surface depends on the geometry of the posts the contact line motion for a droplet spreading over some periodic rough surfaces are also efficiently computed moreover we study the spreading process of an impacting droplet on a microstructured surface a qualitative agreement is achieved between the numerical and experimental results the parallel performance suggests that the proposed solution algorithm is scalable with over 4 000 processors cores with tens of millions of unknowns

asymptotic behaviour of a phase field model with three coupled equations without uniqueness abstract we prove the existence of weak solutions for a phase field model with three coupled equations with unknown uniqueness and state several dynamical systems depending on the regularity of the initial data then the existence of families of global attractors level set depending for the corresponding multi valued semiflows is established applying an energy method finally using the regularizing effect of the problem we prove that these attractors are in fact the same

multi parameter regression survival modeling an alternative to proportional hazards summary it is standard practice for covariates to enter a parametric model through a single distributional parameter of interest for example the scale parameter in many standard survival models indeed the well known proportional hazards model is of this kind in this article we discuss a more general approach whereby covariates enter the model through more than one distributional parameter simultaneously e g scale and shape parameters we refer to this practice as multi parameter regression mpr modeling and explore its use in a survival analysis context we find that multi parameter regression leads to more flexible models which can offer greater insight into the underlying data generating process to illustrate the concept we consider the two parameter weibull model which leads to time dependent hazard ratios thus relaxing the typical proportional hazards assumption and motivating a new test of proportionality a novel variable selection strategy is introduced for such multi parameter regression models it accounts for the correlation arising between the estimated regression coefficients in two or more linear predictors a feature which has not been considered by other authors in similar settings the methods discussed have been implemented in the mpr package in r

phase field modeling and simulation of three phase flow on solid surfaces phase field models are widely used to describe the two phase system the evolution of the phase field variables is usually driven by the gradient flow of a total free energy functional the generalization of the approach to an n phase n 3 system requires some extra consistency conditions on the free energy functional in order for the model to give physically relevant results a projection approach is proposed for the derivation of a consistent free energy functional for the three phase cahn hilliard equations the system is then coupled with the navier stokes equations to describe the three phase flow on solid surfaces with moving contact line an energy stable scheme is developed for the three phase flow system the discrete energy law of the numerical scheme is proved which ensures the stability of the scheme we also show some numerical results for the dynamics of triple junctions and four phase contact lines

the interpretation of multiplicative model parameters as standardized parameters under current conventions relative risk estimates obtained from multiplicative models are interpreted as estimates of a homogeneous effect such interpretations condition on the unverifiable assumption that the relative risk under study is homogeneous an assumption that is not likely to be correct even if the model fits well we propose that such estimates are better interpreted as estimates of standardized relative risks with a bias component that depends on the degree of model misspecification and on the study design to evaluate our proposal we present a study of the maximum likelihood estimators from poisson and logistic regression compared to the population standardized rate ratio the results indicate that our proposed interpretation would in practice be more cautious and accurate than the homogeneous effect interpretation

symmetry classes of variable coefficient nonlinear schrodinger equations a variable coefficient nonlinear schrodinger vcnls equation involving three arbitrary complex functions of space time in 1 1 dimensions is analysed from the point of view of its symmetries all equations of the type studied having non trivial lie point symmetry groups g are identified the symmetry group is shown to be at most five dimensional and only when the equation is equivalent to the nls equation itself or to a rather special complex ginzburg landau equation lie point transformations are used to obtain solutions of specific vcnls equations that should be of interest in nonlinear optics or other branches of physics

error estimates for a finite element discretization of a phase field model for mixtures we derive error estimates for finite element discretizations of phase field models that describe phase transitions in nonisothermal mixtures special attention is paid to the applicability of the result for a large class of models with nonlinear constitutive relations and to an approach that avoids an exponential dependence of the constants in the error estimate on the approximation parameter that models the thickness of the diffuse phase transition region the main assumptions on the model are a convexity condition for a function that can be interpreted as the negative local part of the entropy of the system a suitable regularity of the exact solutions and a spectrum estimate for the operator of the allen cahn equation the spectrum estimate is crucial to avoid the exponential dependence of error constants on the approximation parameters in the model this is done by a technique introduced in x feng and a prohl math comp 73 2004 pp 541 567 for phase transitions of pure materials with linear constitutive relations

interval estimation for a difference between intraclass kappa statistics summary model based inference procedures for the kappa statistic have developed rapidly over the last decade however no method has yet been developed for constructing a confidence interval about a difference between independent kappa statistics that is valid in samples of small to moderate size in this article we propose and evaluate two such methods based on an idea proposed by newcombe 1998 statistics in medicine 17 873 890 for constructing a confidence interval for a difference between independent proportions the methods are shown to provide very satisfactory results in sample sizes as small as 25 subjects per group sample size requirements that achieve a prespecified expected width for a confidence interval about a difference of kappa statistic are also presented

analysis of the cahn hilliard equation with a relaxation boundary condition modeling the contact angle dynamics we analyze the cahn hilliard equation with a relaxation boundary condition modeling the evolution of an interface in contact with the solid boundary an l estimate is established which enables us to prove the global existence of the solution we also study the sharp interface limit of the system the dynamic of the contact point and the contact angle are derived and the results are compared with the numerical simulations

commutation methods applied to the mkdv equation an explicit construction of solutions of the modified korteweg de vries equation given a solution of the ordinary korteweg de vries equation is provided our theory is based on commutation methods i e n 1 supersymmetry underlying miura s transformation that links solutions of the two evolution equations

retrieving topological information for phase field models the phase field approach has become a popular tool in modeling interface motion microstructure evolution and more recently the shape transformation of vesicle membranes under elastic bending energy while it is advantageous to employ phase field models in numerical simu lations to automatically handle topological changes to the microstructures or the configurations of vesicle membranes detecting topological events may also become important for many applications such as those in the simulation of blood cells motivated by such considerations a new quantity is formulated to retrieve some topological information based on the phase field formulation and to capture the occurrence of topological events it can also be used as a control method to avoid unphys ical changes of topology due to the numerical methods should it become necessary for particular practical applications through numerical experiments we demonstrate the effectiveness and the robustness of the new quantity in detecting the topology of fluid bubbles and vesicle membranes

continuity of the temperature in the two phase stefan problem the classical two phase stefan problem a model for ice water melting gives rise to a singular nonlinear partial differential equation which admits a unique weak solution here we prove that this solution and therefore the temperature in the stefan problem are continuous

causal estimation using semiparametric transformation models under prevalent sampling this paper develops methods and inference for causal estimation in semiparametric transformation models for prevalent survival data through estimation of the transformation models and covariate distribution we propose analytical procedures to estimate the causal survival function as the data are observational the unobserved potential outcome survival time may be associated with the treatment assignment and therefore there may exist a systematic imbalance between the data observed from each treatment arm further due to prevalent sampling subjects are observed only if they have not experienced the failure event when data collection began causing the prevalent sampling bias we propose a unified approach which simultaneously corrects the bias from the prevalent sampling and balances the systematic differences from the observational data we illustrate in the simulation study that standard analysis without proper adjustment would result in biased causal inference large sample properties of the proposed estimation procedures are established by techniques of empirical processes and examined by simulation studies the proposed methods are applied to the surveillance epidemiology and end results seer and medicare linked data for women diagnosed with breast cancer

assessment of risks by predicting counterfactuals risk assessment is fundamental to most epidemiological and biomedical investigations in this article risks are assessed in terms of risk difference and risk ratio by predicting counterfactual outcomes models considered for binary outcomes are probit logistic and extreme value regressions new confidence intervals for the effect measures are proposed using the method of variance estimates recovery and evaluated by a simulation study a sas macro is provided for the calculations a risk ratio obtained using counterfactuals is also compared in the simulation with that directly estimated from the modified poisson model to answer a recent concern about the validity of the latter approach two examples are used to illustrate the methods

derivation of the wenzel and cassie equations from a phase field model for two phase flow on rough surface in this paper the equilibrium behavior of an immiscible two phase fluid on a rough surface is studied from a phase field equation derived from minimizing the total free energy of the system when the size of the roughness becomes small we derive the effective boundary condition for the equation by the multiple scale expansion homogenization technique the wenzel and cassie equations for the apparent contact angles on the rough surfaces are then derived from the effective boundary condition the homogenization results are proved rigorously by the convergence theory

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

an improved γ riccati backlund transformation and its applications for the inhomogeneous nonlinear schrodinger model from plasma physics and nonlinear optics abstract the inhomogeneous nonlinear schrodinger type nls model from certain plasmas and optical fibers is investigated with symbolic computation an improved riccati backlund transformation r bt is presented which can generate successively a hierarchy of solutions through algebraic manipulations based on the improved r bt the darboux transformation is obtained the analytic one two soliton like solutions are presented and the physical characteristics of the influences of the coefficient parameters on the propagation of the soliton pulses are discussed graphically

on a navier stokes allen cahn model with inertial effects abstract a mathematical model describing the flow of two phase fluids in a bounded container is considered under the assumption that the phase transition is influenced by inertial effects the model couples a variant of the navier stokes system for the velocity u with an allen cahn type equation for the order parameter relaxed in time in order to introduce inertia at the microscopic level the resulting model is characterized by second order material derivatives which constitute the main difficulty in the mathematical analysis in order to obtain a tractable problem a viscous relaxation term is then included in the phase equation the mathematical results consist in existence of weak solutions in 3d and under additional assumptions existence and uniqueness of strong solutions in 2d a partial characterization of the long time behavior of solutions is also given and in particular some issues related to dissipation of energy are discussed

homogenization of rough boundaries and interfaces homogenization is used to analyze a partial differential equation in a domain with a very rough boundary or interface following the procedure of kohler papanicolaou and varadhan boundary and interface problems in regions with very rough boundaries in multiple scattering and waves in random media p chow w kohler and g papanicolaou eds north holland amsterdam 1981 pp 165 197 and brizzi and chalot homogeneisation de frontiere ph d thesis department of mathematics universite de nice nice france 1978 it is shown that such a boundary or interface can be replaced by an equivalent layer within which a modified differential equation holds the coefficients in this new equation are certain effective parameters such as the effective conductivity the effective dielectric constant the effective refractive index etc these coefficients are determined by the solutions of certain special problems which involve the detailed shape of the boundary or interface this analysis is applied to

a multiscale finite element method for partial differential equations posed in domains with rough boundaries we propose and analyze a finite element scheme of multiscale type to deal with elliptic partial differential equations posed in domains with rough boundaries there is no need to assume that the boundary is periodic in any sense so the method is quite general on the other hand if the boundary is periodic we prove convergence of the scheme

gauge and backlund transformations for the variable coefficient higher order modified korteweg de vries equation a family of higher order modified korteweg de vries equations with variable coefficients t ho mkdv is introduced a one to one correspondence between a real solution of these equations and a complex solution of the variable coefficient higher order korteweg de vries t ho kdv equations is established through a complex miura transformation an auto backlund transformation for these t ho mkdv equations is derived from that of the t ho kdv equations the associated gauge transformations of the corresponding akns systems are presented they enable one to construct a hierarchy of solutions of the t ho mkdv equations from a known hierarchy without solving the differential equations for the wave functions except the first one a new family of higher order evolution equations with an auto backlund transformation is also derived in connection with the gauge transformation of the t ho mkdv equations

flows of incompressible viscous liquids with anisotropic wall slip abstract this paper deals with a boundary value problem for the stokes equations with a general direction dependent navier type slip boundary condition this problem models the steady laminar flow of an incompressible linearly viscous liquid in a bounded domain with an impermeable rough boundary with variable and anisotropic roughness it is proved that the problem has a unique weak solution

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

weak solution of a stochastic 3d cahn hilliard navier stokes model driven by jump noise abstract we investigate a stochastic 2d and 3d cahn hilliard navier stokes system with a multiplicative noise of levy type the model consists of the navier stokes equations for the velocity coupled with a cahn hilliard system for the order phase parameter we prove that the system the existence of weak martingale solution for both 2d and 3d cases the proof of the existence is based on a classical galerkin approximation as well as some compactness methods in the 2d case we prove the pathwise uniqueness of the weak solution

existence of global solutions to the caginalp phase field system with dynamic boundary conditions and singular potentials our aim in this article is to prove the global in time existence of solutions to a caginalp phase field system with dynamic boundary conditions and a singular potential the main difficulty is to prove that the solutions are strictly separated from the singular values of the potential this is achieved by studying an auxiliary elliptic problem

the phase field method in the sharp interface limit the phase field pf method for solidification phenomena is an open formulation based on a free energy functional two common choices for the pf potential here referred to briefly as the caginalp and kobayashi models are compared with respect to their numeric results within the classical sharp interface limit both qualitative and quantitative behavior are addressed and an assessment of the computational effort required to approximate a sharp interface problem is made it is shown that the specific form of the free energy potential does have a strong influence on the convergence of the pf results to their sharp interface limit compliance of the pf solutions with the linear kinetic model for the interface temperature is also investigated a simple one dimensional solidification problem in the presence of kinetic undercooling is solved by the pf model and also by a deforming grid method our results support the view that if care is exercised in formulating the phase temperature coupling there is a high degree of confidence in using the pf method for the numerical modeling of general solidification phenomena

the quasistationary phase field equations with neumann boundary conditions abstract we prove that the quasistationary phase field equations t u u f 2e 1 e w u where w t t 2 1 2 is a double well potential admit a solution when the space dimension n 3 and that the solutions converge for e 0 to solutions of the stefan problem with gibbs thomson law

restricted mean life with adjustment for covariates abstract although the mean is the most widely used measure of location in comparing two distributions its use is essentially precluded in the presence of substantial censoring typical in survival analysis of medical therapies to accommodate censoring irwin 1949 proposed estimation of the expectation of life restricted to a time t using the actuarial estimator of the survival function in this article we examine the restricted mean as an index for comparing survival in two groups and then extend the method to incorporate covariates into the analysis for this purpose it is convenient to depart slightly from the actuarial approach and to consider piecewise exponential models asymptotic properties are explored and the assumption of piecewise exponentiality is shown to be rather mild as departures from the model have a relatively small effect on estimation of the restricted mean the methodology is illustrated using published data from a study conducted by the radiation therapy oncology group rtog

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

the gibbs thompson relation within the gradient theory of phase transitions this paper discusses the asymptotic behavior as 0 of the chemical potentials associated with solutions of variational problems within the van der waals cahn hilliard theory of phase transitions in a fluid with free energy per unit volume given by 2 2 w where is the density the main result is that is asymptotically equal to e d o with e the interfacial energy per unit surface area of the interface between phases the constant sum of principal curvatures of the interface and d the density jump across the interface this result is in agreement with a formula conjectured by m gurtin and corresponds to the gibbs thompson relation for surface tension proved by g caginalp within the context of the phase field model of free boundaries arising from phase transitions

estimating standardized parameters from generalized linear models although the traditional unrestricted non parametric estimators of directly standardized rates and rate differences remain unbiased in sparse data they tend to suffer from instability low precision as a result many authors have proposed more precise estimators based on parametric models for the rates this paper provides a general approach for constructing estimators of standardized parameters using generalized linear models and shows that in some common special cases these model based smoothed estimators can have an exceptionally simple form

an improved method for darboux transformation for the coupled inhomogeneous nonlinear schrodinger system from plasma physics and nonlinear optics abstract the coupled inhomogeneous nonlinear schrodinger type system which can be used to control soliton propagation and interaction in certain plasmas and optical fibers is investigated an improved method for darboux transformation dt is presented in more general forms by constructing an improved riccati type backlund transformation r bt with the n th iterated r bt or the n th iterated dt which is a compact representation for the n soliton like solutions and can generate a series of analytic solutions from a pair of the seed solutions through algebraic manipulations the analytic one two soliton like solutions are provided with the choice of parameters for the soliton solutions the dynamical characteristics of the influences of the inhomogeneous parameters on the propagation of the soliton pulses are discussed graphically

shape instabilities and pattern formation in solidification a new method for numerical solution of the moving boundary problem abstract when a solidification front is advancing into a region of supercooled liquid its shape is subject to instabilities which can lead to complex modes of growth the evaluation of the growth pattern is determined by the interaction of the driving force of the instability due to heat diffusion with the restabilizing force due to surface tension and its full development is a highly nonlinear process a new method for solving the two phase heat diffusion problem under these conditions is described the method is based on a single domain treatment weak formulation of the moving boundary problem with the temperature field near the interface approximated by a piecewise linear function in the spirit of the finite element technique calculated results for a model problem are in excellent agreement with the predictions of an analytical approximation

reconstruction of two time independent coefficients in an inverse problem for a phase field system abstract in this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain r n for the dimension n 3 with a single observation on a subdomain and the sobolev norm of certain partial derivatives of the solutions at a fixed positive time 0 t over the whole spatial domain the proof of these results relies on an appropriate carleman estimate for the phase field system

gauge transformation and the higher order korteweg de vries equation to the family of higher order korteweg de vries kdv equations a new family of higher order mkdv equations depending on a parameter is constructed they are connected by an 2 dependent miura transformation a backlund transformation is also established furthermore a new gauge transformation is associated to this backlund transformation it enables one to derive auto backlund transformations for the families of higher order 2 mkdv and kdv equations respectively for illustration four generations of explicit solutions of the second order kdv equation are presented

quasilinear systems with memory kernels we consider a quasilinear integrodifferential system in non normal form such a system is a generalization of a phase field model with memory and includes as a particular case the system describing the combustion of a material with memory in this paper we study both the direct and the inverse problems our fundamental tools are the theory of analytic semigroups optimal regularity results and fixed point arguments

exponential attractors for a conserved phase field system with memory we consider a conserved phase field system of caginalp type characterized by the assumption that both the internal energy and the heat flux depend on the past history of the temperature and its gradient respectively the model consists of a parabolic integrodifferential equation coupled with a fourth order evolution equation for the phase field this system supplemented with suitable boundary conditions can be interpreted as a dissipative dynamical system in a proper phase space in a previous joint work the last two authors have proved the existence of a global attractor of finite fractal dimension here we show the existence of an exponential attractor by means of the techniques we developed for nonconserved phase field systems with memory

effective contact angle for rough boundary abstract we provide rigorous justification for the classical wenzel equation for the roughness enhanced effective contact angle the minimization of the total surface energy is reformulated into a variational problem as the size of the roughness becomes small we show convergence of the minimizer the limiting minimizer and effective contact angle are explicitly calculated to verify the wenzel equation

prediction in censored survival data a comparison of the proportional hazards and linear regression models although the analysis of censored survival data using the proportional hazards and linear regression models is common there has been little work examining the ability of these estimators to predict time to failure this is unfortunate since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a kaplan meier plot obtained by discretizing the variable in this paper the predictive power of the cox 1972 journal of the royal statistical society series b 34 187 202 proportional hazards estimator and the buckley james 1979 biometrika 66 429 436 censored regression estimator are compared using computer simulations and heuristic arguments it is shown that the choice of method depends on the censoring proportion strength of the regression the form of the censoring distribution and the form of the failure distribution several examples are provided to illustrate the usefulness of the methods

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

computer simulations of phase field drops on super hydrophobic surfaces abstract we present a novel quasi newton continuation procedure that efficiently solves the system of nonlinear equations arising from the discretization of a phase field model for wetting phenomena we perform a comparative numerical analysis that shows the improved speed of convergence gained with respect to other numerical schemes moreover we discuss the conditions that on a theoretical level guarantee the convergence of this method at each iterative step a suitable continuation procedure develops and passes to the nonlinear solver an accurate initial guess discretization performs through cell centered finite differences the resulting system of equations is solved on a composite grid that uses dynamic mesh refinement and multi grid techniques the final code achieves three dimensional realistic computer experiments comparable to those produced in laboratory settings this code offers not only new insights into the phenomenology of super hydrophobicity but also serves as a reliable predictive tool for the study of hydrophobic surfaces

backlund transformation for the non isospectral and variable coefficient non linear schrodinger equation a non linear schrodinger equation nlse with a non isospectral lax pair and variable coefficients is studied this equation is shown to be an integrability condition for an akns system a gamma riccati system and a lax pair these three systems are proved to be equivalent they are all invariant under some generalisation of the konno wadati transformation related to this nlse there is also a variable coefficients evolution equation for the function gamma derived from the gamma riccati system a backlund transformation for this gamma equation has been constructed with this a new backlund transformation for the nlse is presented so that successive generation of new solutions is reduced to integration only

regression analysis with clustered data clustered data are found in many different types of studies for example studies involving repeated measures inter rater agreement studies household surveys crossover designs and community randomized trials analyses based on population average and cluster specific models are commonly used for estimating treatment exposure effects with clustered data this paper discusses conditions when one or both types of models are appropriate for estimating causal effects and when there is agreement between population average and cluster specific analyses applications of survey sampling methods to the robust estimation of standard errors of estimated treatment parameters are discussed

the numerical computation of heteroclinic connections in systems of gradient partial differential equations the numerical computation of heteroclinic connections in partial differential equations pdes with a gradient structure such as those arising in the modeling of phase transitions is considered initially a scalar reaction diffusion equation is studied structural assumptions are made on the problem to ensure the existence of absorbing sets and consequently a global attractor as a result of the gradient structure it is known that if all equilibria are hyperbolic the global attractor comprises the set of equilibria and heteroclinic orbits connecting equilibria to one another thus it is natural to consider direct approximation of the set of equilibria and the connecting orbits results are proved about the fourier spanning basis for branches of equilibria and also for certain heteroclinic connections these results exploit the oddness of the nonlinearity the reaction diffusion equation is then approximated by a galerkin spectral discretization to produce a system of ordinary differential equations

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

abstract approach to evolution equations of phase field type and applications a general system of abstract nonlinear parabolic equations deriving from phase field models of heat transfer in anisotropic fluids with phase transitions is studied through a backward finite differences approximation scheme and existence and uniqueness theorems are proved then applications are presented to two physical situations first a standard heat diffusion problem is briefly discussed mainly as a justification of the choices of the abstract setting second a more interesting transmission problem between two different adjoining fluids is studied under very general compatibility hypotheses and the abstract results are adapted to provide an existence and uniqueness theorem also in this case moreover through convex analysis techniques it is performed a mathematical study of the subdifferential type relations linking the phase fields and the temperatures to the internal energies of the fluids email schimper dragon ian pv cnr it keywords phase field models subdifferential operators abstract evolution equations

effective boundary conditions for laminar flows over periodic rough boundaries effective boundary conditions or wall laws are proposed for a laminar flow over a rough wall with periodic roughness elements these effective conditions are posed on a regularized boundary which allows the details of the wall to be avoided and dramatically reduces the computational cost the effective conditions stem from an asymptotic expansion of the solution which is presented here both first and second order conditions are discussed and tested numerically on bidimensional cases

global existence and asymptotic behavior for the radially symmetric case of a two phase stefan problem with interfacial energy abstract this paper is concerned with global existence in time and asymptotic behavior for the radially symmetric case of a stefan problem with surface tension effects on the interface according to the static gibbs thomson law these problems arise in phase change theory

local minimisers and singular perturbations we construct local minimisers to certain variational problems the method is quite general and relies on the theory of convergence the approach is demonstrated through the model problem it is shown that in certain nonconvex domains n and for e small there exist nonconstant local minimisers u e satisfying u e 1 except in a thin transition layer the location of the layer is determined through the requirement that in the limit u e u 0 the hypersurface separating the states u 0 1 and u 0 1 locally minimises surface area generalisations are discussed with for example vector valued u and anisotropic perturbations replacing u 2

dynamics of layered interfaces arising from phase boundaries the dynamics of a material in two phases is studied in the context of phase field models based on a landau ginzburg free energy functional they consist of a system of two nonlinear diffusion equat

wetting of rough surfaces a homogenization approach the contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests we study the roughness induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory by relying on a variational formulation of the problem we show that the macroscopic contact angle is associated with the solution of two cell problems giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase our results are valid for both chemically heterogeneous and homogeneous surfaces in the latter case a very transparent structure emerges from the variational approach the classical laws of wenzel and cassie baxter give bounds for the optimal energy and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case to the largest one in the hydrophilic case

front tracking finite element method for dendritic solidification 765 abstract a two dimensional finite element method capable of tracking sharp interfaces is developed the method is based on a fixed mesh of bilinear isoparametric elements and is extremely simple and easy to use the interfaces are tracked with a set of marker points that define their position at all times several different approaches to finding the interface position and velocity are discussed and their effect on the convergence rate is examined it is shown through numerical examples that the approximation to the interface position converges with second order accuracy in two dimensional problems as opposed to previously developed finite difference algorithms that are only first order accurate the approximation to the interface velocity is shown to be of first order a number of examples are examined including several that provide a careful comparison with previously published results

phase field method to optimize dielectric devices for electromagnetic wave propagation we discuss a phase field method for shape optimization in the context of electromagnetic wave propagation the proposed method has the same functional capabilities as the level set method for shape optimization the first advantage of the method is the simplicity of computation since extra operations such as re initialization of functions are not required the second is compatibility with the topology optimization method due to the similar domain representation and the sensitivity analysis structural shapes are represented by the phase field function defined in the design domain and this function is optimized by solving a time dependent reaction diffusion equation the artificial double well potential function used in the equation is derived from sensitivity analysis we study four types of 2d or 2 5d axisymmetric optimization problems two are the classical problems of photonic crystal design based on the bloch theory and photonic crystal wave guide design and two are the recent topics of designing dielectric left handed metamaterials and dielectric ring resonators

an integral equation method for the cahn hilliard equation in the wetting problem abstract we present an integral equation approach to solving the cahn hilliard equation equipped with boundary conditions that model solid surfaces with prescribed young s angles the discretization of the system in time using convex splitting leads to a modified biharmonic equation at each time step to solve it we split the solution into a volume potential computed with free space kernels plus the solution to a second kind integral equation skie the volume potential is evaluated with the help of a box based volume fmm method for non box domains the source density is extended by solving a biharmonic dirichlet problem the near singular boundary integrals are computed using quadrature by expansion qbx with fmm acceleration our method has linear complexity in the number of surface volume degrees of freedom and can achieve high order convergence in space with adaptive refinement to manage error from function extension

well posedness results and asymptotic behaviour for a phase transition model taking into account microscopic accelerations we obtain an existence and uniqueness result to fremond s phase transition model which take into account microscopic movements and accelerations moreover the irreversible evolution of the phase variable is considered next we perform an asymptotic analysis on the solution to the above problem as the power of the microscopic acceleration forces goes to zero

standardized estimates from categorical regression models we consider the problem of interpreting categorical regression models such as the polytomous logistic model the continuation ratio model the stereotype model and the cumulative odds model we present a method to convert categorical regression coefficients into estimates of standardized fitted probabilities probability differences and probability ratios we use a delta method approach to estimate standard errors we then present a small simulation study to compare different transforms for setting confidence limits and provide an illustration of our approach in an observational study of drug therapy of polymyositis

a free boundary problem with facets we study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous hamiltonian we find an explicit formula for the hamiltonian prove that the solutions are unique and prove that the limiting free boundary has a facets in every rational direction our choice of problem presents difficulties that require the development of a new uniqueness proof for certain free boundary problems the problem is motivated by physical experiments involving liquid drops on patterned solid surfaces

relevance of the slip condition for fluid flows near an irregular boundary we consider the navier stokes equation in a domain with a rough boundary the roughness is modeled by a small amplitude and small wavelength oscillation with typical scale varepsilon ll 1 for periodic oscillation it is well known that the best homogenized that is regular in varepsilon boundary condition is of navier type such result still holds for random stationary irregularities as shown recently by the first author 5 15 we study here arbitrary irregularity patterns

effective boundary condition at a rough surface starting from a slip condition abstract we consider the homogenization of the navier stokes equation set in a channel with a rough boundary of small amplitude and wavelength it was shown recently that for any non degenerate roughness pattern and for any reasonable condition imposed at the rough boundary the homogenized boundary condition in the limit e 0 is always no slip we give in this paper error estimates for this homogenized no slip condition and provide a more accurate effective boundary condition of navier type our result extends those obtained in basson and gerard varet 2008 6 and gerard varet and masmoudi 2010 13 in which the special case of a dirichlet condition at the rough boundary was examined

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

phase field models for hypercooled solidification abstract properties of the solidification front in a hypercooled liquid so called because the temperature of the resulting solid is below the melting temperature are derived using a phase field diffuse interface model certain known properties for hypercooled fronts in specific materials are reflected within our theories such as the presence of thin thermal layers and the trend towards smoother fronts with less pronounced dendrites when the undercooling is increased within the hypercooled regime both an asymptotic analysis to derive the relevant free boundary problems and a rigorous determination of the inner profile of the diffusive interface are given of particular interest is the incorporation of anisotropy and general microscale interactions leading to higher order differential operators these features necessitate a much richer mathematical analysis than previous theories anisotropic free boundary problems are derived from our models the simplest of which involves determining the evolution of a set a solid particle whose boundary moves with velocity depending on its normal vector considerable attention is given to the identification of surface tension to comparison with previous theories and to questions of stability

hyperbolic phase field dynamics with memory abstract we consider a non conserved phase field system which consists of two nonlinearly coupled hyperbolic integrodifferential equations this model is derived from two basic assumptions the heat flux law is of gurtin pipkin type and the response of the order parameter to the variation of the free energy functional is delayed these hypotheses might be a reasonable attempt to describe for instance the melt of he 4 crystals a suitable initial and boundary value problem is then associated with the system and its well posedness is analyzed in detail

constructing wall laws with domain decomposition or asymptotic expansion techniques abstract this paper is concerned with the numerical simulation of flows of viscous fluids over rough surfaces the proposed methodology introduces consistant equivalent wall laws using domain decomposition techniques with nonmatching grids and local periodicity assumptions the paper describes this approach with its theoretical background studies its limitations and its potential applicability and compares its results to the boundary conditions that are obtained by alternative asymptotic strategies

computation of sharp phase boundaries by spreading the planar and spherically symmetric cases abstract the sharp interface that arises from any of the major transition problems classical or modified stefan etc can be smoothed using the phase field approach as a numerical tool the basic idea is that the thickness of the interface can be regarded as a mathematical free parameter which can be stretched beyond its physical value for computational convenience the computations in one dimensional space and n dimensions with radial symmetry indicate that this is an efficient method for dealing with stiff equations and results in a very accurate interface determination without explicit tracking the question of optimizing the interfacial thickness with respect to grid size is also considered empirically the technique also provides a numerical verification of the concept of an unstable critical radius of solidification

weighted hilbert spaces for the stationary exterior stokes problem with navier slip boundary conditions abstract in this paper we analyze the three dimensional exterior stokes problem with the navier slip boundary conditions describing the flow of a viscous and incompressible fluid past an obstacle where it is assumed that the fluid may slip at the boundary because the flow domain is unbounded we set the problem in weighted spaces in order to control the behavior at infinity of the solutions this functional framework also allows to prescribe various behaviors at infinity of the solutions growth or decay existence and uniqueness of solutions are shown in a hilbert setting which gives the tools for a possible numerical analysis of the problem weighted korn s inequalities are the key point in order to study the variational problem

effective surface and boundary conditions for heterogeneous surfaces with mixed boundary conditions to deal with multi scale problems involving transport from a heterogeneous and rough surface characterized by a mixed boundary condition an effective surface theory is developed which replaces the original surface by a homogeneous and smooth surface with specific boundary conditions a typical example corresponds to a laminar flow over a soluble salt medium which contains insoluble material to develop the concept of effective surface a multi domain decomposition approach is applied in this framework velocity and concentration at micro scale are estimated with an asymptotic expansion of deviation terms with respect to macro scale velocity and concentration fields closure problems for the deviations are obtained and used to define the effective surface position and the related boundary conditions the evolution of some effective properties and the impact of surface geometry peclet schmidt and damkohler numbers are investigated finally comparisons are made between the numerical results obtained with the effective models and those from direct numerical simulations with the original rough surface for two kinds of configurations

analysis of covariance and standardization as instances of prediction in this paper prediction provides the basis for unifying the procedures of covariances adjustment and standardization analysis of covariance is a method of forming predictions from a linear model it is used when qualitative effects are to be studied and the effects of continuous variables are to be adjusted for an essential feature is the division into effects of interest and effects for which adjustment is required covariates may also be qualitative as such they are used implicitly in experimental designs with blocks where treatment effects are adjusted for the effect of blocks the technique of standardization is well known in epidemiology and demography as a method of adjusting explicitly for qualitative effects the same division of effects applies when an analysis that uses generalized linear models is summarized two distinct types of prediction which give identical results in classical linear models are available prediction may be conditional on a fixed value of a covariate or marginal on a distribution of values such as the distribution in the set of data being analysed prediction methods are illustrated by the analysis of a table of proportions by use of a logit model

wall laws for fluid flows at a boundary with random roughness the general concern of this paper is the effect of rough boundaries on fluids we consider a stationary flow governed by incompressible navier stokes equations in an infinite domain bounded by two horizontal rough plates the roughness is modeled by a spatially homogeneous random field with characteristic size e a mathematical analysis of the flow for small e is performed the navier s wall law is rigorously deduced from this analysis this substantially extends former results obtained in the case of periodic roughness notably in 16 17 2007 wiley periodicals inc

relaxation of quasiconvex functional in bv ω ℝp for integrands f x u u in this paper it is shown that if p x u is a quasiconvex function with linear growth then the relaxed functional in bv p of u to int limits omega f x u x nabla u x dx with respect to the l1 topology has an integral representation of the form begin gathered mathfrak f u int limits omega f x u x nabla u x dx int limits sigma u k x u x u x v x dh n 1 x hfill int limits omega f infty x u x dc u hfill end gathered where du u dx u u v dhn 1l u c u the proof relies on a blow up argument introduced by fonseca muller in the case where u w1 1 and on a recent result by alberti showing that the cantor part c u is rank one valued

on a nonlocal phase field system abstract we study the existence uniqueness and continuous dependence on initial data of the solution to a nonlocal phase field system on a bounded domain the system is a gradient flow for a free energy functional with nonlocal interaction also we study the asymptotic behavior of the solution and show the existence of an absorbing set in some metric space