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

study of phase field lattice boltzmann models based on the conservative allen cahn equation conservative phase field cpf equations based on the allen cahn model for interface tracking in multiphase flows have become more popular in recent years especially in the lattice boltzmann lb community this is largely due to their simplicity and improved efficiency and accuracy over their cahn hilliard based counterparts additionally the improved locality of the resulting lb equation lbe for the cpf models makes them more ideal candidates for lb simulation of multiphase flows on nonuniform grids particularly within an adaptive mesh refinement framework and massively parallel implementation in this regard some modifications intended as improvements have been made to the original cpf lbe proposed by geier et al phys rev e 91 063309 2015 pleee81539 375510 1103 physreve 91 063309 which require further examination the goal of the present study is to conduct a comparative investigation into the differences between the original cpf model proposed by geier et al phys rev e 91 063309 2015 pleee81539 375510 1103 physreve 91 063309 and the so called improvements proposed by ren et al phys rev e 94 023311 2016 2470 004510 1103 physreve 94 023311 and wang et al phys rev e 94 033304 2016 2470 004510 1103 physreve 94 033304 using the chapman enskog analysis we provide a detailed derivation of the governing equations in each model and then examine the efficacy of the above mentioned models for some benchmark problems several test cases have been designed to study different configurations ranging from basic yet informative flows to more complex flow fields and the results are compared with finite difference simulations furthermore as a development of the previously proposed cpf lbe model axisymmetric formulations for the proposed model by geier et al phys rev e 91 063309 2015 pleee81539 375510 1103 physreve 91 063309 are derived and presented finally two benchmark problems are designed to compare the proposed axisymmetric model with the analytical solution and previous work we find that the accuracy of the model for interface tracking is roughly similar for different models at high viscosity ratios high density ratios and relatively high reynolds numbers while the original cfp lbe without the additional time dependent terms outperforms the so called improved models in terms of efficiency particularly on distributed parallel machines

spectral distributed lagrange multiplier method algorithm and benchmark tests we extend the formulation of the distributed lagrange multiplier dlm approach for particulate flows to high order methods within the spectral hp element framework we implement the rigid body motion constraint inside the particle via a penalty method the high order dlm method demonstrates spectral convergence rate i e discretization errors decrease exponentially as the order of spectral polynomials increases we provide detailed comparisons between the spectral dlm method direct numerical simulations and the force coupling method for a number of 2d and 3d benchmark flow problems we also validate the spectral dlm method with available experimental data for a transient problem the new dlm method can potentially be very effective in many moving body problems where a smaller number of grid points is required in comparison with low order methods

hybrid confidence regions based on data depth summary we consider the general problem of constructing confidence regions for possibly multi dimensional parameters when we have available more than one approach for the construction these approaches may be motivated by different model assumptions different levels of approximation different settings of tuning parameters or different monte carlo algorithms their effectiveness is often governed by different sets of conditions which are difficult to vindicate in practice we propose two procedures for constructing hybrid confidence regions which endeavour to integrate all such individual approaches the procedures employ the concept of data depth to calibrate the confidence region in two different ways the first rendering its coverage error minimax and the second rendering its coverage error conservative the resulting region reconciles in many important aspects the discrepancies between the various approaches and is robust against misspecification of their governing conditions theoretical and empirical properties of our procedures are investigated in comparison with those of the constituent individual approaches

tests for individual and population bioequivalence based on generalized p values the u s food and drug administration fda has proposed new regulations that address the prescribability and switchability of new formulations of already approved drugs these new criteria are known respectively as population and individual bioequivalence two methods have been proposed in the bioequivalence literature for assessing population and individual bioequivalence that calculate an upper 95 per cent confidence bound for the bioequivalence criterion in question and then test bio equivalence by comparing this bound to the limit established by the fda in this paper we propose applying the generalized test function gtf methodology of tsui and weerahandi journal of the american statistical association 1989 602 607 to this problem to produce tests based on a generalized p value gpv this methodology allows us to construct hypothesis tests in the presence of nuisance parameters using simulation we show that these tests perform well in comparison to the confidence interval methods and have superior power for assessing population bioequivalence copyright 2003 john wiley sons ltd

modelling merging and fragmentation in multiphase flows with surfer we introduce a new numerical method called surfer for the simulation of two and three dimensional flows with several fluid phases and free interfaces between them we consider incompressible fluids obeying the navier stokes equation with newtonian viscosity in the bulk of each phase capillary forces are taken into account even when interfaces merge or break up fluid interfaces are advanced in time using an exactly volume conserving variant of the volume of fluid algorithm thus allowing for full symmetry between fluid phases the navier stokes equation is solved using staggered finite differences on a mac grid and a split explicit time differencing scheme while incompressibility is enforced using an iterative multigrid poisson solver capillary effects are represented as a stress tensor computed from gradients of the volume fraction function this formulation is completely independent of the topology of interfaces and relatively easy to implement in 3d it also allows exact momentum conservation in the discretized algorithm numerical spurious effects or parasite currents are noticed and compared to similar effects in boltzmann lattice gas methods for immiscible fluids simulations of droplets pairs colliding in 2d and in 3d are shown interface reconnection is performed easily despite the large value of capillary forces during reconnection

construction of confidence limits about effect measures a general approach it is widely accepted that confidence interval construction has important advantages over significance testing for the presentation of research results as now facilitated by readily available software however for a number of effect measures procedures are either not available or not satisfactory in samples of small to moderate size in this paper we describe a general approach for estimating a difference between effect measures which can also be used to obtain confidence limits for a risk ratio and a lognormal mean numerical evaluation shows that this closed form procedure outperforms existing methods including the bootstrap

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

marginal inferential models prior free probabilistic inference on interest parameters the inferential models im framework provides prior free frequency calibrated and posterior probabilistic inference the key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown parameters when nuisance parameters are present a marginalization step can reduce the dimension of the auxiliary variable which in turn leads to more efficient inference for regular problems exact marginalization can be achieved and we give conditions for marginal im validity we show that our approach provides exact and efficient marginal inference in several challenging problems including a many normal means problem in nonregular problems we propose a generalized marginalization technique and prove its validity details are given for two benchmark examples namely the behrens fisher and gamma mean problems

fiducial generalized confidence intervals generalized pivotal quantities gpqs and generalized confidence intervals gcis have proven to be useful tools for making inferences in many practical problems although gcis are not guaranteed to have exact frequentist coverage a number of published and unpublished simulation studies suggest that the coverage probabilities of such intervals are sufficiently close to their nominal value so as to be useful in practice in this article we single out a subclass of generalized pivotal quantities which we call fiducial generalized pivotal quantities fgpqs and show that under some mild conditions gcis constructed using fgpqs have correct frequentist coverage at least asymptotically we describe three general approaches for constructing fgpqs a recipe based on invertible pivotal relationships and two extensions of it and demonstrate their usefulness by deriving some previously unknown gpqs and gcis it is fair to say that nearly every published gci can be obtained using one of these recipes as an inte

degradation data analysis based on gamma process with random effects abstract this paper focuses on investigating the gamma degradation model with random effects a generalized p value procedure is proposed to test whether there exist some heterogeneities among the degradation processes of different units using the cornish fisher expansion an approximate confidence interval ci is obtained for the shape parameter the generalized confidence intervals gcis are derived for model parameters and commonly used reliability metrics e g the quantile the reliability function of the lifetime based on the generalized pivotal quantity method those inference procedures are also extended to the accelerated degradation case the performances of the proposed gcis are assessed by monte carlo simulations in the simulation we compared our methods with the wald cis and bootstrap p cis under moderate and large sample sizes it is found that the performance of the gci procedures is better than the wald cis and bootstrap p cis in terms of coverage probabilities finally the proposed procedures are illustrated by two examples

the dynamics of nucleation for the cahn hilliard equation when a constant metastable solution of the cahn hilliard equation is subjected to a spatially localized large amplitude perturbation a transition process may be triggered leading to a globally stable stationary solution in one space dimension the existence and instability of a third stationary solution with the same mass is proved a spike like solution called a canonical nucleus within the class of solutions which are even with respect to the center of the spike it has a one dimensional unstable manifold in addition the process of nucleation by formal arguments using two space scales and two timescales is described the last stage in the process can be approximated by a nonlinear stefan free boundary problem

a dynamic mesh algorithm for curvature dependent evolving interfaces a new finite element method is discussed for approximating evolving interfaces in2nwhose normal velocity equals mean curvature plus a forcing function the method is insensitive to singularity formation and retains the local structure of the limit problem and thus exhibits a computational complexity typical of3n 1without having the drawbacks of front tracking strategies a graded dynamic mesh around the propagating front is the sole partition present at any time step and is significantly smaller than a full mesh time stepping is explicit but stability constraints force small time steps only when singularities develop whereas relatively large time steps are allowed before or past singularities when the evolution is smooth the explicit marching scheme also guarantees that at most one layer of elements has to be added or deleted per time step thereby making mesh updating simple and thus practical performance and potentials are fully documented via a number of numerical simulations in 2d 3d 4d and 8d with axial symmetries they include tori and cones for the mean curvature flow minimal and prescribed mean curvature surfaces with given boundary fattening for smooth driving force and volume constraint

isogeometric analysis of the navier stokes cahn hilliard equations with application to incompressible two phase flows abstract in this work we provide a unified and comparative description of the most prominent phase field based two phase flow models and present our numerical results of the application of galerkin based isogeometric analysis iga to incompressible navier stokes cahn hilliard nsch equations in velocity pressure phase field chemical potential formulation for the approximation of the velocity and pressure fields lbb compatible non uniform rational b spline spaces are used which can be regarded as smooth generalizations of taylor hood pairs of finite element spaces the one step scheme is used for the discretization in time the static and rising bubble in addition to the nonlinear rayleigh taylor instability flow problems are considered in two dimensions as model problems in order to investigate the numerical properties of the scheme

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

generalized fiducial inference for ultrahigh dimensional regression in recent years the ultrahigh dimensional linear regression problem has attracted enormous attention from the research community under the sparsity assumption most of the published work is devoted to the selection and estimation of the predictor variables with nonzero coefficients this article studies a different but fundamentally important aspect of this problem uncertainty quantification for parameter estimates and model choices to be more specific this article proposes methods for deriving a probability density function on the set of all possible models and also for constructing confidence intervals for the corresponding parameters these proposed methods are developed using the generalized fiducial methodology which is a variant of fisher s controversial fiducial idea theoretical properties of the proposed methods are studied and in particular it is shown that statistical inference based on the proposed methods will have correct asymptotic frequentist property in terms of empirical perform

models and confidence intervals for true values in interlaboratory trials we consider the one way random effects model with unequal sample sizes and heterogeneous variances using the method of generalized confidence intervals we develop a new confidence interval procedure for the mean additionally we investigate two alternative models based on different sets of assumptions regarding between group variability and derive generalized confidence interval procedures for the mean these procedures are applicable to small samples statistical simulation is used to demonstrate that the coverage probabilities of these procedures are close enough to the nominal value so that they are useful in practice although the methods are quite general the procedures are explained with the backdrop of interlaboratory studies

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

quasi incompressible cahn hilliard fluids and topological transitions one of the fundamental problems in simulating the motion of sharp interfaces between immiscible fluids is a description of the transition that occurs when the interfaces merge and reconnect it is well known that classical methods involving sharp interfaces fail to describe this type of phenomena following some previous work in this area we suggest a physically motivated regularization of the euler equations which allows topological transitions to occur smoothly in this model the sharp interface is replaced by a narrow transition layer across which the fluids may mix the model describes a flow of a binary mixture and the internal structure of the interface is determined by both diffusion and motion an advantage of our regularization is that it automatically yields a continuous description of surface tension which can play an important role in topological transitions an additional scalar field is introduced to describe the concentration of one of the fluid components and the resulting system of equations couples the euler or navier stokes and the cahn hilliard equations the model takes into account weak non locality dispersion associated with an internal length scale and localized dissipation due to mixing the non locality introduces a dimensional surface energy dissipation is added to handle the loss of regularity of solutions to the sharp interface equations and to provide a mechanism for topological changes in particular we study a non trivial limit when both components are incompressible the pressure is kinematic but the velocity field is non solenoidal quasi incompressibility to demonstrate the effects of quasi incompressibility we analyse the linear stage of spinodal decomposition in one dimension we show that when the densities of the fluids are not perfectly matched the evolution of the concentration field causes fluid motion even if the fluids are inviscid in the limit of infinitely thin and well separated interfacial layers an appropriately scaled quasi incompressible euler cahn hilliard system converges to the classical sharp interface model in order to investigate the behaviour of the model outside the range of parameters where the sharp interface approximation is sufficient we consider a simple example of a change of topology and show that the model permits the transition to occur without an associated singularity

a simple general method for constructing confidence intervals for functions of variance components a simple general method is proposed for constructing confidence intervals for arbitrary functions of variance components in balanced normal theory models the concept of surrogate variables is introduced as part of the description of the method equal tail and shortest length confidence intervals from this method can be computed easily using simulations as an illustration the two way random effects model is considered it is shown that the proposed method produces intervals that are comparable in confidence coefficient and average length to those produced by the best existing methods

inference for the lognormal mean and quantiles based on samples with left and right type i censoring interval estimation of the mean and quantiles of a lognormal distribution is addressed based on a type i singly censored sample a special case of interest is that of a sample containing values below a single detection limit generalized inferential procedures which use maximum likelihood estimation based approximate pivotal quantities and some likelihood based methods are proposed the latter include methodology based on the signed log likelihood ratio test slrt statistic and the modified signed log likelihood ratio test mslrt statistic the merits of the methods are evaluated for a left censored sample using monte carlo simulation for inference concerning the lognormal mean the slrt is to be preferred for left tailed testing generalized inference for right tailed testing and all three approaches provide nearly the same performance for two tailed testing these conclusions hold even when the proportion of censored values is as large as 0 70 for inference concerning quantiles both the generali

generalized p values in significance testing of hypotheses in the presence of nuisance parameters abstract this article examines some problems of significance testing for one sided hypotheses of the form h 0 0 versus h 1 0 where is the parameter of interest in the usual setting let x be the observed data and let t x be a test statistic such that the family of distributions of t x is stochastically increasing in define cx as x t x t x 0 the p value is p x sup 0 pr x cx in the presence of a nuisance parameter there may not exist a nontrivial cx with a p value independent of we consider tests based on generalized extreme regions of the form cx x t x x t x x and conditions on t x x are given such that the p value p x sup 0 pr x cx is free of the nuisance parameter where t is stochastically increasing in we provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions a problem for which the fixed level testing approach

generalized fiducial inference a review and new results abstractr a fisher the father of modern statistics proposed the idea of fiducial inference during the first half of the 20th century while his proposal led to interesting methods for quantifying uncertainty other prominent statisticians of the time did not accept fisher s approach as it became apparent that some of fisher s bold claims about the properties of fiducial distribution did not hold up for multi parameter problems beginning around the year 2000 the authors and collaborators started to reinvestigate the idea of fiducial inference and discovered that fisher s approach when properly generalized would open doors to solve many important and difficult inference problems they termed their generalization of fisher s idea as generalized fiducial inference gfi the main idea of gfi is to carefully transfer randomness from the data to the parameter space using an inverse of a data generating equation without the use of bayes theorem the resulting generalized fiducial distribution gfd can

adaptive identification of nonminimum phase arma models using higher order cumulants alone an adaptive identification algorithm for causal nonminimum phase arma models in additive colored gaussian noise is proposed the algorithm utilizes higher order cumulants of the observed signal alone it estimates the ar and ma parameters successively in each iteration without computing the residual time series the steepest descent method is used for parameter updating

fiducial intervals for variance components in an unbalanced two component normal mixed linear model in this article we propose a new method for constructing confidence intervals for 2 2 and the intraclass correlation 2 2 e2 in a two component mixed effects linear model this method is based on an extension of r a fisher s fiducial argument we conducted a simulation study to compare the resulting interval estimates with other competing confidence interval procedures from the literature our results demonstrate that the proposed fiducial intervals have satisfactory performance in terms of coverage probability as well as shorter average confidence interval lengths overall we also prove that these fiducial intervals have asymptotically exact frequentist coverage probability the computations for the proposed procedures are illustrated using real data examples

a cascaded phase field lattice boltzmann model for the simulation of incompressible immiscible fluids with high density contrast abstract in this work a conservative phase field model for the simulation of immiscible multiphase flows is developed using an incompressible velocity based cascaded lattice boltzmann method clbm extensions are made to the lattice boltzmann lb equations for interface tracking and incompressible hydrodynamics proposed by fakhari et al 1 by performing relaxation operations in central moment space this was motivated by the work of fei et al 2 3 where promising results from such a transformation were observed the relaxation of central moments is defined in a reference frame moving with the fluid while the existing multiple relaxation time 4 5 scheme performs collision in a fixed frame of reference moreover the derivations make use of continuous maxwellian distribution functions as a result the clbm enhances the galilean invariance and stability of the method when high lattice mach numbers are evident the cascaded scheme has been previously used in the literature to simulate multiphase flows based on the pseudo potential model where it allowed for high density and viscosity contrasts to be captured 6 7 here the clbm is implemented within the phase field framework and is verified through the analysis of a layered poiseuille flow the performance of the clbm is then investigated in terms of spurious currents galilean invariance and computational efficiency finally the work of fakhari et al 1 is extended by validating the model s ability to capture the relation between surface tension and the rise velocity of a planar taylor bubble in both stagnant and flowing fluids new counter current results indicate that the rise velocity model of ha ngoc and fabre 8 also applies in this regime

thermodynamically consistent spatial discretization of the one dimensional regularized system of the navier stokes cahn hilliard equations abstract this paper is devoted to the construction of a thermodynamically consistent with non increasing total energy on the discrete level semi discrete approximation continuous in time and discrete in space for the one dimensional regularized system of the navier stokes cahn hilliard equations that describes a compressible isothermal flow of two phase binary fluid with surface effects thermodynamical consistency is achieved using special form of momentum equation with surface force term written in so called potential form results of numerical study are presented

performance analysis of estimation algorithms of nonstationary arma processes the correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive ar moving average ma and arma systems by using estimation residuals in place of unmeasurable noise terms in information vector or matrix we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity ergodicity or existence of higher order moments furthermore we derive the conditions for convergence of the parameter estimation the simulation results validate the convergence theorems proposed

testing variance components in mixed models with generalized p values abstract a procedure for testing one sided hypotheses on variance components in a balanced random effects model is developed the testing is performed on the basis of a generalized p value and involves a one dimensional numerical integration in the special case for which the conventional methods provide an exact test this test is equivalent to the usual f test the test is also generalized bayes in the sense that under a certain diffuse prior the p value is numerically the same as the posterior probability of the null hypothesis

estimation of field reliability based on aggregate lifetime data because of the exponential distribution assumption many reliability databases recorded data in an aggregate way instead of individual failure times each aggregate data point is a summation of a series of collective failures representing the cumulative operating time of one component position from system commencement to the last component replacement the data format is different from traditional lifetime data and the statistical inference is challenging we first model the individual component lifetime by a gamma distribution confidence intervals for the gamma shape parameter can be constructed using a scaled 2 approximation to a modified ratio of the geometric mean to the arithmetic mean while confidence intervals for the gamma rate and mean parameters as well as quantiles are obtained using the generalized pivotal quantity method we then fit the data using the inverse gaussian ig distribution a useful lifetime model for failures caused by degradation procedures for point estimation and inte

exact confidence intervals for the common mean of several normal populations summary the problem of interval estimation of the common mean of several normal populations when the variances are unknown and unequal is considered some new confidence intervals are proposed one of them is centered at the well known graybill deal estimator of the common mean these new intervals and an existing exact confidence interval are numerically compared with respect to their expected lengths based on comparison studies some recommendations are made regarding the choice of the intervals to be used in applications the problem of combining the results of independent investigations for the purpose of a common objective has received considerable attention in the literature in particular it may be necessary to combine the data sets collected by independent agencies to estimate or to test the common parameter of interest this problem arises for example when two or more independent agencies are involved in measuring the effect of a new drug when several measuring instruments are used to measure the products produced by the same production process to assess the average quality or when different laboratories are used to measure the amount of toxic waste in a river meier 1953 gave an illustrative example in which four experiments are used to estimate the mean percentage of albumin in the plasma protein of normal human subjects other examples can be found in the recent papers by eberhardt reeve and spiegelman 1989 and skinner 1991 the former paper gives three examples each of which is concerned with estimating a chemical substance in nonfat milk powder by combining the results of alternative analytical methods the latter gives examples related to clinical trials and determining the density of nitrogen using different laboratory methods in these situations the variances are typically unequal due to the variation in different methods or measuring instruments if it is assumed that the samples collected by independent studies are from normal populations then the problem of interest may be to estimate or test the common mean a of these populations

a semi analytical fourier spectral method for the allen cahn equation in recent years fourier spectral methods have been widely used as a powerful tool for solving phase field equations to improve its effectiveness many researchers have employed stabilized semi implicit fourier spectral sifs methods which allow a much larger time step than a usual explicit scheme our mathematical analysis and numerical experiments however suggest that an effective time step is smaller than a time step specified in the sifs schemes in consequence the sifs scheme is inaccurate for a considerably large time step and may lead to incorrect morphologies in phase separation processes in order to remove the time step constraint and guarantee the accuracy in time for a sufficiently large time step we present a first and a second order semi analytical fourier spectral safs methods for solving the allen cahn equation the core idea of the methods is to decompose the original equation into linear and nonlinear subequations which have closed form solutions in the fourier and physical spaces respectively both the first and the second order methods are unconditionally stable and numerical experiments demonstrate that our proposed methods are more accurate than the stabilized semi implicit fourier spectral method

a systematic look at the gamma process capability indices abstract process capability indices pcis are widely used to measure whether an in control process conforms to manufacturing specifications the normal distribution is assumed in most traditional applications of pcis nevertheless it is not uncommon that some quality characteristics have skewed distributions in such cases the gamma distribution is an appropriate model and percentile based pcis for the gamma process have been studied in the literature in practical applications of pcis it is important to select an appropriate distribution between the normal and the gamma distributions based on historical data in this study we first construct a hypothesis test for model discrimination between the normal and the gamma distributions asymptotic distribution of the test statistic under the gamma process is derived we then consider statistical inference for the percentile based pcis under the gamma process the maximum likelihood method is used for point estimation and the method of generalized pivotal quantities is used for interval estimation we demonstrate the proposed methods by a practical example

one sided tolerance limits in balanced and unbalanced one way random models based on generalized confidence intervals we consider the problem of deriving one sided tolerance intervals in the one way random model with balanced as well as unbalanced data under the usual normality assumptions the problems investigated deal with the computation of such intervals for the observable random variable as well as the unobservable random effect in the one way random model the tolerance limits are derived using the concept of a generalized confidence interval some approximations are derived for the tolerance limits and their performance is investigated by simulation the simulation results show that the proposed tolerance limits are quite satisfactory for practical use

generalized confidence intervals abstract the definition of a confidence interval is generalized so that problems such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal variances under certain conditions the extended definition is shown to preserve a repeated sampling property that a practitioner expects from exact confidence intervals the proposed procedure is also applied to the problem of constructing confidence intervals for the difference in two exponential means and for variance components in mixed models a repeated sampling property of generalized p values is also given with this characterization one can carry out fixed level tests of parameters of continuous distributions on the basis of generalized p values finally pratt s paradox is revisited and a procedure that resolves the paradox is given

on the identifiability of non gaussian arma models using cumulants a fixed set of output cumulants of order greater than two guarantees unique identification of known order causal arma autoregressive moving average models which are driven by unobservable non gaussian i i d noise the models are allowed to be non minimum phase and their outputs may be corrupted by additive colored gaussian noise of unknown covariance the arma parameters can be estimated either by means of linear equations and closed form expressions or by minimizing quadratic cumulant matching criteria the latter approach requires computation of cumulants in terms of the arma parameters which is carried out in the state space using kronecker products

adaptive iir algorithms based on high order statistics recursive estimation algorithms are derived for moving average and autoregressive moving average processes these algorithms can be used for adaptive infinite impulse response iir filtering of non gaussian processes the behavior of these algorithms is illustrated by extensive numerical examples

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

regular article calculation of two phase navier stokes flows using phase field modeling phase field models provide a way to model fluid interfaces as having finite thickness this can allow the computation of interface movement and deformation on fixed grids this paper applies phase field modeling to the computation of two phase incompressible navier stokes flows the navier stokes equations are modified by the addition of the continuum forcing email protected f where c is the composition variable and f is c s chemical potential the equation for interface advection is replaced by a continuum advective diffusion equation with diffusion driven by c s chemical potential gradients the paper discusses how solutions to these equations approach those of the original sharp interface navier stokes equations as the interface thickness e and the diffusivity both go to zero the basic flow physics of phase field interfaces is discussed straining flows can thin or thicken an interface and this must be resisted by a high enough diffusion on the other hand too large a diffusion will overly damp the flow these two constraints result in an upper bound for the diffusivity of o e and a lower bound of o e 2 within these two bounds the phase field navier stokes equations appear to generate an o e error relative to the exact sharp interface equations an o h 2 e 2 numerical method is introduced that is energy conserving in the sense that creation of interface energy by convection is always balanced by an equal decrease in kinetic energy caused by surface tension forcing an o h 4 e 4 compact scheme is introduced that takes advantage of the asymptotic comparatively smooth behavior of the chemical potential for o e accurate phase field models the optimum path to convergence for this scheme appears to be email protected 4 5 the asymptotic rate of convergence corresponding to this is o h 4 5 but results at practical resolutions show that the practical convergence of the method is generally considerably faster than linear extensive analysis and computations show that this scheme is very effective and accurate it allows the accurate calculation of two phase flows with interfaces only two cells wide computational results are given for linear capillary waves and for rayleigh taylor instabilities the first set of computations is compared to exact solutions of the diffuse interface equations and of the original sharp interface equations the rayleigh taylor computations test the ability of the method to compute highly deforming flows these flows include near singular phenomena such as interface coalescences and breakups contact line movement and the formation and breakup of thin wall films grid refinement studies are made and rapid convergence is found for macroscopic flow features such as instability growth rate and propagation speed wavelength and the general physical characteristics of the instability and mass transfer rates

fir system identification using higher order statistics alone this paper focuses on fir system identification in gaussian arma noise using higher order cumulants alone two new types of cumulant based normal equations are established and two algorithms are proposed for ma parameter estimation simulations verify the high performance of the new developments

generalized fiducial inference for wavelet regression we apply fisher s fiducial idea to conduct statistical inference for wavelet regression we first develop a general methodology for handling model selection problems within the fiducial framework with this new methodology we then propose fiduical based methods for performing wavelet curve estimation as well as constructing both pointwise and curvewise confidence intervals it is shown that under some mild regularity conditions both the new fiducial based pointwise and curvewise confidence intervals have asymptotically correct coverage furthermore simulation results show that these new fiducial based methods especially for constructing pointwise confidence intervals also possess promising empirical properties to the best of our knowledge this is the first time that the fiducial idea has been applied to a nonparametric estimation problem

on the exact interval estimation for the difference in paired areas under the roc curves an important measure for comparison of accuracy between two diagnostic procedures is the difference in paired areas under the receiver operating characteristic roc curves non parametric and maximum likelihood methods have been proposed for interval estimation for the difference in paired areas under roc curves however these two methods are asymptotic procedures and their performance in finite sample sizes has not been thoroughly investigated we propose to use the concept of generalized pivotal quantities gpqs to construct an exact confidence interval for the difference in paired areas under roc curves a simulation study is conducted to empirically investigate the probability coverage and expected length of the three methods for various combinations of sample sizes values of the area under the roc curve and correlations simulation results demonstrate that the exact confidence interval based on the concept of gpqs provides not only sufficient probability coverage but also reasonable expected length numerical examples using published data sets illustrate the proposed method

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

on convergent schemes for diffuse interface models for two phase flow of incompressible fluids with general mass densities we are concerned with convergence results for fully discrete finite element schemes suggested in grun and klingbeil j comput phys in press doi 10 1016 j jcp 2013 10 028 they were developed for the diffuse interface model in h abels h garcke and g grun math models methods appl sci 22 2012 1150013 which describes two phase flow of immiscible incompressible viscous fluids we formulate general conditions on discretization spaces and projection operators which allow us to prove compactness of discrete solutions with respect to both time and space and which hence permit us to establish convergence of the scheme to a generalized solution we identify a simple quantitative and physical criterion to decide whether this generalized solution is in fact a weak solution in this case our analysis provides another pathway to establish existence of weak solutions to the aforementioned model in two and in three space dimensions our argument is particularly based on higher regularity results

a fixed grid sharp interface method for bubble dynamics and phase change abstract a numerical method has been developed for direct simulation of bubble dynamics with large liquid to vapor density ratio and phase change the numerical techniques are based on a fixed grid finite volume method capable of treating the interface as a sharp discontinuity the unsteady axisymmetric navier stokes equations and energy equation in both liquid and vapor phases are computed the mass momentum and energy conditions are explicitly matched at the phase boundary to determine the interface shape and movement the cubic b spline is used in conjunction with a fairing algorithm to yield smooth and accurate information of curvatures nondimensional parameters including reynolds weber and jakob numbers are varied to offer insight into the physical and numerical characteristics of the bubble dynamics based on the present sharp interface approach bubble dynamics for density ratio of 1600 or higher with and without phase change can be successfully computed

a novel linear unconditional energy stable scheme for the incompressible cahn hilliard navier stokes phase field model abstract in this paper we propose a linear unconditional energy stable time discretization scheme for cahn hilliard navier stokes model which is a phase field model for two phase incompressible flow based on a lagrange multiplier approach our proposed scheme is linearized by using implicit explicit treatments and the computation of the velocity field u the pressure p the phase function are decoupled using the mathematical induction the bound n l is obtained rigorous error analysis for the variable u p and are carried out in semi discrete form finally some numerical experiments are done to demonstrate the effectiveness for the proposed method