an unconditionally energy stable scheme based on an implicit auxiliary energy variable for incompressible two phase flows with different densities involving only precomputable coefficient matrices abstract we present an energy stable scheme for numerically approximating the governing equations for incompressible two phase flows with different densities and dynamic viscosities for the two fluids the proposed scheme employs a scalar valued auxiliary energy variable in its formulation and it satisfies a discrete energy stability property more importantly the scheme is computationally efficient within each time step it computes two copies of the flow variables velocity pressure phase field function by solving individually a linear algebraic system involving a constant and time independent coefficient matrix for each of these field variables the coefficient matrices involved in these linear systems only need to be computed once and can be pre computed additionally within each time step the scheme requires the solution of a nonlinear algebraic equation about a scalar valued number using the newton s method the cost for this nonlinear solver is very low accounting for only a few percent of the total computation time per time step because this nonlinear equation is about a scalar number not a field function extensive numerical experiments have been presented for several two phase flow problems involving large density ratios and large viscosity ratios comparisons with theory show that the proposed method produces physically accurate results simulations with large time step sizes demonstrate the stability of computations and verify the robustness of the proposed method an implication of this work is that energy stable schemes for two phase problems can also become computationally efficient and competitive eliminating the need for expensive re computations of coefficient matrices even at large density ratios and viscosity ratios

simulations of singularity dynamics in liquid crystal flows a c0 finite element approach in this paper we present a c 0 finite element method for a 2d hydrodynamic liquid crystal model which is simpler than existing c 1 element methods and mixed element formulation the energy law is formally justified and the energy decay is used as a validation tool for our numerical computation a splitting method combined with only a few fixed point iteration for the penalty term of the director field is applied to reduce the size of the stiffness matrix and to keep the stiffness matrix time independent the latter avoids solving a linear system at every time step and largely reduces the computational time especially when direct linear system solvers are used our approach is verified by comparing its computational results with those obtained by c 1 elements and by mixed formulation through numerical experiments of a few other splittings and explicit implicit strategies we recommend a fast and reliable algorithm for this model a number of examples are computed to demonstrate the algorithm

tractography gone wild probabilistic fibre tracking using the wild bootstrap with diffusion tensor mri diffusion tensor magnetic resonance imaging dt mri permits the noninvasive assessment of tissue microstructure and with fibre tracking algorithms allows for the 3 d trajectories of white matter fasciculi to be reconstructed noninvasively probabilistic algorithms allow one to assign a ldquoconfidencerdquo to a given reconstructed pathway but often rely on a priori assumptions about sources of uncertainty in the data bootstrap methods have been proposed as a way of circumventing this problem deriving the uncertainty from the data themselves but acquisition times for data amenable to precise and robust bootstrapping are clinically prohibitive by combining the wild bootstrap recently introduced to the dt mri literature with tractography we show how confidence can be assigned to reconstructed trajectories using data collected in a fraction of the time required for regular bootstrapping we compare in vivo wild bootstrap tracking results with regular tracking results and show that results are comparable this approach therefore allows users who have collected data sets for use with deterministic tracking algorithms rather than those specifically designed for bootstrapping to be able to apply bootstrap analyses and retrospectively assign confidence to their reconstructed trajectories with minimum additional effort

forming post strata via bayesian treed capture recapture models summary for the problem of dual system estimation we propose a bayesian treed capture recapture model to account for heterogeneity of capture probabilities where individual auxiliary information is available the model uses a binary tree to partition the covariate space into homogeneous regions within each of which the capture response can be described adequately by a simple model that assumes equal catchability the attractive features of the proposed model include reduction of correlation bias robustness and practical flexibility as well as simplicity and interpretability in addition it provides a systematic and effective way of forming post strata for the sekar deming estimator of population size we compare the performance of estimators based on this model to those of alternative estimators in three scenarios

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

mass conservative and energy stable finite difference methods for the quasi incompressible navier stokes cahn hilliard system primitive variable and projection type schemes abstract in this paper we describe two fully mass conservative energy stable finite difference methods on a staggered grid for the quasi incompressible navier stokes cahn hilliard q nsch system governing a binary incompressible fluid flow with variable density and viscosity both methods namely the primitive method finite difference method in the primitive variable formulation and the projection method finite difference method in a projection type formulation are so designed that the mass of the binary fluid is preserved and the energy of the system equations is always non increasing in time at the fully discrete level we also present an efficient practical nonlinear multigrid method comprised of a standard fas method for the cahn hilliard equation and a method based on the vanka type smoothing strategy for the navier stokes equation for solving these equations we test the scheme in the context of capillary waves rising droplets and rayleigh taylor instability quantitative comparisons are made with existing analytical solutions or previous numerical results that validate the accuracy of our numerical schemes moreover in all cases mass of the single component and the binary fluid was conserved up to 1 0 8 and energy decreases in time

an efficient scheme for a phase field model for the moving contact line problem with variable density and viscosity abstract in this paper we develop an efficient numerical method for the two phase moving contact line problem with variable density viscosity and slip length the physical model is based on a phase field approach which consists of a coupled system of the cahn hilliard and navier stokes equations with the generalized navier boundary condition 1 2 5 to overcome the difficulties due to large density and viscosity ratio the navier stokes equations are solved by a splitting method based on a pressure poisson equation 11 while the cahn hilliard equation is solved by a convex splitting method we show that the method is stable under certain conditions the linearized schemes are easy to implement and introduce only mild cfl time constraint numerical tests are carried out to verify the accuracy stability and efficiency of the schemes the method allows us to simulate the interface problems with extremely small interface thickness three dimensional simulations are included to validate the efficiency of the method

efficient adaptive energy stable schemes for the incompressible cahn hilliard navier stokes phase field models in this paper we develop a fully adaptive energy stable scheme for cahn hilliard navier stokes system which is a phase field model for two phase incompressible flows consisting a cahn hilliard type diffusion equation and a navier stokes equation this scheme which is decoupled and unconditionally energy stable based on stabilization involves adaptive mesh adaptive time and a nonlinear multigrid finite difference method numerical experiments are carried out to validate the scheme for problems with matched density and non matched density and also demonstrate that cpu time can be significantly reduced with our adaptive approach

a simple em algorithm for capture recapture data with categorical covariates a simple em algorithm is proposed for obtaining maximum likelihood estimates when fitting a loglinear model to data from k capture recapture samples with categorical covariates the method is used to analyze data on screening for the early detection of breast cancer

a lattice boltzmann scheme for incompressible multiphase flow and its application in simulation of rayleigh taylor instability in this paper we propose a new lattice boltzmann scheme for simulation of multiphase flow in the nearly incompressible limit the new scheme simulates fluid flows based on distribution functions the interfacial dynamics such as phase segregation and surface tension are modeled by incorporating molecular interactions the lattice boltzmann equations are derived from the continuous boltzmann equation with appropriate approximations suitable for incompressible flow the numerical stability is improved by reducing the effect of numerical errors in calculation of molecular interactions an index function is used to track interfaces between different phases simulations of the two dimensional rayleigh taylor instability yield satisfactory results the interface thickness is maintained at 3 4 grid spacings throughout simulations without artificial reconstruction steps

an improved multiphase lattice boltzmann flux solver for three dimensional flows with large density ratio and high reynolds number an improved multiphase lattice boltzmann flux solver mlbfs is proposed in this work for effective simulation of three dimensional 3d multiphase flows with large density ratio and high reynolds number as a finite volume scheme the mlbfs originally proposed in 27 applies the finite volume method to solve for macroscopic flow variables directly the fluxes are reconstructed locally at each cell interface by using the standard lbm solutions due to the modeling error of the standard lbm the reconstructed fluxes deviate from those in the navier stokes equations and to compensate this error a complex tensor is introduced in the original mlbfs however the computation of the tensor introduces additional complexity and usually needs a relatively thicker interface thickness to maintain numerical stability which makes the solver be complex and inefficient in the 3d case to remove this drawback in this work a theoretical analysis to the formulations obtained from the chapman enskog expansion is conducted it is shown that the modeling error can be effectively removed by modifying the computation of the equilibrium density distribution function with this improvement the proposed 3d mlbfs not only avoids the calculation of the compensation tensor but also is able to maintain numerical stability with very thin interface thickness several benchmark cases including the challenging droplet impacting on a dry surface head on collisions of binary droplets and droplet splashing on a thin film with density ratio 1000 and reynolds number up to 3000 are studied to validate the proposed solver the obtained results agree well with the published data

an energy stable and convergent finite difference scheme for the phase field crystal equation we present an unconditionally energy stable finite difference scheme for the phase field crystal equation the method is based on a convex splitting of a discrete energy and is semi implicit the equation at the implicit time level is nonlinear but represents the gradient of a strictly convex function and is thus uniquely solvable regardless of time step size we present local in time error estimates that ensure the convergence of the scheme while this paper is primarily concerned with the phase field crystal equation most of the theoretical results hold for the related swift hohenberg equation as well

a phase field model and its numerical approximation for two phase incompressible flows with different densities and viscosities modeling and numerical approximation of two phase incompressible flows with different densities and viscosities are considered a physically consistent phase field model that admits an energy law is proposed and several energy stable efficient and accurate time discretization schemes for the coupled nonlinear phase field model are constructed and analyzed ample numerical experiments are carried out to validate the correctness of these schemes and their accuracy for problems with large density and viscosity ratios

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

an energy law preserving c0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics in this paper we use finite element methods to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain w we reformulate the original model in the weak form which is consistent with the continuous dissipative energy law for the flow and director fields in w 1 2 s w s 0 is an arbitrarily small number this enables us to use convenient conformal c 0 finite elements in solving the problem moreover a discrete energy law is derived for a modified midpoint time discretization scheme a fixed iterative method is used to solve the resulted nonlinear system so that a matrix free time evolution may be achieved and velocity and director variables may be solved separately a number of hydrodynamical liquid crystal examples are computed to demonstrate the effects of the parameters and the performance of the method

a projection fem for variable density incompressible flows abstract this work describes a new finite element projection method for the computation of incompressible viscous flows of nonuniform density one original idea of the proposed method consists in factorizing the density variable partly outside and partly inside the time evolution operator in the momentum equation to prevent spatial discretization errors in the mass conservation to affect the kinetic energy balance of the fluid it is shown that unconditional stability in the incremental version of the projection method is possible provided two projections are performed per time step in particular a second order accurate bdf projection method is presented and its numerical performance is illustrated by test computations and comparisons

brain tractography using q ball imaging and graph theory improved connectivities through fibre crossings via a model based approach brain tractography techniques utilize a set of diffusion weighted magnetic resonance images to reconstruct white matter tracts non invasively and in vivo streamline tracking techniques propagate curves from a seed to imply connectivity to distal voxels alternative approaches have been developed that attempt to quantify connection strength between all voxels and the seed tractography based on graph theory is amongst them despite its potential graph based tracking through complex fibre configurations has not been extensively studied and existing methods have inherent limitations anatomically unlikely connections may be identified in fibre crossing regions by assigning relatively high connection strengths to all crossing populations in this study we discuss these limitations and present a new approach for robustly propagating through fibre crossings as described by the orientation distribution functions odfs derived from q ball imaging each image voxel is treated as a graph node and graph arcs connect neighbouring voxels weights representative of both structural and diffusivity features are assigned to each arc to account for the existence of crossing fibre populations within a voxel complex odfs are decomposed into components representative of single fibre populations and an image multigraph is created the multigraph is searched exhaustively but efficiently to find the strongest paths and assign connectivity strengths between a seed and all the other image voxels a comparison with the existing graph based tractography as well as q ball driven front evolution tractography is performed on simulated data and on human q ball imaging data acquired from five healthy volunteers the new approach improves the connection strengths through fibre crossing regions reducing the strengths of paths that are less anatomically plausible

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

characterizing brain anatomical connections using diffusion weighted mri and graph theory abstract a new methodology based on diffusion weighted magnetic resonance imaging dw mri and graph theory is presented for characterizing the anatomical connections between brain gray matter areas in a first step brain voxels are modeled as nodes of a non directed graph in which the weight of an arc linking two neighbor nodes is assumed to be proportional to the probability of being connected by nervous fibers this probability is estimated by means of probabilistic tissue segmentation and intravoxel white matter orientational distribution function obtained from anatomical mri and dw mri respectively a new tractography algorithm for finding white matter routes is also introduced this algorithm solves the most probable path problem between any two nodes leading to the assessment of probabilistic brain anatomical connection maps in a second step for assessing anatomical connectivity between k gray matter structures the previous graph is redefined as a k 1 partite graph by partitioning the initial nodes set in k non overlapped gray matter subsets and one subset clustering the remaining nodes three different measures are proposed for quantifying anatomical connections between any pair of gray matter subsets anatomical connection strength acs anatomical connection density acd and anatomical connection probability acp this methodology was applied to both artificial and actual human data results show that nervous fiber pathways between some regions of interest were reconstructed correctly additionally mean connectivity maps of acs acd and acp between 71 gray matter structures for five healthy subjects are presented

logistic regression in capture recapture models the effect of population heterogeneity in capture recapture or dual registration models is discussed an estimator of the unknown population size based on a logistic regression model is introduced the model allows different capture probabilities across individuals and across capture times the probabilities are estimated from the observed data using conditional maximum likelihood the resulting population estimator is shown to be consistent and asymptotically normal a variance estimator under population heterogeneity is derived the finite sample properties of the estimators are studied via simulation an application to finnish occupational disease registration data is presented

bootgraph probabilistic fiber tractography using bootstrap algorithms and graph theory bootstrap methods have recently been introduced to diffusion weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model these methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain thereby the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms graph based approaches have been proposed to overcome this drawback of streamline techniques for this reason the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method called bootgraph the acquired data set is thereby converted into a weighted undirected graph by defining a vertex in each voxel and edges between adjacent vertices by means of the cone of uncertainty which is derived using the wild bootstrap a weight is thereafter assigned to each edge two path finding algorithms are subsequently applied to derive connection probabilities while the first algorithm is based on the shortest path approach the second algorithm takes all existing paths between two vertices into consideration tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm the bootgraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints such as a curvature threshold by inheriting the advantages of the bootstrap method and graph theory the bootgraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of streamline tractography algorithms or the assumption of a noise distribution moreover the bootgraph can be applied to common dti data sets without further modifications and shows a high repeatability thus it is very well suited for longitudinal studies and meta studies based on dti

block implicit multigrid solution of navier stokes equations in primitive variables abstract a calculation procedure for rapid computation of steady multidimensional viscous flows is presented the method solves the navier stokes equations in primitive variables using a coupled block implicit multigrid procedure the procedure is applicable to finite difference formulations using staggered locations of the flow variables a smoothing technique called symmetrical coupled gauss seidel scgs is proposed and is empirically observed to provide good smoothing rates the viscous flow in a square cavity with a moving top wall is calculated for a range of reynolds numbers calculations with finite difference grids as large as 321 321 nodes have been made to test the accuracy and efficiency of the calculation scheme the cpu times for these calculations are observed to be significantly smaller than other solution algorithms with primitive variable formulation the calculated flow fields in the cavity are in good agreement with earlier studies of the same flow situation

a conservative phase field method for solving incompressible two phase flows in this paper a conservative phase field method based on the work of sun and beckermann y sun c beckermann sharp interface tracking using the phase field equation j comput phys 220 2007 626 653 for solving the two and three dimensional two phase incompressible navier stokes equations is proposed the present method can preserve the total mass as the cahn hilliard equation but the calculation and implementation are much simpler than that the dispersion relation preserving schemes are utilized for the advection terms while the helmholtz smoother is applied to compute the surface tension force term to verify the proposed method several benchmarks are examined and shown to have good agreements with previous results it also shows that the satisfactions of mass conservations are guaranteed

a time stepping scheme involving constant coefficient matrices for phase field simulations of two phase incompressible flows with large density ratios we present an efficient time stepping scheme for simulations of the coupled navier stokes cahn hilliard equations for the phase field approach the scheme has several attractive characteristics i it is suitable for large density ratios and numerical experiments with density ratios up to 1000 have been presented ii it involves only constant time independent coefficient matrices for all flow variables which can be pre computed during pre processing so it effectively overcomes the performance bottleneck induced by variable coefficient matrices associated with the variable density and variable viscosity iii it completely de couples the computations of the velocity pressure and the phase field function strategy for spectral element type spatial discretizations to overcome the difficulty associated with the large spatial order of the cahn hilliard equation is also discussed ample numerical simulations demonstrate that the current algorithm together with the navier stokes cahn hilliard phase field approach is an efficient and effective method for studying two phase flows involving large density ratios moving contact lines and interfacial topology changes

a novel second order linear scheme for the cahn hilliard navier stokes equations abstract in this paper we consider the cahn hilliard equation coupled with the incompressible navier stokes equation usually known as the cahn hilliard navier stokes chns system the chns system has been widely embraced to investigate the dynamics of a binary fluid mixture by utilizing the modified leap frog time marching method we propose a novel numerical algorithm for solving the chns system in an efficient and accurate manner this newly proposed scheme has several advantages first of all the proposed scheme is linear in time and space such that only a linear algebraic system needs to be solved at each time marching step making it extremely efficient also the existence and uniqueness of numerical solutions are guaranteed for any time step size in addition the scheme is unconditionally energy stable with second order accuracy in time and spectral accuracy in space such that relatively large temporal and spatial mesh sizes can be used to obtain reliable numerical solutions the rigorous proofs for the unconditional energy stable property and solution existence and uniqueness are given furthermore we present several numerical examples to test the proposed numerical algorithm and illustrate its accuracy and efficiency the differences of coarsening dynamics between the cahn hilliard equation and the cahn hilliard navier stokes equations have been investigated as well

a bayesian approach for stochastic white matter tractography white matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging mri images in this paper a novel bayesian modeling approach for white matter tractography is presented the uncertainty associated with estimated white matter fiber paths is investigated and a method for calculating the probability of a connection between two areas in the brain is introduced the main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way theory for estimating global connectivity is also presented as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile

a gradient stable scheme for a phase field model for the moving contact line problem in this paper an efficient numerical scheme is designed for a phase field model for the moving contact line problem which consists of a coupled system of the cahn hilliard and navier stokes equations with the generalized navier boundary condition 1 2 4 the nonlinear version of the scheme is semi implicit in time and is based on a convex splitting of the cahn hilliard free energy including the boundary energy together with a projection method for the navier stokes equations we show under certain conditions the scheme has the total energy decaying property and is unconditionally stable the linearized scheme is easy to implement and introduces only mild cfl time constraint numerical tests are carried out to verify the accuracy and stability of the scheme the behavior of the solution near the contact line is examined it is verified that when the interface intersects with the boundary the consistent splitting scheme 21 22 for the navier stokes equations has the better accuracy for pressure

computation of multiphase systems with phase field models phase field models offer a systematic physical approach for investigating complex multiphase systems behaviors such as near critical interfacial phenomena phase separation under shear and microstructure evolution during solidification however because interfaces are replaced by thin transition regions diffuse interfaces phase field simulations require resolution of very thin layers to capture the physics of the problems studied this demands robust numerical methods that can efficiently achieve high resolution and accuracy especially in three dimensions we present here an accurate and efficient numerical method to solve the coupled cahn hilliard navier stokes system known as model h that constitutes a phase field model for density matched binary fluids with variable mobility and viscosity the numerical method is a time split scheme that combines a novel semi implicit discretization for the convective cahn hilliard equation with an innovative application of high resolution schemes employed for direct numerical simulations of turbulence this new semi implicit discretization is simple but effective since it removes the stability constraint due to the nonlinearity of the cahn hilliard equation at the same cost as that of an explicit scheme it is derived from a discretization used for diffusive problems that we further enhance to efficiently solve flow problems with variable mobility and viscosity moreover we solve the navier stokes equations with a robust time discretization of the projection method that guarantees better stability properties than those for crank nicolson based projection methods for channel geometries the method uses a spectral discretization in the streamwise and spanwise directions and a combination of spectral and high order compact finite difference discretizations in the wall normal direction the capabilities of the method are demonstrated with several examples including phase separation with and without shear in two and three dimensions the method effectively resolves interfacial layers of as few as three mesh points the numerical examples show agreement with analytical solutions and scaling laws where available and the 3d simulations in the presence of shear reveal rich and complex structures including strings

a general theory for modeling capture recapture data from a closed population a general theory for estimating the size of a closed population from multiple recapture data is presented this theory is easily extended to open population models for multiple recapture data estimation is based on a log linear model developed for modeling dependent capture recapture data when capture probabilities vary temporally with behavioral response and are heterogeneous among animals models for complete capture history data are developed along with the first log linear models for removal data the maximum likelihood estimator of the model parameters along with the estimated covariance matrix are presented

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 phase field model for the mixture of two incompressible fluids and its approximation by a fourier spectral method abstract a phase field model for the mixture of two incompressible fluids is presented in this paper the model is based on an energetic variational formulation it consists of a navier stokes system linear momentum equation coupled with a cahn hilliard equation phase field equation through an extra stress term and the transport term the extra stress represents the phase induced capillary effect for the mixture due to the surface tension a fourier spectral method for the numerical approximation of this system is proposed and analyzed numerical results illustrating the robustness and versatility of the model are presented

multi component cahn hilliard system with different boundary conditions in complex domains abstract we propose an efficient phase field model for multi component cahn hilliard ch systems in complex domains the original multi component cahn hilliard system with a fixed phase is modified in order to make it suitable for complex domains in the cartesian grid along with contact angle or no mass flow boundary conditions on the complex boundaries the proposed method uses a practically unconditionally gradient stable nonlinear splitting numerical scheme further a nonlinear full approximation storage multigrid algorithm is used for solving semi implicit formulations of the multi component ch system incorporated with an adaptive mesh refinement technique the robustness of the proposed method is validated through various numerical simulations including multi phase separations via spinodal decomposition equilibrium contact angle problems and multi phase flows with a background velocity field in complex domains

mixture models for estimating the size of a closed population when capture rates vary among individuals nous developpons une parametrisation du melange de lois beta et binomiale qui fournit un cadre inferentiel approprie pour estimer l effectif d une population fermee lorsque les probabilites de capture ou de detection varient entre individus nous ajustons trois classes de modeles de melange beta binomiale logistique normale et modele a classes latentes d une part a des donnees de recapture de lievres d amerique pour en estimer l abondance et d autre part a des comptages d especes d oiseaux pour estimer la richesse specifique dans les deux jeux de donnees les taux de detection varient davantage entre individus lievres ou especes qu entre occasions ou lieux de capture les estimateurs de l effectif de la population et de la richesse specifique sont sensibles aux hypotheses faites sur la distribution sous jacente des probabilites individuelles de detection nous montrons par simulations que les outils habituels d evaluation de la qualite du modele comme la deviance ne sont pas fiables pour choisir entre des modeles de melanges celui qui fournit une inference correcte de l effectif de la population lorsqu elles existent des connaissances a priori sur les causes d heterogeneite des taux de detection doivent etre utilisees pour aider a choisir quelle classe de modeles de melanges utiliser pour l inference

dt mri fiber tracking a shortest paths approach we derive a new fiber tracking algorithm for dt mri that parts with the locally ldquogreedyrdquo paradigm intrinsic to conventional tracking algorithms we demonstrate the ability to precisely reconstruct a diverse range of fiber trajectories in authentic and computer generated dt mri data for which well known conventional tracking algorithms are shown to fail our approach is to pose fiber tracking as a problem in computing shortest paths in a weighted digraph voxels serve as vertices and edges are included between neighboring voxels we assign probabilities weights to edges using a bayesian framework higher probabilities are assigned to edges that are aligned with fiber trajectories in their close proximity we compute optimal paths of maximum probability using computationally scalable shortest path algorithms the salient features of our approach are global optimality unlike conventional tracking algorithms local errors do not accumulate and one ldquowrong turnrdquo does not spell disaster a target point is specified a priori precise reconstruction is demonstrated for extremely low signal to noise ratio impartiality to which of two endpoints is used as a seed and faster computation times than conventional all paths tracking we can use our new tracking algorithm in either a single path tracking mode deterministic tracking or an all paths tracking mode probabilistic tracking

a dti derived measure of cortico cortical connectivity we arm researchers with a simple method to chart a macroscopic cortico cortical connectivity network in living human subjects the researcher provides a diffusion magnetic resonance imaging mri data set and n cortical regions of interest in return we provide an n times n structural adjacency matrix sam quantifying the relative connectivity between all cortical region pairs we also return a connectivity map for each pair to enable visualization of interconnecting fiber bundles the measure of connectivity we devise is 1 free of length bias 2 proportional to fiber bundle cross sectional area and 3 invariant to an exchange of seed and target we construct a 3 d lattice scaffolding graph for white matter by drawing a link between each pair of voxels in a 26 voxel neighborhood for which their two respective principal eigenvectors form a sufficiently small angle the connectivity between a cortical region pair is then measured as the maximum number of link disjoint paths that can be established between them in the white matter graph we devise an efficient edmonds karp like algorithm to compute a conservative bound on the maximum number of link disjoint paths using both simulated and authentic diffusion tensor imaging data we demonstrate that the number of link disjoint paths as a measure of connectivity satisfies properties 1 3 unlike the fraction of intersecting streamlines the measure intrinsic to most existing probabilistic tracking algorithms finally we present connectivity maps of some notoriously difficult to track longitudinal and contralateral fasciculi

diffuse interface model for incompressible two phase flows with large density ratios we investigate the applicability of an incompressible diffuse interface model for two phase incompressible fluid flows with large viscosity and density contrasts diffuse interface models have been used previously primarily for density matched fluids and it remains unclear to what extent such models can be used for fluids of different density thereby potentially limiting the application of these models in this paper the convective cahn hilliard equation and the condition that the velocity field is divergence free are derived from the conservation law of mass of binary mixtures in a straightforward way for fluids with large density and viscosity ratios differences in the equations of motion with a previously derived quasi incompressible model are shown to result from the respective assumptions made regarding the relationship between the diffuse fluxes of two species the convergence properties of the model are investigated for cases with large density ratio quantitative comparisons are made with results from previous studies to validate the model and its numerical implementation tests show that the variation in volume during the computation is of the order of machine accuracy which is consistent with our use of a conservative discretization scheme finite volume methods for the cahn hilliard equation results of the method are compared with previous work for the change in topology of rising bubbles and rayleigh taylor instability additional results are presented for head on droplet collision and the onset of droplet entrainment in stratified flows

phase field model for hele shaw flows with arbitrary viscosity contrast i theoretical approach we present a phase field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular hele shaw cell with asymptotic matching techniques we check the model to yield the right hele shaw equations in the sharp interface limit and compute the corrections to these equations to first order in the interface thickness we also compute the effect of such corrections on the linear dispersion relation of the planar interface we discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase field model to the limiting hele shaw dynamics in particular the convergence appears to be slower for high viscosity contrasts

a second order in time uniquely solvable unconditionally stable numerical scheme for cahn hilliard navier stokes equation we propose a novel second order in time numerical scheme for cahn hilliard navier stokes phase field model with matched density the scheme is based on second order convex splitting for the cahn hilliard equation and pressure projection for the navier stokes equation we show that the scheme is mass conservative satisfies a modified energy law and is therefore unconditionally stable moreover we prove that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme thanks to the simple coupling of the scheme we design an efficient picard iteration procedure to further decouple the computation of cahn hilliard equation and navier stokes equation we implement the scheme by the mixed finite element method ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme

resolution of complex tissue microarchitecture using the diffusion orientation transform dot this article describes an accurate and fast method for fiber orientation mapping using multidirectional diffusion weighted magnetic resonance mr data this novel approach utilizes the fourier transform relationship between the water displacement probabilities and diffusion attenuated mr signal expressed in spherical coordinates the radial part of the fourier integral is evaluated analytically under the assumption that mr signal attenuates exponentially the values of the resulting functions are evaluated at a fixed distance away from the origin the spherical harmonic transform of these functions yields the laplace series coefficients of the probabilities on a sphere of fixed radius alternatively probability values can be computed nonparametrically using legendre polynomials orientation maps calculated from excised rat nervous tissue data demonstrate this technique s ability to accurately resolve crossing fibers in anatomical regions such as the optic chiasm this proposed methodology has a trivial extension to multiexponential diffusion weighted signal decay the developed methods will improve the reliability of tractography schemes and may make it possible to correctly identify the neural connections between functionally connected regions of the nervous system

the use of auxiliary variables in capture recapture and removal experiments the dependence of animal capture probabilities on auxiliary variables is an important practical problem which has not been considered in the development of estimation procedures for capturerecapture and removal experiments in this paper the linear logistic binary regression model is used to relate the probability of capture to continuous auxiliary variables the auxiliary variables could be environmental quantities such as air or water temperature or characteristics of individual animals such as body length or weight maximum likelihood estimators of the population parameters are considered for a variety of models which all assume a closed population testing between models is also considered the models can also be used when one auxiliary variable is a measure of the effort expended in obtaining the sample

resolving fiber crossing using advanced fast marching tractography based on diffusion tensor imaging magnetic resonance diffusion tensor tractography is a powerful tool for the non invasive depiction of the white matter architecture in the human brain however due to limitations in the underlying tensor model the technique is often unable to reconstruct correct trajectories in heterogeneous fiber arrangements such as axonal crossings a novel tractography method based on fast marching fm is proposed which is capable of resolving fiber crossings and also permits trajectories to branch it detects heterogeneous fiber arrangements by incorporating information from the entire diffusion tensor the fm speed function is adapted to the local tensor characteristics allowing in particular to maintain the front evolution direction in crossing situations in addition the fm s discretization error is reduced by increasing the number of considered possible front evolution directions the performance of the technique is demonstrated in artificial data and in the healthy human brain comparisons with standard fm tractography and conventional line propagation algorithms show that in the presence of interfering structures the proposed method is more accurate in reconstructing trajectories the in vivo results illustrate that the elucidated major white matter pathways are consistent with known anatomy and that multiple crossings and tract branching are handled correctly

quantitative evaluation of image based distortion correction in diffusion tensor imaging a statistical method for the evaluation of image registration for a series of images based on the assessment of consistency properties of the registration results is proposed consistency is defined as the residual error of the composition of cyclic registrations by combining the transformations of different algorithms the consistency error allows a quantitative comparison without the use of ground truth specifically it allows a determination as to whether the algorithms are compatible and hence provide comparable registrations consistency testing is applied to evaluate retrospective correction of eddy current induced image distortion in diffusion tensor imaging of the brain in the literature several image transformations and similarity measures have been proposed generally showing a significant reduction of distortion in side by side comparison of parametric maps before and after registration transformations derived from imaging physics and a three dimensional affine transformation as well as mutual information mi and local correlation lc similarity are compared to each other by means of consistency testing the dedicated transformations could not demonstrate a significant difference for more than half of the series considered lc similarity is well suited for distortion correction providing more consistent registrations which are comparable to mi

mixture regression models for closed population capture recapture data in capture recapture studies the use of individual covariates has been recommended to get stable population estimates however some residual heterogeneity might still exist and ignoring such heterogeneity could lead to underestimating the population size n in this work we explore two new models with capture probabilities depending on both covariates and unobserved random effects to estimate the size of a population inference techniques including horvitz thompson estimate and confidence intervals for the population size are derived the selection of a particular model is carried out using the akaike information criterion aic first we extend the random effect model of darroch et al 1993 journal of american statistical association 88 1137 1148 to handle unit level covariates and discuss its limitations the second approach is a generalization of the traditional zero truncated binomial model that includes a random effect to account for an unobserved heterogeneity this approach provides useful tools for inference about n since key quantities such as moments likelihood functions and estimates of n and their standard errors have closed form expressions several models for the unobserved heterogeneity are available and the marginal capture probability is expressed using the logit and the complementary log log link functions the sensitivity of the inference to the specification of a model is also investigated through simulations a numerical example is presented we compare the performance of the proposed estimator with that obtained under model mh of huggins 1989 biometrika 76 130 140

comparison of bootstrap approaches for estimation of uncertainties of dti parameters bootstrap is an empirical non parametric statistical technique based on data resampling that has been used to quantify uncertainties of diffusion tensor mri dti parameters useful in tractography and in assessing dti methods the current bootstrap method repetition bootstrap used for dti analysis performs resampling within the data sharing common diffusion gradients requiring multiple acquisitions for each diffusion gradient recently wild bootstrap was proposed that can be applied without multiple acquisitions in this paper two new approaches are introduced called residual bootstrap and repetition bootknife we show that repetition bootknife corrects for the large bias present in the repetition bootstrap method and therefore better estimates the standard errors like wild bootstrap residual bootstrap is applicable to single acquisition scheme and both are based on regression residuals called model based resampling residual bootstrap is based on the assumption that non constant variance of measured diffusion attenuated signals can be modeled which is actually the assumption behind the widely used weighted least squares solution of diffusion tensor the performances of these bootstrap approaches were compared in terms of bias variance and overall error of bootstrap estimated standard error by monte carlo simulation we demonstrate that residual bootstrap has smaller biases and overall errors which enables estimation of uncertainties with higher accuracy understanding the properties of these bootstrap procedures will help us to choose the optimal approach for estimating uncertainties that can benefit hypothesis testing based on dti parameters probabilistic fiber tracking and optimizing dti methods

a bayesian framework for global tractography we readdress the diffusion tractography problem in a global and probabilistic manner instead of tracking through local orientations we parameterise the connexions between brain regions at a global level and then infer on global and local parameters simultaneously in a bayesian framework this approach offers a number of important benefits the global nature of the tractography reduces sensitivity to local noise and modelling errors by constraining tractography to ensure a connexion is found and then inferring on the exact location of the connexion we increase the robustness of connectivity based parcellations allowing parcellations of connexions that were previously invisible to tractography the bayesian framework allows a direct comparison of the evidence for connecting and non connecting models to test whether the connexion is supported by the data crucially by explicit parameterisation of the connexion between brain regions we infer on a parameter that is shared with models of functional connectivity this model is a first step toward the joint inference on functional and anatomical connectivity

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

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

unified maximum likelihood estimates for closed capture recapture models using mixtures summary agresti 1994 biometrics50 494 500 and norris and pollock 1996a biometrics52 639 649 suggested using methods of finite mixtures to partition the animals in a closed capture recapture experiment into two or more groups with relatively homogeneous capture probabilities this enabled them to fit the models mh mbh norris and pollock and mth agresti of otis et al 1978 wildlife monographs62 1 135 in this article finite mixture partitions of animals and or samples are used to give a unified linear logistic framework for fitting all eight models of otis et al by maximum likelihood likelihood ratio tests are available for model comparisons for many data sets a simple dichotomy of animals is enough to substantially correct for heterogeneity induced bias in the estimation of population size although there is the option of fitting more than two groups if the data warrant it

the removal method for estimating natural populations incorporating auxiliary information the removal method was originally designed to estimate the size of a pest population the technique involves monitoring the decline in the success rate in catching animals as the population is reduced if for example after removing 25 rats from a population the success rate in catching further rats were to drop by a factor of 2 one might guess that the population had declined to half its original size this is the reasoning behind the basic removal estimate in this instance the population size would be estimated at 50 individuals of course it is also possible that the rat population is substantially larger and that the large decline in numbers captured is attributable to another factor the remaining rats for example could be better at avoiding capture thus the removal method like most other techniques for estimating parameters of natural populations is plagued by assumptions that are at best highly questionable furthermore these methods often ignore potentially valuable auxiliary evidence signs of activity such as scats etc can also provide clues as to the size of the remaining population methodology intended to combat simultaneously both these deficiencies is proposed here the basic notion is that when the input for an estimation scheme is extended to include information of more than one type the dependence on the restrictive assumptions associated with the use of any single component will be reduced the statistical methodology involves a standard computer calculation of a maximum likelihood estimate and a slight modification to a common scheme for generating confidence limits the chi squared approximation to the distribution of the maximum likelihood ratio test statistic monte carlo simulations are used to demonstrate that with the inclusion of information on signs of activity the estimation scheme becomes more robust to departures from the assumptions of the removal method

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

some practical aspects of a conditional likelihood approach to capture experiments the use of conditional likelihood methods in the analysis of capture data allows the modeling of capture probabilities in terms of observable characteristics of the captured individuals and the trapping occasions the resulting models may then be used to estimate the size of the population here the use of conditional likelihood procedures to construct models for capture probabilities is discussed and illustrated by an example

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

energy law preserving c0 finite element schemes for phase field models in two phase flow computations we use the idea in 33 to develop the energy law preserving method and compute the diffusive interface phase field models of allen cahn and cahn hilliard type respectively governing the motion of two phase incompressible flows we discretize these two models using a c 0 finite element in space and a modified midpoint scheme in time to increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation under which the discrete energy law can still be derived for these diffusive interface models through an example we demonstrate that the energy law preserving method is beneficial for computing these multi phase flow models we also demonstrate that when applying the energy law preserving method to the model of cahn hilliard type un physical interfacial oscillations may occur we examine the source of such oscillations and a remedy is presented to eliminate the oscillations a few two phase incompressible flow examples are computed to show the good performance of our method

bootstrap white matter tractography boot trac white matter tractography is a noninvasive method for estimating and visualizing the white matter connectivity patterns in the human brain using diffusion tensor imaging dti data sources of experimental noise may induce errors in the measured fiber directions which will reduce the accuracy of the estimated white matter trajectories in this study a statistical nonparametric bootstrap method is described for estimating the dispersion and other errors in white matter tractography results prior studies have derived models of tractography error using the signal to noise ratio snr and diffusion anisotropy of the dti data tractography errors measured using bootstrap methods were generally consistent with an analytic model of tractography error except in areas where branching was evident white matter tractography with bootstrap resampling is also applied to estimate the probabilities of connection between brain regions the approach was used to generate probabilistic connectivity maps between the cerebral peduncles and specific cortical regions