testing serial correlations in high dimensional time series via extreme value theory abstract this paper proposes a simple test for detecting serial correlations in high dimensional time series the proposed test makes use of the robust properties of spearman s rank correlation and the theory of extreme values asymptotic properties of the test statistics are derived under some minor conditions as both the sample size and dimension go to infinity the test is not sensitive to the underlying distribution of the time series so long as the data are continuously distributed in particular the existence of finite order moments of the underlying distribution is not required and asymptotic critical values of the test statistics are available in closed form in finite samples we correct biases of the sample autocorrelations and conduct simulations to study the performance of the proposed test statistics simulation results show that the proposed test statistics enjoy good properties of size and power in finite samples we apply the proposed test to a 92 dimensional series of asset returns finally a simple r code is available to obtain finite sample critical values of the test statistics if needed

testing for high dimensional white noise using maximum cross correlations we propose a new omnibus test for vector white noise using the maximum absolute autocorrelations and cross correlations of the component series based on an approximation by the l norm of a normal random vector the critical value of the test can be evaluated by bootstrapping from a multivariate normal distribution in contrast to the conventional white noise test the new method is proved to be valid for testing departure from white noise that is not independent and identically distributed we illustrate the accuracy and the power of the proposed test by simulation which also shows that the new test outperforms several commonly used methods including the lagrange multiplier test and the multivariate box pierce portmanteau tests especially when the dimension of the time series is high in relation to the sample size the numerical results also indicate that the performance of the new test can be further enhanced when it is applied to pre transformed data obtained via the time series principal component analysis proposed by j chang b guo and q yao arxiv 1410 2323 the proposed procedures have been implemented in an r package

modeling a no slip flow boundary with an external force field abstract a novel technique related to peskin s immersed boundary approach is used to introduce solid surfaces into a simulated flow field the navier stokes equations permit the presence of an externally imposed body force that may vary in space and time forces are chosen to lie along a desired surface and to have a magnitude and direction opposing the local flow such that the flow is brought to rest on an element of the surface for unsteady viscous flow the direct calculation of the needed force is facilitated by a feedback scheme in which the velocity is used to iteratively determine the desired value in particular we determine the surface body force from the relation f x 5 t t 0 u x 5 t dt u x 5 t for surface points x 5 velocity u time t and negative constants and examples are presented which include 2d flow around cylinders 3d turbulent channel flow where one boundary is simulated with a force field and turbulent channel flow over a riblet covered surface while the new method may be applied to complex geometries on a non cartesian mesh we have chosen to use a simple cartesian grid all simulations are done with a spectral code in a single computational domain without any mapping of the mesh

approximating the longest paths in grid graphs abstract in this paper we consider the problem of approximating the longest path in a grid graph that possesses a square free 2 factor by 1 analyzing several characteristics of four types of cross cells and 2 presenting three cycle merging operations and one extension operation we propose an algorithm that finds in an n vertex grid graph g a long path of length at least 5 6 n 2 our approximation algorithm runs in quadratic time in addition to its theoretical value our work has also an interesting application in image guided maze generation

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

modeling multiple time series with applications abstract an approach to the modeling and analysis of multiple time series is proposed properties of a class of vector autoregressive moving average models are discussed modeling procedures consisting of tentative specification estimation and diagnostic checking are outlined and illustrated by three real examples

an isogeometric design through analysis methodology based on adaptive hierarchical refinement of nurbs immersed boundary methods and t spline cad surfaces we explore hierarchical refinement of nurbs as a basis for adaptive isogeometric and immersed boundary analysis we use the principle of b spline subdivision to derive a local refinement procedure which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions we test hierarchical refinement of nurbs for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases using the b spline version of the finite cell method we illustrate the potential of immersed boundary methods as a seamless isogeometric design through analysis procedure for complex engineering parts defined by t spline cad surfaces specifically a ship propeller and an automobile wheel we show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features

a lagrangian particle level set method we present a novel particle level set method for capturing interfaces the level set equation is solved in a lagrangian frame using particles that carry the level set information a key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field the lagrangian description of the level set method is inherently adaptive and exact in the case of solid body motions the efficiency and accuracy of the method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface the simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments

an immersed boundary method with formal second order accuracy and reduced numerical viscosity a formally second order accurate immersed boundary method is presented and tested in this paper we apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first order method the numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high reynolds number flows with immersed boundaries

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

some robust exact results on sample autocorrelations and tests of randomness abstract several exact results on the second moments of sample autocorrelations for both gaussian and non gaussian series are presented general formulae for the means variances and covariances of sample autocorrelations are given for the case where the variables in a sequence are exchangeable bounds for the variances and covariances of sample autocorrelations from an arbitrary random sequence are derived exact and explicit formulae for the variances and covariances of sample autocorrelations from a gaussian white noise are given it is observed that the latter results hold for all spherically symmetric distributions a simulation experiment with gaussian series indicates that normalizing each sample autocorrelation with its exact mean and variance instead of the usual approximate moments can improve considerably the accuracy of the asymptotic n 0 1 distribution to obtain critical values for tests of randomness the exact second moments of rank autocorrelations are also studied

an immersed boundary lattice boltzmann method for the simulation of the flow past an impulsively started cylinder we present a lattice boltzmann method coupled with an immersed boundary technique for the simulation of bluff body flows the lattice boltzmann method for the modeling of the navier stokes equations is enhanced by a forcing term to account for the no slip boundary condition on a non grid conforming boundary we investigate two alternatives of coupling the boundary forcing term with the grid nodes namely the direct and the interpolated forcing techniques the present lb ib methods are validated in simulations of the incompressible flow past an impulsively started cylinder at low and moderate reynolds numbers we present diagnostics such as the near wall vorticity field and the drag coefficient and comparisons with previous computational and experimental works and assess the advantages and drawbacks of the two techniques

simulating free surface flows with sph the sph smoothed particle hydrodynamics method is extended to deal with free surface incompressible flows the method is easy to use and examples will be given of its application to a breaking dam a bore the simulation of a wave maker and the propagation of waves towards a beach arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles the method is explicit and the time steps are therefore much shorter than required by other less flexible methods but it is robust and easy to program

an adaptive version of the immersed boundary method a computational setting for the immersed boundary method employing an adaptive mesh refinement is presented enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested progressively finer rectangular grid patches which dynamically follow the immersed boundary motion the set of equations describing the interaction between a non stationary viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method specially designed for locally refined meshes to an implicit formulation of the immersed boundary method the main contributions of this work concern the formulation and the implementation of a multilevel self adaptive version of the immersed boundary method on locally refined meshes this approach is tested for a particular two dimensional model problem for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary and on the associated uniform mesh built with the resolution of the finest level

numerical simulation of a cylinder in uniform flow in this study a virtual boundary technique is applied to the numerical simulation of stationary and moving cylinders in uniform flow this approach readily allows the imposition of a no slip boundary within the flow field by a feedback forcing term added to the momentum equations in the present work this technique is used with a high order finite difference method effectively eliminating spurious oscillations caused by the feedback forcing when used with spectrally discretized flow solvers very good agreement is found between the present calculations and previous computational and experimental results for steady and time dependent flow at low reynolds numbers

asymptotic covariance structure of serial correlations in multivariate time series summary a simple proof of the asymptotic joint normality of any finite set of serial correlations of a general multivariate second order stationary time series is presented and an explicit formula for the asymptotic covariance between two serial correlations is derived the latter extends bartlett s formula for the asymptotic covariance between two sample cross correlations

a ghost cell immersed boundary method for flow in complex geometry an efficient ghost cell immersed boundary method gcibm for simulating turbulent flows in complex geometries is presented a boundary condition is enforced through a ghost cell method the reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second order accuracy of the base solver both dirichlet and neumann boundary conditions can be treated the current ghost cell treatment is both suitable for staggered and non staggered cartesian grids the accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface numerical results are compared with experimental data and boundary fitted grid results the method is further extended to an existing ocean model mitgcm to simulate geophysical flow over a three dimensional bump the method is easily implemented as evidenced by our use of several existing codes

an implicit boundary approach for viscous compressible high reynolds flows using a hybrid remeshed particle hydrodynamics method abstract we present an implicit boundary particle method with background mesh adaptation we use a brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high reynolds numbers a penalty term is added to the navier stokes equations to impose the boundary conditions the boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid achieving an implicit approach for flow around complex boundaries geometries simulation the main idea of the brinkman penalisation method is to model the solid obstacle as a porous medium the governing equations for the compressible fluid and penalised navier stokes for the porous medium are solved simultaneously without need for interface conditions the accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel poiseuille flow to more complex problems such as the lid driven cavity with high reynolds numbers the reflection and propagation of a compressible shock wave and finally swirling flow in a model two stroke diesel engine the remeshed particle mesh method coupled with brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions

cutfem discretizing geometry and partial differential equations we discuss recent advances on robust unfitted finite element methods on cut meshes these methods are designed to facilitate computations on complex geometries obtained for example from computer

a brinkman penalization method for compressible flows in complex geometries to simulate flows around solid obstacles of complex geometries various immersed boundary methods had been developed their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non body conformal cartesian grids the brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations its main idea is to model solid obstacles as porous media with porosity f and viscous permeability approaching zero it has the pronounced advantages of mathematical proof of error bound strong convergence and ease of numerical implementation with the volume penalization technique in this paper it is extended to compressible flows the straightforward extension of penalizing momentum and energy equations using brinkman penalization with respective normalized viscous h and thermal h t permeabilities produces unsatisfactory results mostly due to nonphysical wave transmissions into obstacles resulting in considerable energy and mass losses in reflected waves the objective of this paper is to extend the brinkman penalization technique to compressible flows based on a physically sound mathematical model for compressible flows through porous media in addition to penalizing momentum and energy equations the continuity equation for porous media is considered inside obstacles in this model the penalized porous region acts as a high impedance medium resulting in negligible wave transmissions the asymptotic analysis reveals that the proposed brinkman penalization technique results in the amplitude and phase errors of order o email protected 1 2 and o h h t 1 email protected 3 4 when the boundary layer within the porous media is respectively resolved or unresolved the proposed method is tested using 1 and 2 d benchmark problems the results of direct numerical simulation are in excellent agreement with the analytical solutions the numerical simulations verify the accuracy and convergence rates

an adaptive wavelet collocation method for fluid structure interaction at high reynolds numbers two mathematical approaches are combined to calculate high rey nolds number incompressible fluid structure interaction a wavelet method to dynamically adapt the computational grid to flow intermittency and obstacle motion and brinkman penalization to enforce solid boundaries of arbitrary complexity we also implement a wavelet based multilevel solver for the poisson problem for the pressure at each time step the method is applied to two dimensional flow around fixed and moving cylinders for reynolds numbers in the range 3 times 10 1 le re le 10 5 the compression ratios of up to 1000 are achieved for the first time it is demonstrated in actual dynamic simulations that the compression scales like re 1 2 over five orders of magnitude while computational complexity scales like re this represents a significant improvement over the classical complexity estimate of re 9 4 for two dimensional turbulence

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state