poisson nernst planck equations for simulating biomolecular diffusion reaction processes i finite element solutions in this paper we developed accurate finite element methods for solving 3 d poisson nernst planck pnp equations with singular permanent charges for simulating electrodiffusion in solvated biomolecular systems the electrostatic poisson equation was defined in the biomolecules and in the solvent while the nernst planck equation was defined only in the solvent we applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules and formulated regular well posed pnp equations an inexact newton method was used to solve the coupled nonlinear elliptic equations for the steady problems while an adams bashforth crank nicolson method was devised for time integration for the unsteady electrodiffusion we numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the nernst planck equation and theoretically proved that the transformed formulation is always associated with an ill conditioned stiffness matrix we also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution the numerical methods are shown to be accurate and stable by various test problems and are applicable to real large scale biophysical electrodiffusion problems

pitfalls of testing non nested hypotheses by the lagrange multiplier method abstract in applied research in econometrics a general model determined from the current knowledge of economic theory often establishes a natural method of embedding a number of otherwise non nested hypotheses under these circumstances significant tests of various hypotheses can be carried out within the classical framework and tests of non nested or separate families of hypotheses do not require development of new statistical methods the application of some suitable variant of likelihood ratio testing procedure will be quite appropriate there are however many ocassions in applied econometrics where the hypotheses under consideration are intended to provide genuine rival explanations of the same given phenomenon and the state of economic theory is not such as to furnish us with a general model that contains both of the rival hypotheses in a natural and theoretically consistent manner a number of investigators have advocated that even when a natural comprehensive model containing both of the hypotheses under consideration cannot be obtained from theoretical considerations it is still appropriate to base significant tests of non nested hypotheses upon a combined model artificially constructed from the rival alternatives moreover in a recent paper on the application of lagrange multiplier lm tests to model specification t s breusch and a r pagan 1980 have claimed that cox s test statistic is connected to an lm or score statistic derived from the application of the lm method to an exponentially combined model earlier employed by a c atkinson 1970 although the use of artificially constructed comprehensive models fortesting separate families of hypotheses is analytically tempting nevertheless it is subject to two major difficulties firstly in many cases of interest in econometrics the structural parameters under the combined hypothesis are not identified secondly the log likelihood function of the artificially constructed model has singularities under both the null and alternative hypotheses the paper firstly examines the derivation of lm statistics in the case of non nested hypotheses and shows that atkinson s general test statistic or breusch and pagan s result can be regarded as an lm test if the parameters of the alternative hypothesis are known the paper also shows that unless all the parameters of the combined models are identified no meaningful test of the separate families of the hypotheses by the artificial embedding procedure is possible and in the identified case an expression for the lm statistic which avoids the problem of the singularity of the information matrix under the null and the alternative hypotheses is obtained the paper concludes that none of the artificially embedding procedures are satisfactory for testing non nested models and should be abandoned it however emphasizes that despite these difficulties associated with the use of artificial embedding procedures cox s original statistic which is not derived as an lm statistic and does not depend on any arbitrary synthetic combination of hypotheses can still be employed as a useful procedure for testing the rival hypotheses often encountered in applied econometrics

a conservative discretization of the poisson nernst planck equations on adaptive cartesian grids in this paper we present a novel hybrid finite difference finite volume method for the numerical solution of the nonlinear poisson nernst planck pnp equations on irregular domains the method is described in two spatial dimensions but can be extended to three dimensional problems as well the boundary of the irregular domain is represented implicitly via the zero level set of a signed distance function and quadtree data structures are used to systematically generate adaptive grids needed to accurately capture the electric double layer near the boundary to handle the nonlinearity in the pnp equations efficiently a semi implicit time integration method is utilized an important feature of our method is that total number of ions in the system is conserved by carefully imposing the boundary conditions by utilizing a conservative discretization of the diffusive and more importantly the nonlinear migrative flux term several numerical experiments are conducted which illustrate that the presented method is first order accurate in time and second order accurate in space moreover these tests explicitly indicate that the algorithm is also conservative finally we illustrate the applicability of our method in the study of the charging dynamics of porous supercapacitors

comparison of local power of alternative tests of non nested regression models the paper derives and compares the local power of three different methods of testing non nested regression models that are available in the literature it shows that the asymptotic power of the orthodox f test against local alternatives is strictly less than that of cox s non nested test or the j test recently proposed by davidson and mackinnon 5 unless the number of non overlapping variables of the alternative hypothesis over the null hypothesis is unity in which case all three tests are shown to be asymptotically equivalent the final section of the paper gives results of monte carlo experiments designed to check the validity of the theoretical findings of the paper and also to shed light on the small sample properties of the cox test and the orthodox test

on the comprehensive method of testing non nested regression models abstract the paper derives the specific form of the exponentially combined likelihood function of two competing multivariate non linear regression models and shows that the application of the comprehensive approach to testing non nested regression models will in general be indeterminate it establishes that in the univariate case there exists a large number of tests of non nested regression models which are consistent in addition to having the same asymptotic distribution under the null hypothesis the paper then derives a set of conditions under which all these consistent tests are asymptotically equivalent not only under the null hypothesis but also under local alternatives as an application of this latter result the paper establishes the asymptotic equivalence of the tests recently proposed by davidson and mackinnon and fisher and mcaleer under local alternatives and shows that within the class of tests considered in the paper these proposed tests possess maximum local power the latter test has this property only when the number of explanatory variables of the true model is not more than that of the false model

a surface patch model for polygonal plates a method of moments surface patch model for polygon plates is presented three methods for segmenting polygon plates are considered also the choice between full surface testing and point matching is discussed as it affects the efficiency and generality of the solution numerical results are compared with measurements and independent calculations for polygonal plates of three different shapes including a wire to plant junction

some aspects of testing non nested hypotheses abstract this paper examines some aspects of testing non nested hypotheses an inequality between the cox and atkinson statistics is noted and the necessary and sufficient condition for the atkinson test to be consistent is derived a new test procedure is also outlined the rest of the paper illustrates the various test statistics their properties and relationships for competing linear regression models

second order poisson nernst planck solver for ion transport the poisson nernst planck pnp theory is a simplified continuum model for a wide variety of chemical physical and biological applications its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community numerous computational algorithms have been constructed for the solution of the pnp equations however in the realistic ion channel context no second order convergent pnp algorithm has ever been reported in the literature due to many numerical obstacles including discontinuous coefficients singular charges geometric singularities and nonlinear couplings the present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second order convergent pnp solver in the ion channel context first a dirichlet to neumann mapping dnm algorithm is designed to alleviate the charge singularity due to the protein structure additionally the matched interface and boundary mib method is reformulated for solving the pnp equations the mib method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces moreover two iterative schemes are utilized to deal with the coupled nonlinear equations furthermore extensive and rigorous numerical validations are carried out over a number of geometries including a sphere two proteins and an ion channel to examine the numerical accuracy and convergence order of the present numerical algorithms finally application is considered to a real transmembrane protein the gramicidin a channel protein the performance of the proposed numerical techniques is tested against a number of factors including mesh sizes diffusion coefficient profiles iterative schemes ion concentrations and applied voltages numerical predictions are compared with experimental measurements

a second order discretization of the nonlinear poisson boltzmann equation over irregular geometries using non graded adaptive cartesian grids in this paper we present a finite difference scheme for the discretization of the nonlinear poisson boltzmann pb equation over irregular domains that is second order accurate the interface is represented by a zero level set of a signed distance function using octree data structure allowing a natural and systematic approach to generate non graded adaptive grids such a method guaranties computational efficiency by ensuring that the finest level of grid is located near the interface the nonlinear pb equation is discretized using finite difference method and several numerical experiments are carried which indicate the second order accuracy of method finally the method is used to study the supercapacitor behaviour of porous electrodes

an efficient scalable numerical algorithm for the simulation of electrochemical systems on irregular domains we present a projection method for the solution of the diffusive transport and reaction equations of electrochemical systems on irregular time dependent domains specific applications include electrodeposition of copper in sub micron trenches as well as any other electrochemical system with an arbitrarily shaped bulk region of dilute electrolyte solution our method uses a finite volume spatial discretization that is second order accurate throughout including a nonuniform region used as a transition to the far field chemical concentrations time integration is performed with a splitting technique that includes a projection step to solve for the electric potential the resulting method is first order accurate in time and is observed to be stable for relatively large time steps furthermore the algorithm complexity scales very respectably with grid refinement and is naturally parallelizable

statistical inference in non nested econometric models the purpose of this paper is to discuss some procedures that are available for testing non nested or separate hypotheses in the statistics and econometrics literature since many of these techniques may also be exploited in other disciplines it is hoped that an elaboration of the principal theoretical findings may make them more readily accessible to researchers in other disciplines several simple examples are used to illustrate the concepts of nested and non nested hypotheses and within the latter category global and partial non nested hypotheses two alternative methods of testing non nested hypotheses are discussed and contrasted the first of these is cox s modification of the likelihood ratio statistic and the second is atkinson s comprehensive model approach a major emphasis is placed on the role of the cox principle of hypothesis testing which enables a broad range of hypotheses to be tested within the same framework the problem associated with the application of the comprehensive model approach to composite non nested hypotheses is also highlighted roy s union intersection principle is presented as a viable method of dealing with this problem simulation results concerning the finite sample properties of various tests are discussed together with an analysis of some attempts to correct the poor size of the cox and related tests

a simulation approach to the problem of computing cox s statistic for testing nonnested models abstract this paper proposes a new procedure for computing the cox statistic for tests of nonnested hypotheses using the method of stochastic simulation the procedure is applicable to a wide class of probability distributions is relatively simple to implement and does not require an analytic derivation of the pseudo true estimators that enter the cox test statistic the paper also contains an application of the proposed method to the test of probit versus logistic formulations of the univariate binary choice models the empirical results show that the simulation method works reasonably well even for a moderate number of replications

an expression for the mutual impedance of coplanar orthogonal surface patches an exact formula is given for the impedance for two orthogonal coplanar piecewise sinusoidal surface patches this algorithm is implemented using a previously published expression for parallel coplanar piecewise sinusoidal surface patches the two algorithms are then used to generate the complete impedance matrix for a rectangular plate

testing separate regression models subject to specification error within the framework of linear regression errors arising from artificial inclusion or exclusion of variables are considered with augmentations or restrictions on a given maintained hypothesis this permits exploitation of relations between tests based on wald and lagrange multiplier principles it is demonstrated that the standard f test though based on biased estimators is nevertheless valid the traditional analysis of misspecification is applied to the linear specialization of tests for separate families of hypotheses an empirical example is provided examining the effect of labour legislation on the growth of canadian trade union membership using annual data for 1925 72 this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item

efficient symmetric discretization for the poisson heat and stefan type problems with robin boundary conditions we present a novel and efficient method for solving the poisson equation the heat equation and stefan type problems with robin boundary conditions over potentially moving arbitrarily shaped domains the method utilizes a level set framework thus it has all of the benefits of a sharp implicitly represented interface such as the ease of handling complex topological changes this method is straightforward to implement and leads to a linear system that is symmetric and positive definite which can be inverted efficiently with standard iterative methods this approach is second order accurate for both the poisson and heat equations and first order accurate for the stefan problem we demonstrate the accuracy in the l 1 and l norms

tests of non nested regression models small sample adjustments and monte carlo evidence abstract it is known that the small sample significance levels of cox type tests of non nested regression models can be much greater than the nominal level adjustments designed to overcome this problem are discussed and two tests are proposed monte carlo evidence on the performance of the tests derived in this paper the davidson mackinnon j test and the fisher mcaleer test is presented the f test applied to the comprehensive model is also included in the simulation experiments

diffuse charge dynamics in electrochemical systems the response of a model microelectrochemical system to a time dependent applied voltage is analyzed the article begins with a fresh historical review including electrochemistry colloidal science and microfluidics the model problem consists of a symmetric binary electrolyte between parallel plate blocking electrodes which suddenly apply a voltage compact stern layers on the electrodes are also taken into account the nernst planck poisson equations are first linearized and solved by laplace transforms for small voltages and numerical solutions are obtained for large voltages the weakly nonlinear limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter epsilon lambdad l where lambdad is the screening length and l the electrode separation at leading order the system initially behaves like an rc circuit with a response time of lambdadl d not lambdad2 d where d is the ionic diffusivity but nonlinearity violates this common picture and introduces multiple time scales the charging process slows down and neutral salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale l2 d in the strongly nonlinear regime controlled by a dimensionless parameter resembling the dukhin number this effect produces bulk concentration gradients and at very large voltages transient space charge the article concludes with an overview of more general situations involving surface conduction multicomponent electrolytes and faradaic processes

the encompassing principle and its application to testing nonnested hypotheses the encompassing principle is used to develop a testing framework which unifies the literature on non nested testing allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist as well as embracing nested hypothesis testing the concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative the analysis is illustrated by an application to two non nested linear regression models and it is shown that the conventional f test as well as all the one degree of freedom non nested tests has an encompassing interpretation and that the f test is a complete parametric encompassing test

testing nested or non nested hypotheses this paper presents a test procedure for nested or non nested hypotheses the test statistic is based on the difference between two estimators of the pseudo true value as defined for instance by sawa this statistic is similar to the usual wald statistic in the case of nested hypotheses and it can be replaced by an asymptotically equivalent one deduced from the score function

direct solution of the discretized poisson neumann problem on a domain composed of rectangles abstract finite difference approximations for the two dimensional poisson neumann problem 1 div grad p q 0on r n grad p g r on r result in a large system of linear equations lp q the n n matrix l is singular with rank l n 1 a solution exists if q satisfies the consistency condition v t q 0 where l t v 0 v 0 a direct solution scheme is described for the case where r can be decomposed into a set of rectangular domains each having a possibly different but constant material coefficient we assume that this problem has to be solved repeatedly for many vectors q the method is efficient in that the number of operations is of order n log n this efficiency is gained by using fast elliptic solvers for each single rectangle and a proper variant of the socalled influence or capacitance matrix technique here on each rectangle a separate poisson neumann problem has to be solved the essential point is the manner in which the consistency condition is enforced for each rectangle the new method has been successfully applied in a code flux to analyze fluid structure interactions

a simplified expression for the self mutual impedance between coplanar and parallel surface monopoles a simplified expression that is valid both for the self and mutual impedances between two coplanar and parallel piecewise sinusoidal pws surface monopoles is presented in contrast to the currently existing two dimensional integral form the present expression involves only a one dimensional integral further the integrand remains regular even for the case of self impedance and does not involve any special functions such as the exponential integral it is in a form suitable for efficient implementation on a computer the expressions are valid when the two surface monopoles are of the same size comparison is made with literature to demonstrate the validity of the expression

a partial differential equation approach to multidimensional extrapolation in this short note a general methodology for multidimensional extrapolation is presented the approach assumes a level set function exists which separates the region of known values from the region to be extrapolated it is shown that arbitrary orders of polynomial extrapolation can be formulated by simply solving a series of linear partial differential equations pdes examples of constant linear and quadratic extrapolation are given

alternative procedures and associated tests of significance for non nested hypotheses this paper attempts to synthesize various procedures for testing non nested hypotheses within the framework of artificial nesting and establishes the result that different tests correspond to different treatments of its identification problem numerical and a priori identification methods are distinguished we derive two modified likelihood ratio tests that are asymptotically equivalent to the cox test and explain the relationship between them the tests are consistent this abstract was borrowed from another version of this item

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

the distributions of the j and cox non nested tests in regression models with weakly correlated regressors abstract this paper examines the asymptotic null distributions of the j and cox non nested tests in the framework of two linear regression models with nearly orthogonal non nested regressors the analysis is based on the concept of near population orthogonality npo according to which the non nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn new distributional results emerge under npo the j and cox tests tend to two different random variables asymptotically each of which is expressible as a function of a nuisance parameter c a n 0 1 variate and a 2 q variate where q is the number of non nested regressors in the alternative model the monte carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under npo by plugging consistent estimates of c into the relevant asymptotic expressions an empirical example illustrates the plug in procedure

mutual impedance of parallel and perpendicular coplanar surface monopoles one dimensional integral formulas are derived for mutual impedance of arbitrary size coplanar parallel and perpendicular surface monopoles the integrals in formulas are expressed as exponential integrals where possible the mutual impedance expression for parallel monopoles is a summation of exponential integrals and one dimensional integrals for perpendicular monopoles the mutual impedance is in closed form containing exponential integrals only the final expressions are in a form suitable for numerical computation since the expressions contain at most one dimensional integrals they can be utilized to reduce the matrix filling time in the moment method formulations especially when inhomogeneous sectioning is preferred additionally they can be used in rectangular surface patch modeling of conducting surfaces with edges which are at an angle to the surface patches providing the angle is small to this end the expressions were utilized in the moment method analysis of linearly tapered slot antennas very good accuracy was obtained with a reduction in computer time

exact tests of a model against nonnested alternatives the results of milliken graybill 1970 are used to develop a general procedure for obtaining exact tests of a linear model against several nonnested and nonlinear alternatives simultaneously the procedure may be extended to test a null model against alternatives in which the dependent variable is subjected to different data transformations arguments are presented in favour of multiple tests