effects of small permanent charge and channel geometry on ionic flows via classical poisson nernst planck models in this work we examine effects of permanent charges on ionic flows through ion channels via a quasi one dimensional classical poisson nernst planck pnp model the geometry of the three dimensional channel is presented in this model to a certain extent which is crucial for the study in this paper two ion species one positively charged and one negatively charged are considered with a simple profile of permanent charges zeros at the two end regions and a constant q 0 over the middle region the classical pnp model can be viewed as a boundary value problem bvp of a singularly perturbed system the singular orbit of the bvp depends on q 0 in a regular way assuming q 0 is small a regular perturbation analysis is carried out for the singular orbit our analysis indicates that effects of permanent charges depend on a rich interplay between boundary conditions and the channel geometry furthermore interesting common features are revealed for q 0 0 only an average quantity of the channel

stability of weak solutions to equations of magnetohydrodynamics with lebesgue initial data abstract we prove the existence the uniqueness and the lipschitz continuous dependence on the initial data of global weak solutions to equations of magnetohydrodynamics mhd with the initial data in the lebesgue spaces

mathematical and numerical study of a corrosion model in this paper we consider a pde system arising in corrosion modelling this system consists in two convection diffusion equations on the densities of charge carriers and a poisson equation on the electric potential boundary conditions are robin boundary conditions we discretize each equation by a finite volume scheme and we prove the convergence of the scheme towards a weak solution to the initial system finally we provide numerical results describing the behaviour of the solutions with respect to an applied voltage

distance maps from unthresholded magnitudes a straightforward algorithm that computes distance maps from unthresholded magnitudes is presented suitable for still images and video sequences while results on binary images are similar to classic euclidean distance transforms the proposed approach does not require a binarization step thus no thresholds are needed and no information is lost in intermediate classification stages experiments include the evaluation of spatial and temporal coherence of distance map values showing better results in both measurements than those obtained with sobel or deriche gradients and classic chessboard distance transforms

finite element solution of the fundamental equations of semiconductor devices in part i of the paper see zlamal 13 finite element solutions of the nonstationary semiconductor equations were constructed two fully discrete schemes were proposed one was nonlinear the other partly linear in this part of the paper we justify the nonlinear scheme we consider the case of basic boundary conditions and of constant mobilities and prove that the scheme is unconditionally stable further we show that the approximate solution extended to the whole time interval as a piecewise linear function converges in a strong norm to the weak solution of the semiconductor equations these results represent an extended and corrected version of results announced without proof in zlamal 14

mathematical studies of poisson nernst planck model for membrane channels finite ion size effects without electroneutrality boundary conditions abstract we study a quasi one dimensional steady state poisson nernst planck model with a local hard sphere potential for ionic flows of two oppositely charged ion species through a membrane channel of particular interest are qualitative properties of ionic flows in terms of individual fluxes j k without assuming electroneutrality boundary conditions for the first order approximation j k 1 in diameter of charged particle of j k our result shows that the quantities v j k 1 and v 2 j k 1 that play critical roles in characterizing ion size effects on ionic flows can be both negative depending sensitively on boundary concentrations and relative ion valences while they are always positive under electroneutrality conditions this new observation indicates that for fixed ion species opposite finite size effects on ionic flows can occur determined further by boundary concentrations numerical simulation is performed to detect some critical potentials closely related to ion size effects numerical simulation results are consistent with our analytical predictions

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

qualitative properties of steady state poisson nernst planck systems mathematical study we examine qualitative properties of solutions of self consistent poisson nernst planck systems including uniqueness in the case of vanishing permanent charge the predominant case studied our results unveil a rich structure inherent in these systems one that is determined by the boundary conditions and the signs of the oppositely charged carrier fluxes a particularly significant special case that of simple boundary conditions is shown to lead to uniqueness and to a complete characterization this case underlies the more complicated cases studied later a contraction mapping principle is included for completeness and allows for an arbitrary permanent charge distribution

structural properties of the one dimensional drift diffusion models for semiconductors this paper is devoted to the analysis of the one dimensional current and voltage drift diffusion models for arbitrary types of semiconductor devices and under the assumption of vanishing generation recombination we show in the course of this paper that these models satisfy structural properties which are due to the particular form of the coupling of the involved systems these structural properties allow us to prove an existence and uniqueness result for the solutions of the current driven model together with monotonicity properties with respect to the total current i of the electron and hole current densities and of the electric field at the contacts we also prove analytic dependence of the solutions on i these results allow us to establish several qualitative properties of the current voltage characteristic in particular we give the nature of the possible bifurcation points of this curve we show that the voltage function is an analytic function of the total current and we characterize the asymptotic behavior of the currents for large voltages as a consequence we show that the currents never saturate as the voltage goes to 00 contrary to what was predicted by numerical simulations by m s mock compel 1 1982 pp 165 174 we also analyze the drift diffusion models under the assumption of quasi neutral approximation we show in particular that the reduced current driven model has at most one solution but that it does not always have a solution then we compare the full and the reduced voltage driven models and we show that in general the quasi neutral approximation is not accurate for large voltages even if no saturation phenomenon occurs finally we prove a local existence and uniqueness result for the current driven model in the case of small generation recombination terms

the existence of liapunov functions for some non conservative positional mechanical systems abstract in this work we establish a liapunov function for the equilibrium for almost all systems x x x y yg x g u r 0 u u r g c 2 0 g 0 0

discontinuous solutions of the navier stokes equations for compressible flow we prove local existence and study properties of discontinuous solutions of the navier stokes equations for one dimensional compressible nonisentropic flow we assume that modulo a step function the initial data is in l2 and the initial velocity and density are in the space bv we show that the velocity and the temperature become smoothed out in positive time and that discontinuities in the density pressure and gradients of the velocity and temperature persist for all time we also show that for stable gases these discontinuities decay exponentially in time more rapidly for smaller viscosities

a mixed method for the mixed initial boundary value problems of equations of semiconductor devices in this article the approximation of nonstationary equations of the semiconductor device with mixed boundary conditions is considered the approximate procedure of this system using a galerkin method that makes use of a mixed finite element method for the potential equation combined with a finite element method for the concentration equations is presented due to the poor regularity properties of the solutions to the semiconductor equations caused by mixed boundary conditions a nonstandard analysis for the semidiscrete galerkin procedure is used existence and uniqueness of the approximate solution is proved a convergence analysis is also given for the method

a poisson nernst planck model for biological ion channels an asymptotic analysis in a three dimensional narrow funnel we wish to predict ionic currents that flow through narrow protein channels of biological membranes in response to applied potential and concentration differences across the channel when some features of channel structure are known we propose to apply singular perturbation analysis to the coupled poisson nernst planck equations which are the basic continuum model of ionic permeation and semiconductor physics in semiconductor physics the problem is a singular perturbation because the ratio of the debye length to the width of the channel is a very small parameter that multiplies the laplacian term in the poisson equation in contrast to semiconductors the atomic scale geometry of narrow ion channels sometimes makes this ratio a large parameter which surprisingly renders the problem a singular perturbation in a different sense we construct boundary layers and match them asymptotically across the different regions of the channel to derive good approximations for fick s and ohm s laws our aim is to e

multiple steady state solutions in a multijunction semiconductor device multiple steady state solutions are constructed for a multijunction semiconductor device using a combination of asymptotic and numerical techniques the multijunction device is modeled by the drift diffusion equations of semiconductor physics in the drift diffusion model three sign alterations of the doping are assumed and a shockley read hall recombination is allowed for in the parameter range for which the current voltage relation is monotonic the quasi neutral approximation to the drift diffusion model is found to be valid and solutions are constructed asymptotically in the limit of large doping densities in contrast in the parameter range for which the current voltage relation is s shaped the quasi neutral approximation is found to poorly approximate solutions to the full model on the middle and lower branches a suitable modification to the quasi neutral approximation is then introduced to describe the middle and lower branches of the current voltage relation under the assumption of no recombi

on strongly reverse biased semiconductor diodes a singular perturbation analysis of the drift diffusion model for stationary flow of charge carriers in a semiconductor device is given an extension of earlier results provides deeper insight into the structure of the solution and the possibility of computing approximations for leakage currents the solvability of the approximating problem is proved

asymptotic analysis of double carrier space charge limited transport in organic light emitting diodes we analyse electron and hole transport in organic light emitting diodes oleds via the driftdiffusion equations we focus on space charge limited transport in which rapid variations in charge car

on the existence of multiple steady state solutions in the theory of electrodiffusion part i the nonelectroneutral case part ii a constructive method for the electroneutral case

finite element approximation to initial boundary value problems of the semiconductor device equations with magnetic influence we shall consider zlamal s approach to the nonstationary equations of the semiconductor device theory under magnetic fields with mixed boundary conditions owing to the reduced smoothness of the electric potential v and carrier densities n and p caused by considering the mixed boundary conditions we must use a nonstandard analysis for this procedure existence as well as uniqueness of the approximate solution is proved the convergence rates obtained in this paper are slower than those previously obtained for pure dirichlet or neumann boundary conditions

using canny s criteria to derive a recursively implemented optimal edge detector a highly efficient recursive algorithm for edge detection is presented using canny s design 1 we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension which can be efficiently implemented by two recursive filters moving in opposite directions in addition to the noise truncature immunity which results the recursive nature of the filtering operations leads with sequential machines to a substantial saving in computational effort five multiplications and five additions for one pixel independent of the size of the neighborhood the extension to the two dimensional case is considered and the resulting filtering structures are implemented as two dimensional recursive filters hence the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm performance measures of this new edge detector are given and compared to canny s filters various experimental results are shown

a bifurcation analysis of the one dimensional steady state semiconductor device equations this paper considers the one dimensional steady state semiconductor device equations modeling a thyristor these equations can be considered as a singularly perturbed boundary value problem the reduced problem is considered in order to derive an approximation to the current voltage curve a bifurcation equation is obtained that completely determines the qualitative structure of the current voltage characteristic a numeric example shows that the developed theory applies to data of realistic magnitude

qualitative properties of steady state poisson nernst planck systems perturbation and simulation study poisson nernst planck pnp systems are considered in the case of vanishing permanent charge a detailed case study based on natural categories described by system boundary conditions and flux is carried out via simulation and singular perturbation analysis our results confirm the rich structure inherent in these systems a natural quantity the quotient of the debye and characteristic length scales serves as the singular perturbation parameter the regions of validity are carefully analyzed by critical comparisons and contrasts between the simulation and the perturbation solution which can be represented in closed form

multiple steady states in one dimensional electrodiffusion with local electroneutrality this paper concerns itself with construction and study of multiple steady states occurring in one dimensional ambipolar electrodiffusion with local electroneutrality constant and equal charge carrier mobilities in the absence of generation recombination piecewise constant fixed change density with four sign alterations is assumed multiple solution branches are constructed via a numerical and asymptotic solution of a system of nonlinear equations resulting from an explicit integration of the appropriate boundary value problem the parameter range in which multiplicity occurs is determined with the aid of asymptotic procedures existence of the appropriate multiple solutions follows from the newton kantorovich theorem

quasi neutral limit to the drift diffusion models for semiconductors with physical contact insulating boundary conditions abstract in this paper the limit of vanishing debye length in a bipolar drift diffusion model for semiconductors with physical contact insulating boundary conditions is studied in one dimensional case the quasi neutral limit zero debye length limit is proved by using the asymptotic expansion methods of singular perturbation theory and the classical energy methods our results imply that one kind of the new and interesting phenomena in semiconductor physics occurs

entropy bounded solutions to the one dimensional compressible navier stokes equations with zero heat conduction and far field vacuum abstract the entropy is one of the fundamental states of a fluid and in the viscous case the equation that it satisfies is highly singular in the region close to the vacuum in spite of its importance in the gas dynamics the mathematical analyses on the behavior of the entropy near the vacuum region were rarely carried out in particular in the presence of vacuum either at the far field or at some isolated interior points it was unknown whether the entropy remains its boundedness the results obtained in this paper indicate that the ideal gases retain their uniform boundedness of the entropy locally or globally in time if the vacuum occurs at the far field only and the density decays slowly enough at the far field precisely we consider the cauchy problem to the one dimensional full compressible navier stokes equations without heat conduction and establish the local and global existence and uniqueness of entropy bounded solutions in the presence of vacuum at the far field only it is also shown that different from the case that with compactly supported initial density the compressible navier stokes equations with slowly decaying initial density can propagate the regularities in inhomogeneous sobolev spaces

a singularly perturbed boundary value problem modelling a semiconductor device this paper is concerned with the static one dimensional modelling of a semiconductor device namely the pn junction when a bias is applied the governing equations are the well known equations describing carrier transport in a semiconductor which consist of a system of ordinary differential equations subject to boundary conditions imposed at the contacts because of the different orders of magnitude of the solution components at the boundaries we scale the components individually and obtain a singular perturbation problem we analyse the equilibrium case zero bias applied and set up approximate models posed as singularly perturbed second order equations by neglecting the hole and electron current densities this makes sense for small forward bias and for moderate reverse bias for the full problem we prove an a priori estimate on the number of electron hole carrier pairs and derive asymptotic expansions as the perturbation parameter tends to zero by setting up the reduced system and the boundary

global existence for 1d compressible isentropic navier stokes equations with large initial data we prove the global existence of weak solutions of the cauchy problem for the navier stokes equations of compressible isentropic flow of a polytropic gas in one space dimension the initial velocity and density are assumed to be in l2 and l2 n bv respectively modulo additive constants in particular no smallness assumptions are made about the intial data in addition we prove a result concerning the asymptotic decay of discontinuities in the solution when the adiabatic constant exceeds 3 2

singular perturbation solutions of steady state poisson nernst planck systems we study the poisson nernst planck pnp system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges assuming point charges and that the debye length is small relative to the domain size we derive an asymptotic formula for the steady state solution by matching outer and boundary layer solutions the case of two ionic species has been extensively studied the uniqueness of the solution has been proved and an explicit expression for the solution has been obtained however the case of three or more ions has received significantly less attention previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations by adopting a methodology that preserves the symmetries of the pnp system we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation due to the simple form of the transcendental equation it can be solved numerically in a straightforward manner our methodology thus provides a standard procedure for solving the pnp system and we illustrate this by solving some practical examples despite the fact that for three ions previous studies have indicated that multiple solutions may exist we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three ion case

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

a complete analysis of a classical poisson nernst planck model for ionic flow abstract in this work we examine the stationary one dimensional classical poisson nernst planck cpnp model for ionic flow a singularly perturbed boundary value problem bvp for the case of zero permanent charge we provide a complete answer concerning the existence and uniqueness of the bvp the analysis relies on a number of ingredients a geometric singular perturbation framework for a reduction to a singular bvp a reduction of the singular bvp to a matrix eigenvalue problem a relation between the matrix eigenvalues and zeros of a meromorphic function and an application of the cauchy argument principle for identifying zeros of the meromorphic function once the zeros of the meromorphic function in a stripe are determined an explicit solution of the singular bvp is available it is expected that this work would be useful for studies of other pnp systems

consistency of semiconductor modeling an existence stability analysis for the stationary van roosbroeck system this paper examines the solution map of the stationary version of the van roosbroeck model for the flow of electrons and holes in a crystalline semiconductor thermodynamic equilibrium and the einstein relations linking mobility and diffusion are assumed to hold for this model incorporated into the model is the quantum statistical assumption that the carrier densities satisfy fermi dirac statistical laws with localization in the boltzmann tail this latter approximation which is seen to be inessential characterizes the conduction and valence bands as nondegenerate the boundary conditions are of two types and correspond to applied potential differences and doping on the contact portions of the device and insulation on the remainder the complete system then involves a coupled set of three nonlinear partial differential equations with their boundary conditions for the electrostatic potential and for the quasi fermi levels corresponding to the electron and hole concentrations in the absence of the classical nondegeneracy approximation the model remains valid but without a natural physical interpretation for two ofthe three dependent variables we demonstrate the existence ofsolutions for this system by associating a solution mapping t such that the fixed points of t define solutions of the system a priori estimates or weak maximum principles permit t to act invariantly on a naturally chosen subset of a hilbert product space the definition of t roughly follows the gummel procedure for uncoupling systems the schauder fixed point theorem is used to prove the existence of a fixed point for t uniqueness is not demonstrated and very possibly does not hold for these systems without special restrictions on the boundary conditions we also introduce a discrete version of the mapping t which is defined in terms of a family of finite difference approximations this mapping enjoys the stability property that it acts invariantly on a rectangular region in euclidean space the dimensions are the same as those specified in the pointwise bounds which define the domain of t a second existence theory framework with quasi constructive aspects is also studied this is based upon pseudomonotone operators the presentation is technology independent except for a section on mos fet devices these typically induce a breakdown ofuniform ellipticity and may be handled by modifications of the major arguments they also exemplify a class of devices for which the electrostatic field is defined on a strictly larger domain than the carriers themselves 1 introduction and model description this paper provides a mathematical analysis of a stationary system solution map which forms the basis for the highly successful computational algorithms used for the numerical solution of the semiconductor system cf bank rose and fichtner 3 our methods involve pointwise stability estimates on solution components organized in such a way that the solution map and a family of discrete approximations may be studied in parallel if desired moreover the weak solution methods do not require regularity theory hence are applicable to physical domains commonly encountered in practice such domains may include re entrant corner points etc and typically induce degenerate elliptic systems we shall also develop the model from physical principles the reason for this is not primarily to compile source material from several different references but rather to indicate clearly to the reader what the level of generality is and to facilitate the discussion of important variations in the device models the models studied herein are reaction diffusion con vection models for which the einstein relations linking carrier mobility and diffusion are assumed to hold the dependent variables of the system include one potential variable inducing an ambient field and two concentration variables for carriers whose convective movement is field dependent this suggests a fairly rich set ofpossible

one dimensional steady state poisson nernst planck systems for ion channels with multiple ion species abstract the one dimensional poisson nernst planck pnp system is a basic model for ion flow through membrane channels if the debye length is much smaller than the characteristic radius of the channel the pnp system can be treated as a singularly perturbed system we provide a geometric framework for the study of the steady state pnp system involving multiple types of ion species with multiple regions of piecewise constant permanent charge special structures of this particular problem are revealed which together with the general framework allows one to reduce the existence and multiplicity of singular orbits to a system of nonlinear algebraic equations near each singular orbit an application of the exchange lemma from the geometric singular perturbation theory gives rise to the existence and local uniqueness of a solution of the singular boundary value problem a new phenomenon on multiplicity and spatial behavior of steady states involving three or more types of ion species is discovered in an example the phenomenon cannot occur when only two types of ion species are involved

electrical structures of interfaces a painleve ii model a painleve ii model derived out of the classical nernst planck system is applied in the context of boundary value problems that describe the electric field distribution in a region x 0 occupied by an electrolyte for privileged flux ratios of the ion concentrations the auto backlund transformation admitted by the painleve ii equation may be applied iteratively to construct exact solutions to classes of physically relevant boundary value problems these representations involve in turn either yablonskii vorob ev polynomials or classical airy functions the requirement that the electric field distribution and ion concentrations in these representations be non singular imposes constraints on the physical parameters these are investigated in detail along with asymptotic properties

geometric singular perturbation approach to steady state poisson nernst planck systems boundary value problems of a one dimensional steady state poisson nernst planck pnp system for ion flow through a narrow membrane channel are studied by assuming the ratio of the debye length to a characteristic length to be small the pnp system can be viewed as a singularly perturbed problem with multiple time scales and is analyzed using the newly developed geometric singular perturbation theory within the framework of dynamical systems the global behavior is first studied in terms of limiting fast and slow systems it is rather surprising that a complete set of integrals is discovered for the nonlinear limiting fast system this allows a detailed description of the boundary layers for the problem the slow system itself turns out to be a singularly perturbed one too which indicates that the singularly perturbed pnp system has three different time scales a singular orbit zeroth order approximation of the boundary value problem is identified based on the dynamics of limiting fast and slow

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

global well posedness of the cauchy problem for the navier stokes equations of nonisentropic flow with discontinuous initial data abstract we prove the global existence uniqueness and continuous dependence on initial data for discontinuous solutions of the navier stokes equations for nonisentropic compressible flow in one space dimension a great deal of information is obtained concerning the qualitative behavior of the solution including an analysis of the convection and evolution of jump discontinuities the derivation of sharp rates of smoothing and the l asymptotic behavior

quasi neutral limit to the drift diffusion models for semiconductors with physical contact insulating boundary conditions and the general sign changing doping profile abstract the quasi neutral limit in a bipolar drift diffusion model for semiconductors with physical contact insulating boundary conditions the general sign changing doping profile and general initial data which allow the presence of the left and right boundary layers and the initial layers is studied in the one dimensional case the dynamic structure stability of the solution with respect to the scaled debye length is proven by the asymptotic analysis of singular perturbation and the entropy energy method the key point of the proof is to use sufficiently the fact that the length of the boundary layer is very small in a short time period

a direct matrix method for computing analytical jacobians of discretized nonlinear integro differential equations in this article we present a simple direct matrix method for analytically computing the jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro differential equations the method is based on a formulation of the discretized equations in vector form using only matrix vector products and component wise operations by applying simple matrix based differentiation rules the matrix form of the analytical jacobian can be calculated with little more difficulty than required to compute derivatives in single variable calculus after describing the direct matrix method we present numerical experiments demonstrating the computational performance of the method discuss its connection to the newton kantorovich method and apply it to illustrative 1d and 2d example problems from electrochemical transport

a singular perturbation analysis of the fundamental semiconductor device equations in this paper we present a singular perturbation analysis of the fundamental semiconductor device equations which form a system of three second order elliptic differential equations subject to mixed neumann dirichlet boundary conditions the system consists of poisson s equation and the continuity equations and describes potential and carrier distributions in an arbitrary emiconductor device the singular perturbation parameter is the minimal normed debye length of the device under consideration using matched asymptotic expansions we demonstrate the occurrence of internal layers at surfaces across which the impurity distribution appearing as an inhomogeneity of poisson s equation has a jump discontinuity these surfaces are called junctions and the occurrence of boundary layers at semiconductor oxide interfaces we derive the layer equations and the reduced problem charge neutral approximation and give existence proofs for these problems the layer solutions which characterize the solutions of the s

a finite element approximation theory for the drift diffusion semiconductor model two sided estimates are derived for the approximation of solutions to the drift diffusion steady state semiconductor device system which are identified with fixed points of gummel s solution map the approximations are defined in terms of fixed points of numerical finite element discretization maps by use of a calculus developed by krasnosel skii and his coworkers it is possible both to locate approximations near fixed points in an a priori manner as well as fixed points near approximations in an a posteriors manner these results thus establish a nonlinear approximation theory in the energy norm with rate keyed to what is possible in a standard linear theory this analysis provides a convergence theory for typical computational approaches in current use for semiconductor simulation

on the one dimensional current driven semiconductor equations the steady state semiconductor equations in one dimension are examined subject to a given current through the device supplemented by dirichlet boundary conditions on one end of the device solutions to this current driven model are identified as the fixed points of a mapping t and uniqueness of solutions for the unipolar model is shown for arbitrary currents by demonstrating that t is unconditionally a contraction for both the uni and the bipolar model existence of solutions close to thermodynamic equilibrium is shown this means that for the one dimensional unipolar current driven model the situation is complementary to that for the potential driven model where it is possible to show existence of solutions for arbitrary applied potentials and uniqueness close to thermodynamic equilibrium only for the unipolar case iteration with the mapping t defines an algorithm for the solution of this model which is unconditionally convergent to the unique solution if it exists

unsteady analytical solutions to the poisson nernst planck equations it is shown that the poisson nernst planck equations for a single ion species can be formulated as one equation in terms of the electric field this previously not analyzed equation shows similarities to the vector burgers equation and is identical with it in the one dimensional case several unsteady exact solutions for one and multidimensional cases are presented besides new mathematical insights which these first known unsteady solutions give they can serve as test cases in computer simulations to analyze numerical algorithms and to verify code

uniform asymptotic error estimates for semiconductor device and electrochemistry equations abstract the paper is organized as follows section 1 sets up the problem our purpose and results and the existing results in the literature section 2 gives the notations used in the paper sections 3 and 4 set up the problem in the case of a symmetric piecewise constant junction and recall the associated asymptotic expansion in section 5 our method is introduced and uniform asymptotic error estimates for a symmetric piecewise constant junction are derived section 6 is an application of our technique for the case of a biological membrane with a constant concentration of fixed charges uniform asymptotic error estimates are also proved to hold in that case a brief summary and conclusion are given in the appendix we give the proofs of the lemmas which are used in sections 5 and 6

global well posedness of the cauchy problem for the equations of a one dimensional viscous heat conducting gas with lebesgue initial data we study the cauchy problem for the one dimensional equations of a viscous heat conducting gas in the lagrangian mass coordinates with the initial data in the lebesgue spaces we prove the existence the uniqueness and the lipschitz continuous dependence on the initial data of global weak solutions 1 main theorems we study the existence the uniqueness and the lipschitz continuous dependence on initial data of global weak solutions to the cauchy problem for the system of one dimensional quasilinear equations of a viscous polytropic ideal gas in a strip qt r 0 t t vx

numerical algorithms based on galerkin methods for the modeling of reactive interfaces in photoelectrochemical pec solar cells abstract this work concerns the numerical solution of a coupled system of self consistent reaction drift diffusion poisson equations that describes the macroscopic dynamics of charge transport in photoelectrochemical pec solar cells with reactive semiconductor and electrolyte interfaces we present three numerical algorithms mainly based on a mixed finite element and a local discontinuous galerkin method for spatial discretization with carefully chosen numerical fluxes and implicit explicit time stepping techniques for solving the time dependent nonlinear systems of partial differential equations we perform computational simulations under various model parameters to demonstrate the performance of the proposed numerical algorithms as well as the impact of these parameters on the solution to the model

series solution of painleve ii in electrodiffusion conjectured convergence a perturbation series solution is constructed with the use of airy functions for a nonlinear two point boundary value problem arising in an established model of steady electrodiffusion in one dimension with two ionic species carrying equal and opposite charges the solution includes a formal determination of the associated electric field which is known to satisfy a form of the painleve ii differential equation comparisons with the numerical solution of the boundary value problem show excellent agreement following termination of the series after a sufficient number of terms for a much wider range of values of the parameters in the model than suggested by previously presented analysis or admitted by previously presented approximation schemes these surprising results suggest that for a wide variety of cases a convergent series expansion for the painleve transcendent describing the electric field has been obtained a suitable weighting of error measures for the approximations to the field and its first derivative provides a monotonically decreasing overall measure of the error in a subset of these cases it is conjectured that the series does converge for this subset