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

the existence of solitary wave solutions of delayed camassa holm equation via a geometric approach abstract this paper is concerned with the camassa holm equation which is a model for shallow water waves we first establish the existence of solitary wave solutions for the equation without delay and then we prove the existence of solitary wave solutions for the equation with a special local delay convolution kernel and a special nonlocal delay convolution kernel by using the method of dynamical system especially the geometric singular perturbation theory and invariant manifold theory according to the relationship between solitary wave and homoclinic orbit the camassa holm equation is transformed into the ordinary differential equations with fast variables by using the variable substitution it is proved that the equation with disturbance also possesses homoclinic orbit and there exists solitary wave solution of the delayed camassa holm equation

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

exchange lemmas for singular perturbation problems with certain turning points abstract in this work singular perturbation problems with a certain type of turning point are studied from a geometric point of view we first describe the delay phenomenon initially studied by pontryagin of dynamics near the slow manifold possessing the turning points based on the local properties of such turning points and the center manifold theory for general invariant manifolds developed by chow liu and yi we extend the well known exchange lemma first formulated by jones and kopell for problems with normally hyperbolic slow manifolds to problems with this type of turning point applications to singular boundary value problems with turning points are discussed

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

tracking invariant manifolds with differential forms in singularly perturbed systems abstract a technique is developed for finding homoclinic orbits in singularly perturbed systems the desired orbit lies near a singular solution that has both fast and slow time scales the orbit is to be constructed as the transverse intersection of a center stable and center unstable manifold which requires tracking the invariant manifolds near the singular solution the main technical advance is the exchange lemma which allows one to convert information about transversality of manifolds associated with the singular limit equations to information about behavior of the invariant manifold as it leaves a neighborhood of a slow segment of the singular solution the computations for this lemma are done with the use of differential forms and the lemma is applied to prove the existence of a homoclinic orbit in a class of singularly perturbed equations

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

density functional theory of charged hard sphere fluids an approximate electrostatic es excess free energy functional for charged hard sphere fluids is presented this functional is designed for systems with large density variations but may also be applied to systems without such variations based on the rosenfeld method of perturbation about a bulk homogeneous reference fluid y rosenfeld j chem phys 98 8126 1993 the new es functional replaces the reference fluid densities with a functional of the particle densities called the rfd functional the first order direct correlation function dcf in the particle densities is computed using as input the first and second order dcfs in rho i x the inhomogeneous densities defined by the rfd functional because this formulation imposes no a priori constraints on the form of the rfd functional it is valid for any choice of rho i x the rfd functional may be chosen 1 so that the input dcfs that is dcfs in rho i x may be approximated and 2 so the combination of rho i x and input dcfs yields a good estimate of the first order dcf in the particle densities in this way the general problem of finding the excess free energy functional has been replaced by the specific problem of choosing a rfd functional we present a particular rfd functional that together with bulk formulations for the input dcfs accurately reproduces the results of monte carlo simulations

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

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

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

oscillation for a second order neutral differential equation with impulses we consider a certain type of second order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations called impulses as a matter of fact some particular non impulsive cases of the system are oscillatory already thus we are interested in finding adequate impulse controls under which our system remains oscillatory

interval criteria for oscillation of second order nonlinear neutral differential equations some new oscillation criteria are established in this paper for the second order nonlinear neutral delay differential equation r t x t p t x t q t f x t 0 where and are nonnegative constants r p q c t0 r and f c r r these results are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results about neutral and delay differential equations in particular several examples that dwell upon the sharp conditions of our results are also included

a note on oscillation criteria of second order nonlinear neutral delay differential equations in recent years many results on oscillation criteria of second order nonlinear neutral delay differential equations have been obtained but some of these criteria are incorrect due to a mistake in a crucial auxiliary result this note examines several of these results provides some counterexamples and points out what causes the problems

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

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

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

invariant manifolds and singularly perturbed boundary value problems boundary value problems for singularly perturbed equations often have singular solutions with internal and boundary layers this paper addresses the question of when singular solutions to such prob

a stochastic optimization model for real time operation of reservoirs using uncertain forecasts a real time operation model primarily useful for daily operation of reservoirs is developed this model is based on a chance constraint formulation and assumes a particular form of the linear decision rule it uses the conditional distribution function cdf of actual streamflows conditioned on the forecasted values these cdf s are constructed by incorporating the statistical properties of forecast errors for different time steps the objective considered is the minimization of weighted probable deviations from storage and release targets these weights are surrogates for the actual loss functions and the probable deviations are functions of the reliability levels specified in the model with the use of target values for release and storage this model is capable of using a release policy that is a subset of a seasonal policy and overcomes the myopic short sighted nature of operation simulation of actual operation using this model for a hypothetical reservoir demonstrates the feasibility and efficiency of this approach this model is shown to be applicable for a system of reservoirs the restrictions associated with the use of a linear decision rule are shown to be invalid for this model

largest well posed spaces for the general diffusion system with nonlocal interactions abstract the authors derive a general diffusion gd system with nonlocal interactions of special structure via energetic variational approach and observe that there exist two critical values of s i e s 1 2 1 for the nonlocal interactions where s 1 2 reflects how strong nonlocal property we have and s 1 affects the linearization and choice of initial data spaces the authors also establish the global existence and uniqueness of mild solution

philos type oscillation criteria for emden fowler neutral delay differential equations philos type oscillation criteria are established for the emden fowler neutral delay differential equation x t c 1x t q 1 t y email protected a 1y email protected q 2 t y email protected b 1y email protected 0 t t 0 where x t y t p t y email protected the results obtained here essentially improve some known results in the literature in particular two interesting examples that point out the importance of our results are also included

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

gevrey regularity of mild solutions to the parabolic elliptic system of drift diffusion type in critical besov spaces abstract this paper is devoted to studying analyticity of mild solutions to the parabolic elliptic system of drift diffusion type with small initial data in critical besov spaces more precisely by using multilinear singular integrals and fourier localization argument we show that global in time mild solutions are gevrey regular i e e t 1 v e t 1 w l t b p r 2 n p r n l t 1 b p r n p r n for all 1 p 2 n and 1 r where 1 is the fourier multiplier whose symbol is given by 1 i 1 n i as a corollary we obtain decay estimates of mild solutions in critical besov spaces without using cumbersome recursive estimation of higher order derivatives