entropic particle transport higher order corrections to the fick jacobs diffusion equation transport of point size brownian particles under the influence of a constant and uniform force field through a planar three dimensional channel with smoothly varying axis symmetric periodic side walls is investigated here we employ an asymptotic analysis in the ratio between the difference of the widest and the most narrow constriction divided through the period length of the channel geometry we demonstrate that the leading order term is equivalent to the fick jacobs approximation by use of the higher order corrections to the probability density we show that in the diffusion dominated regime the average transport velocity is obtained as the product of the zeroth order fick jacobs result and the expectation value of the spatially dependent diffusion coefficient d x which substitutes the constant diffusion coefficient in the common fick jacobs equation the analytic findings are corroborated with the precise numerical results of a finite element calculation of the smoluchowski diffusive particle dynamics occurring in a reflection symmetric sinusoidal shaped channel

the product form for sojourn time distributions in cyclic exponential queues consider a closed cyclic queuing system consisting of m exponential queues the laplace stieltjes transform of the joint distribution of the consecutive sojourn times of a customer at the m queues is determined and shown to have a product form the proof is based on a reversibility argument

exact dimensional reduction of linear dynamics application to confined diffusion in their stochastic versions dynamical systems take the form of the linear dynamics of a probability distribution we show that exact dimensional reduction of such systems can be carried out and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior disappearing under typical coarse graining application is made to non uniform quasi low dimensional diffusion resulting in a systematic extension of the classical fick jacobs approximate reduction to an exact subdynamics

projecting diffusion along the normal bundle of a plane curve the purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized fick jacob s equation obtained by projecting the two dimensional diffusion equation along the normal directions of an arbitrary curve on the plane

on the characterizing properties of the permanental polynomials of graphs abstract let g be a graph and a g the adjacency matrix of g the permanental polynomial of g is defined as g x per x i a g if two graphs g and h have the same permanental polynomial then g is called a per cospectral mate of h a graph g is said to be characterized by its permanental polynomial if all the per cospectral mates of g are isomorphic to g it is shown that complete graphs stars regular complete bipartite graphs and odd cycles are characterized by their permanental polynomials we prove that in general the permanental polynomial cannot characterize the paths and even cycles in particular for each l 1 and m 2 we can find non isomorphic per cospectral mates of p 4 l 3 and c 4 m respectively when we restrict our consideration to connected graphs both the paths and even cycles c 4 l 2 are characterized by their permanental polynomials

permanental polynomials of graphs abstract the first section surveys recent results on the permanental polynomial of a square matrix a i e per xi a the second section concerns the permanental polynomial of the adjacency matrix of a graph the final section is an introduction to the permanental polynomial of the laplacian matrix of a graph an appendix lists some of these latter polynomials

diffusion in a two dimensional channel with curved midline and varying width reduction to an effective one dimensional description diffusion in a narrow two dimensional channel with a midline that need not be straight and a width that may vary is reduced to an effective one dimensional equation of motion this equation takes the form of the fick jacobs equation with a spatially varying effective diffusivity the effective diffusivity includes a contribution that comes from the slope of the midline as well as the usual term stemming from variations in the channel width along the length of the channel our derivation of our equation of motion is completely rigorous and is based on an asymptotic expansion in a small dimensionless parameter that characterizes the channel width for a channel that has a straight midline or wall our equation of motion reduces to zwanzig s equation r zwanzig j phys chem 96 3926 1992 our derivation therefore provides a rigorous proof of the validity of the latter equation finally the equation of motion is solved analytically for channels with curved midline and constant width

effective diffusion on riemannian fiber bundles the purpose of this paper is to provide equations to model the evolution of effective diffusion over a riemannian fiber bundle under the hypothesis of infinite diffusion rate along compact fibers these equations are obtained by projecting the diffusion equation onto the base manifold of the fiber bundle the projection or dimensional reduction is achieved by integrating the diffusion equation along the fibers of the bundle this work generalizes an put into a general framework previous work on effective diffusion over channels and the interfaces between curved surfaces

on the permanental sum of graphs abstract let g be a graph and a g the adjacency matrix of g the polynomial g x per x i a g is called the permanental polynomial of g and the permanental sum of g is the summation of the absolute values of the coefficients of g x in this paper we investigate properties of permanental sum of a graph prove recursive formulas to compute the permanental sum of a graph and show that the ordering of graphs with respect to permanental sum furthermore we determine the upper and lower bounds of permanental sum of unicyclic graphs and the corresponding extremal unicyclic graphs are also determined

on the bivariate permanent polynomials of graphs abstract in 1980 balasubramanian and parthasarathy introduced the bivariate permanent polynomials of graphs and conjectured that this polynomial is a graph characterizing polynomial that is any two graphs with the same bivariate permanent polynomial are isomorphic in this paper we give counterexamples to this conjecture by a computer search furthermore we show that several well known families of graphs are determined by the bivariate permanent polynomial complete graphs complete bipartite graphs regular complete multipartite graphs cycles and their complements

per spectral characterizations of graphs with extremal per nullity abstract a graph g is said to be determined by its permanental spectrum if any graph having the same permanental spectrum as g is isomorphic to g in this paper we introduce the permanental nullity of a graph the multiplicity of the number zero in the permanental spectrum of a graph to study graphs determined by their permanental spectra first we determine all graphs of order n whose permanental nullities are n 2 n 3 n 4 and n 5 respectively then we show that all graphs with the permanental nullity n 2 n 3 or n 5 and all non bipartite graphs with the permanental nullity n 4 are determined by their permanental spectra in particular we prove that the complete bipartite graphs are determined by their permanental spectra

kinetic equations for diffusion in the presence of entropic barriers we use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers the result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers we analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description the corresponding kinetic equation named the fick jacobs equation is obtained and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries the method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature

biased diffusion in confined media test of the fick jacobs approximation and validity criteria we study biased diffusive transport of brownian particles through narrow spatially periodic structures in which the motion is constrained in lateral directions the problem is analyzed under the perspective of the fick jacobs equation which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one dimensional diffusion the validity of this approximation based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure is analyzed by comparing the different time scales that characterize the problem a validity criterion is established in terms of the shape of the structure and of the applied force it is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure the criterion can be visualized by means of a diagram representing the regions where the fick jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure

extended fick jacobs equation variational approach we derive an extended fick jacobs equation for the diffusion of noninteracting particles in a two and symmetric three dimensional channels of varying cross section a x using a variational approach the result is a diffusion differential equation of second order in only one space longitudinal coordinate this equation is tested on the task of calculating the stationary flux through a hyperboloidal tube and its solution is compared with that of other methods

computing the permanental polynomials of graphs let m be an nn matrix with entries mij i j 1 2 n the permanent of m is defined to be per m i 1nmi i where the sum is taken over all permutations of 1 2 n the permanental polynomial of m is defined by per xinm where in is the identity matrix of size n in this paper we give recursive formulas for computing permanental polynomials of the laplacian matrix and the signless laplacian matrix of a graph respectively

the time for a round trip in a cycle of exponential queues in 1 chow obtained the steady state distribution of the cycle time of a customer in a closed tandem queue composed of two exponential fifo servers and populated by an arbitrary fixed number of customers the present paper gives the generalization of chow s result by means of a different proof to the case of arbitrarily many exponential servers

which graphs are determined by their spectrum for almost all graphs the answer to the question in the title is still unknown here we survey the cases for which the answer is known not only the adjacency matrix but also other types of matrices such as the laplacian matrix are considered

technical note on normalizing constants in queueing networks we present a method for deriving the normalizing constant for the state space probabilities in a closed markovian queueing network with constant service rates our method produces a much simpler expression than any obtained previously this expression takes the form of a sum of only m terms if the visitation rate to service rate ratios are distinct and is easily generalized to the degenerate case the expression also yields a closed form solution for time delay distributions in cyclic networks of any length and with any number of customers

approximations of the generalized fick jacobs equation we analyze the generalized fick jacobs equation obtained by a rigorous mapping of the diffusion equation in a quasi one dimensional quasi 1d narrow 2d or 3d channel with varying cross section a x onto the longitudinal coordinate x we show that for constructing approximations and understanding their applicability in practice it is crucial to study the 2d 3d density inside the channel in the regime of stationary flow we present algorithms enabling us to derive approximate formulas for the effective diffusion coefficient involving derivatives of a x higher than a ensuremath x and give examples for 2d channels effects of the boundary conditions at the ends of a finite channel and the case of nonsmooth a x are also discussed

highly unique network descriptors based on the roots of the permanental polynomial in this paper we examine the zeros of permanental polynomials as highly unique network descriptors we employ exhaustively generated networks and demonstrate that our defined graph measures based on the moduli of the zeros of permanental polynomials are quite efficient when distinguishing graphs structurally in this work we continue with a line of research that relates to the search of almost complete graph invariants these highly unique network measures may serve as a powerful tool for tackling graph isomorphism