some examples of kinetic schemes whose diffusion limit is il in s exponential fitting this paper is concerned with diffusive approximations of some numerical schemes for several linear or weakly nonlinear kinetic models which are motivated by wide range applications including radiative transfer or neutron transport run and tumble models of chemotaxis dynamics and vlasov fokker planck plasma modeling the well balanced method applied to such kinetic equations leads to time marching schemes involving a scattering s matrix itself derived from a normal modes decomposition of the stationary solution one common feature these models share is the type of diffusive approximation their macroscopic densities solve drift diffusion systems for which a distinguished numerical scheme is il in scharfetter gummel s exponential fitting discretization we prove that these well balanced schemes relax within a parabolic rescaling towards such type of discretization by means of an appropriate decomposition of the s matrix hence are asymptotic preserving

mean exit times for particles driven by weakly colored noise consider a particle whose velocity is an ornstein uhlenbeck process with correlation time varepsilon 2 frac dx dt frac sigma z varepsilon qquad frac dz dt frac z varepsilon 2 frac sqrt 2 xi t varepsilon where xi t is gaussian white noise this represents brownian motion with memory i e a non markovian brownian motion singular perturbation techniques reduce the mean exit time problem to a boundary layer problem which turns out to be the half range expansion problem for the fokker planck operator this is solved via complex variable theory it is found that the spatial density has a milne extrapolation length varepsilon sigma zeta tfrac 1 2 varepsilon sigma 1 46035 cdots where zeta is the riemann zeta function it is also found that the average time at which x t first escapes an interval a 0 b ven that it starts at x 0 0 and z 0 z 0 is e t text ex frac 1 2 sigma 2 left a varepsilo

an aggregate label setting policy for the multi objective shortest path problem we consider label setting algorithms for the multi objective shortest path problem with any number of sum and bottleneck objectives we propose a weighted sum aggregate ordering of the labels specifically tailored to combine sum and bottleneck objectives we show that the aggregate order leads to a consistent reduction of solution times up to two thirds with respect to the classical lexicographic order

asymptotic solution of the wang uhlenbeck recurrence time problem a langevin particle is initiated at the origin with positive velocity its trajectory is terminated when it returns to the origin in 1945 wang and uhlenbeck posed the problem of finding the joint probability density function pdf of the recurrence time and velocity naming it the recurrence time problem we show that the short time asymptotics of the recurrence pdf is similar to that of the integrated brownian motion solved in 1963 by mckean we recover the long time t ensuremath 3 2 decay of the first arrival pdf of diffusion by solving asymptotically an appropriate variant of mckean s integral equation

first passage times for correlated random walks and some generalizations it is generally difficult to solve fokker planck equations in the presence of absorbing boundaries when both spatial and momentum coordinates appear in the boundary conditions in this note we analyze a simple exactly solvable model of the correlated random walk and its continuum analogue it is shown that one can solve for the moments recursively in one dimension in exact analogy with first passage problems for the fokker planck equation although the boundary conditions are somewhat more complicated further generalizations are suggested to multistate random walks

eigenvalues and eigenfunctions of the fokker planck equation for the extremely underdamped brownian motion in a double well potential the eigenvalues and eigenfunctions of the fokker planck equation describing the extremely underdamped brownian motion in a symmetric double well potential are investigated by transforming the fokker planck equation to energy and position coordinates and by performing a suitable averaging over the position coordinate a differential equation depending only on energy is derived for finite temperatures this equation is solved by numerical integration whereas in the weak noise limit an analytic result for the lowest nonzero eigenvalue is obtained furthermore by using a boundary layer theory near the critical trajectory the correction term to the zero friction limit result is found

the analytic solutions of some boundary layer problems in the theory of brownian motion the authors give analytic solutions of the generalised albedo and milne problems for the uhlenbeck ornstein process and discuss the relation between these and the original wang uhlenbeck 1945 problem of determining the distribution of first passage times

differential geometry of viscoelastic models with fractional order derivatives viscoelastic materials with memory effect are studied based on the fractional rheonomic geometry the geometric objects are regarded as basic quantities of fractional viscoelastic models i e the metric tensor and torsion tensor are interpreted as the strain and the fractional strain rate respectively the generalized viscoelastic equations are expressed by the geometric objects especially the basic constitutive equations such as voigt and maxwell models can be derived geometrically from the generalized equation this leads to the fact that various viscoelastic models can be unified into one geometric expression

multi objective vehicle routing problems routing problems such as the traveling salesman problem and the vehicle routing problem are widely studied both because of their classic academic appeal and their numerous real life applications similarly the field of multi objective optimization is attracting more and more attention notably because it offers new opportunities for defining problems this article surveys the existing research related to multi objective optimization in routing problems it examines routing problems in terms of their definitions their objectives and the multi objective algorithms proposed for solving them

a multicriteria pareto optimal path algorithm abstract in this paper we present an algorithm for finding in a multicriteria network pareto optimal paths one each for each efficient objective vector validation of the algorithm and two illustrative examples are included computational experience is also reported this algorithm is a generalization of an earlier one for the bicriterion case

the density profile for the klein kramers equation near an absorbing wall we derive asymptotic series for the expansion coefficients of a function in terms of the pagani functions which occur in the boundary layer solutions of the klein kramers equation the results enable us to determine the density profile in the stationary solution of this equation near an absorbing wall from the numerically determined velocity distribution at the wall with an accuracy of about 2 we also obtain information about the analytic behavior of the density profile this profile increases near the wall with the square root of the distance to the wall finally the asymptotic analysis leads to an understanding of the slow convergence of variational approximations to the solution of the absorbing wall problem and of the exponents that occur when one studies the variational approximations to various quantities of interest as functions of the number of terms in the variational ansatz this is used to obtain a better variational estimate for the density at the wall

the analytic structure of the stationary kinetic boundary layer for brownian particles near an absorbing wall a method for solving kinetic boundary layer problems for the 1d klein kramers equation the kinetic equation for brownian particles was proposed a few years ago by marshall and watson 1987 for the special case of particles moving under the influence of a constant or zero external force in this paper the authors apply this method to a number of classical stationary boundary layer problems for completely or partially absorbing walls these are the milne problem in which a current flows towards the wall from infinity and the albedo problem in which particles are injected into the system at the wall with a prescribed velocity distribution the solutions are known to be non analytic at the wall for zero normal velocity the authors pay particular attention to the nature of this singularity for several special cases the results are compared with results obtained by approximate methods

an exact method for the biobjective shortest path problem for large scale road networks abstract the biobjective shortest path problem bsp is the problem of finding one to one paths from a start node to an end node while simultaneously minimizing two conflicting objective functions we present an exact recursive method based on implicit enumeration that aggressively prunes dominated solutions our approach compares favorably against a top performer algorithm on two large testbeds from the literature and efficiently solves the bsp on large scale networks with up to 1 2 million nodes and 2 8 million arcs additionally we describe how the algorithm can be extended to handle more than two objectives and prove the concept on networks with up to 10 objectives

parameters estimation for a new anomalous thermal diffusion model in layered media in this paper we study an inverse problem of parameters estimation for a new time fractional heat conduction model in multilayered medium in the anomalous thermal diffusion model we consider the fractional derivative boundary conditions and the conduction obeys modified fourier law with riemannliouville fractional operator of different order in each layer for the direct problem we construct an effective finite difference scheme by using the balance method to deal with the discontinuity interface for the inverse problem we apply the nonlinear conjugate gradient ncg method with different conjugated coefficients to simultaneously identify the fractional exponent in each layer finally we use experimental data to verify the effectiveness of the proposed technique in which the jacobian matrix is achieved by a derivative free approach we analyze the sensitivity coefficients and the convergence behaviors of the ncg algorithm the simulation results confirm that the fractional heat conduction model with estimated parameters gives a more accurate fitting than the classical counterpart and the ncg method is a feasible and effective technique for the inverse problem of parameters estimation in fractional model

a rigorous model for prediction of viscosity of oil based hybrid nanofluids abstract oil based hybrid nanofluids play an important role in heat transfer in cooling systems and lubrication therefore various experimental investigations are conducted to estimate their viscosity however such measurements can be carried out on limited types of oil based hybrid nanofluids and often are time consuming and expensive the main objective of this paper is to develop a rigorous data driven method based on an advanced genetic programming gp called multigene genetic programming mggp to predict the viscosity of newtonian oil based hybrid nanofluids which has not previously been used in this area a comparative analysis was performed using the gene expression programming gep multi variate linear regression mlr methods and various correlations 679 experimental data points with different nanoparticles and oil based fluids were collected from literature to develop the artificial intelligent ai models the new approach showed superior performance in estimating of the relative viscosity of oil based hybrid nanofluids in comparison with all correlations methods furthermore the mggp results for the test dataset r 0 991 rmse 0 05 pi 0 643 were more accurate than those obtained from the gep r 0 975 rmse 0 083 pi 0 696 and mlr r 0 912 rmse 0 153 pi 1 respectively the sensitivity analysis was also performed demonstrating that the volume fraction p i s 0 849 d v 1 10 079 temperature p i s 0 463 d v 2 9 966 and nanoparticles size p i s 0 420 d v 3 6 092 are the most significant factors in assessing relative viscosity respectively

exact solution of the reaction diffusion problem for a particle generating band on a surface by riemann hilbert matching the existence of a class of exact solutions for diffusion reaction problems is demonstrated for the example of a band the method may be applied to any particle source which can be analytically mapped to a band or a disc situated on an infinite plane a simple asymptotic expression for the experimentally measurable collector efficiency current current response function has been found

semiflexible polymer in the half plane and statistics of the integral of a brownian curve a continuum model of a polymer with non zero bending energy fluctuating without overhangs in the half plane is considered the exact partition function is obtained from the marshall watson solution of the klein kramers equation for brownian motion in the half space the partition function contains information on probabilities associated with the integral of a brownian curve and reproduces sinai s t 5 4 result for the asymptotic first passage time density the t 5 2 dependence of a different passage probability implies a first order polymer adsorption transition for short range pinning potentials

the growth of small droplets from a gas mixture results and estimates for very small radii abstract to test and to complement the moment method for solving kinetic equations in the space outside of a sphere that absorbs one component out of a gas mixture we develop a solution method especially suitable for radii smaller or not much larger than a mean free path the method is used to calculate the stationary current towards an absorbing sphere suspended in a gas mixture that is in equilibrium far from the sphere for the simplest kinetic equation a variant of the linear bgk equation and for radii below two mean free paths this procedure gives the current towards the sphere to within an accuracy of at most a few tenths of a percent for radii around two mean free paths the new results agree with those of a variant of the moment method for lower radii discrepancies of up to a few percent are found our new method does not work for the klein kramers equation a kinetic equation for brownian particles for the latter equation we obtain an estimate for the current at very low radii from the free space solution by uhlenbeck and ornstein its numerical evaluation strongly indicates an analytic behavior for small radii different from the one found in the bgk case

the kinetic boundary layer for the linearized boltzmann equation around an absorbing sphere we construct approximate solutions of the linearized boltzmann equation for a gas outside of a completely absorbing sphere a simple model for a liquid droplet growing in a supersaturated vapor the solutions are linear combinations of two chapman enskog type solutions which carry heat and particle currents and boundary layer eigenfunctions that decay with increasing distance from the sphere on a distance of the order of a mean free path to construct the boundary layer eigenfunctions and the linear combination that satisfies the boundary condition at the sphere we expand the solution in burnett functions and truncate the resulting system of equations for the expansion coefficients for one particular truncation prescription which generalizes grad s 13 moment scheme good initial convergence with increasing order of truncation is obtained for both moderately small and large radii of the sphere the results for small radii extrapolate smoothly toward the known limit of zero radius we present results for the reaction rate the particle current arriving at the sphere divided by the density at infinity and for the density and temperature profiles in the boundary layer the explicit calculations are carried out for maxwell molecules but the method appears to be suitable for more general intermolecular potentials

the influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet we extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background the method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses the release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state the kinetic equation describing the vapor is the stationary klein kramers equation for brownian particles diffusing in a temperature gradient by means of an expansion in burnett functions this equation is transformed into a set of coupled algebrodifferential equations by numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface in view of the intrinsic numerical instability of the system of equations a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest the procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon the effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small of the order of 1 but well outside of the margin of error of the method

parameter estimation for the fractional schrodinger equation using bayesian method in this paper the fractional schrodinger equation is studied the bayesian method is put forward to estimate some relevant parameters of the equation results show that the estimated values can fit well with the exact solution the varying initial values and maximum iterations have little effect on the estimated results it indicates that the bayesian method is efficient for the multi parameter estimation for the fractional schrodinger equation this method can also be used to estimate parameters for the fractional schrodinger equation in other potential field

first passage times for the uhlenbeck ornstein process a numerical solution is obtained for the laplace transformed backward kramers equation from which the mean first passage time may be obtained the main difficulties are associated with a the parabolic nature of the time development operator and b the existence of a double structure in the solution near the absorbing barrier both of these difficulties are resolved by computational methods derived from boundary layer theory the reliability of the method is assessed by comparing its results with an earlier analytic solution for the case of a uniform force field the authors also present the results for a harmonic force field for which no analytic solution is yet known

the distribution of exit times for weakly colored noise we analyze the exit time first passage time problem for the ornstein uhlenbeck model of brownian motion specifically consider the positionx t of a particle whose velocity is an ornstein uhlenbeck process with amplitude and correlation time e2 dx dt sigma z varepsilon dz dt z varepsilon 2 2 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 xi t varepsilon where t is gaussian white noise let the exit timetex be the first time the particle escapes an interval a t by directly solving the fokker planck equation in brief after taking a laplace transform we use singular perturbation methods to reduce the fokker planck equation to a boundary layer problem this boundary layer problem turns out to be a half range expansion problem which we solve via complex variable techniques this yields the laplace transform off t to within a transcendentally smallo e a e e b e error we then obtainf t by inverting the transform order by order in e in particular by lettingb we obtain the solution to wang and uhlenbeck s unsolved problem b througho e2 2 a1 this solution is f t erf left frac a varepsilon sigma alpha varepsilon sigma z 0 2 sigma t varepsilon 2 kappa 1 mathord left vphantom 1 2 right kern nulldelimiterspace 2 right for frac t varepsilon 2 1 andf 1 otherwise here 1 2 1 4603 where is the riemann zeta function and the constant is 0 22749

the kinetic boundary layer for the klein kramers equation a new numerical approach we explore a numerical technique for determining the structure of the kinetic boundary layer of the klein kramers equation for noninteracting brownian particles in a fluid near a wall that absorbs the brownian particles the equation is of interest in the theory of diffusion controlled reactions and of the coagulation of colloidal suspensions by numerical simulation of the langevin equation equivalent to the klein kramers equation we amass statistics of the velocities at the first return to the wall and of the return times for particles injected into the fluid at the wall with given velocities the data can be used to construct the solutions of the standard problems at an absorbing wall the milne and the albedo problem we confirm and extend earlier results by burschka and titulaer obtained by a variational method vexed by the slow convergence of the underlying eigenfunction expansion we briefly discuss some further boundary layer problems that can be attacked by exploiting the results reported here

half range completeness for the fokker planck equation half range completeness theorems are proved for eigenfunctions associated to the one dimensional fokker planck equation in a semi infinite medium existence and uniqueness results for perfectly absorbing partially absorbing and purely specularly reflecting boundary conditions are deduced for the stationary and time dependent problems similar results are obtained for a slab geometry

prediction of the effective parameters of the nanofluids using the generalized stochastic perturbation method abstract the paper presents the results concerning a new problem of homogenization of the fluids filled with a random volume fraction of nanoparticles we use a variety of probabilistic and statistical methods applied for numerical determination of the effective physical properties of different fluids filled with nanoparticles the new probabilistic approach in the form of a higher order stochastic perturbation method is employed here which is based on a higher order taylor expansion of input random quantities and the resulting homogenized parameters using a general order series with random coefficients it is contrasted with the monte carlo simulation and analytical symbolic integration all computer methods are used to determine up to the fourth probabilistic moments and coefficients for effective specific heat viscosity heat conductivity and mass density for some nanofluids of modern technological importance the volume fraction of the nanoparticles is treated in this study as the input gaussian parameter truncated to the positive values and uniquely defined by the expectation where its coefficient of variation is an additional parameter in our analysis computational experiments are performed here using computer algebra system maple and they demonstrate a very good agreement of the probabilistic characteristics computed using analytical perturbation and simulation methods

the algebra of two symmetric matrices proving completeness and deriving syzygies for a set of invariants of the riemann tensor a large number of riemann tensor invariants can be written as traces of products of two 3 3 matrices representing the weyl tensor and the weyl like square of the ricci tensor it is pointed out that finding a complete set i for all of these invariants is a simple consequence of the more general problem of finding a complete set of symmetric matrices m in terms of which all symmetric matrix polynomials in these two matrices can be expressed such a set is constructed and a formal proof of its completeness is given several matrix identities and a scalar syzygy obtained recently by sneddon are rederived and their interrelationships clarified they are shown to be ultimately consequences of the cayley hamilton theorem a minimal set of invariants that must be contained in the complete set of invariants of the general problem is identified and it is concluded that no set proposed so far is complete

the kinetic boundary layer for the fokker planck equation with absorbing boundary the fokker planck equation for the distribution of position and velocity of a brownian particle is a particularly simple linear transport equation its normal solutions and an apparently complete set of stationary boundary layer solutions can be determined explicitly by a numerical algorithm we select linear combinations of them that approximately fulfill the boundary condition for a completely absorbing plane wall and that approach a linearly increasing position space density far from the wall various aspects of these approximate solutions are discussed in particular we find that the extrapolated asymptotic density reaches zero at a distance xm beyond the wall we find xm 1 46 in units of the velocity persistence length of the brownian particle this study was motivated by certain problems in the theory of diffusion controlled reactions and the results might be used to test approximate theories employed in that field

half range completeness for the fokker planck equation with an external force this paper deals with a generalization of a classical result obtained by r beals and v protopopescu for the fokker planck equations to the case in which a constant external force is present

on a multicriteria shortest path problem abstract multicriteria shortest path problems have not been treated intensively in the specialized literature despite their potential applications in fact a single objective function may not be sufficient to characterize a practical problem completely for instance in a road network several parameters as time cost distance etc can be assigned to each arc clearly the shortest path may be too expensive to be used nevertheless the decision maker must be able to choose some solution possibly not the best for all the criteria in this paper we present two algorithms for this problem one of them is an immediate generalization of the multiple labelling scheme algorithm of hansen for the bicriteria case based on this algorithm it is proved that any pair of nondominated paths can be connected by nondominated paths this result is the support of an algorithm that can be viewed as a variant of the simplex method used in continuous linear multiobjective programming a small example is presented for both algorithms

the time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems abstract in this paper a time fractional fourier law is obtained from fractional calculus according to the fractional fourier law a fractional heat conduction equation with a time fractional derivative in the general orthogonal curvilinear coordinate system is built the fractional heat conduction equations in other orthogonal coordinate systems are readily obtainable as special cases in addition we obtain the solution of the fractional heat conduction equation in the cylindrical coordinate system in terms of the generalized h function using integral transformation methods the fractional heat conduction equation in the case 0 1 interpolates the standard heat conduction equation 1 and the localized heat conduction equation 0 finally numerical results are presented graphically for various values of order of fractional derivative

the covariant form of the klein kramers equation and the associated moment equations we provide a covariant coordinate free formulation of the many dimensional klein kramers equation for the phase space distribution of a brownian particle we construct a complete set of eigenfunctions of the collision operator adapted to the coordinate system which involve covariant tensorial hermite polynomials the klein kramers equation can then be reformulated as a system of coupled equations for the expansion coefficients with respect to this system truncation of this system of moment equations and application of a subsidiary condition yields a covariant generalization of grad s thirteen moment equations as an application we give the explicit form of these equations for spherically symmetric stationary solutions in spherical coordinates we briefly comment on possible extensions of our treatment to slightly more complicated cases

generalized viscoelastic models their fractional equations with solutions recently fractional calculus fc has encountered much success in the description of complex dynamics in particular fc has proved to be a valuable tool to handle viscoelastic aspects in this paper we construct fractional rheological constitutive equations on the basis of well known mechanical models especially the maxwell the kelvin voigt the zener and the poynting thomson model to this end we introduce a fractional element in addition to the standard purely elastic and purely viscous elements as we proceed to show many of the fractional differential equations which we obtain by this construction method admit closed form analytical solutions in terms of fox h functions of the minag leffler type

the structure of the stationary kinetic boundary layer for the linear bgk equation recently very accurate numerical methods for solving kinetic boundary layer problems for linear kinetic equations have been developed to test such methods detailed information about exactly solvable models can be very helpful to this purpose the authors present results for the stationary 1d linear bgk equation obtained by the singular eigenfunction method that extend results already known in the literature both in scope and in precision special attention is paid to the nature of the singularity in the distribution function for small velocities near the boundary this singularity cannot be reproduced exactly by the numerical methods available explicit expressions are presented for the milne problem and for the albedo problem with input particles of a single velocity they compare the results with those of a recently developed variant of the two stream moment method they find excellent agreement except close to the singularity for many quantities of interest the accuracy obtainable by the novel two stream moment method cannot be reproduced with comparable numerical effort by evaluation of the exact solution

green s function approach to the solution of the time dependent fokker planck equation with an absorbing boundary abstract the solution of the time dependent multivelocity fokker planck equation in plane geometry with an absorbing boundary is formulated in terms of the infinite medium green s function and the boundary distribution the boundary distribution is to be determined by solving an integral equation it is shown that the velocity moments such as density current and energy density can be expressed in terms of three reduced distributions which depend on the longitudinal velocity component only numerical results for monovelocity pulsed and steady sources are presented

parameter estimation for the generalized fractional element network zener model based on the bayesian method abstract in the present study an inverse problem to estimate parameters in the zener model of viscoelasticity based on the generalized fractional element gfe network is studied the bayesian method is proposed to obtain the optimal estimation of the viscoelastic parameters three examples are performed to certify the validity of the method all numerical results lead to an excellent fitting between the calculative results and experimental data it is shown that the bayesian method is feasible in the inverse problem of parameter estimation for the fractional constitutive equation and the gfe network zener model is efficient in the modeling of the viscoelastic behavior

directed self organized critical patterns emerging from fractional brownian paths abstract we discuss a family of clusters c corresponding to the region whose boundary is formed by a fractional brownian path y i and by the moving average function y n i 1 n k 0 n 1 y i k our model generates fractal directed patterns showing spatio temporal complexity and we demonstrate that the cluster area length and duration exhibit the characteristic scaling behavior of soc clusters the function cn i acts as a magnifying lens zooming in or out the avalanches formed by the cluster construction rule where the magnifying power of the zoom is set by the value of the amplitude window n on the basis of the construction rule of the clusters c n i y i y n i and of the relationship among the exponents we hypothesize that our model might be considered to be a generalized stochastic directed model including the dhar ramaswamy dr model and the stochastic models as particular cases as in the dr model the growth and annihilation of our clusters are obtained from the set of intersections of two random walk paths and we argue that our model is a variant of the directed self organized criticality scheme of the dr model

linear and nonlinear diffusion and reaction diffusion equations from discrete velocity kinetic models two velocity kinetic models are used to derive in the appropriate limit the equations which govern the macroscopic density of fluid systems such equations are obtained from an asymptotic expansion in powers of a small parameter related to the microscopic mean free path it is shown that the density of a fluid interacting with a non equilibrium background satisfies a linear diffusion equation and that the hierarchy of equations arising from the asymptotic expansion can be completely solved by a recursive scheme for a system of interacting particles a nonlinear diffusion equation is obtained and some of its solutions are analysed finally the density of a system of particles undergoing chemical reactions is shown to satisfy a nonlinear equation which formally coincides with the reaction diffusion equation proposed ad hoc at the macroscopic level

partial range completeness and existence of solutions to two way diffusion equations separating variables to solve a two way diffusion equation leads to a nonstandard eigenvalue problem in one variable it is shown that the eigenfunctions having negative eigenvalues are complete on the part of the domain where initial conditions are imposed while those with positive eigenvalues are complete where final conditions are imposed the corresponding exponentially growing and exponentially decaying solutions may be used to expand arbitrary solutions on semi infinite intervals in the time variable a natural iterative procedure for obtaining solutions on finite intervals is shown to converge in some cases a linearly growing solution must also be taken into account

parameter estimation for the fractional fractal diffusion model based on its numerical solution in this paper we mainly consider a problem of parameter estimation for the fractional fractal diffusion model used to describe the anomalous diffusion in porous media the bayesian method is proposed to estimate parameters for the fractional fractal diffusion model based on its numerical solution firstly the center box difference method is employed to solve the fractional fractal diffusion equation subject to the initial boundary conditions then we apply the bayesian method to estimate three parameters for the model simultaneously that is the fractional order the fractal dimension d f and the structure parameter to testify the validity of the results for the model s parameter estimation experimental data from the fast desorption process of methane in coal are used it is shown that the numerical results modeled with parameters given by the bayesian method coincide well with the desorption experimental data indicating that the bayesian method is efficient and valid in identifying multi parameter for the fractional fractal diffusion model besides the fractional fractal diffusion model is demonstrated to be more capable than the classical fick s model to describe the anomalous diffusion behavior of gas in coal to clarify the parameters effect on the relative diffusion amount of methane for the fractional fractal diffusion model parameter sensitivity analysis is also carried out this paper provides a specific and efficient parameter estimation method for the fractional fractal diffusion model

on a special class of bicriterion path problems abstract in this paper we are concerned with a special class of bicriterion path problems for the considered class of bicriterion problems at least one of the objectives is type maxmin for the other one besides an objective type maxmin also a minsum and a minratio type objective are considered two algorithms are presented for the considered class of bicriterion path problems the first one only determines the minimal complete set of nondominated paths and the second one determines the entire set of nondominated paths both algorithms can be used for any type of bicriterion path problems since one of the objectives is type maxmin and an algorithm exists to determine the best path for the other objective computational statistics for the three types of considered bicriterion path problems are also presented

an accurate two stream moment method for kinetic boundary layer problems of linear kinetic equations the authors develop a method for solving 1d kinetic boundary layer problems for linear equations that uses separate hermite moment expansions in the velocity variable for particles moving towards and away from a plane wall this so called two stream method is tested for two especially simple kinetic equations the linear bgk equation and the klein kramers equation the kinetic equation for brownian particles for both of these equations extensive exact information is available for two simple boundary layer problems the milne and the albedo problem a comparison of these exact results with those obtained with this version of the two stream moment method shows that the accuracy obtainable by this method exceeds that of earlier methods by several orders of magnitude in particular the method allows them to obtain accurate results not only for the moments of the distribution function but also for the distribution function itself

phase space diffusion in a system with a partially permeable wall a new boundary condition for a diffusive system with a partially permeable wall described by the klein kramers equation is proposed the green functions for such a system are given and a generalization to the system with a series of walls is briefly discussed it is shown that the well known boundary condition for the case of a partially absorbing wall which gives the so called radiation boundary condition for the diffusion equation cannot be used for the system under consideration

a comparison of heuristic best first algorithms for bicriterion shortest path problems abstract a variety of algorithms have been proposed to solve the bicriterion shortest path problem this article analyzes and compares the performance of three best first label setting algorithms that accept heuristic information to improve efficiency these are namoa moa and tung chew s algorithm tc a set of experiments explores the impact of heuristic information in search efficiency and the relative performance of the algorithms the analysis reveals that namoa is the best option for difficult problems its time performance can benefit considerably from heuristic information though not in all cases the performance of tc is similar but somewhat worse however the time performance of moa is found to degrade considerably with the use of heuristic information in most cases explanations are provided for these phenomena

a bayesian analysis of monte carlo correlation times for the two dimensional ising model abstract we present a new bayesian analysis of the high accuracy data of nightingale and blote for the correlation times of the two dimensional ising model to determine the value of the dynamical critical exponent we demonstrate the crucial role played by the nightingale blote assumption that odd terms disappear in their expression for the correlation time as a function of the size of the system we obtain differing results for the existence of logarithmic corrections and the value of the dynamical critical exponent depending on whether or not that assumption is valid

a drop of ink falls from my pen it comes to earth i know not when the authors obtain for a brownian particle in a uniform force field the mean and asymptotic first passage times as functions of the particle s initial position and velocity with the recurrence times given as a special case they discuss the region of phase space for which the diffusion model of brownian motion provides an adequate approximation and conclude that there is no possibility of obtaining the recurrence times within that model they find that the nature of the boundary value problem is profoundly altered when the motion is treated as a process in phase rather than configuration space because the time development operator is then parabolic rather than elliptic they argue that such a change in the treatment of brownian motion places it within the sphere of transport theory rather than diffusion theory and that consequently results such as ours have relevance to the study of phenomena such as radiative transfer and neutron transport

flux to a trap the flux of particles to a single trap is investigated for two systems 1 particles in 3d space which jump a fixed step lengthl the rayleigh flight and are adsorbed by a spherical surface and 2 particles on a lattice jumping to nearest neighbor sites with a single adsorbing site initially the particles are uniformly distributed outside the traps when the jump length goes to zero both processes go over to regular diffusion and the first case yields the diffusive flux to a sphere as solved by smoluchowski for nonzero step length the flux for large times is given by a modified form of smoluchowski s result with the effective radius replaced byr cl wherec 0 29795219 andcl is the milne extrapolation length for this problem for the second problem a similar expression for the flux is found with the effective trap radius a function of the lattice sc bcc fcc being considered

flow of a viscoelastic fluid with the fractional maxwell model between two side walls perpendicular to a plate the unsteady flow of a viscoelastic fluid with the fractional maxwell model between two side walls perpendicular to a plate is investigated exact solutions for the velocity field are established by means of the fourier and laplace transforms the similar solutions for maxwell and newtonian fluids can be obtained as limiting cases of our results in the absence of side walls all solutions that have been determined reduce to those corresponding to the motion over an infinite plate

overview of theoretical models for reaction rates there is enormous recent interest in the development of models for rate processes because rates are an almost universal characterization in the physical and biological sciences in this paper we provide an introduction to several of the problems to be discussed in greater depth by other speakers at a symposium held at the national institutes of health on may 6 8 1985 this review will focus on 1 the smoluchowski model for reaction rates together with its extension by onsager 2 first passage time formalism for discrete and continuous master equations and fokker planck equations 3 the kramers model and its extensions 4 diffusion in the presence of trapping centers

half range expansion analysis for langewin dynamics in the high friction limit with a singular absorbing boundary condition noncharacteristic case we consider the dynamics of a brownian particle given by the langevin equation in a strip under the effects of a deterministic force the trajectories of particles originate at a source whose spatial location in the phase space coincides with the location of adsorbing boundaries this leads to singular behavior of trajectories in the high friction limit we use the half range expansion technique and systematic asymptotics to solve a boundary value problem for the fokker planck operator and to calculate the steady state transition probability density the mean time to absorption and the distribution of exit points we do not make assumptions about other parameters in the problem except that they areo 1 relative to the friction coefficient we calculate explicitly the correct location of the milne type extrapolation for absorbing boundary conditions for the smoluchowski approximation to the langevin equation

multi objective minmax robust combinatorial optimization with cardinality constrained uncertainty abstract in this paper we develop two approaches to find minmax robust efficient solutions for multi objective combinatorial optimization problems with cardinality constrained uncertainty first we extend an existing algorithm for the single objective problem to multi objective optimization we propose also an enhancement to accelerate the algorithm even for the single objective case and we develop a faster version for special multi objective instances second we introduce a deterministic multi objective problem with sum and bottleneck functions which provides a superset of the robust efficient solutions based on this we develop a label setting algorithm to solve the multi objective uncertain shortest path problem we compare both approaches on instances of the multi objective uncertain shortest path problem originating from hazardous material transportation

mechanism of complicated volume deformation in polymers and its fractional time based description abstract in tension and compression of polymers some abnormal phenomena of volume changes were often observed and its mechanism is still unclear in this paper based on the thermodynamics principle it is shown that the combined effects of internal energy and entropy are the basic reason of causing the anomaly in polymers moreover to describe the complicated deformation through a simple model and have a correct modelization of mechanical behaviors a volume strain model is presented in which the variation of volume strain resulted from the combined effects is characterized through a fractional integral expression comparison between fitting results and experimental results reveals the proposed model can describe the volume deformation of polymers

the tricriterion shortest path problem with at least two bottleneck objective functions abstract the focus of this paper is on the tricriterion shortest path problem where two objective functions are of the bottleneck type for example minmax or maxmin the third objective function may be of the same kind or we may consider for example minsum or maxprod let p n be the complexity of a classical single objective algorithm responsible for this third function where n is the number of nodes and m be the number of arcs of the graph an o m 2 p n algorithm is presented that can generate the minimal complete set of pareto optimal solutions finding the maximal complete set is also possible optimality proofs are given and extensions for several special cases are presented computational experience for a set of randomly generated problems is reported

a novel nonlinear regression model of svr as a substitute for ann to predict conductivity of mwcnt cuo water hybrid nanofluid based on empirical data abstract an ideal regression method should have several characteristics including precision accuracy and generalization in many studies in the field of nanofluid the precision of models is more highlighted nevertheless a lack of generalization may lead to over fitted models in this paper two nonlinear regression methods namely the ann and svr are employed to predict the thermal conductivity of mwcnt cuo water hybrid nanofluid with temperature and volume fraction it is seen that precision of svr ann approaches are able to be compared however svr generalization is more convenient compared to ann because svr method utilizes less parameters hence svr can show better persistence to overfitting in little size datasets compared to ann therefore svr is more authentic approach for the regression with little size datasets

hydrodynamic singular regimes in 1 1 kinetic models and spectral numerical methods classical results from spectral theory of stationary linear kinetic equations are applied to efficiently approximate two physically relevant weakly nonlinear kinetic models a model of chemotaxis involving a biased velocity redistribution integral term and a vlasov fokker planck vfp system both are coupled to an attractive elliptic equation producing corresponding mean field potentials spectral de compositions of stationary kinetic distributions are recalled based on a variation of case s elementary solutions for the first model and on a sturm liouville eigenvalue problem for the second one well balanced godunov schemes with strong stability properties are deduced moreover in the stiff hydrodynamical scaling an hybridized algorithm is set up for which asymptotic preserving properties can be established under mild restrictions on the computational grid several numerical validations are displayed including the consistency of the vfp model with burgers hopf dynamics on the velocity field after blowup of the macroscopic density into dirac masses

the vacuum einstein equations as closed ideals of matrix valued differential forms the vacuum einstein equations are written as a closed differential ideal of three dimensional matrices of differential forms allowing the weyl tensor to appear explicitly in the equations possible uses of this formulation are indicated

chapman enskog as an application of the method for eliminating fast variables although the chapman enskog treatment of the boltzmann equation is one of the first examples of the elimination of fast variables it is not usually presented consistently from that point of view here it is developed systematically as a special case of the general method for eliminating fast variables from nonlinear equations as a result certain ambiguities can be remedied first it is inconsistent with the separation of time scales to extend the phenomenological description of the gas by including some of the higher moments of the distribution function such as the heat flow in the application to the relativistic boltzmann equation the dilemma concerning the choice of the lowest order approximation is resolved in the final section it is demonstrated that unsystematic elimination of fast variables leads to secular terms

a numerical approach to study the kramers equation for finite geometries boundary conditions and potential fields the kramers equation for the phase space function which models the dynamics of an underdamped brownian particle is the subject of our study numerical solutions of this equation for natural boundaries unconfined geometries have been well reported in the literature but not much has been done on the kramers equation for finite confining geometries which require a set of additional constraints imposed on the phase space function at physical boundaries in this paper we present numerical solutions for the kramers equation with a variety of potential fields namely constant linear harmonic and periodic in the presence of fully absorbing and fully reflecting boundary conditions bcs the choice of the numerical method and its implementation take into consideration the type of bcs in order to avoid the use of ghost points or artificial conditions we study and assess the conditions under which the numerical method converges various aspects of the solutions for the phase space function are presented with figures and discussed in detail