irreducible representations of brauer algebras irreducible representations of brauer algebras are constructed by using the induced representation and the linear equation method as examples some matrix representations of brauer algebras df n with f or 5 are presented

transformation coefficients of permutation groups the eigenfunction method is used to calculate the transformation coefficients m 1 2 m1 m2 from the yamanouchi basis of the permutation group sf1 f2 to the sf1 f2 sf1 sf2 irreducible basis a program in fortran is written and tables of the transformation coefficients for the permutation group sf up to f 6 are given possible applications of the transformation coefficients are sketched

the induced representations of brauer algebras and the clebsch gordan coefficients of induced representations of from with are discussed the induction coefficients idcs or the outer product reduction coefficients of with up to a normalization factor are derived by using the linear equation method weyl tableaux for the corresponding gel fand basis of so n are defined the assimilation method for obtaining clebsch gordan coefficients of so n in the gel fand basis for no modification rule involved couplings from idcs of brauer algebras is proposed some isoscalar factors of for the resulting irrep with are tabulated

faxen s theorem for nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow a generalization of the fax en s theorem to the nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow is presented from this result expressions for the velocity autocorrelation function vaf and the time dependent diffusion coefficient of the particle can be obtained we analyze the behavior of the vaf and the time dependent diffusion coefficient for different physical regimes of the suspending fluid the relevance of the theorem to microrheology is discussed

no many scallop theorem collective locomotion of reciprocal swimmers to achieve propulsion at low reynolds number a swimmer must deform in a way that is not invariant under time reversal symmetry this result is known as the scallop theorem however there is no many scallop theorem we demonstrate here that two active particles undergoing reciprocal deformations can swim collectively moreover polar particles also experience effective long range interactions these results are derived for a minimal dimers model and generalized to more complex geometries on the basis of symmetry and scaling arguments we explain how such cooperative locomotion can be realized experimentally by shaking a collection of soft particles with a homogeneous external field

brownian motion in a rotating flow the langevin equations for a particle of an arbitrary shape and the correlation functions for the fluctuating forces torques or force torque acting on the particle in a rotating flow are derived from the semimicroscopic level of coarse graining by using fluctuating hydrodynamics in order to obtain the solution of the navier stokes langevin equation valid over the entire flow region use is made of the method of matched asymptotic expansions in f a2 v 1 2 1 the cases of slow and rapid rotation are analyzed it is shown that the fluctuation dissipation theorems hold up to the order of f a2 v 1 2 in both slow and rapid rotation and that the diffusivity tensor depends on the angular velocity of the fluid and becomes anisotropic

non canonical subgroup restrictions of the unitary group u nm u n m a reduction of the inner product space of the permutation group on an n particle system has been used to develop a scheme for obtaining the states spanning a general irreducible representation of the unitary group u nm in terms of those spanning the product representations of u n x u m since relatively straightforward methods are now available for determining the clebsch gordan coefficients for the permutation groups this procedure is viable as special cases of the general expression algebraic expressions for the reduction of identity and alternating representations of u nm are obtained

simple swimmer at low reynolds number three linked spheres we propose a very simple one dimensional swimmer consisting of three spheres that are linked by rigid rods whose lengths can change between two values with a periodic motion in a nonreciprocal fashion which breaks the time reversal symmetry as well as the translational symmetry we show that the model device can swim at low reynolds number this model system could be used in constructing molecular sized machines

a statistical mechanical theory of slow dynamics near the glass transition abstract a statistical mechanical theory of slow dynamics near the glass transition in two kinds of glass forming systems m molecular systems and s suspensions of colloids is presented from a unified point of view based on the tokuyama mori projection operator method the exact diffusion equations for the coherent and the incoherent intermediate scattering functions are first derived whose memory functions are convolutionless in time and contain the correlation effects due to the hydrodynamic interactions in s the analytic expressions of the memory functions are then calculated within the mode coupling theory mct approximation and are shown to coincide with the conventional ones obtained by mct alternative mode coupling equations are thus obtained in m and s separately self diffusion is also discussed alternative equations for the mean square displacement and the non gaussian parameter are also derived within mct approximation all results in both the systems are compared with those obtained by mct

the gel fand basis and matrix elements of the graded unitary group u m n projection operators with correct normalisation are constructed for obtaining the gel fand basis mod nu m of the graded unitary group u m n each u m n gel fand basis vector mod nu m for an f particle system uniquely corresponds to a non standard basis vector mod nu m of the permutation group s f the matrix element of the generator ei 1i of u m n between the two gel fand basis vectors mod nu m and mod nu m is proportional to the overlap between the two non standard basis vectors mod nu m and mod nu m of s f explicit formulae are given for the normalisation constant in the projection operator as well as for the matrix elements of the generator ei 1i of the graded unitary group u m n which is the extension of the gel fand tsetlin formula for the ordinary unitary group u m

analytical expressions for some multiplicity free isoscalar factors of sf sf 1 an algebraic routine for the evaluation of analytical expressions for isoscalar factors isfs of sf sf 1 is formulated based on the linear equation method lem and the analytical continuation of the rank f as examples isfs of sf sf 1 for the coupling f 1 1 f 1 1 f 1 1 f 2 2 f 2 1 1 f 2 1 1 are tabulated the results demonstrate that the number of isf tables can be greatly reduced compared with corresponding numerical results produced using other methods

comparison of the tokuyama mori type projection operator method to that of mori type near the glass transition abstract two types of projection operator methods mori type and tokuyama mori type are tested for studying the slow dynamics of a single particle in complex systems near the glass transition from a unified point of view based on the mean field theory recently proposed by the present author the molecular and brownian dynamics simulations and the corresponding solutions of the mode coupling theory developed by employing mori type formalism are compared consistently disagreement is found for the mean square displacements in stage thus validity of both types is fully investigated near the glass transition from a new standpoint

on the theory of brownian motion in compressible fluids abstract within the framework of the theory of hydrodynamic fluctuations the brownian motion of a spherical particle in a compressible fluid has been considered taking into account the action of a harmonic potential the general relations for the velocity autocorrelation function and mean square displacement of a brownian particle have been established by means of the solutions of the generalized langevin equation the analysis for the time evolution of the correlations has been performed both on large and small time scales on a large time scale the asymptotic expansions describing the persistent correlations have been found to arbitrary order in t n 2 the transition to the system without potential has been studied and the conditions for realization of the diffusion regime of correlations have been clarified on a small time scale a consistent limit procedure for the velocity autocorrelation function has been used which leads in a straightforward manner to the well known result given by the equipartition theorem

biorthogonal coupling coefficients of uq n the coupling wigner clebsch gordan coefficients and their isofactors for the unitary quantum algebras uq n with the repeating irreducible representations in the coproduct decomposition are considered generalizing the u n case the biorthogonal systems of the uq n isofactors with the dual multiplicity labels are constructed by means of the recoupling technique in terms of the isofactors with simpler multiplicity structure a first construction correlated with the inverted littlewood richardson rules gives the bilinear combinations of isofactors after applying the proportionality of the q recoupling racah coefficients to the boundary q isofactors an alternative recursive construction gives the nonorthogonal q isofactors satisfying the most elementary boundary conditions and proportional to the uq n 1 recoupling coefficients for some less restricted values of parameters some multiplicity free and more general uq n recoupling coefficients are found the blocks bilinear combinations of which equal to the resubducing coefficients of the complementary chains of q algebras are proposed to use for the orthonormalization of some uq n biorthogonal isofactors including the general uq 3 case

multiplicity free uq n coupling coefficients the coupling wigner clebsch gordan coefficients of the unitary quantum algebras uq n are considered the tensorial properties of the generator powers and their ordered products used in the explicit projectors and weight lowering procedures are established different expressions for the multiplicity free isofactors of uq n coupling coefficients those coupling an arbitrary and symmetric representations are derived explicit expression of the arbitrary isofactors in terms of their boundary values are proposed proportionality of the semistretched isofactors to the stretched q recoupling coefficients of uq n 1 q analogues of 9j symbols is demonstrated the stretched isofactors of uq 3 are expressed in terms of clebsch gordan coefficients of uq 2

brownian motion in a fluid in simple shear flow abstract we study brownian motion of a sphere suspended in a fluid in stationary homogeneous flow using hydrodynamic fluctuation theory we derive a langevin equation and show that the fluctuation dissipation theorem is modified by the macroscopic homogeneous flow it is found that the strength of the random force is no longer given in terms of the shear dependent friction coefficient alone as it is when the unperturbed fluid is at rest the modification originates from the tensile nature of the macroscopic flow as a special case we analyze the langevin equation for the simple shear case in detail and give the velocity autocorrelation function and the mean square displacement of the sphere for some special time regimes the possibility to defince a diffusion coefficient in these regimes is also discussed

the induction coefficients of the hecke algebra and the clebsch gordan coefficients of the quantum group suq n i special gel fand basis a general procedure for evaluating the induction coefficients idcs or the outer product reduction coefficients of the hecke algebra hf q of the af 1 type is formulated based on the linear equation method analytical expressions for the idc s of hf q are tabulated for f 4 it is also proved that these idcs are the clebsch gordan coefficients for the special gel fand basis of the quantum group suq n

irreducible tensor operators for the quantum algebras su 2 q irreducible tensor operators of su 2 q are defined based on the coproduct and are constructed by using the jordan schwinger mapping

time dependent self diffusion in model suspensions of highly charged brownian particles abstract a quantitative comparison is reported between the predictions of two theories of the time dependent self diffusion properties of suspensions of highly charged brownian particles the first theory based on the overdamped n body fokker planck dynamics involves a mode mode coupling approximation for the time dependent self friction function whereas the second one makes use of short time conditions derived from the n body smoluchowski equation in both cases the relevant dynamic properties can be expressed in terms solely of the radial distribution function g r this quantity is first calculated using the rescaled mean spherical approximation rmsa by comparing with computer simulation results for g r it is found that the rmsa becomes increasingly inaccurate as the freezing transition is approached we observe however that the rmsa itself provides a device to fit the simulation results for g r using this procedure the time dependent self diffusion coefficient calculated from both theories is in good agreement with brownian dynamics simulations

convergence in competition models with small diffusion coefficients abstract it is well known that for reaction diffusion 2 species lotka volterra competition models with spatially independent reaction terms global stability of an equilibrium for the reaction system implies global stability for the reaction diffusion system this is not in general true for spatially inhomogeneous models we show here that for an important range of such models for small enough diffusion coefficients global convergence to an equilibrium holds for the reaction diffusion system if for each point in space the reaction system has a globally attracting hyperbolic equilibrium this work is planned as an initial step towards understanding the connection between the asymptotics of reaction diffusion systems with small diffusion coefficients and that of the corresponding reaction systems

the clebsch gordan coefficient for su m n gel fand basis the outer product reduction coefficients orc of the graded state permutation group which differ from the orc of the ordinary permutation group only in signs have been identified with the clebsch gordan coefficients cgc for the special gel fand basis of the graded unitary group su m n the cgc for a general gel fand basis of su m n can be easily obtained from those for the special one tables of the su m n cgc are presented which are valid for arbitrary m and n

varying total population enhances disease persistence qualitative analysis on a diffusive sis epidemic model abstract this paper performs qualitative analysis on an sis epidemic reaction diffusion system with a linear source in spatially heterogeneous environment the main feature of our model lies in that its total population number varies compared to its counterpart proposed by allen et al 2 the uniform bounds of solutions are derived based on which the threshold dynamics in terms of the basic reproduction number is established and the global stability of the unique endemic equilibrium is discussed when spatial environment is homogeneous in particular the asymptotic profile of endemic equilibria is determined if the diffusion rate of the susceptible or infected population is small or large the theoretical results show that a varying total population can enhance persistence of infectious disease and therefore the disease becomes more threatening and harder to control

intrinsic lie group and nuclear collective rotation about intrinsic axes for any lie group g is so called intrinsic lie group g is introduced g and g being commutative and anti isomorphic it is shown that in the parameter space of a lie group g the corresponding intrinsic lie group g is just the second parameter group the general relations between the first and second parameter groups are derived in a simple way for the group so 3 there is the intrinsic lie group so 3 the infinitesimal generators of so 3 are precisely the components of the angular momentum in the intrinsic coordinate system therefore the intrinsic lie group so 3 provides an appropriate mathematical formalism for the description of collective rotations of nuclei about their intrinsic axes

on the motion and brownian motion of n spheres in a viscous fluid abstract an extension of faxen s theorem is given for the case that n spheres move with arbitrary velocities through a fluid in non uniform steady flow explicit expressions for the friction and mutual friction tensors valid to order r 3 where r is a typical distance between spheres are obtained together with this extension these expressions contain 2 3 and 4 sphere contributions brownian motion of n spheres as a consequence of fluid fluctuations is discussed on the basis of the relationships derived

coefficients of fractional parentage for u m p n q u m n u p q and u m n u m u n the outer product reduction coefficients orc which reduce the representation rep induced from the irreps of the permutation groups s f1 and s f2 into the irreps of s f1 f2 are shown to be the indirect coupling coefficients for the u m p n q u m n u p q irreducible basis the non standard orc for reducing the rep induced from the non standard irreps of s f13 s f1 s f3 and s f24 s f2 s f4 into that of s f s f12 s f34 with fij fi fj f f12 f34 are identified with the u f u f12 u f34 clebsch gordan coefficient for the special gel fand bases of u f12 and u f34 the u m p n q u m n u p q cfp as well as its special case the u m p u m u p cfp are identified with the s f s f12 s f34 outer product isoscalar factor the u m n u m u n cfp are obtained from the u m n u m u n cfp by simply changing all the partition labels for u n into their conjugates interchanging rows with columns and taking into account a phase change the cfp can be calculated from the orc numerical values of the one body cfp for systems with up to six particles are tabulated

reduction of inner product representations of unitary groups a direct method for the reduction of inner products of irreducible representations irreps of unitary groups has been proposed using the duality between the permutation and unitary groups a canonical tensor basis set has been used to obtain a closed expression for the clebsch gordan coefficients of u n this expression involves the subduction coefficients arising in the outer product reduction of sn1 sn2 sn1 n2 of the permutation groups the symmetrization coefficients of u n and matrix elements of the standard representation of sn the expression holds good for an inner product reduction of irreps of u n and is independent of n the method has been illustrated with examples

noisy swimming at low reynolds numbers small organisms e g bacteria and artificial microswimmers move due to a combination of active swimming and passive brownian motion considering a simplified linear three sphere swimmer we study how the swimmer size regulates the interplay between self driven and diffusive behavior at low reynolds number starting from the kirkwood smoluchowski equation and its corresponding langevin equation we derive formulas for the orientation correlation time the mean velocity and the mean square displacement in three space dimensions the validity of the analytical results is illustrated through numerical simulations tuning the swimmer parameters to values that are typical of bacteria we find three characteristic regimes i brownian motion at small times ii quasiballistic behavior at intermediate time scales and iii quasidiffusive behavior at large times due to noise induced rotation our analytical results can be useful for a better quantitative understanding of optimal foraging strategies in bacterial systems and they can help to construct more efficient artificial microswimmers in fluctuating fluids

a duality consistent phase convention for complex conjugation in sun we have argued that a simple phase convention for all involutive mappings can be chosen so the algebra of inner product couplings in sun is identical to that for outer products in sl pure real phases with a single 1 entry in any row or column can represent the permutation matrix for transposition in order of the two component irreducible representations irreps in a binary coupling the matrix for association in sl with respect to the alternating group al the derome sharp matrix and the 1jm factor the latter two are required by complex conjugation in sun in our previous work we have proposed specific prescriptions for assigning the phase under transposition and association and have shown them to be consistent with duality in this work we propose a duality consistent prescription for assigning the phase of the derome sharp matrix and thus of the 1jm factor which is related to it by association

spectral bound and reproduction number for infinite dimensional population structure and time heterogeneity spectral bounds of quasi positive matrices are crucial mathematical threshold parameters in population models that are formulated as systems of ordinary differential equations the sign of the spectral bound of the variational matrix at 0 decides whether at low density the population becomes extinct or grows another important threshold parameter is the reproduction number mathcal r which is the spectral radius of a related positive matrix as is well known the spectral bound and mathcal r 1 have the same sign provided that the matrices have a particular form the relation between spectral bound and reproduction number extends to models with infinite dimensional state space and then holds between the spectral bound of a resolvent positive closed linear operator and the spectral radius of a positive bounded linear operator we also extend an analogous relation between the spectral radii of two positive linear operators which is relevant for discrete time models we illustrate the general theory

overdamped van hove function of colloidal suspensions the generalized hydrodynamic theory for collective diffusion of a monodisperse colloidal suspension is developed in the framework of the onsager machlup theory of time dependent fluctuations the time evolution of the intermediate scattering function f k t is derived as a contraction of the description involving the instantaneous particle number concentration the particle current and the stress tensor of the brownian fluid as state variables we show that the proper overdamped limit of this equation requires the explicit separation of the stress tensor in its mutually orthogonal kinetic and configurational contributions analogous results also follow for the self intermediate scattering function f s k t we show that neglecting the non markovian part of the configurational stress tensor memory one recovers the single exponential memory approximation based on sum rules derived from the smoluchowski equation for both f s k t and f k t we suggest simple approximate manners to relate the collective and the self memory functions leading to vineyard like approximate relations between f s k t and f k t

theory of dynamic arrest in colloidal mixtures we present a first principles theory of dynamic arrest in colloidal mixtures based on the multicomponent self consistent generalized langevin equation theory of colloid dynamics m a chavez rojo and m medina noyola phys rev e 72 031107 2005 m a chavez rojo and m medina noyola phys rev e76 039902 2007 we illustrate its application with a description of dynamic arrest in two simple model colloidal mixtures namely hard sphere and repulsive yukawa binary mixtures our results include observation of the two patterns of dynamic arrest one in which both species become simultaneously arrested and the other involving the sequential arrest of the two species the latter case gives rise to mixed states in which one species is arrested while the other species remains mobile we also derive the bifurcation or fixed point equations for the nonergodic parameters of the system which takes the surprisingly simple form of a system of coupled equations for the localization length of the particles of each species the solution of this system of equations indicates unambiguously which species is arrested finite localization length and which species remains ergodic infinite localization length as a result we are able to draw the entire ergodic nonergodic phase diagram of the binary hard sphere mixture

brownian dynamics divergence of mobility tensor abstract the mobility tensor for many spheres suspended in a viscous fluid is considered an analytical formula for the divergence of this tensor is derived it is then applied in calculations of long time collective diffusion coefficient of hard sphere suspension by means of brownian dynamics method

dependence of the friction tensor on the rotation of a frame of reference abstract is is argued that the expression for the friction tensor of a sphere immerssed in a fluid depends on the choice of the frame of reference and in particular its rotation the relation between the friction tensor in the laboratory frame and the corotating frame which have been derived by different authors respectively is explicitly given memory effects are found to play a crucial role in the transformation from one frame of reference to another

a statistical mechanical theory of self diffusion in glass forming liquids abstract a statistical mechanical theory of self diffusion in glass forming liquids is presented a non markov linear langevin equation is derived from a newton equation by employing the tokuyama mori projection operator method the memory function is explicitly written in terms of the force force correlation functions the equations for the mean square displacement the mean fourth displacement and the non gaussian parameter are then formally derived the present theory is applied to the glass transitions in the glass forming liquids to discuss the crossover phenomena in the dynamics of a single particle from a short time ballistic motion to a long time self diffusion process via a caging stage the effects of the renormalized friction coefficient on self diffusion are thus explored with the aid of analyses of the simulation results by the mean field theory proposed recently by the present author it is thus shown that the relaxation time of the renormalized memory function is given by the relaxation time it is also shown that for times longer than the relaxation time the dynamics of a single particle is identical to that discussed in the suspensions

on the basic reproduction number of reaction diffusion epidemic models the basic reproduction number r 0 serves as a threshold parameter of many epidemic models for disease extinction or spread the purpose of this paper is to investigate r 0 for spatial reaction

subduction coefficients of birman wenzl algebras and racah coefficients of the quantum groups oq n and spq 2m i subduction coefficients irreducible representations of birman wenzl algebras cf r q in the non standard basis are discussed a procedure for evaluating subduction coefficients sdcs or the transformation coefficients between standard and non standard basis of birman wenzl algebras is formulated based on the linear equation method sdcs of cf r q with f 4 are derived racah coefficients of the quantum groups oq n and spq 2m can be obtained from sdcs of birman wenzl algebras cf r q by using the schur weyl brauer duality relation between birman wenzl algebras cf r q and the quantum groups oq n and spq 2m

relations for clebsch gordan and racah coefficients in suq 2 and yang baxter equations relations are exploited among clebsch gordan cg and racah coefficients in the algebra suq 2 known as a deformation of su 2 these are used to show that the yang baxter yb relation for the irf interaction round a face model results from one of the symmetry relations for the 9 j symbol specific to suq 2 and that in an asymptotic limit this yb relation becomes the yb relation for the two dimensional vertex model the racah coefficient which has a particularly simple dependence on q is efficiently used such that an asymptotic limit of the racah coefficient is the cg coefficient and another limit gives the factorized s matrix of the vertex model

the clebsch gordan coefficients and isoscalar factors of the graded unitary group su m n it is pointed out that the clebsch gordan coefficients cgc of the permutation group are the coefficients which couple irreducible bases irb of su m n and su p q to the irb of su mp nq mp np and the outer product reduction coefficients orc of the permutation group are the coefficients which couple the irb of su m n and su p q into the irb of su m p n q the orc of permutation groups with due modification in signs are the cgc for the special gel fand basis of su m n the isoscalar factor isf for the permutation group chain s f contains implies s f1 s f2 is the isf for the graded unitary group chain su mp nq mq np contains implies su m n su p q and the outer product isf for the group chain s f contains implies s f1 s f2 is the isf for su mp nq mq np contains implies su m n x su p q all these coefficients can be calculated easily and some are already available

classification selection rules and symmetry properties of the clebsch gordan coefficients of symmetric group new analytical expressions for clebsch gordan coefficients cgcs of symmetric group are formulated based on the racah factorization lemma as examples cgcs for the coupling f 1 1 f 1 1 and f 1 1 f 2 2 are tabulated we have introduced a new technique called the clebsch gordan sequences cgss cgss provide a partial understanding of vanishing of cgcs and an explanation of new symmetry properties of multiplicity free cgcs

su mn su m su n isoscalar factors and s f1 f2 s f1 s f2 isoscalar factors a simple relation is found between the isoscalar factor isf of the unitary group and those of the permutation group i e the su mn su m su n isf is equal to the s f1 f2 s f1 s f2 isf since the values of s f1 f2 s f1 s f2 isf are independent of m and n one arrives at an important conclusion that the values of su mn su m su n isf are also independent of m and n therefore they can be calculated for all m and n by a single stroke instead of one m and one n at a time an eigenfunction metho for evaluating the su mn su m su n isf is given which can be easily translated into a computer program

multiple scales analysis of the fokker planck equation for simple shear flow abstract we extend the multiple time scales formalism originally introduced for the fokker planck equation by wycoff and balazs physica a 146 1987 175 to the case of simple shear flow the analysis is carried out for small values of the stokes number st a dimensionless measure of the inertia of a brownian particle the probability density is expanded in terms of hermite functions of the fluctuation velocity the difference between the actual particle velocity and the unperturbed flow velocity at its location and consequently the structure of the multiple scales hierarchy differs from the analogous equilibrium problem with a conservative forcing the multiple scales solutions are compared to a small st expansion of the exact solutions for two canonical initial conditions we also obtain the form of the smoluchowski equation correct to o st for the effects of particle inertia modifications to the scheme for hydrodynamically interacting particles are discussed

coupling subduction and induction transformations for group representations the basis of a representation space of any group may be chosen according to its decomposition into representations of the group and a subgroup chain coupling recoupling subduction and resubduction factors are each shown to arise as a result of schur s lemmas and a particular group subgroup structure when induction and mackey s subgroup theorem are considered new transformation factors occur those of induction and reinduction key properties of these factors are given together with their relationship with double coset matrix elements

on the construction of wavefunctions in the six quark system a method for calculating the fractional parentage coefficients for many quark systems in the scheme ucst 12 contains implies ucs 6 ut 2 contains implies uc 3 us 2 ut 2 based on the complementarity of the permutation sn and unitary u n groups is developed the scalar factors of the clebsch gordan coefficients for the chain of groups u mn contains implies u m u n are shown to be independent of the ranks mn and m and n of the groups and to be determined by the young schemes associated with them tables of fractional parentage coefficients for low states of the six quark 6q system are presented

clebsch gordan coefficients for the permutation group a non genealogical method is proposed for the reduction of the inner product representations of the permutation group sn this method of determining the clebsch gordan coefficients has been found to be recursive only within a given series as such it permits the direct reduction of products of large dimensional representations

motion of a sphere in a viscous incompressible fluid at low reynolds number abstract we study the motion of a sphere in a viscous incompressible fluid at low reynolds number on the basis of the equation of motion derived by basset and boussinesq we show that the motion after a sudden impulse deviates strongly from the exponential solution of the stokes equation of motion if the mass of the sphere is not much larger than the mass of the displaced fluid we relate this to the form of the relaxation spectrum

path integral method applied to the brownian rotation of a symmetric top abstract the conditional probability density function in angular velocities space is obtained in an exact and closed expression for a symmetric top undergoing brownian motion the distribution turns out to be non gaussian we obtain the distribution function by shifting the problem of solving stochastic differential equations to the problem of solving ordinary differential equations this is done using the method of path integrals developed by feynman and hibbs for quantum mechanics

threshold dynamics of a diffusive siri model with nonlinear incidence rate abstract this work is concerned with the dynamics of a diffusive siri epidemic model with nonlinear incidence rate we first establish the well posedness of the model then we show the basic reproduction number r 0 is a threshold parameter for the stability of the model in fact the disease free equilibrium is globally asymptotically stable when r 0 1 while the phenomena of uniform persistence occurs when r 0 1 if r 0 1 the disease free equilibrium is globally asymptotically stable under some assumptions we also clarify the relationship between r 0 and the local basic reproduction number moreover we establish the local and global stability of the endemic equilibrium provided that all parameters of this model are constants

hydrodynamic interactions and some new periodic structures in three particle sediments abstract it is well known that the motion of three particles sedimenting in a stokes fluid is of a simple periodic function of time if the initial configuration is a horizontal equilateral triangle we use the method of induced forces to show that if this ititial configuration is made less symmetric then many much more complex structures which are still periodic in time may result which involve a sequence of inequivalent configurations this confirms that the horizontal isosceles triangle configuration is remarkably robust against perturbations

scalar factors for non canonical subgroup restriction of unitary group a procedure has been outlined for obtaining the scalar factors reduced wigner coefficients of the unitary group u nm contains implies u n x u m this has been done at the permutation group level for sn down arrow sn x sn and the equality between the scalar factors of these two groups has been exploited it has been shown that the scalar factors can be uniquely expressed in terms of the inner and outer product coupling coefficients of the permutation group the ambiguity due to multiplicity is resolved at the level of the above coefficients

a new young diagrammatic method for kronecker products of and a new simple young diagrammatic method for kronecker products of o n and sp 2m is proposed based on the representation theory of brauer algebras a general procedure for the decomposition of the tensor products of representations for o n and sp 2m is outlined which is similar to that for u n known as the littlewood rules together with trace contractions from a brauer algebra and some modification rules given by king

the casimir invariants and gel fand basis of the graded unitary group su m n in the space of f particle product states the casimir invariants of the graded unitary group su m n are functions of the class operators of the graded coordinate permutation group s f which are equal to the class operators of the graded state permutation group s f formulae for the quadratic and cubic casimir invariants are given it is shown that in general the eigenvalue formulae for the u m n casimir invariants as functions of the partition can be obtained from those for u m n by simply changing the argument of the functions from m n to m n the quasi standard basis of s f is identified with the gel fand basis of su m n i e the irreducible basis classified according to the group chain su m n contains implies su m n 1 contains implies su m contains implies su 2 contains implies u 1 the special gel fand basis of su m n for which the weight is restricted to 1 1 1 can be easily obtained from the gel fand basis of su m n with due allowances for modifying sign factors arising from the grading the construction of a general su m n gel fand basis is also discussed

evolution of a semilinear parabolic system for migration and selection without dominance the semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus without dominance is investigated the population occupies a finite habitat of arbitrary dimensionality and shape i e a bounded open domain in r d the selection coefficients depend on position the drift and diffusion coefficients may depend on position the primary focus of this paper is the dependence of the evolution of the gene frequencies on the strength of selection relative to that of migration it is proved that if migration is sufficiently strong i e is sufficiently small and the migration operator is in divergence form then the allele with the greatest spatially averaged selection coefficient is ultimately fixed the stability of each vertex i e an equilibrium with exactly one allele present is completely specified the stability of each edge equilibrium i e one with exactly two alleles present is fully described when either i migration is sufficiently weak i e is sufficiently large or ii the equilibrium has just appeared as increases the existence of unexpected complex phenomena is established even if there are only three alleles and migration is homogeneous and isotropic corresponding to the laplacian i as increases arbitrarily many changes of stability of the edge equilibria and corresponding appearance of an internal equilibrium can occur and ii the conditions for protection or loss of an allele can both depend nonmonotonically on neither of these phenomena can occur in the diallelic case

van hove function of colloidal mixtures exact results abstract a general theory for the collective diffusion of a polydisperse colloidal suspension is developed in the framework of the generalized langevin equation formalism of time dependent fluctuations the time evolution of the intermediate scattering functions f k t is derived as a contraction of the description involving the instantaneous particle number concentration the particle current and the kinetic and the configurational components of the stress tensor of the brownian species as state variables analogous results also follow for the self intermediate scattering functions f s k t we show that neglecting the non markovian part of the configurational stress tensors memory one obtains the multicomponent generalization of the single exponential memory approximation sexp based on sum rules derived from the smoluchowski equation for both f s k t and f k t as an illustrative example the sexp is applied to a simple model binary mixture of colloidal particles interacting through repulsive yukawa pair potentials the results are compared with brownian dynamics simulations

the clebsch gordan coefficients of permutation groups s 2 s 6 the clebsch gordan cg coefficients of the permutation groups s 2 s 6 are calculated by using the eigenfunction method phases have been chosen in a consistent way to exhibit as many symmetries for the coefficients as is possible including non multiplicity free cases the cg coefficients of s 2 s 5 and those for 321 321 to 321 5 of s 6 are tabulated in the square root form of rationals these tables together with the s 6 contains implies s 5 isoscalar factors published earlier provide a complete tabulation of the s 2 s 6 cg coefficients given in the young yamanouchi basis

a spatial seirs reaction diffusion model in heterogeneous environment abstract we propose a susceptible exposed infected recovered susceptible seirs reaction diffusion model where the disease transmission and recovery rates can be spatially heterogeneous the basic reproduction number r 0 is connected with the principal eigenvalue of a linear cooperative elliptic system threshold type results on the global dynamics in terms of r 0 are established the monotonicity of r 0 with respect to the diffusion rates of the exposed and infected individuals which does not hold in general is established in several cases finally the asymptotic profile of the endemic equilibrium is investigated when the diffusion rate of the susceptible individuals is small our results reveal the importance of the movement of the exposed and recovered individuals in disease dynamics as opposed to most of previous works which solely focused on the movement of the susceptible and infected individuals

hydrodynamic interactions in brownian dynamics i periodic boundary conditions for computer simulations abstract because of the long range nature of hydrodynamic interactions the problem of boundary conditions on a finite simulation cell of a hydrodynamically dense suspension of particles in brownian motion is quite as complicated as the analogous problem in simulation of the statistical mechanics of charged and dipolar systems one resolution of this problem is to use periodic boundary conditions and to view them as a way of describing a physical system composed of a large spherical array of periodic replicas of the simulation cell the hydrodynamic interactions are calculated using the quasi static linearized navier stokes equation this requires that the suspending fluid velocity remains small throughout the array that the sum of the particle velocities in the simulation cell be zero is insufficient to force boundedness of the fluid velocity as the array becomes large boundedness in the array of the suspending fluid velocity is achieved if a rigid wall boundary condition is applied at the outer edge of the array as the array becomes large with this condition the net particle velocity equals zero condition is not needed the condition allows lattice sum representations for the suspending fluid velocity to be derived these lattice sums are absolutely and rapidly convergent and periodic representations of the velocity in the array with boundary condition allow calculation of mobility tensors which are also periodic and can be evaluated numerically in tolerable amounts of computer time a major effect of these calculations is to identify the physical model system corresponding to a truly periodic fluid velocity and mobility tensor as a large array with rigid wall boundary condition

dynamics and asymptotical profiles of an age structured viral infection model with spatial diffusion abstract in this paper we propose an age since infection virus model with fickian diffusion and assume that all the parameters depend on the environment then we adopt the semigroup theory and the classical renewal process to compute the next generation operator r x the basic reproduction r 0 is the spectral radius of r x furthermore we clarify the relationship between r 0 and r x and investigate asymptotical profile of the basic reproduction number r 0 associated with the diffusion rate d in main part we show that r 0 is a threshold value the virus free steady state e0 is globally asymptotically stable if r 0 1 otherwise the endemic steady state e is globally attractive finally we use backward euler method to perform some numerical examples to illustrate the theoretical results

mean field theory of glass transitions abstract the experimental and the simulation results for the mean square displacements in various systems are analyzed near glass transitions by employing the mean field theory recently proposed by comparing different glass transitions with each other from a unified point view it is then shown that the mean square displacements obey a logarithmic growth followed by a power law growth of a super diffusion type in relaxation stage it is also shown that although the long time self diffusion coefficients are approximately described by a singular function of a control parameter with the same critical exponent for different systems where the singular point depends on the system no divergence of any characteristic times such as a relaxation time is found near the singular point nor the glass transition point a crossover point over which the supercooled liquid phase appears is also predicted theoretically it is thus suggested that the present theory provides an useful tool to understand phenomena near the glass transition within the framework of the mean square displacements

the fluctuation dissipation theorem for non markov processes and their contractions the role of the stationarity condition abstract a demonstration is given of the equivalence between the stationarity condition of an n dimensional stochastic process a t defined as the solution of a generalized langevin equation with random initial values with the second fluctuation dissipation theorem as a result it is shown that a similar relation also holds for any stochastic process obtained as a projection of a t into a subspace of the original space

on extremal paths for stochastic processes that involve step potentials and the generalized hamilton jacobi equation abstract from the behavior of extremal paths across a boundary defined by a finite step potential we obtain by means of a least action principle a first integral of the euler lagrange equation a conservation principle this first integral gives the geometrical properties which are refraction and reflexion laws for extremal paths across the boundary and also it leads to a generalized hamilton jacobi equation for the extremal action

statics and tracer diffusion in binary suspensions of polystyrene spheres experiment vs theory abstract extensive measurements of the static and dynamic field autocorrelation function of dilute bidisperse suspensions of charged polystyrene spheres obtained by static and dynamic light scattering experiments are discussed in terms of the two component macroion fluid model the suspensions under study consist of a small amount of large spheres immersed in a system of small spheres for these suspensions the self scattering function at short and intermediate times can be determined by dynamic light scattering dls performed at large wavenumbers the self scattering function contains information on the tracer diffusion of both small and large spheres the experimentally observed self scattering functions of the binary mixtures are compared with theoretical calculations based on the so called single exponential approximation sexp the sexp is based on the exact short time behavior of the single particle dynamics and within it the dynamic properties are entirely expressed in terms of the partial static structure functions the latter are calculated using the extended rescaled mean spherical approximation rmsa for colloidal mixtures good agreement between experimental data and the sexp theory has been found

relaxation in a glassy binary mixture comparison of the mode coupling theory to a brownian dynamics simulation we solved the mode coupling equations for the kob andersen binary mixture using structure factors calculated from brownian dynamics simulations of the same system we found as was previously observed that the mode coupling temperature t c inferred from simulations is about two times greater than that predicted by the theory however we find that many time dependent quantities agree reasonably well with the predictions of the mode coupling theory if they are compared at the same reduced temperature epsilon t t c t c and if epsilon is not too small specifically the simulation results for the incoherent intermediate scattering function the mean square displacement the relaxation time and the self diffusion coefficient agree reasonably well with the predictions of the mode coupling theory we find that there are substantial differences for the non gaussian parameter at small reduced temperatures the probabilities of the logarithm of single particle displacements demonstrate that there is hopping like motion present in the simulations and this motion is not predicted by the mode coupling theory the wave vector dependent relaxation time is shown to be qualitatively different from the predictions of the mode coupling theory for temperatures where hopping like motion is present

irreducible representations of hecke algebras in the nonstandard basis and subduction coefficients irreducible representations of hecke algebras of the type an 1 hn q are discussed in the nonstandard basis some subduction coefficients i e the transformation coefficients between the standard and nonstandard base of hn q are derived by using the linear equation method

analytic results for the three sphere swimmer at low reynolds number the simple model of a low reynolds number swimmer made from three spheres that are connected by two arms is considered in its general form and analyzed the swimming velocity force velocity response power consumption and efficiency of the swimmer are calculated both for general deformations and also for specific model prescriptions the role of noise and coherence in the stroke cycle is also discussed

periodic fundamental solution of the linear navier stokes equations we derive expressions for the periodic fundamental solution of the linear navier stokes equations for point sources located at the lattice points of a simple cubic lattice we cast the solution which was first found by hasimoto in a form suitable for fast numerical computation the proposed algorithm is useful for computer simulations of fluid suspensions with periodic boundary conditions

asymptotic laws and preasymptotic correction formulas for the relaxation near glass transition singularities within the mode coupling theory mct for the dynamics of simple liquids the leading corrections to the asymptotic solutions for the relaxation in the vicinity of an ideal glass transition are derived the formulas are used to determine the range of validity of the scaling law description of the mct results for the a and b processes in glass forming systems solutions of the mct equations of motion are calculated for a hard sphere colloidal suspension model and compared with the derived analytical results the leading order formulas are shown to describe the major qualitative features of the bifurcation scenario near the transition and the leadingplus next to leading order formulas are demonstrated to give a quantitative description of the evolution of structural relaxation for the model s1063 651x 97 06005 4

a simple derivation of the quantum clebsch gordan coefficients for su 2 q to su 2 q the quantum deformation of su 2 the van der waerden method for calculating the clebsch gordan cg coefficients is genaralized the polynomial basis for irreducible representations of su 2 q the relevant polynomial invariants and the deduction of the q analog of the cg coefficients are given