a hybrid molecular and continuum method for low reynolds number flows abstract a novel hybrid method is proposed and developed combining the continuum boundary singularity method bsm and the molecular direct simulation monte carlo method dsmc for low reynolds number flows in the transition regime the flow about a single cylinder is used to test the proposed hybrid method the dsmc is applied to an annular region enclosing the cylinder and the bsm is employed to solve the entire flow domain the parameters used in the dsmc and in the coupling procedure such as the number of simulated particles the cell size and the size of the coupling zone are determined by inspecting the convergence rate and accuracy of obtained solution it is observed that in the partial slip flow regime the results from the hybrid method match the ones from the bsm combined with the heuristic partial slip boundary conditions for higher knudsen numbers the differences in velocity and pressure drop between the hybrid and continuum bsm are significant that justify the use of hybrid method

adaptive mesh and algorithm refinement using direct simulation monte carlo adaptive mesh and algorithm refinement amar embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement amr hierarchy the coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of amr direct simulation monte carlo dsmc is used as the particle algorithm embedded within a godunov type compressible navier stokes solver several examples are presented and compared with purely continuum calculations

bosonization techniques on algebraic curves and conformal field theories the bosonization of b c systems is studied with conformal weight on riemann surfaces in which the moduli space is parametrized by the branch points algebraic curves besides being interesting in itself the problem is related to perturbative string theories and to nonfree conformal field theories on the complex plane with the insertion of certain spin fields called the twist fields the method of differentials is proposed which allows a complete treatment of the b c systems on algebraic curves with local abelian monodromy group it can be nevertheless applied also to more general algebraic curves allowing the computation of the green s functions and shedding some light about the structure of the twist fields in the general case the connections between our formalism and the solutions of the riemann monodromy problem used to find out the conformal blocks of conformal field theories are pointed out

analytic fields on riemann surfaces ii the properties of analytic fields on a riemann surface represented by a branch covering of 1 are investigated in detail branch points are shown to correspond to the vertex operators with simple conformal properties as applications we compute determinants of bar partial j operators forzn symmetric surfaces and obtain various representations for the two loop measure in the bosonic string theory together with various identities for theta functions of hyperelliptic surfaces we also present an integral representation for the quantum part of the twist field correlation functions which describe propagation of the string on the orbifold background we also calculate the quantum part of the structure constants of the twist field operator algebra generalizing the results of dixon friedan martinec and shenker

on the effective size of a non weyl graph we show how to find the coefficient of the leading term of the resonance asymptotics using the method of pseudo orbit expansion for quantum graphs which do not obey weyl asymptotics for a non weyl graph we develop a method to reduce the number of edges of a corresponding directed graph through this method we prove bounds on the above coefficient depending on the structure of the graph for graphs with the same lengths of internal edges we explicitly find the positions of the resolvent resonances

non weyl microwave graphs one of the most important characteristics of a quantum graph is the average density of resonances l where l denotes the length of the graph this is a very robust measure it does not depend on the number of vertices in a graph and holds also for most of the boundary conditions at the vertices graphs obeying this characteristic are called weyl graphs using microwave networks that simulate quantum graphs we show that there exist graphs that do not adhere to this characteristic such graphs are called non weyl graphs for standard coupling conditions we demonstrate that the transition from a weyl graph to a non weyl graph occurs if we introduce a balanced vertex a vertex of a graph is called balanced if the numbers of infinite leads and internal edges meeting at a vertex are the same our experimental results confirm the theoretical predictions of e b davies and a pushnitski analysis and pde 4 729 2011 and are in excellent agreement with the numerical calculations yielding the resonances of the networks

self duality of the sl 2 hitchin integrable system at genus 2 we revisit the hitchin integrable system 11 21 whose phase space is the bundle cotangent to the moduli space of holomorphic sl 2 bundles over a smooth complex curve of genus 2 as shown in 18 may be identified with the 3 dimensional projective space of theta functions of the 2nd order i e we prove that the hitchin system on possesses a remarkable symmetry it is invariant under the interchange of positions and momenta this property allows to complete the work of van geemen previato 21 which basing on the classical results on geometry of the kummer quartic surfaces specified the explicit form of the hamiltonians of the hitchin system the resulting integrable system resembles the classic neumann systems which are also self dual its quantization produces a commuting family of differential operators of the 2nd order acting on homogeneous polynomials in four complex variables as recently shown by van geemen dejong 11 these operators realize the knizhnik zamolodchikov bernard hitchin connection for group su 2 and genus 2 curves

arguments towards a c theorem from branch point twist fields a fundamental quantity in 1 1 dimensional quantum field theories is zamolodchikov s c function a function of a renormalization group distance parameter r which interpolates between ultraviolet and infrared fixed points its value is usually interpreted as a measure of the number of degrees of freedom of a model at a particular energy scale the c theorem establishes that c r is a monotonically decreasing function of r and that its derivative may only vanish at quantum critical points r 0 and r at those points c r becomes the central charge of the conformal field theory which describes the critical point in this communication we argue that a different function proposed by calabrese and cardy defined in terms of the two point function which involves the branch point twist field and the trace of the stress energy tensor has exactly the same qualitative features as c r

pure gauge su 2 seiberg witten theory and modular forms we identify the spectral curve of pure gauge su 2 seiberg witten theory with the weierstrass curve c l z 1 z z and thereby obtain explicitely a modular form from which the moduli space parameter u and lattice parameters a and ad can be derived in terms of modular respectively theta functions we further discuss its relationship with the c 2 triplet model conformal field theory

hybrid continuum molecular simulations of transient gas flows with rarefaction an adaptively coupled continuum molecular approach for compressible viscous flows in transient calculations is presented the continuum domain is described by the unsteady compressible navier stokes equations and the molecular domain is solved by direct simulation monte carlo a strategy is described to extend the overlapped schwarz method with dirichlet dirichlet boundary condition coupling procedure to transient simulations the method has been successfully validated against full direct simulation monte carlo results for transient simulations of a one dimensional shock tube and a two dimensional pressure driven slit flow a sensitivity analysis showed that the used overlapped schwarz coupling method with dirichlet dirichlet boundary conditions is only weakly sensitive to various parameters e g the exact position of the continuum molecular interface the size of the overlap region and the scatter in the molecular solution which is a clear advantage over the more commonly used flux based coupling technique another advantage of the chosen coupling method is that the continuum and molecular time steps can be decoupled and that in general a coupling time step can be used that is much larger than the molecular time step the study performed also highlighted a limit of the method it was found to be necessary to keep the courant number based on the coupling time step the cell size in the continuum region and the molecular most probable velocity below 1 to avoid instabilities

determinant bundles and virasoro algebras we consider the interplay of infinite dimensional lie algebras of virasoro type and moduli spaces of curves suggested by string theory we will see that the infinitesimal geometry of determinant bundles is governed by virasoro symmetries the mumford forms are just invariants of these symmetries the representations of virasoro algebra define twisted d modules on moduli spaces thesed modules are equations on correlators in conformal field theory

an asymptotic preserving automatic domain decomposition method for the vlasov poisson bgk system with applications to plasmas in this work we present an efficient strategy to deal with plasma physics simulations in which localized departures from thermodynamical equilibrium are present the method is based on the introduction of intermediate regions which allows smooth transitions between kinetic and fluid zones in this paper we extend domain decomposition techniques obtained through dynamic coupling and buffer zones to the study of plasmas and moreover we combine them with asymptotic preserving and asymptotically accurate strategies for the time integration we use a hybrid scheme in which both kinetic and fluid descriptions are considered and coupled together while the kinetic model is solved by asymptotic preserving and accurate methods in order to guarantee high efficiency and accuracy in all regimes the numerical scheme is validated and its performances are analyzed by numerical simulations

development and verification of a coupled dsmc ns scheme using unstructured mesh an efficient and accurate parallel coupled dsmc ns method using three dimensional unstructured grid topology is proposed and verified for the simulation of high speed gas flows involving continuum and rarefied regimes a domain overlapping strategy taking advantage of unstructured data format with dirichlet dirichlet type boundary conditions based on two breakdown parameters is used iteratively to determine the choice of solvers in the spatial domain the selected breakdown parameters for this study include 1 a local maximum knudsen number defined as the ratio of the local mean free path and local characteristic length based on property gradient and 2 a thermal non equilibrium indicator defined as the ratio of the difference between translational and rotational temperatures to the translational temperature a supersonic flow m 4 over a quasi 2 d 25 wedge is employed as the first step in verifying the present coupled method the results of simulation using the coupled method are in excellent agreement with those of the pure dsmc method which is taken as the benchmark solution effects of the size of overlapping regions and the choice of breakdown parameters on the convergence history are discussed results show that the proposed iteratively coupled method predicts the results more accurately as compared to the one shot coupled method which has been often used in practice further a realistic 3 d nitrogen flow which two near continuum parallel orifice jets underexpand into a near vacuum environment is simulated using the present coupled method to demonstrate its capability finally developments in extending the present method are also outlined in this paper

a multiscale kinetic fluid solver with dynamic localization of kinetic effects this paper collects the efforts done in our previous works 7 9 10 to build a robust multiscale kinetic fluid solver our scope is to efficiently solve fluid dynamic problems which present non equilibrium localized regions that can move merge appear or disappear in time the main ingredients of the present work are the followings ones a fluid model is solved in the whole domain together with a localized kinetic upscaling term that corrects the fluid model wherever it is necessary this multiscale description of the flow is obtained by using a micro macro decomposition of the distribution function 9 the dynamic transition between fluid and kinetic descriptions is obtained by using a time and space dependent transition function to efficiently define the breakdown conditions of fluid models we propose a new criterion based on the distribution function itself several numerical examples are presented to validate the method and measure its computational efficiency

holomorphic bundles and many body systems we show that spin generalization of elliptic calogero moser system elliptic extension of gaudin model and their cousins are the degenerations of hitchin systems applications to the constructions of integrals of motion angle action variables and quantum systems are discussed the constructions of classical systems are motivated by conformal field theory and their quantum counterparts can be thought of as being the degenerations of the critical level knizhnik zamolodchikov bernard equations

free field representation for massive integrable models a new approach to massive integrable models is considered it allows one to find symmetry algebras which define the spaces of local operators and to get general integral representations for form factors in thesu 2 thirring and sine gordon models

appendix resonances on a simple graph we study the scattering problem on a graph consisting of a line with a finite length appendix the two parts are coupled through boundary conditions depending on three parameters the motion on the line is free while the appendix supports a potential the appendix bound states give rise to a ladder of resonances we construct the resolvent and solve the corresponding pole condition for a weak coupling in general the condition only admits an analytic solution in particular cases we find the pole positions numerically for a linear potential and show that the poles eventually return to the real axis when the coupling strength increases

entanglement entropy and conformal field theory we review the conformal field theory approach to entanglement entropy in 1 1 dimensions we show how to apply these methods to the calculation of the entanglement entropy of a single interval and the generalization to different situations such as finite size systems with boundaries and the case of several disjoint intervals we discuss the behaviour away from the critical point and the spectrum of the reduced density matrix quantum quenches as paradigms of non equilibrium situations are also considered

a particle particle hybrid method for kinetic and continuum equations we present a coupling procedure for two different types of particle methods for the boltzmann and the navier stokes equations a variant of the dsmc method is applied to simulate the boltzmann equation whereas a meshfree lagrangian particle method similar to the sph method is used for simulations of the navier stokes equations an automatic domain decomposition approach is used with the help of a continuum breakdown criterion we apply adaptive spatial and time meshes the classical sod s 1d shock tube problem is solved for a large range of knudsen numbers results from boltzmann navier stokes and hybrid solvers are compared the cpu time for the hybrid solver is 3 4 times faster than for the boltzmann solver

entanglement entropy of non unitary conformal field theory here we show that the renyi entanglement entropy of a region of large size l in a one dimensional critical model whose ground state breaks conformal invariance such as in those described by non unitary conformal field theories behaves as ceff n 1 2n log l where ceff c 24delta 0 is the effective central charge c which may be negative is the central charge of the conformal field theory and delta 0 is the lowest holomorphic conformal dimension in the theory we also obtain results for models with boundaries and with a large but finite correlation length and we show that if the lowest conformal eigenspace is logarithmic then there is an additional term proportional to log log l these results generalize the well known expressions for unitary models we provide a general proof and report on numerical evidence for a non unitary spin chain and an analytical computation using the corner transfer matrix method for a non unitary lattice model we use a new algebraic technique for studying the branching that arises within the replica approach and find a new expression for the entanglement entropy in terms of correlation functions of twist fields for non unitary models

form factors deformed knizhnik zamolodchikov equations and finite gap integration we study the limit of asymptotically free massive integrable models in which the algebra of nonlocal charges turns into affine algebra the form factors of fields in that limit are described by kz equations on level 0 we show the limit to be connected with finite gap integration of classical integrable equations

hidden quantum group symmetry and integrable perturbations of conformal field theories the hidden quantum group symmetry in the quantum sine gordon model is found this symmetry provides the possibility to restrict the operator algebra of the model to subalgebras it is shown that these subalgebras are massive deformations of minimal conformal field theories

finite cloud method a true meshless technique based on a fixed reproducing kernel approximation we introduce fixed moving and multiple fixed kernel techniques for the construction of interpolation functions over a scattered set of points we show that for a particular choice of nodal volumes the fixed moving and multiple fixed kernel approaches are identical to the fixed moving and multiple fixed least squares approaches a finite cloud method which combines collocation with a fixed kernel technique for the construction of interpolation functions is presented as a true meshless technique for the numerical solution of partial differential equations numerical results are presented for several one and two dimensional problems including examples from elasticity heat conduction thermoelasticity stokes flow and piezoelectricity copyright 2001 john wiley sons ltd

fokker planck dsmc algorithm for simulations of rarefied gas flows a fokker planck based particle monte carlo algorithm was devised recently for simulations of rarefied gas flows by the authors 1 3 the main motivation behind the fokker planck fp model is computational efficiency which could be gained due to the fact that the resulting stochastic processes are continuous in velocity space this property of the model leads to simulations where the computational cost becomes independent of the knudsen number kn 3 however the fokker planck model which can be seen as a diffusion approximation of the boltzmann equation becomes less accurate as kn increases in this study we propose a hybrid fokker planck direct simulation monte carlo fp dsmc solution method which is applicable for the whole range of kn the objective of this algorithm is to retain the efficiency of the fp scheme at low kn kn 1 and to employ conventional dsmc at high kn kn 1 since the computational particles employed by the fp model represent the same data as in dsmc the coupling between the two methods is straightforward the new ingredient is a switching criterion which would ideally result in a hybrid scheme with the efficiency of the fp method and the accuracy of dsmc for the whole kn range here we adopt the number of collisions in a given computational cell and for a given time step size as a decision criterion in order to switch between the fp model and dsmc for assessment of the hybrid algorithm different test cases including flow impingement and flow expansion through a slit were studied both accuracy and efficiency of the model are shown to be excellent for the presented test cases

theta functions modular invariance and strings we use quillen s theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory in particular we show that the spin structure dependence of the chiral dirac determinant on a riemann surface is given by riemann s theta function we use this result to investigate the modular invariance of multiloop heterotic string amplitudes

the mumford form and the polyakov measure in string theory an explicit formula is derived for the mumford form on the moduli space of algebraic curves according to the belavin knizhnik theorem this gives a formula for the polyakov bosonic string measure

the analysis of elliptic families i metrics and connections on determinant bundles in this paper we construct the quillen metric on the determinant bundle associated with a family of elliptic first order differential operators we also introduce a unitary connection on and calculate its curvature our results will be applied to the case of dirac operators in a forthcoming paper

the analysis of elliptic families ii dirac operators eta invariants and the holonomy theorem in this paper we specialize the results obtained in bf1 to the case of a family of dirac operators we first calculate the curvature of the unitary connection on the determinant bundle which we introduced in bf1

algorithm refinement for stochastic partial differential equations ii correlated systems we analyze a hybrid particle continuum algorithm for a hydrodynamic system with long ranged correlations specifically we consider the so called train model for viscous transport in gases which is based on a generalization of the random walk process for the diffusion of momentum this discrete model is coupled with its continuous counterpart given by a pair of stochastic partial differential equations at the interface between the particle and continuum computations the coupling is by flux matching giving exact mass and momentum conservation this methodology is an extension of our stochastic algorithm refinement ar hybrid for simple diffusion f alexander a garcia d tartakovsky algorithm refinement for stochastic partial differential equations i linear diffusion j comput phys 182 2002 47 66 results from a variety of numerical experiments are presented for steady state scenarios in all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm for a non stochastic version i e using only deterministic continuum fluxes the long range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude

hermitian symplectic geometry and extension theory here we give brief account of hermitian symplectic spaces showing that they are intimately connected to symmetric as well as self adjoint extensions of a symmetric operator furthermore we find an explicit parametrization of the lagrange grassmannian in terms of the unitary matrices this allows us to explicitly describe all self adjoint boundary conditions for the schrodinger operator on the graph in terms of a unitary matrix we show that the asymptotics of the scattering matrix can be expressed simply in terms of this unitary matrix

quantum group symmetries and non local currents in 2d qft we construct and study the implications of some new non local conserved currents that exist is a wide variety of massive integrable quantum field theories in 2 dimensions including the sine gordon theory and its generalization to affine toda theory these non local currents provide a non perturbative formulation of the theories the symmetry algebras correspond to the quantum affine kac moody algebras thes matrices are completely characterized by these symmetries formals matrices for the imaginary coupling affine toda theories are thereby derived the application of theses matrices to perturbed coset conformal field theory is studied non local charges generating the finite dimensional quantum group in the liouville theory are briefly presented the formalism based on non local charges we describe provides an algernative to the quantum inverse scattering method for solving integrable quantum field theories in 2d

logarithmic torus amplitudes abstractfor the example of the logarithmic triplet theory at c 2 the chiral vacuumtorus amplitudes are analysed it is found that the space of these torus amplitudes isspanned by the characters of the irreducible representations as well as a function thatcan be associated to the logarithmic extension of the vacuum representation a fewimplications and generalisations of this result are discussed 1 introduction during the last twenty years much has been understood about the struc ture of rational conformal eld theories rational conformal eld theories are characterisedby the property that they have only nitely many irreducible highest weight representationsof the chiral algebra or vertex operator algebra and that every highest weight represen tation is completely decomposable into irreducible representations the structure of thesetheories is well understood in particular the characters of the irreducible representationstransform into one another under modular transformations 1 see also 2 and the modulars matrix determines the fusion rules via the verlinde formula 3 a general proof for thishas only recently been given in 4 on the other hand it is clear that rational conformal eld theories are rather special andit is therefore important to understand the structure of more general classes of conformal eld theories one such class are the rational logarithmic theories that possess only nitelymany indecomposable representations but for which not all highest weight representationsare completely decomposable the name logarithmic comes from the fact that their chiralcorrelation functions typically have logarithmic branch cuts the rst example of a non rational logarithmic conformal eld theory was found in 5 see also 6 and the rstrational example that shall also concern us in this paper was constructed in 7 for somerecent reviews see 8 9 10 from a physics point of view logarithmic conformal eldtheories appear naturally in various models of statistical physics for example in the theory

a combined continuum dsmc technique for multiscale analysis of microfluidic filters a multiscale method that combines continuum fluid models with the direct simulation monte carlo dsmc method is presented the continuum regions are treated by stokes equations and a scattered point based finite cloud method is employed to solve the stokes equations the continuum and dsmc regions are combined by an overlapped schwarz alternating method with dirichlet dirichlet type boundary conditions a scattered point interpolation scheme is developed to interpolate the solution between subdomains the convergence characteristics of the multiscale approach are investigated in detail specifically the dependence of convergence on the overlap size the dsmc noise and the number of time steps employed in the dsmc algorithm are studied while the convergence depends weakly on the dsmc noise and the overlap size the number of dsmc time steps simulated in each coupling iteration should be selected so that the total time steps simulated until convergence of the coupled process is close to the time constant of the dsmc subsystem steady state analysis of microfluidic filters is studied in detail using the multiscale approach the multiscale approach is also applied for the simulation of a membrane with an array of microfluidic filters and a dual stage microfluidic device with an array of microfluidic filters for particle trapping and sorting

clebsch gordan coefficients and racah coefficients for the su 2 and su 1 1 groups as the discrete analogues of the poschl teller potential wavefunctions the clebsch gordan coefficients cgc and the racah coefficients for the su 2 and su 1 1 groups are studied as functions of a discrete variable it has been shown that cgc for su 2 and su 1 1 groups may be considered to be discrete analogues of wavefunctions for the one dimensional schrodinger equation with the poschl teller potential expressions for cgc and 6j symbols of the su 1 1 group have been found through the hahn and racah polynomials consideration is given to the asymptotic properties of eigenvalues and eigenfunctions of the hamiltonian of an asymmetric top and of the bargmann moshinsky operator omega

non weyl asymptotics for quantum graphs with general coupling conditions inspired by a recent result of davies and pushnitski we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices we derive a criterion for the asymptotics to be of a non weyl character we show that for balanced vertices with permutation invariant couplings the asymptotics is non weyl only in the case of kirchhoff or anti kirchhoff conditions while for graphs without permutation symmetry numerous examples of non weyl behaviour can be constructed furthermore we present an insight into what makes the kirchhoff anti kirchhoff coupling particular from the resonance point of view finally we demonstrate a generalization to quantum graphs with unequal edge weights

generation of the maxwellian inflow distribution this paper presents several efficient exact acceptance rejection methods for generating the maxwellian inflow distribution the velocity distribution of gas molecules crossing a plane the new methods are demonstrated to be computationally faster and more accurate than the schemes commonly used for open boundary conditions in particle simulations

bosonic field propagators on algebraic curves in this paper we investigate the theory of massless scalar fields on nondegenerate algebraic curves the propagator is written in terms of the parameters appearing in the polynomial defining the curve this provides an alternative to the language of theta functions the main result is the derivation of a third kind differential normalized in such a way that its periods around the homology cycles are purely imaginary all the physical correlation functions of the scalar fields can be expressed in terms of this object this paper contains a detailed analysis of the techniques necessary to study field theories on algebraic curves a simple expression of the scalar field propagator is found in a particular case in which the algebraic curves have zn internal symmetry and one of the fields is located at a branch point

moduli spaces of meromorphic functions and determinant of laplacian the hurwitz space is the moduli space of pairs x f where x is a compact riemann surface and f is a meromorphic function on x we study the laplace operator delta df 2 of the flat singular riemannian manifold x df 2 we define a regularized determinant for delta df 2 and study it as a functional on the hurwitz space we prove that this functional is related to a system of pde which admits explicit integration this leads to an explicit expression for the determinant of the laplace operator in terms of the basic objects on the underlying riemann surface the prime form theta functions the canonical meromorphic bidifferential and the divisor of the meromorphic differential df the proof has several parts that can be of independent interest as an important intermediate result we prove a decomposition formula of the type of burghelea friedlander kappeler for the determinant of the laplace operator on flat surfaces with conical singularities and euclidean or conical ends we introduce and study the s matrix s lambda of a surface with conical singularities as a function of the spectral parameter lambda and relate its behavior at lambda 0 with the schiffer projective connection on the riemann surface x we also prove variational formulas for eigenvalues of the laplace operator of a compact surface with conical singularities when the latter move

vertex representations of quantum affine algebras we construct vertex representations of quantum affine algebras of ade type which were first introduced in greater generality by drinfeld and jimbo the limiting special case of our construction is the untwisted vertex representation of affine lie algebras of frenkel kac and segal our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations in the case of the quantum affine algebra of type a we introduce vertex operators corresponding to all the roots and determine their commutation relations this provides an analogue of a chevalley basis of the affine lie algebra unk n in the basic representation