the q deformation of quantum mechanics of one degree of freedom the q quantum mechanics of the one degree of freedom is studied among others the holomorphic representation of q deformed heisenberg weyl algebra and its realization by covariant berezin symbols is described

a lattice boltzmann method for immiscible multiphase flow simulations using the level set method we consider the lattice boltzmann method for immiscible multiphase flow simulations classical lattice boltzmann methods for this problem e g the colour gradient method or the free energy approach can only be applied when density and viscosity ratios are small moreover they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node in contrast our approach simulates the flow using a single field and separates the fluid phases by a free moving interface the scheme is based on the lattice boltzmann method and uses the level set method to compute the evolution of the interface to couple the fluid phases we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice boltzmann framework various simulations are presented to validate the numerical scheme e g two phase channel flows the young laplace law for a bubble and viscous fingering in a hele shaw cell the results show that the method is feasible over a wide range of density and viscosity differences

coherent states of the q canonical commutation relations for theq deformed canonical commutation relationsa f a g 1 q f g 1 qa g a f forf g in some hilbert space we consider representations generated from a vector satisfyinga f where we show that such a representation exists if and only if 1 moreover for 1 these representations are unitarily equivalent to the fock representation obtained for 0 on the other hand representations obtained for different unit vectors are disjoint we show that the universal c algebra for the relations has a largest proper closed two sided ideal the quotient by this ideal is a naturalq analogue of the cuntz algebra obtained forq 0 we discuss the conjecture that ford this analogue should in fact be equal to the cuntz algebra itself in the limiting casesq 1 we determine all irreducible representations of the relations and characterize those which can be obtained via coherent states

a p q oscillator realization of two parameter quantum algebras it is noted that the study of a quantum algebra sup q 2 with two independent deformation parameters p q leads to a p q oscillator realization for it the analysis is extended to the p q analogues of su 1 1 osp 2 1 and the centreless virasoro algebra the standard single parameter q deformations are obtained in the limit p q

remarks on the number operator for generalized quons we construct the number operator for particles obeying infinite statistics defined by a generalized q deformation of the heisenberg algebra and prove the positivity of the norm of linearly independent state vectors

unsteady immiscible multiphase flow validation of a multiple relaxation time lattice boltzmann method the lattice boltzmann modeling of immiscible multiphase flows needs to be further validated especially when density variation occurs between the different flow phases from this perspective the goal of this research is to introduce the multiple relaxation time operator into a lattice boltzmann model in order to improve its numerical stability in the presence of large density and viscosity ratios essentially this research shows that the introduction of this operator greatly improves the numerical stability of the approach compared to the original single relaxation time collision operator in many lattice boltzmann research studies multiphase lattice boltzmann methods are validated using a reduced number of test cases and unsteady flow test cases are frequently omitted before much more complex flow configurations are simulated in this context several test cases are proposed to evaluate the behavior of a lattice boltzmann method for simulating immiscible multiphase flows with high density and viscosity ratios these are 1 two phase couette flow 2 three phase laplace law 3 three phase zalesak disk 4 two phase flow between oscillating plates 5 two phase capillary wave and 6 the two phase oscillating cylindrical bubble the first two involve a steady regime and the remaining four an unsteady regime

bilinear forms clifford algebras q commutation relations and quantum groups abstract constructions are described which associate algebras to arbitrary bilinear forms generalising the usual clifford and heisenberg algebras quantum groups of symmetries are discussed both as deformed enveloping algebras and as quantised function spaces a classification of the equivalence classes of bilinear forms is also given

semi implicit linearized multiple relaxation time formulation of lattice boltzmann schemes for mixture modeling a lattice boltzmann model for mixture modeling is developed by applying the multiple relaxation time mrt approach to the hamel model which allows one to derive from a general framework different model equations independently proposed like the gross krook model and the sirovich model by imposing some physical constraints the mrt lattice boltzmann hamel model reduces to the generalized mrt lattice boltzmann gross krook model involving the local maxwellian centered on the barycentric velocity which allows one to tune independently the species diffusivity the mixture kinematic viscosity and the mixture bulk viscosity reducing the number of moving particles over the total is possible to deal effectively with mass particle ratios far from unity and for this reason to model the pressure driven diffusion a convenient numerical approach is proposed for solving the developed model which essentially widens the stability range of conventional schemes in terms of dimensionless relaxation frequencies by solving explicitly the advection operator together with the nonlinear terms of the collisional operator and solving implicitly the residual linear terms in this way the calculations are drastically reduced and the operative matrices can be computed once for all at the beginning of the calculation implying moderate additional computational demand following this approach a semi implicit linearized backward euler scheme ideal for parallel implementations is proposed in order to achieve the previous results the asymptotic analysis recently suggested for analyzing the macroscopic equations corresponding to lattice boltzmann schemes in the low mach number limit proves to be an effective tool some numerical tests are reported for proving the consistency of the proposed method with both the fick model and maxwell stefan model in the macroscopic limit

bose like oscillator in fractional dimensional space the system of a fractional dimensional bose like oscillator of one degree of freedom whose canonical variables satisfy the general wigner commutation relations is investigated momentum position uncertainty relations are obtained for states without definite parity the well known one dimensional heisenberg uncertainty principle is retained but for odd and even states momentum position uncertainty inequalities depending on the dimension of the space are obtained the motions of both the free particle and the harmonic oscillator in a fractional dimensional space are studied through the probability density function the existence of compression spread of the probability density for dimensions d 1 is shown fractional dimensional bose like operators are also deduced they together with the reflection operator form an r deformed heisenberg algebra with a deformation parameter depending on the dimension of the space

turning bosons into fermions exclusion statistics fractional statistics and the simple harmonic oscillator motivated by haldane s exclusion statistics we construct creation and annihilation operators for g ons using a bosonic algebra we find that g ons appear due to the breaking of a discrete symmetry of the original bosonic system this symmetry is intimately related to the braid group and we demonstrate a link between exclusion statistics and fractional statistics

on quantization of simple harmonic oscillators a general framework is presented of quantizing the system of a simple harmonic oscillator various methods of quantization so far proposed are accommodated here in a unified form some remarks are also made on quantization for the case of more than one oscillator

positive representations of general commutation relations allowing wick ordering we consider the problem of representing in hilbert space commutation relations of the form graphics where the tklij are essentially arbitrary scalar coefficients examples comprise the q canonical commutation relations introduced by greenberg bozejko and speicher and the twisted canonical anti commutation relations studied by pusz and woronowicz as well as the quantum group s u 2 using these relations any polynomial in the generators ai and their adjoints can uniquely be written in wick ordered form in which all starred generators are to the left of all unstarred ones in this general framework we define the fock representation as well as coherent representations we develop criteria for the natural scalar product in the associated representation spaces to be positive definite and for the relations to have representations by bounded operators in a hilbert space we characterize the relations between the generators ai not involving a i which are compatible with the basic relations the relations may also be interpreted as defining a non commutative differential calculus for generic coefficients tklij however all differential forms of degree 2 and higher vanish we exhibit conditions for this not to be the case and relate them to the ideal structure of the wick algebra and conditions of positivity we show that the differential calculus is compatible with the involution iff the coefficients t define a representation of the braid group this condition is also shown to imply improved bounds for the positivity of the fock representation finally we study the kms states of the group of gauge transformations defined by aj exp it aj

generalized commutators and deformation of strong coupling superconductivity we consider quantum deformation of a strong coupling superconductivity model based on creation annihilation operators which satisfy generalized commutator relations it is found that the nature of the superconducting phase transition can be changed from the usual second order to a first order transition if the deformation parameter exceeds a certain critical value metastable normal and superconducting states can exist when the transition is of the first order

analysis and reduction of the spurious current in a class of multiphase lattice boltzmann models we show that the spurious current present near a curved interface in a class of multiphase lattice boltzmann lb models is due to the insufficient isotropy of the discrete gradient operator a method of obtaining highly isotropic gradient operators on a lattice is given numerical simulations show that both the magnitude and the spatial extent of the spurious current are significantly reduced as gradient operators of increasingly higher order of isotropy is adopted in multiphase lb models

wavelet representations and fock space on positive matrices abstract we show that every biorthogonal wavelet determines a representation by operators on hilbert space satisfying simple identities which captures the established relationship between orthogonal wavelets and cuntz algebra representations in that special case each of these representations is shown to have tractable finite dimensional co invariant doubly cyclic subspaces further motivated by these representations we introduce a general fock space hilbert space construction which yields creation operators containing the cuntz toeplitz isometries as a special case

an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

wigner quantum oscillators we present three groups of non canonical quantum oscillators the position and momentum operators of each group generate basic lie superalgebras namely sl 1 3 osp 1 6 and osp 3 2 the sl 1 3 oscillators have finite energy spectrum and finite dimensions the osp 1 6 oscillators are related to the para bose statistics the internal angular momentum s of the osp 3 2 oscillators takes no more than three half integer values in a particular representation s 1 2

on c algebras generated by pairs of q commuting isometries we consider the c algebras and generated respectively by isometries s1 s2 satisfying the relation s 1s2 qs2s 1 with q 1 the deformed cuntz relation and by isometries s1 s2 satisfying the relation s2s1 qs1s2 with q 1 we show that is isomorphic to the cuntz toeplitz c algebra for any q 1 we further prove that if and only if either q1 q2 or in the second part of our paper we discuss the complexity of the representation theory of we show that is wild for any q in the circle q 1 and hence that is not nuclear for any q in the circle

singular limit of the porous medium equation with a drift abstract we study the stiff pressure limit of a nonlinear drift diffusion equation where the density is constrained to stay below the maximal value one the challenge lies in the presence of a drift and the consequent lack of monotonicity in time in the limit a hele shaw type free boundary problem emerges which describes the evolution of the congested zone where density equals one we discuss pointwise convergence of the densities as well as the bv regularity of the limiting free boundary

endomorphisms of b h ii finitely correlated states on on we identify sets of conjugacy classes of ergodic endomorphisms of b h where h is a fixed separable hilbert space they correspond to certain equivalence classes of pure states on the cuntz algebras onwherenis the powers index these states called finitely correlated states and strongly asymptotically shift invariant states are defined and characterized the subsets of these states defining shifts will in general be identified in a later work but here an interesting cross section for the conjugacy classes of shifts called diagonalizable shifts is introduced and studied

on crossed product of algebras the concept of a crossed tensor product of algebras is studied from a few points of view some related constructions are considered crossed enveloping algebras and their representations are discussed applications to the noncommutative geometry and particle systems with generalized statistics are indicated

irreducible representations of the extended poincare parasuperalgebra we classify and explicitly construct all the irreducible hermitian representations of the extended poincar parasuperalgebra these representations which include the representations of the usual extended poincar superalgebra as a particular case can serve as a group theoretical foundation of parasupersymmetric quantum field theory i e as a general viewpoint to reformulate the quantum field theory and quantum mechanics of identical particles on the general basis of paraquantization and supersymmetry

multiphase flow modeling of spinodal decomposition based on the cascaded lattice boltzmann method abstract a new multiphase lattice boltzmann model based on the cascaded collision operator is developed to study the spinodal decomposition of critical quenches in the inertial hydrodynamic regime the proposed lattice boltzmann model is able to investigate simulations of multiphase spinodal decomposition with a very high reynolds number the law governing the growth of the average domain size i e l t is studied numerically in the late time regime when multiple immiscible fluids are considered in the spinodal decomposition it is found numerically that the growth exponent is inversely proportional to the number n of immiscible fluids in the system in fact 6 n 7 is a simple law that matches the numerical results very well even up to n 20 as the number of immiscible fluids increases the corresponding drop in the connectivity of the various fluid domains is believed to be the main factor that drives and slows down the growth rate various videos that accurately demonstrate spinodal decomposition with different transport mechanisms are provided see appendix a the remarks and statement made in this research are based on the analysis of 5120 numerical simulations and the postprocessing of about 3 5 tb of data

realizability of a model in infinite statistics following greenberg and others we study a space with a collection of operatorsa k satisfying the q mutator relations a l a k a l k l corresponding forq 1 to classical bose and fermi statistics we show that then n matrixa n q representing the scalar products ofn particle states is positive definite for alln ifq lies between 1 and 1 so that the commutator relations have a hilbert space representation in this case this has also been proved by fivel and by bozejko and speicher we also give an explicit factorization ofa n q as a product of matrices of the form 1 q jt 1 with 1 j n andt a permutation matrix in particular a n q is singular if and only ifq m 1 for some integerm of the formk 2 k 2 k n

maximum modulus principle for holomorphic functions on the quantum matrix ball we describe the shilov boundary ideal for a q analog of the algebra of holomorphic functions on the unit ball in the space of n n matrices and show that its c envelope is isomorphic to the c algebra of continuous functions on the quantum unitary group u q n

discrete lattice effects on the forcing term in the lattice boltzmann method we show that discrete lattice effects must be considered in the introduction of a force into the lattice boltzmann equation a representation of the forcing term is then proposed with the representation the navier stokes equation is derived from the lattice boltzmann equation through the chapman enskog expansion several other existing force treatments are also examined

the energy operator for a model with a multiparametric infinite statistics in this paper we consider an energy operator a free hamiltonian in the second quantized approach for the multiparameter quon algebras aia j qija jai ij i j i with qij i ji any hermitian matrix of deformation parameters we obtain an elegant formula for normally ordered sometimes called wick ordered series expansions of number operators which determine a free hamiltonian as a main result see theorem 1 we prove that the number operators are given with respect to a basis formed by generalized lie elements by certain normally ordered quadratic expressions with coefficients given precisely by the entries of the inverses of gram matrices of multiparticle weight spaces this settles a conjecture by meljanac s and perica a 1994 j phys a math gen 27 4737 44 these gram matrices are hermitian generalizations of the varchenko matrices associated with a quantum symmetric bilinear form of diagonal arrangements of hyperplanes the solution of the inversion problem of such matrices in meljanac s and svrtan d 1996 math commun 1 1 24 theorem 2 2 17 leads to an effective formula for the number operators studied in this paper the one parameter case in the monomial basis was studied by zagier stanciu and moller

a harnack inequality approach to the regularity of free boundaries part ii flat free boundaries are lipschitz soit u une solution faible d un probleme aux limites libres du type u 0 sur u 0 et sur u 0 et soit le long de la frontiere libre f la relation u v g u x est satisfaite au sens faible alors si f est proche du graphe d une fonction de lipschitz dans la boule unite b 1 de r n f est le graphe d une fonction de lipschitz dans b 1 2

wick product for commutation relations connected with yang baxter operators and new constructions of factors we analyze a certain class of von neumann algebras generated by selfadjoint elements for satisfying the general commutation relations such algebras can be continuously embedded into some closure of the set of finite linear combinations of vectors where is an orthonormal basis of a hilbert space the operator which represents the vector is denoted by and called the wick product of the operators we describe explicitly the form of this product also we estimate the operator norm of for finally we apply these two results and prove that under the assumption all the von neumann algebras considered are ii 1 factors

q gaussian processes non commutative and classical aspects we examine for 1 q 1 q gaussian processes i e families of operators non commutative random variables where the a t fulfill the q commutation relations for some covariance function equipped with the vacuum expectation state we show that there is a q analogue of the gaussian functor of second quantization behind these processes and that this structure can be used to translate questions on q gaussian processes into corresponding and much simpler questions in the underlying hilbert space in particular we use this idea to show that a large class of q gaussian processes possesses a non commutative kind of markov property which ensures that there exist classical versions of these non commutative processes this answers an old question of frisch and bourret fb

noncommutative levy processes for generalized particularly anyon statistics let t mathbb r d let a function qt 2 to mathbb c satisfy q s t overline q t s and q s t 1 a generalized statistics is described by creation operators partial t dagger and annihilation operators t t in t which satisfy the q commutation relations partial s partial dagger t q s t partial dagger t partial s delta s t partial s partial t q t s partial t partial s partial dagger s partial dagger t q t s partial dagger t partial dagger s from the point of view of physics the most important case of a generalized statistics is the anyon statistics for which q s t is equal to q if s t here q in mathbb c q 1 we start the paper with a detailed discussion of a q fock space and operators partial t dagger partial t t in t in it which satisfy the q commutation relations next we consider a noncommutative stochastic process white noise omega t partial t dagger partial t lambda partial t dagger partial t t in t here lambda in mathbb r is a fixed parameter the case 0 corresponds to a q analog of brownian motion while 0 corresponds to a centered q poisson process we study q hermite q charlier respectively polynomials of infinitely many noncommutatative variables omega t t in t the main aim of the paper is to explain the notion of independence for a generalized statistics and to derive corresponding levy processes to this end we recursively define q cumulants of a field xi t t in t this allows us to define a q levy process as a field xi t t in t whose values at different points of t are q independent and which possesses a stationarity of increments in a certain sense we present an explicit construction of a q levy process and derive a nualart schoutens type chaotic decomposition for such a process

regularity of the free boundary in parabolic phase transition problems in this paper we start the study of the regularity properties of the free boundary for parabolic two phase free boundary problems may be the best known example of a parabolic two phase free boundary problem is the stefan problem a simplified model describing the melting or solidification of a material with a solid liquid interphase the concept of solution can be stated in several ways classical solution weak so lution on divergence form or viscosity solution and as usual one would like to prove that the weak solutions that may be constructed are in fact as smooth and classical as possible locally a classical solution of the stefan problem may be described as following on the unit cylinder q1 b1 1 1 we have two complementary domains and qi separated by a smooth surface s oi2 nq1 in fl and qi we have two smooth solutions ul and u2 of the heat equations

generalized exclusion and hopf algebras we propose a generalized oscillator algebra at the roots of unity with generalized exclusion and we investigate the braided hopf structure we find that there are two solutions these are the generalized exclusions of the bosonic and fermionic types we also discuss the covariance properties of these oscillators

quasistatic droplets in randomly perforated domains we consider the hele shaw problem in a randomly perforated domain with zero neumann boundary conditions a homogenization limit is obtained as the characteristic scale of the domain goes to zero specifically we prove that the solutions as well as their free boundaries converge uniformly to those corresponding to a homogeneous and anisotropic hele shaw problem set in mathbb r d the main challenge when deriving the limit lies in controlling the oscillations of the free boundary this is overcome first by extending de giorgi nash moser type estimates to perforated domains and second by proving the almost sure non degenerate growth of the solution near its free boundary

some free boundary problems recast as nonlocal parabolic equations abstract in this work we demonstrate that a class of some one and two phase free boundary problems can be recast as nonlocal parabolic equations on a submanifold the canonical examples would be one phase hele shaw flow as well as its two phase analog we also treat nonlinear versions of both one and two phase problems in the special class of free boundaries that are graphs over r d we give a precise characterization that shows their motion is equivalent to that of a solution of a nonlocal fractional nonlinear parabolic equation for functions on r d our main observation is that the free boundary condition defines a nonlocal operator having what we call the global comparison property a consequence of the connection with nonlocal parabolic equations is that for free boundary problems arising from translation invariant elliptic operators in the positive and negative phases one obtains in a uniform treatment for all of the problems one and two phase a propagation of modulus of continuity for viscosity solutions of the free boundary flow

on boson algebras as hopf algebras certain types of generalized undeformed and deformed boson algebras which admit a hopf algebra structure are introduced together with their fock type representations and their corresponding r matrices it is also shown that a class of generalized heisenberg algebras including those underlying physical models such as that of calogero sutherland is isomorphic with one of the types of boson algebra proposed and can be formulated as a hopf algebra

lattice boltzmann modeling with discontinuous collision components hydrodynamic and advection diffusion equations irrespective of the nature of the modeled conservation laws we establish first the microscopic interface continuity conditions for lattice boltzmann lb multiple relaxation time link wise collision operators with discontinuous components equilibrium functions and or relaxation parameters effective macroscopic continuity conditions are derived for a planar implicit interface between two immiscible fluids described by the simple two phase hydrodynamic model and for an implicit interface boundary between two heterogeneous and anisotropic variably saturated soils described by richard s equation comparing the effective macroscopic conditions to the physical ones we show that the range of the accessible parameters is restricted e g a variation of fluid densities or a heterogeneity of the anisotropic soil properties when the interface is explicitly tracked the interface collision components are derived from the leading order continuity conditions among particular interface solutions a harmonic mean value is found to be an exact lb solution both for the interface kinematic viscosity and for the interface vertical hydraulic conductivity function we construct simple problems with the explicit and implicit interfaces matched exactly by the lb hydrodynamic and or advection diffusion schemes with the aid of special solutions for free collision parameters

the lp boundary value problems on lipschitz domains abstract let be a bounded lipschitz domain in r n we develop a new approach to the invertibility on l p of the layer potentials associated with elliptic equations and systems in as a consequence for n 4 and 2 n 1 n 1 e p 2 where e 0 depends on we obtain the solvability of the l p neumann type boundary value problems for second order elliptic systems the analogous results for the biharmonic equation are also established

q deformed classical lie algebras and their anyonic realization all classical lie algebras can be realized a la schwinger 1965 in terms of fermionic oscillators we show that the same can be done for their q deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice the deformation parameter q is a phase related to the anyonic statistical parameter a crucial role in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the undeformed ones the entire procedure works even on one dimensional chains in such a case q can also be real

howe duality for the quantum groups uqu m n uqu m a dual pair is defined to be a pair of mutually centralizing subgroups of the real symplectic group let g g be a dual pair of reductive groups in which g is also compact and consider the decomposition of the metaplectic representation of the symplectic group into gg irreducibles each such irreducible is a tensor product of an irreducible of g with one of g and it turns out there is a bijective correspondence between them a particular irreducible of g only occurring with a particular one of g and vice versa this so called howe duality is here generalized to the quantum group case uqu m n uqu m for q not a root of unity a metaplectic representation for this dual pair is given in terms of the q oscillator algebra and a uqu m n uqu m covariant heisenberg weyl algebra is also constructed and realized on fock space the heart of the proof lies in showing that uqu m n and uqu m are essentially mutual commutants on fock space the duality follows using the compactness of uqu m the proof is i

study of quommutators of quantum variables and generalized derivatives a general deformation of the heisenberg algebra is introduced with two deformed operators instead of just one this is generalized to many variables and permits the simultaneous existence of coherent states and the transposition of creation operators

regularity of one phase stefan problem near lipschitz initial data in this paper we show that starting from lipschitz initial free boundary with small lipschitz constant the solution of the one phase stefan problem st immediately regularizes and is smooth in space and time for a small positive time

on wick algebras with additional twisted commutation relations we study the construction of the c symmetric creation and annihilation operators which form a wick algebra with some additional relations this wick algebra is an algebra of the operators which act on the associative algebra of polynomials with noncommutative variables divided by an ideal generated by quadratic relations between the variables as a result the consistency conditions for such a representation are obtained the creators and annihilator have to preserve ideal where which leads us to consistency conditions

contractivity properties of ornstein uhlenbeck semigroup for general commutation relations we study a certain class of von neumann algebras generated by selfadjoint elements i a i a i where a i a i satisfy the general commutation relations

a duality for endomorphisms of von neumann algebras we consider endomorphisms of von neumann algebras let m be a von neumann algebra represented on a hilbert space h and let m be the corresponding commutant let end m be given and suppose m has a cyclic vector in h such that the corresponding state leaves invariant then there is a dual completely positive mapping on m which we find and describe each of the two and has an associated spectral group and we show that the group for is contained in that for we consider the following three restrictions on i is a shift on m ii is strongly ergodic and iii is ergodic we give spectral theoretic conditions on using the two groups described above to fall into each of the three classes we also show that the two groups are conjugacy invariants and we discuss the case of cocycle conjugacy

regularity of the free boundary for the one phase hele shaw problem abstract in this paper we prove that in a local neighborhood lipschitz continuous free boundary of a solution of the one phase hele shaw problem is indeed smooth if the solution is lipschitz continuous and non degenerate in the neighborhood

extended poincare parasuperalgebra with central charges and invariant wave equations we describe irreducible representations of the extended poincare parasuperalgebra ppsa which includes an arbitrary number n of parasupercharges n n n 2 central charges and an internal symmetry group we also discuss wave equations which are invariant with respect to the ppsa and propose a parasupersymmetric generalization of the wess zumino model for arbitrary p and n

quantum spin chains with quantum group symmetry we consider actions of quantum groups on lattice spin systems we show that if an action of a quantum group respects the local structure of a lattice system it has to be an ordinary group even allowing weakly delocalized quasi local tails of the action we find that there are no actions of a properly quantum group commuting with lattice translations the non locality arises from the ordering of factors in the quantum groupc algebra and can be made one sided thus allowing semi local actions on a half chain under such actions localized quantum group invariant elements remain localized hence the notion of interactions invariant under the quantum group and also under translations recently studied by many authors makes sense even though there is no global action of the quantum group we consider a class of such quantum group invariant interactions with the property that there is a unique translation invariant ground state under weak locality assumptions its gns representation carries no unitary representation of the quantum group

exclusion statistics operator algebras and fock space representations we study exclusion statistics within the second quantized approach we consider operator algebras with positive definite fock space and restrict them in a such a way that certain state vectors in fock space are forbidden ab initio we describe three characteristic examples of such exclusion namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space e g the calogero sutherland type of exclusion statistics exclusion in the single oscillator fock space where some states in single oscillator fock space are forbidden e g the gentile realization of exclusion statistics and a combination of these two exclusions e g green s realization of para fermi statistics for these types of exclusions we discuss the extended haldane statistics parameters g recently introduced by two of us in 1996 mod phys lett a 11 3081 and associated counting rules within these three types of exclusions in fock space the original haldane exclusion statistics cannot be realized

generalized deformed oscillator and nonlinear algebras the harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied the eigenstates and eigenvalues of the deformed oscillator are calculated this generalized deformed oscillator algebra is used to create nonlinear deformation of the classical su 2 algebra the deformed boson realizations of an arbitrary nonlinear su 2 algebra are calculated the algebra of the q deformed oscillator is a special case of the generalized deformed oscillator algebra

ϕ derivations on operators on q fock space we study the q creation and q annihilation derivatives of operators on q fock space and then the derivatives are derivations with respect to the q wick product where is a homomorphism with respect to the q wick product which provide interesting non trivial examples of abstract derivation

three dimensional multi relaxation time mrt lattice boltzmann models for multiphase flow in this paper three dimensional 3d multi relaxation time mrt lattice boltzmann lb models for multiphase flow are presented in contrast to the bhatnagar gross krook bgk model a widely employed kinetic model in mrt models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted as a result the mrt models offer a significant improvement in numerical stability of the lb method for simulating fluids with lower viscosities we show through the chapman enskog multiscale analysis that the continuum limit behavior of 3d mrt lb models corresponds to that of the macroscopic dynamical equations for multiphase flow we extend the 3d mrt lb models developed to represent multiphase flow with reduced compressibility effects the multiphase models are evaluated by verifying the laplace young relation for static drops and the frequency of oscillations of drops the results show satisfactory agreement with available data and significant gains in numerical stability

uniqueness and existence results on the hele shaw and the stefan problems in this paper we introduce a notion of viscosity solutions for the one phase hele shaw and stefan problems when there is no surface tension we prove the uniqueness and existence of the solutions for both problems and the uniform convergence of solutions of porous medium equation to those of the hele shaw problem

on certain quantum deformations of gl n r in this article all deformations of the general linear group subject to certain restrictions which in particular ensure a smooth passage to the lie group limit are obtained representations are given in terms of certains sets of creation and annihilation operators these creation and annihilation operators may belong to a generalization of the q quark type or q hadronic type with q boson or q fermion behavior this leads to a natural definition of q direct sums of q algebras

the spectrum of the algebra of skew differential operators and the irreducible representations of the quantum heisenberg algebra the left spectrum of a wide class of the algebras of skew differential operators is described as a sequence we determine and classify all the algebraically irreducible representations of the quantum heisenberg algebra over an arbitrary field

fock representations of the superalgebra sl n 1 m its quantum analogue uq sl n 1 m and related quantum statistics fock space representations of the lie superalgebra sl n 1 m and of its quantum analogue uq sl n 1 m are written down the results are based on a description of these superalgebras via creation and annihilation operators the properties of the underlying statistics are briefly discussed

minimality of the data in wavelet filters abstract orthogonal wavelets or wavelet frames for l2 r are associated with quadrature mirror filters qmf a set of complex numbers which relate the dyadic scaling of functions on r to the z translates in this paper we show that generically the data in the qmf systems of wavelets are minimal in the sense that the data cannot be nontrivially reduced the minimality property is given a geometric formulation in the hilbert space l2 z and it is then shown that minimality corresponds to irreducibility of a wavelet representation of the algebra o 2 and so our result is that this family of representations of o 2 on the hilbert space l2 z is irreducible for a generic set of values of the parameters which label the wavelet representations

infinite statistics and the su 1 1 phase operator a few years ago agarwal 1991 phys rev a 44 8398 showed that the susskind glogower phase operators expressible in terms of bose operators provide a realization of the algebra for particles obeying infinite statistics in this paper we show that the su 1 1 phase operators constructed in terms of the elements of the su 1 1 lie algebra also provide a realization of the algebra for infinite statistics there are many realizations of the su 1 1 algebra in terms of single or multimode bose operators three of which are discussed along with their corresponding phase states the susskind glogower phase operator is a special case of the su 1 1 phase operator associated with the holstein primakoff realization of su 1 1

jacobson generators fock representations and statistics of sl n 1 the properties of a statistics related to the class a of simple lie algebras t d palev preprint jinr e17 10550 1977 hep th 9705032 are further investigated the description of each sl n 1 is carried out via generators a1 an which we call jacobson generators with respect to these generators the definition of a fock space of sl n 1 is given it is proved that the fock spaces wp p n are the simple symmetric finite dimensional modules of sl n 1 the pauli principle of the underlying statistics is formulated within each wp operators b p i ai p i 1 n called quasi bose creation and annihilation operators caos are defined then limp b p i bi where bi are ordinary bose caos therefore a statistics appears as an approximation of bose statistics with caos acting in finite dimensional state spaces we indicate that the p 1 quasi bose operators b 1 1 b 1 n are natural operators for the description of hard core bose models and of the related heisenberg spin models we argue th

multiple relaxation time lattice boltzmann model for multiphase flow the lattice boltzmann method has shown promise in simulating multiphase flows however when using the bhatnagar gross krook bgk collision operator and polynomial equilibria numerical stability problems have been shown to occur as the relaxation time is decreased some authors have suggested the use of multiple relaxation time mrt models in lieu of the bgk collision operator which employs a single relaxation time to enhance numerical stability in this paper a mrt lattice boltzmann model for multiphase flow is developed and evaluated for accuracy in several test problems including oscillating liquid cylinders and capillary waves it is shown that the mrt model is able to achieve numerically stable results at lower viscosities relative to the corresponding bgk model

a variational inequality approach to hele shaw flow with a moving boundary this paper is concerned with the study of a mathematical model of the injection of fluid into a finite hele shaw cell the mathematical problem is one of solving laplace s equation in an unknown region whose boundary changes with time by a transformation of the dependent variable an elliptic variational inequality formulation of the moving boundary problem is obtained the variational inequality is shown to have a unique solution up to the time at which the cell is filled regularity results for the solution of the inequality are obtained by studying a penalty approximation of the inequality

on commutators of wick products on ccr and car algebras in this paper we study the q commutator of wick products on the ccr canonical commutation relation algebra and on the car canonical anticommutation relation algebra we obtain a formula on q commutator of wick products in terms of wick products of monomials of lower order moreover we give a relation of double q commutator

example of infinite statistics i give a second quantized example of infinite statistics in which any representation of the symmetric group can occur for identical particles and discuss the properties of the example

regularity for the one phase hele shaw problem from a lipschitz initial surface in this paper we show that if the lipschitz constant of the initial free boundary is small then for small positive time the solution is smooth and satisfies the hele shaw equation in the classical sense a key ingredient in the proof which is of independent interest is an estimate up to order of magnitude of the speed of the free boundary in terms of initial data

the hele shaw problem as a mesa limit of stefan problems existence uniqueness and regularity of the free boundary we study a hele shaw problem with a mushy region obtained as a mesa type limit of one phase stefan problems in exterior domains we deal with both neumann and dirichlet data and show pointwise convergence of the stefan solutions to the hele shaw solution we make no assumptions on the geometry topology or connectivity of the injection slot

theory of the lattice boltzmann equation symmetry properties of discrete velocity sets the lattice boltzmann equation replaces continuous particle velocity space by a finite set the velocity distribution function then varies over a finite dimensional vector space instead of over an infinite dimensional function space the number of linearly independent moments of the distribution function in a lattice boltzmann model cannot exceed the number of velocities finite dimensionality therefore necessarily induces linear dependences among the moments that do not exist in a continuous theory given a finite velocity set it is important to know which moments are free of these dependences elementary group theory is applied to the solution of this problem it is found that decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group makes it straightforward to uncover linear dependences among the moments the construction of some standard two and three dimensional models is reviewed from this viewpoint and procedures for constructing higher dimensional models are suggested

multirange multi relaxation time shan chen model with extended equilibrium the work presents simulations with the multirange shan chen model developed by sbragaglia et al 2007 18 which improved the shan chen model for the proper surface tension term also by introducing the matrix collision operator and extended equilibrium density distribution function the density ratio is increased from 100 to 160 the multi relaxation time mrt method attracted the attention of researchers due to several advantages such as better stability simulations with prandtl number different from unity and possibilities to improve the accuracy of the scheme compared with bgk single time relaxation model our recent results have shown that the combination of mrt methods with multiphase flow models can improve the achievable gas liquid density ratio