parasupercoherent states and color supergroups parabosonic coherent states are illustrated from the displacement operator point of view such a construction requires the use of the green cusson ansatze a specific representation of parastatistics leading to color supergroups a comparison with a previous result is shown through the annihilation operator and the minimum uncertainty contexts the extension to the parasupersymmetric case is also considered

lie structures in parasupersymmetric quantum mechanics i the standard supersymmetrization procedure parasupersymmetric quantum mechanics leads to the construction of new lie structures that are called lie parasuperalgebras they are characterized by double commutation relations between even and odd generators and include as particular substructures the usual lie superalgebras oscillatorlike systems in one spatial dimension are especially exploited in order to put such structures in evidence but n dimensional extensions are easily determined these developments in the standard supersymmetrization procedure will be considered first and the spin orbit coupling one will be considered in a subsequent article j beckers and n debergh j math phys 1991

conformal o 3 2 symmetry of the two dimensional inverse square potential it is shown that the dynamical systems describing a point mass moving in a repulsive inverse square potential in a plane and a free relativistic massless particle are isomorphic to each other the obvious conformal invariance of the massless particle appears as a hidden dynamical symmetry of the inverse square potential

transformations of some induced osp 3 2 modules in an so 3 sp 2 basis the modules of the orthosymplectic lie superalgebra osp 3 2 induced from finite dimensional irreducible submodules of the stability subalgebra so 3 gl 1 are investigated the corresponding infinite dimensional irreducible or indecomposable modules the kac modules and the related typical and atypical modules are studied in detail every such module is decomposed into a direct sum of either indecomposable or irreducible modules of the even subalgebra so 3 sp 2 for each of these infinite dimensional or finite dimensional irreducible or indecomposable modules relations are written down giving the transformations of the basis under the action of the algebra generators

prediction of steady state flow of real gases in randomly heterogeneous porous media abstract we consider steady state flow of real gases through bounded randomly heterogeneous porous media such flow is described by a nonlinear partial differential equation with the random coefficient medium s permeability and source terms subject to randomly prescribed boundary conditions prior to applying stochastic analysis the problem is linearized by means of the kirchhoff transformation which allows us to obtain the exact expressions for an effective upscaled gas permeability in particular for one two and three dimensional mean uniform flows in infinite statistically homogeneous and isotropic domains the resulting effective permeability is given by harmonic geometric and arithmetic averages respectively the influence of statistical anisotropy of the random permeability field and domain s boundaries on the effective gas permeability is also investigated

perturbation theory for the effective diffusion constant in a medium of random scatterers we develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random medium the random medium contains point scatterers of density uniformly distributed throughout the material the tracer is a langevin particle subjected to the quenched random force generated by the scatterers via our perturbative analysis we determine when the random potential can be approximated by a gaussian random potential we also develop a self similar renormalization group approach based on thinning out the scatterers this scheme is similar to that used with success for diffusion in gaussian random potentials and agrees with known exact results to assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

integrators for lie poisson or dynamical systems abstract we reformulate the ge marsden 1988 lie poisson integration algorithm in terms of algebra variables alone and show how to implement it for regular quadratic lie algebras to arbitrary order and for arbitrary lie algebras to first order we also describe two generalizations of ruth s method 1983 that can be used to generate very fast algorithms

three level coupled systems and parasupersymmetric shape invariance a class of bound state problems which represents the coupling of a three level atom with a two dimensional system involving two shape invariant potentials is introduced we consider second order parasupersymmetric quantum mechanical models and using an algebraic formulation for shape invariant potential systems resolve the eigenvalue problem for these coupled systems considering two possible kinds for the coupling hamiltonian linear and nonlinear in the potential ladder operators an application is given for a couple of shape invariant potentials harmonic oscillator morse potentials

perturbation theory for effective diffusivity in random gradient flows we investigate a result for the effective diffusivity of particles in a random gradient flow previously obtained by an intuitively plausible renormalization group argument and very accurately verified by numerical simulation we show that to two loop order the result is consistent with a direct perturbation theory calculation to the same order in perturbation theory we also derive a ward identity which guarantees the equality of the ratio of the effective diffusivity to the renormalized coupling with the ratio of the corresponding bare values the invariance of this ratio under renormalization was an important feature of the successful renormalization group calculation

effective conductivity of many component composites by a random walk method an extension to the many component case is given for a random walk algorithm which was recently introduced to calculate the effective conductivity of random mixtures with two finite conductivity components the many component algorithm has been tested for the case in which the conductivity distribution is generated by taking n component conductivities and assigning them at random with equal probability to the sites of a lattice of size 303 simulations have been done with n 10 100 1000 and 27 000 numerical results obtained by using the proposed random walk algorithm are shown to be in close agreement with those obtained using the conventional finite difference method

continuum derrida approach to drift and diffusivity in random media by means of rather general arguments based on an approach due to derrida that makes use of samples of finite size we analyse the effective diffusivity and drift tensors in certain types of random media in which the motion of the particles is controlled by molecular diffusion and a local flow field with known statistical properties the power of the derrida method is that it uses the equilibrium probability distribution which exists for each finite sample to compute asymptotic behaviour at large times in the infinite medium in certain cases where this equilibrium situation is associated with a vanishing microcurrent our results demonstrate the equality of the renormalization processes for the effective drift and diffusivity tensors this establishes for those cases a ward identity previously verified only to two loop order in perturbation theory in certain models the technique can also be applied to media in which the diffusivity exhibits spatial fluctuations we derive a simple relationship between the effective diffusivity in this case and that for an associated gradient drift problem that provides an interesting constraint on previously conjectured results

hamiltonian structures and stability for rigid bodies with flexible attachments the dynamics of a rigid body with flexible attachments is studied a general framework for problems of this type is established in the context of poisson manifolds and reduction a simple model for a rigid body with an attached linear extensible shear beam is worked out for illustration second the energy casimir method for proving nonlinear stability is recalled and specific stability criteria for our model example are worked out the poisson structure and stability results take into account vibrations of the string rotations of the rigid body their coupling at the point of attachment and centrifugal and coriolis forces

effective permittivity of log normal isotropic random media a method of deriving the effective permittivity epsilon eff of log normal d dimensional isotropic media is developed the approach is based on applying the regularized green function technique for the laplace operator the feasibility of exact determining of the effective permittivity is analysed by deriving epsilon eff at third order in the log permittivity variance it is shown that the 3d effective permittivity is a functional of the spectrum of inhomogeneities and therefore cannot be expressed by a closed formula in particular the formula for the effective permittivity discussed previously by landau and lifshitz 1960 and matheron 1967 deviates from the exact one in the third order term

stochastic diagrammatic analysis of groundwater flow in heterogeneous porous media the diagrammatic approach is an alternative to standard analytical methods for solving stochastic differential equations governing groundwater flow with spatially variable hydraulic conductivity this approach uses diagrams instead of abstract symbols to visualize complex multifold integrals that appear in the perturbative expansion of the stochastic flow solution and reduces the original flow problem to a closed set of equations for the mean and the covariance functions diagrammatic analysis provides an improved formulation of the flow problem over conventional first order series approximations which are based on assumptions such as constant mean hydraulic gradient infinite flow domain and neglect of cross correlation terms this formulation includes simple schemes like finite order diagrammatic perturbations that account for mean gradient trends and boundary condition effects as well as more advanced schemes like diagrammatic porous media description operators which contain infinite order correlations in other words diagrammatic analysis covers not only the cases where low order diagrams lead to good approximations of flow but also those situations where low order perturbation is insufficient and a more sophisticated analysis is needed diagrams lead to a nonlocal equation for the mean hydraulic gradient in terms of which necessary conditions are formulated for the existence of an effective hydraulic conductivity three dimensional flow in an isotropic bounded domain with dirichlet boundary conditions is considered and an integral equation for the mean hydraulic head is derived by means of diagrams this formulation provides an explicit expression for the boundary effects within the three dimensional flow domain in addition to these theoretical results the numerical performance of the diagrammatic approach is tested and useful insight is obtained by means of one dimensional flow examples where the exact stochastic solutions are available

homogenization of richards equation in permeability fields with different connectivities 1 large scale modeling of transient flow in the unsaturated zone is important for the estimation of the water budget and solute transport in the vadose zone upscaled flow models need to capture the impact of small scale heterogeneities which are not resolved by the model on large scale flow we perform upscaling of the richards equation in heterogeneous porous media with continuous distributions of the soil hydraulic parameters using homogenization theory and stochastic averaging techniques we restrict the analysis to flow regimes in which the capillary equilibrium assumption holds on the small scale in order to account for effects of capillary entry pressure we apply the brooks corey model for the soil retention and relative permeability curves and consider leverett scaling for the coupling of intrinsic permeability and entry pressure for this model we derive and analyze the ensemble averaged parameter functions for the macroscopic flow equations the effects of a definite entry pressure vanish with increasing variance of the log intrinsic permeability we compare the statistically averaged parameter functions to numerically calculated effective functions for parameter fields with different connectivity properties these results illustrate that soils with well connected coarse materials differ in the relative permeability from those with well connected fine materials or those without particular connectedness

conformal invariance conditions for spinor fields with gauge freedom the global invariance conditions are given for the j j spinor fields with gauge freedom invariant under subgroups of c 3 1 we formulate two propositions concerning the nonexistence of nontrivial fields with and without compact gauge freedom and apply them to the maximal noncompact subgroups of c 3 1 we also determine explicitly the most general o 4 and o 2 o 4 invariant j j spinor fields with compact gauge freedom

representation theory of superconformal quantum mechanics the analogy between the representations of su 1 1 1 and su 2 2 1 is explained and used to suggest the latter as a spectrum supergroup of superconformal relativistic quantum mechanics for systems with rotational degrees of freedom

finite dimensional lie poisson approximations to vlasov poisson equations many of the basic equations of conservative continuum mechanics euler vlasov poisson vlasov maxwell mhd etc are hamiltonian systems with respect to lie poisson brackets on dual spaces of infinite dimensional lie algebras the development of lie poisson integrators for finite dimensional lie poisson systems has shown that they are superior in the numerical simulations of these systems especially with regard to long term phenomena this paper shows how to truncate one of these systems the vlasov poisson equation of plasma physics to a finite dimensional lie poisson system this requires replacing the functions on single particle phase space with their poisson bracket lie algebra structure by a finite dimensional lie algebra replacing the densities by their moments of order up to k about a fixed reference point corresponds to replacing the functions by their taylor expansions up to order k unfortunately these truncated taylor expansions do not form a lie algebra since the functions which vanish through order k do not form an ideal under poisson bracket geometrically this corresponds to the fact that canonical transformations which fix the reference point do not form a normal subgroup introducing the location of a reference point in phase space as an extra variable and truncating with respect to this moving point turns out to decouple the location from shape coordinates of a lump of density in phase space as far as the poisson bracket is concerned one can then replace the shape coordinates by a finite number of moments the central result of the paper is a construction of the decoupling map described above in the general context of the decomposition of a lie group as a product of subgroups the main theorem is first proved by the general theory of poisson reduction then by explicit calculation and lastly by showing that the poisson isomorphism follows from the lift of a natural groupoid isomorphism the groupoid aspect of the theory also provides natural poisson maps useful in the application of ruth type integration techniques which do not seem easily derivable from the general theory of poisson reduction 1994 john wiley sons inc

numerical integration of lie poisson systems while preserving coadjoint orbits and energy in this paper we apply geometric integrators of the rkmk type to the problem of integrating lie poisson systems numerically by using the coadjoint action of the lie group g on the dual lie algebra mbox normalsize mathfrak g to advance the numerical flow we devise methods of arbitrary order that automatically stay on the coadjoint orbits first integrals known as casimirs are retained to machine accuracy by the numerical algorithm within the proposed class of methods we find integrators that also conserve the energy these schemes are implicit and of second order nonlinear iteration in the lie algebra and linear error growth of the global error are discussed numerical experiments with the rigid body and a finite dimensional truncation of the euler equations for a two dimensional 2d incompressible fluid are used to illustrate the properties of the algorithm

on remarkable properties of invariance superalgebras for the harmonic oscillator starting from the orthosymplectic superalgebra osp 3 4 the authors rigorously explain the correspondence between two superalgebras as invariance superalgebras of the one dimensional quantum harmonic oscillator i e osp 2 2 sh 2 2 and osp 3 2 the study of the corresponding root systems as well as their properties with respect to their even or odd characters gives them remarkable properties for the enclosed subsuperalgebras of osp 3 4 such properties and correspondences can be extended to the n dimensional context

on p 2 generalized deformed parafermions and exotic statistics generalized deformed parafermions of order two are analysed according to the lie super algebras they generate a classification of the subtended exotic statistics is then given and for each of them remarkable embedded lie structures are pointed out

on non relativistic conformal symmetries and invariant tensor fields the largest symmetry group of the schrodinger equation the so called schrodinger group is analysed in connection with invariant 2forms 1 forms and 0 2 symmetric tensors through the beckers harnad perroud winternitz global method 1978 developed in the relativistic conformal context invariant fields and potentials are obtained and discussed in the physical context of schrodinger electromagnetism through the corresponding infinitesimal method specific attention is paid to magnetic monopole dynamical symmetries these results are obtained in correspondence with the subalgebra classification determined by using the patera winternitz zassenhaus algorithm 1975 the accent is put on the maximal subalgebras of the schrodinger algebra

fourth order symplectic integration abstract in this paper we present an explicit fourth order method for the integration of hamilton s equations this method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state that is the integration step is an explicit symplectic map although the result is first derived for a specific type of hamiltonian it is shown to be quite general in particular the results can be applied to any lie group

on the geometry of the hamilton jacobi equation and generating functions in this paper we develop a geometric version of the hamilton jacobi equation in the poisson setting specifically we geometrize what is usually called a complete solution of the hamilton jacobi equation we use some well known results about symplectic groupoids in particular cotangent groupoids as a keystone for the construction of our framework our methodology follows the ambitious program proposed by weinstein in mechanics day waterloo on 1992 volume 7 of fields institute communications american mathematical society providence 1996 in order to develop geometric formulations of the dynamical behavior of lagrangian and hamiltonian systems on lie algebroids and lie groupoids this procedure allows us to take symmetries into account and as a by product we recover results from channell and scovel phys d 50 1 80 88 1991 ge indiana univ math j 39 3 859 876 1990 ge and marsden phys lett a 133 3 134 139 1988 but even in these situations our approach is new a theory of generating functions for the poisson structures considered here is also developed following the same pattern solving a longstanding problem of the area how to obtain a generating function for the identity transformation and the nearby poisson automorphisms of poisson manifolds a direct application of our results gives the construction of a family of poisson integrators that is integrators that conserve the underlying poisson geometry these integrators are implemented in the paper in benchmark problems some conclusions current and future directions of research are shown at the end of the paper

higher order susy linearized nonlinear heisenberg algebras and coherent states using an iterative construction of the first order intertwining technique we find k parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the oscillator plus k additional levels at arbitrary positions below e0 it is seen that the natural ladder operators for these systems give place to polynomial nonlinear algebras and it is shown that these algebras can be linearized the coherent states construction is performed in the nonlinear and linearized cases

on clifford algebras and unitary lie superalgebras constructions of semidirect sums of p 2p clifford algebras cl2n cln have recently appeared in supersymmetric developments moreover they are also related to specific properties on realizations of green cusson s ansatze when parabosons of order p are concerned the author shows that such semidirect sums are isomorphic to unitary lie superalgebras he also gives a corresponding realization in terms of the basis elements of cl2n 2q 2 cl2m 2q 2 n 2m or n 2m 1 each case is discussed according to the parity of p i e p 2q or p 2q 1

multidimensional generalized superalgebras the multidimensional analogues of the one dimensional generalized superalgebras are considered in the framework of quantum mechanics

stochastic analysis of spatial variability in two dimensional steady groundwater flow assuming stationary and nonstationary heads two dimensional steady groundwater flow in a confined aquifer with spatially variable transmissivity t is analyzed stochastically using spectral analysis and the theory of intrinsic random functions conditions that ensure a stationary statistically homogeneous head process are derived and using two convenient forms for the covariance function of the ln t process the head covariance function is studied in addition the head variogram is obtained for a particular nonstationary case and the asymptotic head variogram is derived under very general conditions results are compared to those obtained by gelhar 1976 for one and two dimensional phreatic flow and bakr et al 1978 for one and three dimensional confined flow multidimensional flow analysis results in a significantly reduced head variance the head correlation remains high over much greater distances than the ln t correlation the variogram obtained when stationary heads are assumed is identical to that obtained for nonstationary heads for dimensionless lag distances up to 2 times the correlation scale of the log transmissivity the variogram for nonstationary heads continues to grow logarithmically as lag distance increases independent of the form of the input covariance in the nonstationary case the conditions for stationarity are contrasted with the corresponding results obtained for the one and three dimensional cases of gutjahr and gelhar 1981 the head variance calculated from the stationary theory is found to agree with that of previous monte carlo simulations

quantum dynamics of parasupersymmetric and shape invariant coupled systems a class of bound state problems which represents the coupling of a three level atom with a two dimensional system involving two shape invariant potentials was introduced in a previous paper in this paper we considered second order parasupersymmetric quantum mechanical models and two possible kinds for the coupling hamiltonian linear and nonlinear in the potential ladder operators in the present paper using an algebraic formulation for shape invariant potential systems we study the quantum dynamics of these coupled systems and obtain the temporal behaviour of some dynamical variables related with the atom and the coupling potentials an application is given for a couple of shape invariant potentials poschl teller self similar potentials

the oscillator model for the lie superalgebra sh 2 2 and charlier polynomials we investigate an algebraic model for the quantum oscillator based upon the lie superalgebra sh 2 2 known as the heisenberg weyl superalgebra or the algebra of supersymmetric quantum mechanics and its fock representation the model offers some freedom in the choice of a position and a momentum operator leading to a free model parameter using the technique of jacobi matrices we determine the spectrum of the position operator and show that its wavefunctions are related to charlier polynomials cn with parameter 2 some properties of these wavefunctions are discussed as well as some other properties of the current oscillator model

probability density functions of hydraulic head and velocity in three dimensional heterogeneous porous media 1 in this study we assess probability density functions of hydraulic heads and specific discharges in three dimensional bounded heterogeneous porous media by monte carlo mc simulation we discuss their empirical shapes and demonstrate that the intuitive use of obvious information on boundedness leads to parametric distribution functions which fit surprisingly well on the basis of statistical moments of hydraulic heads and velocities up to fourth order we discuss the spatial dependence of the empirical distributions and their dependence on the variance of log conductivity comparison of the first and second central moment to the results from classical numerical first order second moment fosm analysis reveals that fosm predicts these moments surprisingly close for hydraulic heads on the basis of this fact we demonstrate that fitting the chosen parametric distributions for hydraulic heads to fosm moments is promising for the sake of estimating exceedance probabilities our mc scenarios vary in variance of log conductivity 0 125 to 5 0 in the type of multivariate dependence in correlation scale and types of boundary conditions our study illustrates that in contrast to the common assumption fosm is a reasonable choice for evaluating multivariate and univariate moments for heads if used in conjunction with additional information on distribution shapes in the absence of utilizable additional information we demonstrate that second moment methods are mostly inadequate for assessing distributions accurately significant deviations from gaussian distributions occurred for discharge components even at a variance of log conductivity as low as 0 125 and we found that the distributions of transverse discharge components are extremely fat tailed the observed non gaussianity questions the results of approximate approaches in solute flux and dispersion studies where velocity fields are assumed to be multi gaussian and then directly represented by or generated from their covariances the main implication is to apply more accurate schemes such as exact non local methods extensive mc or higher order stochastic galerkin approaches and to include higher order moments at least if no additional assumptions on the shape of distributions are available or justifiable

analysis of flow through heterogeneous random aquifers 2 unsteady flow in confined formations the direct problem of determining the head field in a formation of given stationary isotropic random structure is solved approximately for unsteady flow conditions under restrictive assumptions of sufficiently small conductivity variance and average head gradient slowly varying in time and space closed form expressions are derived for the effective conductivity or storativity and for the head variogram two types of unsteady flow are considered transients and periodic flows in the case of transients it is assumed that initially the head is constant no flow and that ultimately the flow becomes uniform it is found that the effective conductivity and transmissivity are time dependent and drop from the arithmetic mean initially to the steady state value during a relaxation time the latter is much larger for one dimensional flows than for two or three dimensional ones the head variogram also relaxes from the one corresponding to the initial lack of correlation to the steady state variogram during a relaxation time which grows with the lag while in three dimensional structure the relaxation time scales are relatively short and steady state analysis can be used accurately even under transient conditions the tendency to steady state may be very slow in the case of transmissivity because of its large integral scale hence steady state analysis for transients might not be warranted for regional transient flows in the case of periodic flows of seasonal nature the head gradient is assumed to be made up from a steady component and a periodic one if the amplitude of the latter is sufficiently small compared to the steady one steady state value of effective transmissivity and storativity can be adopted the head variogram has also its steady state form for large lags and quasisteady for small lags hence the variogram lies between the steady one steady component of head gradient and the quasisteady one instantaneous head gradient

lowest weight representations of super schrodinger algebras in one dimensional space lowest weight modules in particular verma modules over the n 1 2 super schrodinger algebras in 1 1 dimensional spacetime are investigated the reducibility of the verma modules is analyzed via explicitly constructed singular vectors the classification of the irreducible lowest weight modules is given for both massive and massless representations a vector field realization of the n 1 2 super schrodinger algebras is also presented

on the heisenberg and orthosymplectic superalgebras of the harmonic oscillator the new invariance superalgebra osp 2 2n sh 2 2n for an n dimensional quantum harmonic oscillator is proposed and the corresponding supersymmetric hamiltonian is constructed this superalgebra is related to the structure osp 3 2n recently studied by englefield j phys a 21 1309 1988 by interchanging the even and odd characters of the fundamental generators belonging to the heisenberg superalgebra sh 2 2n the connection between both structures is established and its consequences exploited the specific cases n 1 2 3 are discussed and compared with recent contributions some general conclusions are also summarized

the use of field theoretic methods for the study of flow in a heterogeneous porous medium the effects of heterogeneities on the steady state flow of a single fluid in a porous medium are examined it is argued that incomplete knowledge of the permeability requires the use of a stochastic model of the system it is shown that the problem may be written as a field theory which allows a perturbation series to be expressed by diagrammatic means this allows the calculation of effective permeability the mean pressure and the pressure variance the method as well as recovering familiar results gives a formal means of improving the approximation and approaching more complex systems

symmetries and supersymmetries of the quantum harmonic oscillator the supersymmetric version of the one dimensional harmonic oscillator is studied by taking into account its conformal properties the largest superalgebra of symmetries and supersymmetries is derived as osp 2 2 square operator sh 1 the semidirect sum of osp 2 2 and the heisenberg superalgebra through a one to one correspondence between the nonrelativistic free case and the harmonic oscillator description the authors deduce the expected supersymmetries of the schrodinger equation the above structure appears as the largest spectrum generating superalgebra of the harmonic oscillator and its representation within an energy basis is given the physical three dimensional case is also considered when the maximal set of super symmetries is required and this case is compared with recent work

superalgebras and the supersymmetric harmonic oscillator the bound states of the d dimensional supersymmetric oscillator with a bosonic and fermionic component are shown to span an irreducible representation of osp 3 2d which contains the supersymmetric hamiltonian the representation branches in two infinite dimensional irreducible representations of osp 2 2d and osp 1 2d subalgebras the one dimensional case is used to exhibit s 2 subalgebras with representations both finite and infinite dimensional which are reducible but indecomposable the supersymmetry associated with the radial equation of the d dimensional oscillator is considered and states having a fixed angular momentum in each sector provide an irreducible representation space for an osp 2 2 superalgebra and osp 1 2 subalgebra

on schrodinger superalgebras using the supersymplectic framework of berezin kostant and others two types of supersymmetric extensions of the schrodinger algebra itself a conformal extension of the galilei algebra were constructed an i type extension exists in any space dimension and for any pair of integers n and n it yields an n n n superalgebra which generalizes the n 1 supersymmetry gauntlett et al found for a free spin 1 2 particle as well as the n 2 supersymmetry of the fermionic oscillator found by beckers et al in two space dimensions new exotic or ij type extensions arise for each pair of integers and yielding an n 2 superalgebra of the type discovered recently by leblanc et al in nonrelativistic chern simons theory for the magnetic monopole the symmetry reduces to o 3 osp 1 1 and for the magnetic vortex it reduces to o 2 osp 1 2

statistical behaviors for renormalization of correlated permeability field abstract in this article the statistical properties for the renormalized permeability obtained from the renormalization of the correlated permeability field are investigated in contrast to the uncorrelated porous media the scaling of the variance of the renormalized permeability field exhibits a crossover behavior when the correlation lengths are larger compared with the domain scale covered by the renormalization procedure the variance of the renormalized permeability will decrease slowly and the scaling exponent will be close to zero as the renormalization number increases the covered domain scale will eventually become larger than the correlation lengths and then the scaling property will transit to the uncorrelated case the convergent values of the renormalized permeability for isotropic and anisotropic correlated media are also investigated both the theoretical analysis and the simulation results show that larger correlation length in one direction will lead to a larger convergent value in the corresponding direction for the log normal permeability field numerical simulations show that the crossover scaling and also the convergent value for the renormalized permeability can be fitted very well by simple mathematical functions

finite mode analogs of 2d ideal hydrodynamics coadjoint orbits and local canonical structure abstract the algebraic finite mode hydrodynamic type systems that have o n integrals of motion for o n n modes and are intrinsically connected with two dimensional ideal fluid flows are studied special emphasis is given on the structure of their phase space and the problem of finding proper dynamical variables for its description in connection with appropriate problems for the original hydrodynamic equations various possibilities for embedding in the space of canonical variables are demonstrated on the simplest example of the su 3 model giving the finite dimensional analogs of clebsch variables

analysis of flow through heterogeneous random aquifers by the method of embedding matrix 1 steady flow the statistical structures of the hydraulic conductivity head gradient specific discharge and head fields are analyzed with the aid of a simplified model consisting of a collection of spherical in three dimensions and cylindrical in two dimensions blocks of different conductivity and diameter set at random and independently in space results of a previous work for the effective conductivity and unbounded formations dagan 1979 are recovered and given a rational derivation the influence of the aquifer boundary and nonuniform average flows are examined for the first time the growth of the head variance with distance from boundary in two dimensional flows is compared with that of the monte carlo simulations of smith and freeze 1979

hall littlewood symmetric functions and the bkp equation the connection between solutions of the bkp equation and hall littlewood symmetric functions is utilised in a unified approach to soliton and polynomial solutions this is analogous to the wronskian formulation of the solution of the kp equation as a by product two novel expressions for certain hall littlewood functions in terms of pfaffians are derived

parastatistics and the clifford algebra unitary group approach to the many electron correlation problem it is shown that the clifford algebra unitary group approach which is based on the subgroup chain u 2n so 2n 1 so 2n u n may be described in terms of the para fermi algebra applications to the development of efficient algorithms for the evaluation of matrix elements of u n generators and of their products are also briefly discussed

a fast algorithm for the estimation of the equivalent hydraulic conductivity of heterogeneous media fast upscaling of hydraulic conductivity is a recurrent problem in modeling flow through heterogeneous porous media we propose a new renormalization technique it is based on the iterative application of the cardwell and parsons 1945 bounds on elementary groups of cells the combination of the bounds with a heuristic formula allows anisotropy to be taken into account the new technique is tested and compared with other fast techniques among the tested techniques the two most reliable ones are the tensorial renormalization and the new simplified renormalization the numerical efficiency of the simplified renormalization leads us to recommend it when a diagonal tensor of equivalent conductivity is sufficient

stochastic models of subsurface flow infinite versus finite domains and stationarity stochastic solutions of the differential equation describing one dimensional flow through a porous medium with spatially variable hydraulic conductivity which is represented by a stationary statistically homogeneous random process are developed using several techniques the analytical approximations using first order analysis propagation of error covariance differential equations and variogram analysis all yield consistent results which demonstrate the important effects of boundary conditions and conditioning using the theory of intrinsic random functions stochastic solutions are developed for the case when the logarithm of the hydraulic conductivity is a three dimensional stationary random field in contrast to the one dimensional case it is found that the resulting three dimensional head perturbation will be locally stationary under very general conditions results from the one dimensional analytical solutions are found to be in agreement with previous monte carlo simulations for a flow system of finite length the solution based on linearization in the logarithm of hydraulic conductivity proved to be very robust showing reasonable agreement with monte carlo results even for the largest input standard deviation of lnk 4 6

perturbation schemes for flow in random media we utilize a many body style formalism to compute the long range effective diffusivity kappa e for dispersal of a passive scalar field in a random irrotational flow with molecular diffusivity by comparing the theoretical results with the outcome of computer simulations we show that a renormalization group approach that includes an appropriate vertex renormalization is superior to low order perturbation theory and to the hartree fock approximation and gives a rather accurate method of computing kappa e for a range of parameter values

invariant vector fields and the prolongation method for supersymmetric quantum systems the kinematical and dynamical symmetries of equations describing the time evolution of quantum systems such as the supersymmetric harmonic oscillator in one space dimension and the interaction of a non relativistic spin one half particle in a constant magnetic field are reviewed from the point of view of the vector field prolongation method generators of supersymmetries are then introduced so that we get lie superalgebras of symmetries and supersymmetries this approach does not require the introduction of grassmann valued differential equations but a specific matrix realization and the concept of dynamical symmetry the jaynes cummings model and supersymmetric generalizations are then studied we show how it is closely related to the preceding models lie algebras of symmetries and supersymmetries are also obtained

mathcal n 2 galilean superconformal algebras with a central extension supersymmetric extensions of galilean conformal algebra gca specified by spin l and dimension of space d are investigated duval and horvathy showed that the l 1 2 gca has two types of supersymmetric extensions called standard and exotic recently masterov introduced a centerless super gca for arbitrary l which corresponds to the standard extension we show that masterov s super gca has two types of central extensions depending on the parity of 2l we then introduced a novel super gca for arbitrary l corresponding to the exotic extension it is shown that the exotic superalgebra also has two types of central extensions depending on the parity of 2l furthermore we give a realization of the standard and exotic super gcas in terms of their subalgebras finally we present an supersymmetric extension of gca with central extensions

effective hydraulic conductivity of a randomly heterogeneous porous medium 1 the effective hydraulic conductivity of a randomly heterogeneous isotropic porous medium has been calculated by means of a new perturbative technique which differs greatly from that commonly used in the approach developed we construct the perturbation series for a seepage velocity and then utilize darcy s law for calculating pressure on the basis of the analysis of high order approximations it is shown that in the general case the effective conductivity in the large scale limit does depend on the form of the correlation function thus the widespread landau lifshitz matheron formula which operates on the conjecture that the first two terms of the perturbation series are those for the taylor series expansion of an exponential function proves to be invalid the calculations were carried out in a space of arbitrary dimension the dependence of the effective conductivity on the variance has been obtained up to the third order approximation inclusive in terms of a conductivity logarithm for convenience and simplification of series analysis the feynman diagrammatic technique was developed and utilized in a one dimensional 1d case our result in the large scale limit when a heterogeneity scale is small enough with respect to the characteristic scale of groundwater flow gives an exact formula for the effective conductivity

moment invariants for the vlasov equation moment invariants functions of the moments of a vlasov distribution that are invariant under sp 6 are classified using young diagrams the connection between the moment invariants and the poincare invariants is established an application using the moment invariants as phase space coordinates is considered for a matching section in a particle beam accelerator and a lie poisson numerical integration algorithm for the moment dynamics is proposed

on the harmonic oscillator and its invariance superalgebras the author determines the largest kinematical and dynamical invariance lie superalgebras characterizing n dimensonal harmonic oscillators when the spin orbit supersymmetrization procedure is under study these considerations essentially add new heisenberg superstructures in the case of an arbitrary even number of spatial dimensions

on unitary lie superalgebras from the spin orbit supersymmetrisation procedure from the basis elements of a clifford algebra cl n the authors generate a grading leading to a unitary lie superalgebra when n is even such a construction is motivated by the understanding of the specific properties of the fermionic variables in the so called spin orbit coupling procedure of supersymmetrisation in n 2 supersymmetric quantum mechanics the n odd case is also considered and some specific examples are discussed

renormalization group analysis of macrodispersion in a directed random flow we apply field theoretic methods to the calculation of the effective diffusivity macrodispersion coefficient in a random flow we show how this approach can be utilized to calculate a perturbation series for the effective diffusivity of conservative tracers in an incompressible velocity field with nonvanishing mean the first order i e one loop approximation of this series coincides with classical results derived by gelhar and axness and dagan a renormalization group rng approach is utilized and the results are compared to the classical first order perturbation theory for a moderate variability of the permeability the renormalized theory predicts only small corrections to the longitudinal dispersivity however the transverse dispersivity can be larger than that predicted by the first order perturbation theory by several orders of magnitude we compare these values to the outcome of monte carlo simulations and find that the rng predictions are in much better though not perfect accordance with the results of simulations moreover the results are in good quantitative agreement with reported observations from the borden site field experiment

super theta functions and the weil representation we show that the super theta function of levin 1987 is a matrix coefficient of the super heisenberg group

a search for shape invariant solvable potentials the author investigates a simple method of constructing potentials which is related to the work of bhattacharjie and sudarshan 1962 and for which the schrodinger equation can be solved in terms of known special functions it turns out that this method can be related to supersymmetric quantum mechanics and this relationship can help to decide which special functions satisfying linear homogeneous second order differential equations can be solutions of the schrodinger equation with potentials of the form v x w2 x w x the author illustrates this procedure with the example of orthogonal polynomials and obtains explicit expressions of wavefunctions of a wide class of shape invariant potentials

prediction of steady state flow in nonuniform geologic media by conditional moments exact nonlocal formalism effective conductivities and weak approximation we consider the effect of measuring randomly varying local hydraulic conductivities k x on one s ability to predict steady state flow within a bounded domain driven by random source and boundary functions more precisely we consider the prediction of local hydraulic head h x and darcy flux q x by means of their unbiased ensemble moments h x and q x conditioned on measurements of k x these predictors satisfy a deterministic flow equation in which q x x h x r x where x is a relatively smooth unbiased estimate of k x and r x is a residual flux we derive a compact integral expression for r x which is rigorously valid for a broad class of k x fields including fractals it demonstrates that q x is nonlocal and non darcian so that an effective hydraulic conductivity does not generally exist we show analytically that under uniform mean flow the effective conductivity may be a scalar a symmetric or a nonsymmetric tensor or a set of directional scalars which do not form a tensor we demonstrate numerically that in two dimensional mean radial flow it may increase from the harmonic mean of k x near interior and boundary sources to the geometric mean far from such sources for cases where r x can neither be expressed nor approximated by a local expression we propose a weak integral approximation closure which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of k x measurements increase the nonlocal deterministic flow equation can be solved numerically by standard methods our theory shows clearly how the scale of grid discretization should relate to the scale quantity and quality of available data after providing explicit approximations for the second moments of head and flux prediction errors we conclude by discussing practical methods to compute x from noisy measurements of k x and to calculate required second moments of the associated estimation errors when k x is lognormal

dynamics of free surfaces in random porous media we consider free surface flow in random porous media by treating hydraulic conductivity of a medium as a random field with known statistics we start by recasting the boundary value problem in the form of an integral equation where the parameters and domain of integration are random our analysis of this equation consists of expanding the random integrals in taylor s series about the mean position of the free boundary and taking the ensemble mean to quantify the uncertainty associated with such predictions we also develop a set of integro differential equations satisfied by the corresponding second ensemble moments the resulting moment equations require closure approximations to be workable we derive such closures by means of perturbation expansions in powers of the variance of the logarithm of hydraulic conductivity though this formally limits our solutions to mildly heterogeneous porous media our analytical solutions for one dimensional flows demonstrate that such perturbation expansions may remai

effective diffusivity in non isotropic gradient flows we study the effective diffusivity tensor for particles in a random gradient flow that statistically lacks rotational symmetry the effective diffusivity tensor is computed up to two loop order in perturbation theory and the ward identity that relates this tensor to the effective coupling is verified to the same order we re examine the renormalization group calculation that produced a very accurate numerical value for the effective diffusivity in the rotationally symmetric case and formulate two versions based on distinct divisions of the random potential field that gives rise to the flow both types of renormalization group calculation give good results when compared with numerical simulations however at two loop order in perturbation theory the two methods differ in detail from each other and from the exact perturbation calculation this is in contrast to the corresponding results in the isotropic case

first passage time in a two layer system as a first step in the first passage problem for passive tracer in stratified porous media we consider the case of a two dimensional system consisting of two layers with different convection velocities using a lattice generating function formalism and a variety of analytic and numerical techniques we calculate the asymptotic behavior of the first passage time probability distribution we show analytically that the asymptotic distribution is a simple exponential in time for any choice of the velocities the decay constant is given in terms of the largest eigenvalue of an operator related to a half space green s function for the anti symmetric case of opposite velocities in the layers we show that the decay constant for system lengthl crosses over froml 2 behavior in the diffusive limit tol 1 behavior in the convective regime where the crossover lengthl is given in terms of the velocities we also have formulated a general self consistency relation from which we have developed a recursive approach which is useful for studying the short time behavior

on chains of orthosymplectic lie superalgebras and the n dimensional quantum harmonic oscillator triplets of embedded orthosymplectic lie superalgebras are singled out and analyzed in terms of their respective even and odd root systems the corresponding chains of embeddings are considered for arbitrary integers m and n for both m n and m n it is shown that the second member inside each triplet is always in a one to one correspondence with the semidirect sum of the third member and the associated heisenberg superalgebra that is characterized by the same entries m and n for arbitrary m n invariance superalgebras of the n dimensional harmonic oscillator are recovered and their one to one correspondence associated with a recent character reversal phenomenon linking these invariance superstructures is rigorously explained specific and general cases as well as conclusions are presented

coherent states for the harmonic oscillator representations of the orthosymplectic supergroup osp 1 2n r coherent states for the harmonic oscillator representations of the noncompact supergroup osp 1 2n r are introduced and the invariant integration measure is calculated by studying transformation properties of supercoset variables the generalized bogoliubov transformation for mixed systems of bosons and fermions is also obtained an example for the simple harmonic oscillator is given

stochastic modeling of groundwater flow by unconditional and conditional probabilities 1 conditional simulation and the direct problem mathematical modeling of groundwater flow in heterogeneous porous formations of large extent is investigated the formation properties hydraulic conductivity transmissivity as well as flow variables head specific discharge solute concentration are regarded as random variables subjected to uncertainty the main aim of the study is to analyze the influence of conditional probability of input variables upon the statistical structure of the dependent variables the unconditional probability density functions are supposed to be stationary multivariate normal while conditioning accounts for the measured values at a few points of the formation two problems of groundwater flow are discussed in part 1 conditional simulation and the direct problem for steady flow analytical results are obtained by using perturbation approximations average uniform head gradient flows as well as recharge and flow to wells are discussed in unconditional modeling the input variable the conductivity or transmissivity log is regarded as stationary and is represented by its constant mean and variogram the ensemble of formations on which statistical calculations are carried out represents all aquifers with same probability density distributions in conditional modeling the measured values at a few points are kept fixed and uncertainty prevails only at other points consequently statistical computations are performed for the subensemble of aquifers which preserve the measured values and as a result both input and output variables are nonstationary the main effect of conditioning is to reduce the variance i e the uncertainty of these variables this effect is particularly important in the case of flow toward wells application of the modeling method to field problems is outlined

on k 3 4 coherent states for the harmonic oscillator a new construction of perelomov s generalised coherent states 1986 is considered for one dimensional harmonic oscillators admitting the heisenberg weyl group as invariance lie group exploiting the niederer maximal kinematical invariance group 1973 for such physical systems the author deduce further characteristics on the heisenberg states through the use of the fundamental perelomov state mod k k with k 3 4 the author explicitly gets new normalisation factor and measure for the heisenberg generalised coherent states the real lie algebras so 2 1 square operator h 2 so 2 1 and h 2 play a prominent role in this study

lie structures in parasupersymmetric quantum mechanics ii the spin orbit coupling supersymmetrization procedure the spin orbit coupling supersymmetrization procedure is considered in parasupersymmetric quantum mechanics describing oscillatorlike systems the superposition of bosonic and parafermionic degrees of freedom is mainly studied in the cases of two and three spatial dimensions but the n dimensional case is also determined new lie superalgebras and lie parasuperalgebras are pointed out they differ from those already obtained in connection with the standard procedure of supersymmetrization studied in part i of this series j beckers and n debergh j math phys 1991

evaluation of the path integral for flow through random porous media we present a path integral formulation of darcy s equation in one dimension with random permeability described by a correlated multivariate lognormal distribution this path integral is evaluated with the markov chain monte carlo method to obtain pressure distributions which are shown to agree with the solutions of the corresponding stochastic differential equation for dirichlet and neumann boundary conditions the extension of our approach to flow through random media in two and three dimensions is discussed

irreducible representations of the poincare parasuperalgebra we explicitly describe all the irreducible unitary representations of the poincare parasuperalgebra i e the parasupersymmetric extension of the lie algebra of the poincare group this parasuperalgebra includes as a particular case the usual poincare superalgebra and can serve as the group theoretical foundation of parasupersymmetric quantum field theory

so 4 reduction of the yang mills equations for the classical gauge groups we show that the reduction of the su n so n and sp n yang mills equations in compactified minkowski space by certain realizations of the so 4 subgroup of the conformal group leads to systems of ordinary differential equations the reduced systems are interpretable as hamiltonian systems with symmetry constrained so that the momentum map equals zero explicit solutions for these systems are given

finite and infinite dimensional representations of the orthosymplectic superalgebra osp 3 2 the shift operator technique is used to give a complete analysis of all finite and infinite dimensional irreducible representations of the orthosymplectic superalgebra osp 3 2 for all cases the star or grade star conditions for the algebra are investigated only two finite dimensional representations are grade star representations if the representation space is required to be a graded hilbert space when the even part is so 3 sp 2 r su 2 su 1 1 an infinite class of infinite dimensional star representations is found one of them can be realized in terms of two valued functions of a complex variable this representation reduces to the sum of two metaplectic representations of sp 2 we show that it is precisely this metaplectic representation for osp 3 2 which gives the spin energy eigenstates for the one dimensional harmonic oscillator with spin 1 2 states