simulation of three dimensional liquid sloshing flows using a strongly implicit calculation procedure a coupled strongly implicit solution strategy for unsteady three dimensional free surface flows has been developed based on an artificial compressibility formulation for the incompressible navier stokes equations a pseudotime term has been used in the continuity equation to permit time accurate calculations to be achieved the scheme appears capable of tracking the free surface reasonably accurately inside a partially filled spherical container undergoing a general rotating motion characteristic of that experienced by a spin stabilized satellite five different free surface calculations have been presented

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

deformations of algebras defined by tilting bundles abstract in this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles we do this in two settings first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal deformation of that scheme and then expanding this result to c equivariant deformations over schemes with a good c action in both these situations the endomorphism algebra of the lifted tilting bundle produces a deformation of the original endomorphism algebra and this is a graded deformation in the c equivariant case we apply our results to rational surface singularities generalising the deformed preprojective algebras of crawley boevey and holland and also to symplectic situations where the deformations produced are related to symplectic reflection algebras

boundary element analysis of nonlinear water wave problems a new boundary element technique based on green s formula is applied to the analysis of nonlinear water wave problems the problems are formulated mathematically as two dimensional nonlinear initial boundary value problems in terms of a velocity potential assuming the fluid to be inviscid and incompressible and the flow to be irrotational in the present paper two kinds of wave making problems are analysed 1 a tsunami generated by sea bed elevation 2 generation propagation and run up on a vertical wall of a solitary wave numerical results obtained by the present method are compared with available experimental data and analytical solutions excellent agreements are obtained

constraint qualifications in quasidifferentiable optimization the classical linearization procedure for differentiable nonlinear programming problems can be naturally generalized to the quasidifferentiable case as in the classical case one has to impose so called constraint qualifications on the constraint functions in order to ensure that optimality of a feasible point implies optimality of the nullvector for the corresponding quasilinearized problem we present various constraint qualifications in a unified setting propose a new one and investigate the relations between these conditions

stability analysis of a multibody system model for coupled slosh vehicle dynamics abstract the coupled slosh vehicle dynamics of a rigid body in planar atmospheric flight carrying a sloshing liquid is considered as a multibody system with the sloshing motion modelled as a simple pendulum the coupled non linear equations for the four degree of freedom multibody system are derived using the method of lagrangian dynamics careful non dimensionalization reveals two crucial parameters that determine the extent of coupling between the rigid body and slosh modes and also two important frequency parameters using a two parameter continuation method critical combinations of these four parameters for which the coupled slosh vehicle dynamics can become unstable are computed results are displayed in the form of neutral stability curves stability boundaries in parameter space and an analytical expression incorporating the four parameters that represents the neutral stability curves is obtained reduced order linearized models and key transfer functions are derived in an effort to understand the instability phenomenon physically the sloshing motion is seen to induce a static instability sometimes called tumbling in the vehicle pitch dynamics depending on the slosh mass fraction and the location of the slosh pendulum hinge point above the rigid vehicle center of mass

superpotentials calabi yau algebras and pbw deformations abstract the paper 9 by bocklandt schedler and wemyss considers path algebras with relations given by the higher derivations of a superpotential giving a condition for such an algebra to be calabi yau in particular they show that the algebra c v g for v a finite dimensional c vector space and g a finite subgroup of gl v is morita equivalent to a path algebra with relations given by a superpotential and is calabi yau for g sl v in this paper we extend these results giving a condition for a pbw deformation of a calabi yau koszul path algebra with relations given by a superpotential to have relations given by a superpotential and proving these are calabi yau in certain cases we apply our methods to symplectic reflection algebras where we show that every symplectic reflection algebra is morita equivalent to a path algebra whose relations are given by the higher derivations of an inhomogeneous superpotential in particular we show these are calabi yau regardless of the deformation parameter also for g a finite subgroup of gl 2 c not contained in sl 2 c we consider pbw deformations of a path algebra with relations which is morita equivalent to c x y g we show there are no non trivial pbw deformations when g is a small subgroup

higher symplectic reflection algebras and non homogeneous n koszul property abstract we study a class of associative algebras associated to finite groups acting on a vector space these algebras are non homogeneous n koszul algebra generalizations of symplectic reflection algebras p etingof v ginzburg symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism invent math 147 2002 243 348 the koszul property was generalized to homogeneous algebras of degree n 2 in r berger koszulity for nonquadratic algebras j algebra 239 2001 705 734 in the present paper the extension of the koszul property to non homogeneous algebras is realized through a pbw theorem this pbw theorem is the generalization to the n case of a quadratic result obtained by braverman and gaitsgory a braverman d gaitsgory poincare birkhoff witt theorem for quadratic algebras of koszul type j algebra 181 1996 315 328 see also a polishchuk l positselski quadratic algebras univ lecture ser vol 37 amer math soc providence ri 2005 we work in the general setting where the ground ring is an arbitrary von neumann regular ring

upwind differencing scheme for the time accurate incompressible navier stokes equations the two dimensional incompressible navier stokes equations are solved in a time accurate manner using the method of pseudocompres sibility using this method subiterations in pseudotime are required to satisfy the continuity equation at each time step an upwind differencing scheme based on flux difference splitting is used to compute the convective terms the upwind differencing is biased based on the sign of the local eigenvalue of the jacobian matrix of the convective fluxes both third order and fifth order differencing schemes are used on the convective fluxes throughout the grid s interior the equations are solved using an implicit line relaxation scheme this solution scheme is stable and is capable of running at large time steps in pseudo time leading to fast convergence for each physical time step a variety of computed results are presented to validate the present scheme results for the flow over an oscillating plate are compared with the exact analytic solution and good agreement is seen excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure flow solutions over a circular cylinder with vortex shedding are also presented finally the flow past an airfoil at 90 angle of attack is computed

closed form modeling of fluid structure interaction with nonlinear sloshing potential flow closed form modeling of the dynamics of a structure coupled to a rigid container carrying a fluid with a free surface is addressed the coupling of the fluid s equations of motion with the structure s equations of motion is accomplished by building a boundary value problem for the instantaneous interaction pressure all nonlinearities are taken into account and large displacement nonlinear sloshing effects are considered no simplifications are made in field equations and boundary conditions this is a complementary study to a previous work presented by the authors the boundary conditions for the interaction pressure when the container has curved walls are developed the fluid is modeled as potential flow with modified rayleigh damping the end result of the analysis is a set of first order differential equations for the motion of both the structure and the fluid numerical examples with circular containers are presented

reduction of quasidifferentials and minimal representations some criterias for the non minimality of pairs of compact convex sets of a real locally convex topological vector space are proved based on a reduction technique via cutting planes and excision of compact convex subsets following an example of j grzybowski we construct a class of equivalent minimal pairs of compact convex sets which are not connected by translations

on shapiro s results in quasidifferential calculus several necessary minimum conditions for quasidifferentiable programming problems are discussed some statements of shapiro 1986 are shown to be incorrect

directional derivative estimates for the optimal value function of a quasidifferentiable programming problem this paper is concerned with the optimal value function arising in the primal decomposition of a quasidifferentiable programming problem in particular estimates for the upper dini directional derivative of this function are derived they involve certain lagrange multipliers occurring in the necessary minimum conditions to the lower level problems this study generalizes some previously published results on this subject

koszulity for nonquadratic algebras abstract it is known that a koszul algebra is defined as being a quadratic algebra with a pure resolution of the ground field in this paper we extend koszulity to algebras whose relations are homogeneous of degree s 2 a cubic artin schelter regular algebra has motivated our work generalized koszulity is connected to lattice distributivity and to confluence a generalized symmetric algebra is proved to be generalized koszul and the bimodule version of the generalized koszul resolution is used for investigating its hochschild homology

generalized coordinate forms of governing fluid equations and associated geometrically induced errors the governing equations of fluid flow may be cast into various forms upon application of a generalized coordinate mapping these forms are the nonconservation law form nclf and strong weak and chain rule conservation law forms sclf wclf crclf respectively this paper describes the geometrically induced errors resulting from the failure to satisfy a certain consistency condition for each of these four forms and also demonstrates the ability of the crclf to produce exactly the same numerical solution as the wclf provided a condition is met on where to evaluate the transformation metrics it is also demonstrated that considerably fewer arithmetic operations are required to advance the solution from n to n 1 when the crclf is used in com parison to both the sclf and wclf he effort devoted to the field of computational fluid dynamics is progressing at an ever increasing rate at certain points in time during this natural evolution of numerical methods schemes and ideas it is sometimes in structive to pause to reflect upon past work in an attempt to gain the proper perspective it is important that this reflection reaches all of the way to the fundamental rules and practices used to develop numerical techniques some of these practices are often taken for granted much too soon after their in troduction into the literature only through a global view of this past effort can subtle mutually experienced problem areas and possible causes be identified the present work deals with the numerical solution to the transformed fluid flow equations i e euler equations etc using the finite difference approach the transformed equations are obtained through application of a generalized mapping from physical coordinates to computational coordinates at the time of application of the mapping to the original equations and prior to choosing the numerical in tegration scheme the analyst must decide in which form the equations should be written the choices are the non conservation law form nclf strong conservation law form sclf weak conservation law form wclf and chain rule conservation law form crclf this decision is one of the fundamental practices alluded to in the previous paragraph the present work illustrates how such a fundamental decision can strongly influence both the amount of analysis required to develop a consistent algorithm and the number of arithmetic operations required to execute the algorithm in addition it is shown that large solution errors and in some cases instabilities can result from failure to implement the results of such an analysis

poincare birkhoff witt theorem for quadratic algebras of koszul type abstract in this paper we prove a general poincare birkhoff witt theorem for quadratic koszul algebras the result is similar to that obtained by polischuk and positselsky but the proof is entirely different and uses algebraic deformation theory in particular we obtain a new proof of the classical pbw theorem for lie algebras based on deformation theory

primitive variable strongly implicit calculation procedure for viscous flows at all speeds a coupled solution procedure is described for solving the compressible form of the time dependent twodimensional navier stokes equations in body fitted curvilinear coordinates this approach employs the strong conservation form of the governing equations but uses primitive variables m v p t rather than the more traditional conservative variables p pw pv et as unknowns a coupled modified strongly implicit procedure cmsip is used to efficiently solve the newton linearized algebraic equations it appears that this procedure is effective for mach numbers ranging from the incompressible limit mx 0 01 to supersonic generally smoothing was not needed to control spatial oscillations in pressure for subsonic flows despite the use of central differences dual time stepping was found to further accelerate convergence for steady flows sample calculations including steady and unsteady low mach number internal and external flows and a steady shock boundarylayer interaction flow illustrate the capability of the present solution algorithm