the reduction of binary fuzzy relations and its applications this paper introduces the concept of t reduction of binary fuzzy relations and establishes its properties it presents an approach to providing the one valued restoration of any boundary transitive and t asymmetric binary fuzzy relation by its t reduction a theoretical basis for this approach is established showing that t reduction is the smallest fuzzy relation whose t transitive closure coincides with the given binary fuzzy relation and where an nxn fuzzy relation on a finite universe with cardinality n can be represented by n 1 values this approach opens up an original way for constructing the membership functions of certain binary fuzzy relations important examples for the application of this concept are given

modified signed log likelihood ratio summary the signed log likelihood ratio r for a one dimensional interest parameter can be modified as r r r log u r so that r is asymptotically standard normally distributed with error of order o n 3 2 u being interpretable as a test statistic a new more direct derivation of this result is given which leads to a more explicit expression for u and provides a better handle on the error term the relation of the tail area approximation determined by r to a generalization of the lugannani rice approximation is discussed and the applicability of r to the analysis of residual variation is indicated

a stable fsi algorithm for light rigid bodies in compressible flow abstract in this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid structure interactions of light rigid bodies and inviscid compressible flow the new algorithm is stable even for bodies with zero mass and zero moments of inertia the approach is based on a local characteristic projection of the force on the rigid body and is a natural extension of the recently developed algorithm for coupling compressible flow and deformable bodies 1 2 3 the new algorithm advances the solution in the fluid domain with a standard upwind scheme and explicit time stepping the newton euler system of ordinary differential equations governing the motion of the rigid body is augmented by added mass correction terms this system which is very stiff for light bodies is solved with an a stable diagonally implicit runge kutta scheme the implicit system there is one independent system for each body consists of only 3 d d 2 scalar unknowns in d 2 or d 3 space dimensions and is fast to solve the overall cost of the scheme is thus dominated by the cost of the explicit fluid solver normal mode analysis is used to prove the stability of the approximation for a one dimensional model problem and numerical computations confirm these results in multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body these tensors which depend on certain surface integrals of the fluid impedance couple the translational and angular velocities of the body numerical results in two space dimensions based on the use of moving overlapping grids and adaptive mesh refinement demonstrate the behavior and efficacy of the new scheme these results include the simulation of the difficult problems of shock impingement on an ellipse and a more complex body with appendages both with zero mass

partial ordering in l underdeterminate sets abstract the purpose of this paper is to improve results on fuzzy partial orderings obtained by zadeh in 9 we overcome the difficulties connected with the axioms of antisymmetry and linearity moreover if the underlying lattice l is a complete residuated lattice we establish a szpilrajn theorem i e any l fuzzy partial ordering has a linear extension in opposition to zadeh s our point of view is that an axiom of antisymmetry without a reference to a concept of equality is meaningless therefore we first introduce the category lus cf 2 which can be considered as a mathematical model of fuzzy equality and subsequently we specify the axioms of l fuzzy partial orderings with respect to the frame given by lus the axioms we use clearly display the usefulness of having a zadeh like complementation and as a consequence the usefulness of a positivistic and nonintuitionistic frame of study an example concerning l rn which we give clearly shows that the lus version of the szpilrajn theorem cannot be reduced to a fuzzification of an already existing theorem but provides us with additional information

transitivity bounds in additive fuzzy preference structures transitivity plays a crucial role in preference modeling and related fields in this paper we discuss this property in the general context of additive fuzzy preference structures of particular interest is the decomposition of a large preference relation r in its symmetric part i indifference relation and its asymmetric part p strict preference relation by means of a so called indifference generator i given the type of transitivity of a large preference relation r w r t a conjunctor and a generator we establish basic lower bounds and general upper bounds on the transitivity of p and i these bounds are due to the careful design of generic counterexamples moreover we identify the situations in which these bounds are effectively reached thereby establishing connections with interesting properties such as dominance bisymmetry the 1 lipschitz property and rotation invariance

fuzzy sets and vague environments abstract in this paper we propose a natural approach to handle imprecise numbers as they arise for example from measurements fuzzy sets turn out to be a canonical representation for such imprecise numbers that are induced by taking different tolerance or error bounds into account fuzzy sets are induced by scaling factors that describe the magnitude of the imprecision on the other the scaling factors can be derived from given fuzzy sets so that we have a correspondence between scaling factors and fuzzy sets when these concepts are applied to control problems the max min rule is rediscovered as an interpolation technique viewing fuzzy control as an interpolation technique in vague environments enables us to validate various concepts for the design and tuning of fuzzy controllers and also suggests new methods based on clear semantics

numerical simulation of coupled fluid solid problems abstract a multi grid finite volume method is presented for the prediction of coupled fluid solid problems in complex geometries whereby a unified finite volume approach based on the concept of block structured grids is employed for the handling of the complexity of the geometry and the fluid solid coupling a high numerical efficiency is obtained with a non linear multi grid method using a pressure correction based scheme as a smoother a number of numerical experiments were used to verify the accuracy and numerical efficiency of the method additionally to illustrate the capabilities of the approach results for two practical applications are presented

space time finite element techniques for computation of fluid structure interactions we describe the space time finite element techniques we developed for computation of fluid structure interaction fsi problems among these techniques are the deforming spatial domain stabilized space time dsd sst formulation and its special version and the mesh update methods including the solid extension mesh moving technique semmt also among these techniques are the block iterative quasi direct and direct coupling methods for the solution of the fully discretized coupled fluid and structural mechanics equations we present some test computations for the mesh moving techniques described we also present numerical examples where the fluid is governed by the navier stokes equations of incompressible flows and the structure is governed by the membrane and cable equations overall we demonstrate that the techniques we have developed have increased the scope and accuracy of the methods used in computation of fsi problems 2005 elsevier b v all rights reserved

parallel computation of three dimensional flows using overlapping grids with adaptive mesh refinement this paper describes an approach for the numerical solution of time dependent partial differential equations in complex three dimensional domains the domains are represented by overlapping structured grids and block structured adaptive mesh refinement amr is employed to locally increase the grid resolution in addition the numerical method is implemented on parallel distributed memory computers using a domain decomposition approach the implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors a modified bin packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors all components of the amr algorithm such as error estimation regridding and interpolation are performed in parallel the parallel time stepping algorithm is illustrated for initial boundary value problems involving a linear advection diffusion equation and the nonlinear reactive euler equations numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach exact solutions of the advection diffusion equation are constructed and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids different numbers of refinement levels and refinement ratios and different numbers of processors the problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the euler equations and a problem involving the initiation of a detonation from a hot spot in a t shaped pipe is considered to demonstrate the numerical approach for the reactive case for both problems the accuracy of the numerical solutions is assessed quantitatively through an estimation of the errors from a grid convergence study the parallel performance of the approach is examined for the shock diffraction problem

curvilinear immersed boundary method for simulating fluid structure interaction with complex 3d rigid bodies the sharp interface curvib approach of ge and sotiropoulos l ge f sotiropoulos a numerical method for solving the 3d unsteady incompressible navier stokes equations in curvilinear domains with complex immersed boundaries journal of computational physics 225 2007 1782 1809 is extended to simulate fluid structure interaction fsi problems involving complex 3d rigid bodies undergoing large structural displacements the fsi solver adopts the partitioned fsi solution approach and both loose and strong coupling strategies are implemented the interfaces between immersed bodies and the fluid are discretized with a lagrangian grid and tracked with an explicit front tracking approach an efficient ray tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies numerical experiments are carried out for two fsi problems vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions for both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements the numerical experiments suggest that both the properties of the structure mass geometry and the local flow conditions can play an important role in determining the stability of the fsi algorithm under certain conditions the fsi algorithm is unconditionally unstable even when strong coupling fsi is employed for such cases however combining the strong coupling iteration with under relaxation in conjunction with the aitken s acceleration technique is shown to effectively resolve the stability problems a theoretical analysis is presented to explain the findings of the numerical experiments it is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the fsi algorithm the stabilizing role of under relaxation is also clarified and the upper bound of the under relaxation coefficient required for stability is derived

a stable partitioned fsi algorithm for incompressible flow and deforming beams an added mass partitioned amp algorithm is described for solving fluid structure interaction fsi problems coupling incompressible flows with thin elastic structures undergoing finite deformations the new amp scheme is fully second order accurate and stable without sub time step iterations even for very light structures when added mass effects are strong the fluid governed by the incompressible navier stokes equations is solved in velocity pressure form using a fractional step method large deformations are treated with a mixed eulerian lagrangian approach on deforming composite grids the motion of the thin structure is governed by a generalized euler bernoulli beam model and these equations are solved in a lagrangian frame using two approaches one based on finite differences and the other on finite elements the key amp interface condition is a generalized robin mixed condition on the fluid pressure this condition which is derived at a continuous level has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers special treatment of the amp condition is required to couple the finite element beam solver with the finite difference based fluid solver and two coupling approaches are described a normal mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains and it is shown that the amp scheme is stable independent of the ratio of the mass of the fluid to that of the structure a traditional partitioned tp scheme using a dirichlet neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large a series of benchmark problems of increasing complexity are considered to illustrate the behavior of the amp algorithm and to compare the behavior with that of the tp scheme the results of all these benchmark problems verify the stability and accuracy of the amp scheme results for one benchmark problem modeling blood flow in a deforming artery are also compared with corresponding results available in the literature

on the compositional characterization of complete fuzzy pre orders complete pre orders can be characterized in terms of the transitivity of the corresponding strict preference and indifference relations in this paper we investigate this characterization in a fuzzy setting we consider two types of completeness weak completeness and strong completeness and decompose a fuzzy pre order by means of an indifference generator in particular a frank t norm in the weakly complete case we identify the strongest type of transitivity of the indifference and strict preference relations in function of the generator used for constructing them in the strongly complete case we lay bare a stronger type of transitivity of the strict preference relation we conclude the paper with a rather negative result there is no hope to obtain a compositional characterization of weakly complete fuzzy pre orders and hence also not of fuzzy pre orders in general

a compendium of fuzzy weak orders representations and constructions the present paper gives a state of the art overview of representation and construction results for fuzzy weak orders we do not assume that the underlying domain is finite instead we concentrate on results that hold in the most general case that the underlying domain is possibly infinite this paper presents three fundamental representation results each of which also provides a construction method i score function based representations ii inclusion based representations iii representations by decomposition into crisp linear orders and fuzzy equivalence relations which also facilitates a pseudo metric based construction

a stable and accurate partitioned algorithm for conjugate heat transfer abstract we describe a new partitioned approach for solving conjugate heat transfer cht problems where the governing temperature equations in different material domains are time stepped in an implicit manner but where the interface coupling is explicit the new approach called the champ scheme conjugate heat transfer advanced multi domain partitioned is based on a discretization of the interface coupling conditions using a generalized robin mixed condition the weights in the robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme the interface treatment combines ideas from optimized schwarz methods for domain decomposition problems together with the interface jump conditions and additional compatibility jump conditions derived from the governing equations for many problems i e for a wide range of material properties grid spacings and time steps the champ algorithm is stable and second order accurate using no sub time step iterations i e a single implicit solve of the temperature equation in each domain in extreme cases e g very fine grids with very large time steps it may be necessary to perform one or more sub iterations each sub iteration generally increases the range of stability substantially and thus one sub iteration is likely sufficient for the vast majority of practical problems the champ algorithm is developed first for a model problem and analyzed using normal mode theory the theory provides a mechanism for choosing optimal parameters in the mixed interface condition a comparison is made to the classical dirichlet neumann dn method and where applicable to the optimized schwarz os domain decomposition method for problems with different thermal conductivities and diffusivities the champ algorithm outperforms the dn scheme for domain decomposition problems with uniform conductivities and diffusivities the champ algorithm performs better than the typical os scheme with one grid cell overlap the champ scheme is also developed for general curvilinear grids and cht examples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach

saddlepoint approximations to the cdf of some statistics with nonnormal limit distributions abstract in standard saddlepoint approximations to the cumulative distribution function of a random variable the normal distribution has appeared to play a special role in this article we consider what happens when the normal base distribution is replaced by an arbitrary base distribution generalized versions of several standard formulas are presented the choice of a chi squared base or an inverse gaussian base is then considered in detail the generalized approximations are compared in two examples a linear combination of chi squared variables and the first passage time distribution for a random walk the former example considers approximations using the chi squared base that are slightly more accurate than their normal based counterparts in the latter example approximations based on the inverse gaussian are considerably more accurate than their normal based counterparts

galerkin differences for acoustic and elastic wave equations in two space dimensions abstract the galerkin difference method a finite element method built using standard galerkin projection techniques but employing nonstandard basis functions was originally developed for one space dimension in 1 here the method is extended to two space dimensions using a tensor product construction theoretical and computational evidence shows the method behaves as expected for the acoustic wave equation for the elastic wave equation the approximations are found to be at least as accurate as predicted but with a free surface the scheme may exhibit an unexpected superconvergence extension to curvilinear mapped grids is also considered for acoustics in all cases the use of a tensor product construction allows for efficient solution of the linear system involving the mass matrix which implies optimal linear time solutions with respect to the number of degrees of freedom

on the structure of f indistinguishability operators abstract some properties concerning the structure of f indistinguishability operators are analyzed it is shown that any of such operators is generated by a family of fuzzy subsets this result since it gives the way to construct f indistinguishabilities facilitates new applications of fuzzy relations the links between f indistinguishability operators and a kind of generalized metrics in the unit interval which are also explored are used to define the canonical generators of an f indistinguishability operator that is the fuzzy partition associated with the operator

moving overlapping grids with adaptive mesh refinement for high speed reactive and non reactive flow we consider the solution of the reactive and non reactive euler equations on two dimensional domains that evolve in time the domains are discretized using moving overlapping grids in a typical grid construction boundary fitted grids are used to represent moving boundaries and these grids overlap with stationary background cartesian grids block structured adaptive mesh refinement amr is used to resolve fine scale features in the flow such as shocks and detonations refinement grids are added to base level grids according to an estimate of the error and these refinement grids move with their corresponding base level grids the numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from fixed parameter space to moving physical space the mapped equations are solved numerically using a second order extension of godunov s method the stiff source term in the reactive case is handled using a runge kutta error control scheme we consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid in the latter case the newton euler equations describe the motion of the center of mass of the each body and the rotation about it and these equations are integrated numerically using a second order predictor corrector scheme numerical boundary conditions at slip walls are described and numerical results are presented for both reactive and non reactive flows that demonstrate the use and accuracy of the numerical approach

a cut cell finite volume finite element coupling approach for fluid structure interaction in compressible flow we present a loosely coupled approach for the solution of fluid structure interaction problems between a compressible flow and a deformable structure the method is based on staggered dirichlet neumann partitioning the interface motion in the eulerian frame is accounted for by a conservative cut cell immersed boundary method the present approach enables sub cell resolution by considering individual cut elements within a single fluid cell which guarantees an accurate representation of the time varying solid interface the cut cell procedure inevitably leads to non matching interfaces demanding for a special treatment a mortar method is chosen in order to obtain a conservative and consistent load transfer we validate our method by investigating two dimensional test cases comprising a shock loaded rigid cylinder and a deformable panel moreover the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset finally we propose a three dimensional fluid structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations

a stable partitioned fsi algorithm for rigid bodies and incompressible flow part ii general formulation abstract a stable partitioned algorithm is developed for fluid structure interaction fsi problems involving viscous incompressible flow and rigid bodies this added mass partitioned amp algorithm remains stable without sub iterations for light and even zero mass rigid bodies when added mass and viscous added damping effects are large the scheme is based on a generalized robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body added mass effects are handled in the robin condition by inclusion of a boundary integral term that depends on the pressure added damping effects due to the viscous shear forces on the body are treated by inclusion of added damping tensors that are derived through a linearization of the integrals defining the force and torque added damping effects may be important at low reynolds number or for example in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small in this second part of a two part series the general formulation of the amp scheme is presented including the form of the amp interface conditions and added damping tensors for general geometries a fully second order accurate implementation of the amp scheme is developed in two dimensions based on a fractional step method for the incompressible navier stokes equations using finite difference methods and overlapping grids to handle the moving geometry the numerical scheme is verified on a number of difficult benchmark problems

a level set approach to eulerian lagrangian coupling we present a numerical method for coupling an eulerian compressible flow solver with a lagrangian solver for fast transient problems involving fluid solid interactions such coupling needs arise when either specific solution methods or accuracy considerations necessitate that different and disjoint subdomains be treated with different eulerian or lagrangian schemes the algorithm we propose employs standard integration of the eulerian solution over a cartesian mesh to treat the irregular boundary cells that are generated by an arbitrary boundary on a structured grid the eulerian computational domain is augmented by a thin layer of cartesian ghost cells boundary conditions at these cells are established by enforcing conservation of mass and continuity of the stress tensor in the direction normal to the boundary the description and the kinematic constraints of the eulerian boundary rely on the unstructured lagrangian mesh the lagrangian mesh evolves concurrently driven by the traction boundary conditions imposed by the eulerian counterpart several numerical tests designed to measure the rate of convergence and accuracy of the coupling algorithm are presented as well general problems in one and two dimensions are considered including a test consisting of an isotropic elastic solid and a compressible fluid in a fully coupled setting where the exact solution is available

maxima and minima in fuzzified linear orderings the paper studies the notions of fuzzy maxima minima suprema and infima in the setting of fuzzified linear orderings the main result shows that in fuzzified linear orders satisfying certain reasonable assumptions the fuzzy maxima and minima of all non empty fuzzy sets are non empty

representations and constructions of similarity based fuzzy orderings this contribution advocates the dissemination of similarity based fuzzy orderings a generalized concept of fuzzy orderings which appears to be unavoidable as soon as the classical correspondences between preorderings equivalence relations and orderings are taken into account in contrast to earlier papers on the topic this paper is focused on representation and construction results which once more demonstrate the feasibility of the proposed concept

conditional extensions of fuzzy preorders abstract the problem of embedding incomplete into complete relations has been an important topic of research in the context of crisp relations and their applications several variations of the acclaimed szpilrajn s theorem have been provided inclusive of the case when some order conditions between elements are imposed on the extension we extend the analysis of that topic by alcantud to the fuzzy case by appealing to generators to decompose fuzzy preference relations into strict preference and indifference relations we give general extension results for the corresponding concept of compatible extension of a fuzzy reflexive relation then we investigate the conditions under which compatible order extensions exist such that certain elements are connected by the asymmetric part resp and certain other elements by the symmetric part to respective elements with degree 1

a plea for the use of lukasiewicz triplets in the definition of fuzzy preference structures ii the identity case abstract it has been shown in the first part of this paper that the concept of a fuzzy preference structure is only meaningful provided that the de morgan triplet involved contains a continuous archimedean triangular norm having zero divisors or hence a transform of the ukasiewicz triangular norm in this second part additional arguments for this statement are supplied in what we call the identity case is the identity mapping and the involutive negator is the standard negator first it is shown that the use of a continuous non archimedean triangular norm having zero divisors in the definition of a fuzzy preference structure indeed is possible secondly using such a triangular norm implies that at least in the square 0 4 5 2 it actually behaves as the ukasiewicz triangular norm furthermore an important transformation theorem indicates that any fuzzy preference structure with respect to a de morgan triplet containing such a continuous non archimedean triangular norm having zero divisors can be transformed into a fuzzy preference structure with respect to the standard ukasiewicz triplet these additional arguments conclude in a convincing way our plea for the use of ukasiewicz triplets in the definition of fuzzy preference structures

fuzzy preference structures without incomparability abstract in this paper we establish important relationships between the basic properties of the components of a fuzzy preference structure without incomparability this study is carried out for the fuzzy preference structures introduced recently by de baets van de walle and kerre a set of remarkable theorems gives detailed insight in the relationships between the sup t transitivity of the fuzzy preference and indifference relations and the sup t transitivity of the fuzzy large preference relation several paths of thought involving t norms with or without zero divisors are explored and where required illustrative counterexamples confirm the falsity of certain implications finally we introduce the t n ferrers property of a binary fuzzy relation and show that the fuzzy preference and fuzzy large preference relations share certain types of this ferrers property

a stable partitioned fsi algorithm for rigid bodies and incompressible flow part i model problem analysis a stable partitioned algorithm is developed for fluid structure interaction fsi problems involving viscous incompressible flow and rigid bodies this added mass partitioned amp algorithm remains stable without sub iterations for light and even zero mass rigid bodies when added mass and viscous added damping effects are large the scheme is based on a generalized robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body added mass effects are handled in the robin condition by inclusion of a boundary integral term that depends on the pressure added damping effects due to the viscous shear forces on the body are treated by inclusion of added damping tensors that are derived through a linearization of the integrals defining the force and torque added damping effects may be important at low reynolds number or for example in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small in this first part of a two part series the properties of the amp scheme are motivated and evaluated through the development and analysis of some model problems the analysis shows when and why the traditional partitioned scheme becomes unstable due to either added mass or added damping effects the analysis also identifies the proper form of the added damping which depends on the discrete time step and the grid spacing normal to the rigid body the results of the analysis are confirmed with numerical simulations that also demonstrate a second order accurate implementation of the amp scheme

a formal study of linearity axioms for fuzzy orderings abstract this contribution is concerned with a detailed investigation of linearity axioms for fuzzy orderings different existing concepts are evaluated with respect to three fundamental correspondences from the classical case linearizability of partial orderings intersection representation and one to one correspondence between linearity and maximality as a main result we obtain that it is virtually impossible to simultaneously preserve all these three properties in the fuzzy case if we do not require a one to one correspondence between linearity and maximality however we obtain that an implication based definition appears to constitute a sound compromise in particular if ukasiewicz type logics are considered

deforming composite grids for solving fluid structure problems we describe a mixed eulerian lagrangian approach for solving fluid structure interaction fsi problems the technique which uses deforming composite grids dcg is applied to fsi problems that couple high speed compressible flow with elastic solids the fluid and solid domains are discretized with composite overlapping grids curvilinear grids are aligned with each interface and these grids deform as the interface evolves the majority of grid points in the fluid domain generally belong to background cartesian grids which do not move during a simulation the fsi dcg approach allows large displacements of the interfaces while retaining high quality grids efficiency is obtained through the use of structured grids and cartesian grids the governing equations in the fluid and solid domains are evolved in a partitioned approach we solve the compressible euler equations in the fluid domains using a high order godunov finite volume scheme we solve the linear elastodynamic equations in the solid domains using a second order upwind scheme we develop interface approximations based on the solution of a fluid solid riemann problem that results in a stable scheme even for the difficult case of light solids coupled to heavy fluids the fsi dcg approach is verified for three problems with known solutions an elastic piston problem the superseismic shock problem and a deforming diffuser in addition a self convergence study is performed for an elastic shock hitting a fluid filled cavity the overall fsi dcg scheme is shown to be second order accurate in the max norm for smooth solutions and robust and stable for problems with discontinuous solutions for a wide range of constitutive parameters

explicit synchronous partitioned algorithms for interface problems based on lagrange multipliers abstract traditional explicit partitioned schemes exchange boundary conditions between subdomains and can be related to iterative solution methods for the coupled problem as a result these schemes may require multiple subdomain solves acceleration techniques or optimized transmission conditions to achieve sufficient accuracy and or stability we present a new synchronous partitioned method derived from a well posed mixed finite element formulation of the coupled problem we transform the resulting differential algebraic equation dae to a hessenberg index 1 form in which the algebraic equation defines the lagrange multiplier as an implicit function of the states using this fact we eliminate the multiplier and reduce the dae to a system of explicit odes for the states explicit time integration both discretizes this system in time and decouples its equations as a result the temporal accuracy and stability of our formulation are governed solely by the accuracy and stability of the explicit scheme employed and are not subject to additional stability considerations as in traditional partitioned schemes we establish sufficient conditions for the formulation to be well posed and prove that classical mortar finite elements on the interface are a stable choice for the lagrange multiplier we show that in this case the condition number of the schur complement involved in the elimination of the multiplier is bounded by a constant the paper concludes with numerical examples illustrating the approach for two different interface problems

an added mass partition algorithm for fluid structure interactions of compressible fluids and nonlinear solids we describe an added mass partitioned amp algorithm for solving fluid structure interaction fsi problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements the computational approach is a mixed eulerian lagrangian scheme that makes use of deforming composite grids dcg to treat large changes in the geometry in an accurate flexible and robust manner the current work extends the amp algorithm developed in banks et al 1 for linearly elasticity to the case of nonlinear solids to ensure stability for the case of light solids the new amp algorithm embeds an approximate solution of a nonlinear fluid solid riemann fsr problem into the interface treatment the solution to the fsr problem is derived and shown to be of a similar form to that derived for linear solids the state on the interface being fundamentally an impedance weighted average of the fluid and solid states numerical simulations demonstrate that the amp algorithm is stable even for light solids when added mass effects are large the accuracy and stability of the amp scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi analytical solution that is obtained for a rotating solid disk immersed in a fluid the scheme is applied to the simulation of a planar shock impacting a light elliptical shaped solid and comparisons are made between solutions of the fsi problem for a neo hookean solid a linearly elastic solid and a rigid solid the ability of the approach to handle large deformations is demonstrated for a problem of a high speed flow past a light thin and flexible solid beam

incremental approach for radial basis functions mesh deformation with greedy algorithm mesh deformation is an important element of any fluidstructure interaction simulation in this article a new methodology is presented for the deformation of volume meshes using incremental radial basis function rbf based interpolation a greedy algorithm is used to select a small subset of the surface nodes iteratively two incremental approaches are introduced to solve the rbf system of equations 1 block matrix inversion based approach and 2 modified lu decomposition approach the use of incremental approach decreased the computational complexity of solving the system of equations within each greedy algorithm s iteration from o n3 to o n2 results are presented from an accuracy study using specified deformations on a 2d surface mesh deformations for bending and twisting of a 3d rectangular supercritical wing have been demonstrated outcomes showed the incremental approaches reduce the cpu time up to 67 as compared to a traditional rbf matrix solver finally the proposed mesh deformation approach was integrated within a fluidstructure interaction solver for investigating a flow induced cantilever beam vibration

reduction of fuzzy automata by means of fuzzy quasi orders abstract in our recent paper we have established close relationships between state reduction of a fuzzy automaton and resolution of a particular system of fuzzy relation equations in that paper we have also studied reductions by means of those solutions which are fuzzy equivalences in this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi orders generally fuzzy quasi orders and fuzzy equivalences are equally good in the state reduction but we show that right and left invariant fuzzy quasi orders give better reductions than right and left invariant fuzzy equivalences we also show that alternate reductions by means of fuzzy quasi orders give better results than alternate reductions by means of fuzzy equivalences furthermore we study a more general type of fuzzy quasi orders weakly right and left invariant ones and we show that they are closely related to determinization of fuzzy automatons we also demonstrate some applications of weakly left invariant fuzzy quasi orders in conflict analysis of fuzzy discrete event systems

direct numerical simulation of particulate flows with an overset grid method abstract we evaluate an efficient overset grid method for two dimensional and three dimensional particulate flows for small numbers of particles at finite reynolds number the rigid particles are discretised using moving overset grids overlaid on a cartesian background grid this allows for strongly enforced boundary conditions and local grid refinement at particle surfaces thereby accurately capturing the viscous boundary layer at modest computational cost the incompressible navier stokes equations are solved with a fractional step scheme which is second order accurate in space and time while the fluid solid coupling is achieved with a partitioned approach including multiple sub iterations to increase stability for light rigid bodies through a series of benchmark studies we demonstrate the accuracy and efficiency of this approach compared to other boundary conformal and static grid methods in the literature in particular we find that fully resolving boundary layers at particle surfaces is crucial to obtain accurate solutions to many common test cases with our approach we are able to compute accurate solutions using as little as one third the number of grid points as uniform grid computations in the literature a detailed convergence study shows a 13 fold decrease in cpu time over a uniform grid test case whilst maintaining comparable solution accuracy

a plea for the use of lukasiewicz triplets in the definition of fuzzy preference structures i general argumentation abstract the generalization of the concept of a classical or crisp preference structure to that of a fuzzy preference structure expressing degrees of strict preference indifference and incomparability among a set of alternatives requires the choice of a de morgan triplet i e of a triangular norm and an involutive negator the resulting concept is only meaningful provided that this choice allows the representation of truly fuzzy preferences more specifically one of the degrees of strict preference indifference or incomparability should always be unconstrained to the preference modeller this intuitive requirement is violated when choosing a triangular norm without zero divisors since in that case fuzzy preference structures reduce to classical preference structures and hence none of the degrees can be freely assigned furthermore it is shown that the choice of a continuous non archimedean triangular norm having zero divisors is not compatible with our basic requirement the sets of degrees of strict preference indifference and incomparability in 0 1 are always bounded from above by a value strictly smaller than 1 these fundamental results imply that when working with a continuous triangular norm only archimedean ones having zero divisors are suitable candidates these arguments sufficiently support our plea for the use of ukasiewicz triplets in the definition of fuzzy preference structures

an introduction to vague complemented ordered sets abstract the purpose of this paper is to introduce a theory of fuzzily defined complement operations on nonempty sets equipped with fuzzily defined ordering relations many valued equivalence relation based fuzzy ordering relations also called vague ordering relations provide a powerful and a comprehensive mathematical modelling of fuzzily defined partial ordering relations for this reason starting with a nonempty set x equipped with a many valued equivalence relation and a vague ordering relation a fuzzily defined complement operation called a vague complement operation on x will be formulated by means of the underling many valued equivalence relation and vague ordering relation because of the fact that the practical implementations of vague complement operations basically depend on their representation properties a considerable part of this paper is devoted to the representations of vague complement operations in addition to this the present paper provides various nontrivial examples for vague complements and introduces a many valued logical interpretation of quantum logic as a real application of vague complements

numerically stable fluid structure interactions between compressible flow and solid structures we propose a novel method to implicitly two way couple eulerian compressible flow to volumetric lagrangian solids the method works for both deformable and rigid solids and for arbitrary equations of state the method exploits the formulation of 11 which solves compressible fluid in a semi implicit manner solving for the advection part explicitly and then correcting the intermediate state to time t n 1 using an implicit pressure obtained by solving a modified poisson system similar to previous fluid structure interaction methods we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a no slip constraint unlike previous methods however we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled symmetric indefinite system similar to 17 which only handles incompressible flow we also show that under a few reasonable assumptions this system can be made symmetric positive definite by following the methodology of 16 because our method handles the fluid structure interactions implicitly we avoid introducing any new time step restrictions and obtain stable results even for high density to mass ratios where explicit methods struggle or fail we exactly conserve momentum and kinetic energy thermal fluid structure interactions are not considered at the fluid structure interface and hence naturally handle highly non linear phenomenon such as shocks contacts and rarefactions

an arbitrary lagrangian eulerian finite element approach for fluid structure interaction phenomena the present contribution is concerned with the design of a family of consistent fluid structure interaction algorithms based on a unique temporal and spatial discretization of the governing equations the characterization of the moving fluid structure interface is realized by means of the arbitrary lagrangian eulerian technique the spatial discretization is performed with the finite element method whereby either a first order upwind scheme or the classical second order upwind petrov galerkin technique are used to discretize the linearized fluid equations while the standard bubnov galerkin method is applied to the structural equations in order to streamline coupling the structure is discretized in a velocity based fashion the temporal discretization of both the fluid and the structural equations is embedded in the generalized framework by making use of classical newmark approximations in time to quantify the sources of error of the proposed algorithms systematic studies in terms of the one dimensional piston model problem are presented copyright 2003 john wiley sons ltd

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

a non commutative and non idempotent theory of quantale sets in fuzzy set theory non idempotency arises when the conjunction is interpreted by arbitrary t norms there are many instances in mathematics where set theory ought to be non commutative and or non idempotent the purpose of this paper is to combine both ideas and to present a theory of non commutative and non idempotent quantale sets among other things standard concepts like fuzzy preorders and fuzzy equivalence relations will be exhibited as special cases more specifically the category q set is investigated where q is an arbitrary involutive quantale objects quantale sets are pairs consisting of a set and a q valued equality with a suitable symmetry axiom three important properties of q set are shown it is complete cocomplete and has the epi extremal mono factorization property its subcategory s q set of separated quantale sets is reflective in q set and shares the same fundamental properties with q set in particular s q set is also a complete and cocomplete epi extremal mono category the objects of the category q set are interesting categories in their own right two categorical frameworks for objects of q set are exhibited first it is shown that q valued equalities arise from q valued preorders with self adjoint extents by symmetrization which leaves q valued equalities invariant here sets with quantale preorders are shown to be b categories with base b being a specific quantaloid the second approach is based on involutive quantaloids a combination of two well known things quantaloids and ordered categories with involution in this context quantale sets are precisely symmetric b categories w r t appropriately chosen quantaloid b with involution further the cauchy completion preserves the symmetry axiom for a large class of involutive quantales which include quantic frames our non commutative generalization of frames and all left continuous t norms there exist at least two monads on q set the singleton monad and quasi singleton monad which are of special interest for fuzzy set theory the kleisli category associated with the singleton monad is the non commutative and non idempotent analogue of higgs topos while the eilenberg moore category of the quasi singleton monad permits the internalization of lukasiewicz negation as truth arrow finally an application of quantale sets to c algebras is given and the change of base is treated

infereni on full or partial parameters based on the standardized signed log likelihood ratio on etudie des tests et des limites de confiance bases sur la statistique du rapport de log vraisemblance signee en ajustant cette statistique de telle sorte qu a un ordre superieur d approximation la distribution normale standard soit valable

an analysis of a new stable partitioned algorithm for fsi problems part i incompressible flow and elastic solids stable partitioned algorithms for fluid structure interaction fsi problems are developed and analyzed in this two part paper part i describes an algorithm for incompressible flow coupled with compressible elastic solids while part ii discusses an algorithm for incompressible flow coupled with structural shells importantly these new added mass partitioned amp schemes are stable and retain full accuracy with no sub iterations per time step even in the presence of strong added mass effects e g for light solids the numerical approach described here for bulk compressible solids extends the scheme of banks et al 1 2 for inviscid compressible flow and uses robin mixed boundary conditions with the fluid and solid solvers at the interface the basic amp robin conditions involving a linear combination of velocity and stress are determined from the outgoing solid characteristic relation normal to the fluid solid interface combined with the matching conditions on the velocity and traction two alternative forms of the amp conditions are then derived depending on whether the fluid equations are advanced with a fractional step method or not the stability and accuracy of the amp algorithm is evaluated for linearized fsi model problems the full nonlinear case being left for future consideration a normal mode analysis is performed to show that the new amp algorithm is stable for any ratio of the solid and fluid densities including the case of very light solids when added mass effects are large in contrast it is shown that a traditional partitioned algorithm involving a dirichlet neumann coupling for the same fsi problem is formally unconditionally unstable for any ratio of densities exact traveling wave solutions are derived for the fsi model problems and these solutions are used to verify the stability and accuracy of the corresponding numerical results obtained from the amp algorithm for the cases of light medium and heavy solids