high order methods for low reynolds number flows around moving obstacles based on universal meshes summary we propose a family of methods for simulating two dimensional incompressible low reynolds number flow around a moving obstacle whose motion is prescribed the methods make use of a universal mesh a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle s boundary the resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off the shelf time integrators we demonstrate the approach by using taylor hood elements to approximate the fluid velocity and pressure to integrate in time we consider implicit runge kutta schemes as well as a fractional step scheme we illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations copyright 2015 john wiley sons ltd

on l subsets and tl subalgebras this is a continuation of yu s 1993 work on tl subalgebras we define and discuss another kind of homomorphism and isomorphism of tl subalgebras where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l we also give two methods for generating tl subalgebras

a three field stabilized finite element method for fluid structure interaction elastic solid and rigid body limit summary we propose a full eulerian framework for solving fluid structure interaction fsi problems based on a unified formulation in which the fsis are modelled by introducing an extra stress in the momentum equation the obtained three field velocity pressure and stress system is solved using a stabilized finite element method the key feature of this unified formulation is the ability to describe different kind of interactions between the fluid and the structure which can be either elastic or a perfect rigid body without the need of treating this last case via penalization the level set method combined with a dynamic anisotropic mesh adaptation is used to track the fluid solid interface copyright 2015 john wiley sons ltd

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

the fixed mesh ale approach for the numerical approximation of flows in moving domains in this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization and therefore the formulation to be presented falls within the category of fixed grid methods even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed grid method our approach can be applied together with any technique to impose approximately boundary conditions although we also describe the one we actually favor our main concern is to properly account for the advection of information as the domain boundary evolves to achieve this we use an arbitrary lagrangian eulerian framework the distinctive feature being that at each time step results are projected onto a fixed background mesh that is where the problem is actually solved

improved fractional step method for simulating fluid structure interaction using the pfem summary numerical difficulties are present in the particle finite element method even though it has been shown to be a powerful and effective approach to simulating fluid structure interaction to overcome problems of mass loss on the free surface and the added mass effect an improved fractional step method fsm that handles added mass terms in a mathematically exact way is developed a further benefit is that no assumptions regarding the structural response are made in handling added mass terms thus it is straightforward to incorporate material nonlinearity in fluid structure interaction fsi under this approach patch tests and comparisons with experimental data are presented in order to verify and validate the improved fsm for fsi applications the computational cost of this approach is shown to be negligible compared with the other aspects of the fsm particularly when the size of the structure and the fluid structure interface is small relative to the volume of fluid copyright 2014 john wiley sons ltd

connecting fuzzy preorders fuzzy consequence operators and fuzzy closure and co closure systems abstract the relations between fuzzy preorders fuzzy consequence operators fuzzy closure systems and co closure systems lattice structures are studied given a continuous t norm we will prove that the complete lattice of all fuzzy preorders is isomorphic with a subfamily of the complete lattice of fuzzy consequence operators moreover we will show that it is possible to embed both structures in the class of fuzzy closure systems by a lattice dual monomorphism between semilattices a solution to the following open problem when two families of fuzzy possible valuations produce the same fuzzy implication relation is given concept of interior operator of a fuzzy consequence operator is suggested and a characterization of the previous open problem through interior operator is shown

l fuzzy closure systems this paper studies the generalization of fuzzy closure operators and fuzzy closure systems introduced by belohlavek in 2001 and introduces the concepts of strong l fuzzy closure systems and strong l fuzzy closure operators it is shown that a strong l fuzzy closure system is precisely the fuzzy system in opposition to the crisp system and a strong l fuzzy closure operator is a suitable closure operator that has a close relation to a strong l fuzzy closure system it is also shown that there is a galois correspondence between the category of strong l fuzzy closure system spaces and that of strong l fuzzy closure spaces

adaptively weighted numerical integration in the finite cell method abstract with adaptively weighted aw numerical integration for a given set of quadrature nodes order and domain of integration the quadrature weights are obtained by solving a system of suitable moment fitting equations in least square sense the moments in the moment equations are approximated over a simplified domain that is homeomorphic to the original domain and then are corrected for the deviation from the original domain using shape sensitivity analysis in this paper we demonstrate the application of aw integration scheme in the context of the finite cell method which must perform numerical integration over arbitrary domains without meshing the standard integration technique employed in fcm is the characteristic function method that converts the continuous integrand over a complex domain into a discontinuous integrand over a simple box domain then well known integrand adaptivity techniques are employed to integrate the resulting discontinuous integrand over the box domain although this method is simple to implement it becomes computationally very expensive for realistic complex 3d domains such as sculptures bones and engines in contrast in aw scheme the quadrature weights directly adapt to the complex geometric domain without the need to making the integrand discontinuous leading to superior computational properties in this paper we demonstrate the computational efficiency of aw over the characteristic function method as it requires fewer subdivisions and less time to achieve a given accuracy in both two and three dimensions in addition aw offers a number of advantages including flexibility in the choice of quadrature points and basis functions

fuzzy relations and fuzzy groups abstract given a group s we consider fuzzy relations on s that is maps from s s into 0 1 of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on s s we prove that if is a fuzzy subset of s and is the strongest fuzzy relation on s that is a fuzzy relation on then is a fuzzy subgroup if and only if is a fuzzy subgroup a number of other results are obtained about the interrelationships between fuzzy relations on s including the weakest fuzzy relation and fuzzy subgroups on s s

fuzzy groups some group theoretic analogs abstract we introduce the concepts of 1 order of a fuzzy subgroup of a finite group 2 a fuzzy abelian group and 3 a fuzzy solvable group we obtain some results involving these notions which are analogs of results from group theory also we prove analogs of two basic theorems of group theory namely cayley s theorem and lagrange s theorem

a symmetric method for weakly imposing dirichlet boundary conditions in embedded finite element meshes summary in this paper we propose a way to weakly prescribe dirichlet boundary conditions in embedded finite element meshes the key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation relatively small and can be fixed a priori moreover the formulation is symmetric for symmetric problems an additional element discontinuous stress field is used to enforce the boundary conditions in the poisson problem additional terms are required in order to guarantee stability in the convection diffusion equation and the stokes problem the proposed method is then easily extended to the transient navier stokes equations copyright 2012 john wiley sons ltd

characterizations of l convex spaces via domain theory abstract we provide some new characterizations of l convex spaces by using the way below relation in domain theory for this purpose we first study the notion of domain finiteness in the lattice valued case and then introduce three kinds of spaces algebraic l closure spaces restricted l hull spaces and l entailment spaces these three spaces are shown to be categorically isomorphic to l convex spaces additionally we introduce the notion of l polytopes and prove that a subcollection of a dense l convex structure is a base if and only if it contains all l polytopes these results indicate that in the study of the theory of fuzzy convex spaces fuzzy domain theory has important applications

degree dependent network growth from preferential attachment to explosive percolation we present a simple model of network growth and solve it by writing the dynamic equations for its macroscopic characteristics such as the degree distribution and degree correlations this allows us to study carefully the percolation transition using a generating functions theory the model considers a network with a fixed number of nodes wherein links are introduced using degree dependent linking probabilities pk to illustrate the techniques and support our findings using monte carlo simulations we introduce the exemplary linking rule pk k with between 1 and this parameter may be used to interpolate between different regimes for negative links are most likely attached to high degree nodes on the other hand in case 0 nodes with low degrees are connected and the model asymptotically approaches a process undergoing explosive percolation

tl subrings and tl ideals part 1 basic concepts abstract in 25 27 we put forward a rudimentary frame of the theory of tl subalgebras in 26 we established a theory of tl subgroups and tl subgroups in this paper we will continue our work in concern with basic ideas provided in 25 27 introduce the notions of tl subrings and tl ideals of a ring and study some of their properties where t is an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l

from scale free to erdos renyi networks we analyze a model that interpolates between scale free and erdos r enyi networks the model introduced generates a one parameter family of networks and allows one to analyze the role of structural heterogeneity analytical calculations are compared with extensive numerical simulations in order to describe the transition between these two important classes of networks finally an application of the proposed model to the study of the percolation transition is presented

an immersed boundary method with formal second order accuracy and reduced numerical viscosity a formally second order accurate immersed boundary method is presented and tested in this paper we apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first order method the numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high reynolds number flows with immersed boundaries

generalized synchronization in complex dynamical networks via adaptive couplings abstract this paper investigates generalized synchronization of three typical classes of complex dynamical networks scale free networks small world networks and interpolating networks the proposed synchronization strategy is to adjust adaptively a node s coupling strength based on the node s local generalized synchronization information by taking the auxiliary system approach and using the lyapunov function method we prove that for any given initial coupling strengths the generalized synchronization can take place in complex networks consisting of nonidentical dynamical systems it is demonstrated that the coupling strengths are affected by topologies of the networks furthermore it is found that there are hierarchical features in the processes of generalized synchronization in scale free networks because of their highly heterogeneous distributions of connection degree finally we discuss in detail how a network s degree of heterogeneity affects its generalization synchronization behavior

a bubble stabilized finite element method for dirichlet constraints on embedded interfaces we examine a bubble stabilized finite element method for enforcing dirichlet constraints on embedded interfaces by embedded we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh as such the robust imposition of dirichlet constraints using a lagrange multiplier field is not trivial to focus issues we consider a simple one sided problem that is representative of a wide class of evolving interface problems the bulk field is decomposed into coarse and fine scales giving rise to coarse scale and fine scale one sided sub problems the fine scale solution is approximated with bubble functions permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method importantly the method is simple to implement readily extends to multiple dimensions obviates the need to specify any free stabilization parameters and can lead to a symmetric positive definite system of equations the performance of the method is then examined through several numerical examples the accuracy of the lagrange multiplier is compared to results obtained using a local version of the domain integral method the variational multiscale approach proposed herein is shown to both stabilize the lagrange multiplier and improve the accuracy of the post processed fluxes copyright 2006 john wiley sons ltd

an extension principle for closure operators this led several authors to investigate the closure systems and the closure operators in the framework of fuzzy set theory the resulting researches give an elegant and powerful treatment of notions such as those of fuzzy w x subalgebras necessity measures and envelopes for example see 1 4 and w x 11 let s be any set and denote by p s and f s the class of the subsets and the class of the fuzzy subsets of s respectively in this paper we propose an extension principle enabling us to extend any classical operator j p s a p s to an operator j f s a f s in such a way that j is a closure operator if and only if j is a closure operator also we

normalization of fuzzy algebras in this work the notion of fuzzy algebra is investigated given an algebra a and a poset s a fuzzy algebra over a is an s set f over the base set a of a such that every cut x a f x a a s is a subalgebra of a some consequences are derived a particular notion of equivalence between two fuzzy algebras is studied which is more perspicuous than the notion of isomorphism a set of properties which appear to be desirable for a fuzzy algebra is settled the main theorem of the paper says that every fuzzy algebra is normalizable i e another fuzzy algebra may be constructed which is equivalent to the former and which satisfies all the desired properties

scale free networks by super linear preferential attachment rule abstract a network growth model with geographic limitation of accessible information about the status of existing nodes is investigated in this model the probability k of an existing node of degree k is found to be super linear with k k and 1 when there are links from new nodes the numerical results show that the constructed networks have typical power law degree distributions p k k and the exponent depends on the constraint level an analysis of local structural features shows the robust emergence of scale free network structure in spite of the super linear preferential attachment rule this local structural feature is directly associated with the geographical connection constraints which are widely observed in many real networks

universal meshes a method for triangulating planar curved domains immersed in nonconforming meshes summary we introduce a new method to triangulate planar curved domains that transforms a specific collection of triangles in a background mesh to conform to the boundary in the process no new vertices are introduced and connectivities of triangles are left unaltered the method relies on a novel way of parameterizing an immersed boundary over a collection of nearby edges with its closest point projection to guarantee its robustness we require that the domain be c2 regular the background mesh be sufficiently refined near the boundary and that specific angles in triangles near the boundary be strictly acute the method can render both straight edged and curvilinear triangulations for the immersed domain the latter includes curved triangles that conform exactly to the immersed boundary and ones constructed with isoparametric mappings to interpolate the boundary at select points high order finite elements constructed over these curved triangles achieve optimal accuracy which has customarily proven difficult in numerical schemes that adopt nonconforming meshes aside from serving as a quick and simple tool for meshing planar curved domains with complex shapes the method provides significant advantages for simulating problems with moving boundaries and in numerical schemes that require iterating over the geometry of domains with no conformity requirements the same background mesh can be adopted to triangulate a large family of domains immersed in it including ones realized over several updates during the coarse of simulating problems with moving boundaries we term such a background mesh as a universal mesh for the family of domains it can be used to triangulate universal meshes hence facilitate a framework for finite element calculations over evolving domains while using only fixed background meshes furthermore because the evolving geometry can be approximated with any desired order numerical solutions can be computed with high order accuracy we present demonstrative examples using universal meshes to simulate the interaction of rigid bodies with stokesian fluids copyright 2014 john wiley sons ltd

erosion of synchronization coupling heterogeneity and network structure we study the dynamics of network coupled phase oscillators in the presence of coupling frustration it was recently demonstrated that in heterogeneous network topologies the presence of coupling frustration causes perfect phase synchronization to become unattainable even in the limit of infinite coupling strength here we consider the important case of heterogeneous coupling functions and extend previous results by deriving analytical predictions for the total erosion of synchronization our analytical results are given in terms of basic quantities related to the network structure and coupling frustration in addition to fully heterogeneous coupling where each individual interaction is allowed to be distinct we also consider partially heterogeneous coupling and homogeneous coupling in which the coupling functions are either unique to each oscillator or identical for all network interactions respectively we demonstrate the validity of our theory with numerical simulations of multiple network models and highlight the interesting effects that various coupling choices and network models have on the total erosion of synchronization finally we consider some special network structures with well known spectral properties which allows us to derive further analytical results

eulerian formulation using stabilized finite element method for large deformation solid dynamics this paper describes an eulerian formulation for large deformation solid dynamics in the present eulerian approach an advective equation is solved using the stream upwind petrov galerkin finite element method the eulerian finite element method is applied to path dependent solid analyses such as impact bar and ductile necking problems these computational results using the eulerian finite element method are compared with the results obtained from using the lagrangian finite element method and an eulerian formulation based on a finite difference method copyright 2007 john wiley sons ltd

approximate imposition of boundary conditions in immersed boundary methods we analyze several possibilities to prescribe boundary conditions in the context of immersed boundary methods as basic approximation technique we consider the finite element method with a mesh that does not match the boundary of the computational domain and therefore dirichlet boundary conditions need to be prescribed in an approximate way as starting variational approach we consider nitsche s methods and we then move to two options that yield non symmetric problems but that turned out to be robust and efficient the essential idea is to use the degrees of freedom of certain nodes of the finite element mesh to minimize the difference between the exact and the approximated boundary condition

weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes this is the accepted version of the following article codina r and baiges j 2015 weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non matching meshes int j numer meth engng 104 624 654 doi 10 1002 nme 4815 which has been published in final form at http onlinelibrary wiley com doi 10 1002 nme 4815 abstract

immersed interface methods for stokes flow with elastic boundaries or surface tension a second order accurate interface tracking method for the solution of incompressible stokes flow problems with moving interfaces on a uniform cartesian grid is presented the interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids the interface is represented by a cubic spline along which the singularly supported elastic or surface tension force can be computed the stokes equations are then discretized using the second order accurate finite difference methods for elliptic equations with singular sources developed in our previous paper siam j numer anal 31 1994 pp 1019 1044 the resulting velocities are interpolated to the interface to determine the motion of the interface an implicit quasi newton method is developed that allows reasonable time steps to be used

lattices of fuzzy subgroupoids fuzzy submonoids and fuzzy subgroups we redefine the sup min product of fuzzy subsets and discuss the redefined sup min products of fuzzy subgroupoids fuzzy submonoids and fuzzy subgroups in addition we study lattice structures of the lattices of fuzzy subgroupoids fuzzy submonoids and fuzzy subgroups

on strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method we consider a problem stemming from recent models of phase transitions in stimulus responsive hydrogels wherein a sharp interface separates swelled and collapsed phases extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly fit the interface geometry are emphasized attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface we show that as the reciprocal interfacial mobility vanishes it plays the role of a penalty parameter enforcing a pure dirichlet constraint eventually triggering oscillations in the interfacial velocity we also examine alternative formulations employing a lagrange multiplier to enforce this constraint it is shown that the most convenient choice of basis for the lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms suggesting a lack of stability in the discrete formulation under such conditions neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux fortunately the adaptation and use of local domain integral methodologies considerably improves the flux evaluations several example problems are presented to compare and contrast the various techniques and methods

an immersed interface method for simulating the interaction of a fluid with moving boundaries in the immersed interface method boundaries are represented as singular force in the navier stokes equations which enters a numerical scheme as jump conditions recently we systematically derived all the necessary spatial and temporal jump conditions for simulating incompressible viscous flows subject to moving boundaries in 3d with second order spatial and temporal accuracy near the boundaries sheng xu z jane wang systematic derivation of jump conditions for the immersed interface method in three dimensional flow simulation siam j sci comput 2006 in press in this paper we implement the immersed interface method to incorporate these jump conditions in a 2d numerical scheme we study the accuracy efficiency and robustness of our method by simulating taylor couette flow flow induced by a relaxing balloon flow past single and multiple cylinders and flow around a flapping wing our results show that 1 our code has second order accuracy in the infinity norm for both the velocity and the pressure 2 the addition of an object introduces relatively insignificant computational cost 3 the method is equally effective in computing flow subject to boundaries with prescribed force or boundaries with prescribed motion

comparing fuzzy and crisp deduction systems abstract the connections between the fuzzy deduction systems and the crisp deduction systems are examined we show that there is a natural way to associate to every fuzzy deduction system a crisp deduction system and to every crisp deduction system a fuzzy deduction system

galois connections among fuzzy groups similarities distances given a set s we define galois connections between the lattices of the fuzzy subgroups of transformations in s the lattice of the similarities in s and the lattice of the distances in s

on synchronizability and heterogeneity in unweighted networks abstract synchronization in classes of continuous time dynamical unweighted networks with different topologies is investigated a synchronization optimal network model based on rewiring of links is proposed compared with other networks it exhibits a stronger synchronizability we presented link density and investigated the correlation of synchronizability link density and heterogeneity in degree distribution in this work it will be shown that synchronizability of type i networks is independent of heterogeneity in the degree distribution when the link density is smaller than 0 02 synchronizability and link density are proportional when the link density is larger than 0 025 heterogeneity decides the curve slope the synchronizability of type ii networks is drastically enhanced by enhancing the link density when the link density is smaller than 0 025 however synchronizability increases weakly by enhancing the link density when the link density is larger than 0 025

fuzzy submonoids fuzzy preorders and quasi metrics let l be a residuated lattice then given a monoid m we define a galois connection from the lattice of the compatible l preorders in m and the lattice of l submonoids of m given a set s we define a galois connection between the lattice of the l preorders in s and the lattice of l submonoids of the monoid ss i a link with the notion of quasi metric is also established

fuzzy counterparts of hull operators and interval operators in the framework of l convex spaces abstract for fuzzy counterparts of hull operators and interval operators two types of fuzzy hull operators and one type of fuzzy interval operators are proposed firstly the concept of l hull operators is introduced and the resulting category is shown to be isomorphic to that of l convex spaces secondly considering the graded inclusions of l subsets the notion of l ordered hull operators is presented which is shown to be categorically isomorphic to strong l convex structures finally the concept of l interval operators is introduced and it is shown that there is a galois correspondence between the category of l interval spaces and that of l convex spaces in particular the category of arity 2 l convex spaces can be reflectively embedded into that of l interval spaces

on fuzzy ideals and fuzzy bi ideals in semigroups abstract in this paper we give some properties of fuzzy ideals and fuzzy bi ideals of semigroups and characterize semigroups that are left duo left simple and semilattices of subsemigroups in terms of fuzzy ideals and fuzzy bi ideals

from unweighted to weighted networks with local information abstract in this paper we analyze an evolving model with local information which can generate a class of networks by choosing different values of the parameter p the model introduced exhibits the transition from unweighted networks to weighted networks because the distribution of the edge weight can be widely tuned with the increase in the local information the degree correlation of the network transforms from assortative to disassortative we also study the distribution of the degree strength and edge weight which all show crossover between exponential and scale free finally an application of the proposed model to the study of the synchronization is considered it is concluded that the synchronizability is enhanced when the heterogeneity of the edge weight is reduced

explosive synchronization with partial degree frequency correlation networks of kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of their corresponding vertices exhibit so called explosive synchronization behavior which is now under intensive investigation here we study and discuss explosive synchronization in a situation that has not yet been considered namely when only a part typically a small part of the vertices is subjected to a degree frequency correlation our results show that in order to have explosive synchronization it suffices to have degree frequency correlations only for the hubs the vertices with the highest degrees moreover we show that a partial degree frequency correlation does not only promotes but also allows explosive synchronization to happen in networks for which a full degree frequency correlation would not allow it we perform a mean field analysis and our conclusions were corroborated by exhaustive numerical experiments for synthetic networks and also for the undirected and unweighed version of a typical benchmark biological network namely the neural network of the worm caenorhabditis elegans the latter is an explicit example where partial degree frequency correlation leads to explosive synchronization with hysteresis in contrast with the fully correlated case for which no explosive synchronization is observed

a characterization of fuzzy subgroups abstract an ordinary subgroup of a group g is 1 a subset of g 2 closed under the group operation in a fuzzy subgroup it is precisely these two notions that lose their deterministic character a fuzzy subgroup of a group g associates with each group element a number the larger the number the more certainly that element belongs to the fuzzy subgroup the closure property is captured by the inequality x y t x y in a rosenfeld s original definition t was the function minimum however any t norm t provides a meaningful generalization of the closure property two classes of fuzzy subgroups are investigated the fuzzy subgroups in one class are subgroup generated those in the other are function generated each fuzzy subgroup in these classes satisfies the above inequality with t given by t a b max a b 1 0 while the two classes look different each fuzzy subgroup in either is isomorphic to one in the other it is shown that a fuzzy subgroup satisfies the above inequality with t minimum if and only if it is subgroup generated of a very special type finally these notions are applied to some abstract pattern recognition problems

a fictitious domain method for dirichlet problem and applications abstract in this article we discuss the solution of the dirichlet problem for a class of elliptic operators by a lagrange multiplier fictitious domain method this approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries the resulting saddle point system can be solved by an uzawa conjugate gradient algorithm in the case of two dimensional problems a quasi optimal preconditioner has been found by fourier analysis and numerical experiments confirm its nice scaling properties the resulting methodology is applied to a nonlinear time dependent problem namely the flow of a viscous plastic medium in a cylindrical pipe showing the potential of this methodology for some classes of nonlinear problems

the immersed interface method for elliptic equations with discontinuous coefficients and singular sources the authors develop finite difference methods for elliptic equations of the form nabla cdot beta x nabla u x kappa x u x f x in a region omega in one or two space dimension

on fuzzy regular subsemigroups of a semigroup abstract since a rosenfeld proposed the concept of fuzzy subgroup in 1971 there has been considerable development of fuzzy algebra in particular n kuraki discussed fuzzy biideals and the fuzzy semiprime ideal of a semigroup we introduce the concepts of fuzzy regular subsemigroups fuzzy weakly regular subsemigroups fuzzy completely regular subsemigroups and fuzzy weakly completely regular subsemigroups and investigate some of their algebraic properties

high order finite element methods for moving boundary problems with prescribed boundary evolution abstract we introduce a framework for the design of finite element methods for two dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy both in space and in time at the core of our approach is the use of a universal mesh a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immersed domain by adjusting a small number of mesh elements in the neighborhood of the moving boundary the resulting method maintains an exact representation of the prescribed moving boundary at the discrete level or an approximation of the appropriate order yet is immune to large distortions of the mesh under large deformations of the domain the framework is general making it possible to achieve any desired order of accuracy in space and time by selecting a preferred and suitable finite element space on the universal mesh for the problem at hand and a preferred and suitable time integrator for ordinary differential equations we illustrate our approach by constructing a particular class of methods and apply them to a prescribed boundary variant of the stefan problem we present numerical evidence for the order of accuracy of our schemes in one and two dimensions

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

fuzzy semiprime ideals in semigroups abstract in this paper we shall introduce the notion of fuzzy semiprimality in a semigroup which is an extension of semiprimality in it and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality

from regular to growing small world networks abstract we propose a growing model which interpolates between one dimensional regular lattice and small world networks the model undergoes an interesting phase transition from large to small worlds we investigate the structural properties by both theoretical predictions and numerical simulations our growing model is a complementarity for the important static watts strogatz network model

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

efficient implementation of finite element methods on nonmatching and overlapping meshes in three dimensions in recent years a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on nonmatching or overlapping meshes examples of such methods are the fictitious domain method the extended finite element method and nitsche s method in all these methods integrals must be computed over cut cells or subsimplices which is challenging to implement especially in three space dimensions in this note we address the main challenges of such an implementation and demonstrate good performance of a fully general code for automatic detection of mesh intersections and integration over cut cells and subsimplices as a canonical example of an overlapping mesh method we consider nitsche s method which we apply to poisson s equation and a linear elastic problem

erosion of synchronization in networks of coupled oscillators we report erosion of synchronization in networks of coupled phase oscillators a phenomenon where perfect phase synchronization is unattainable in steady state even in the limit of infinite coupling an analysis reveals that the total erosion is separable into the product of terms characterizing coupling frustration and structural heterogeneity both of which amplify erosion the latter however can differ significantly from degree heterogeneity finally we show that erosion is marked by the reorganization of oscillators according to their node degrees rather than their natural frequencies

computing the lattice of all fixpoints of a fuzzy closure operator we present a fast bottom up algorithm to compute all fixpoints of a fuzzy closure operator in a finite set over a finite chain of truth degrees along with the partial order on the set of all fixpoints fuzzy closure operators appear in several areas of fuzzy logic and its applications including formal concept analysis fca that we use as a reference area of application in this paper several problems in fca such as computing all formal concepts from data with graded attributes or computing non redundant bases of all attribute dependencies can be reduced to the problem of computing fixpoints of particular fuzzy closure operators associated with the input data the development of a general algorithm that is applicable in particular to these problems is the ultimate purpose of this paper we present the algorithm its theoretical foundations and experimental evaluation

stabilized finite element approximation of transient incompressible flows using orthogonal subscales abstract in this paper we present a stabilized finite element method to solve the transient navier stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales the latter are approximately accounted for so as to end up with a stable finite element problem which in particular allows to deal with convection dominated flows and the use of equal velocity pressure interpolations three main issues are addressed the first is a method to estimate the behavior of the stabilization parameters based on a fourier analysis of the problem for the subscales secondly the way to deal with transient problems discretized using a finite difference scheme is discussed finally the treatment of the nonlinear term is also analyzed a very important feature of this work is that the subgrid scales are taken as orthogonal to the finite element space in the transient case this simplifies considerably the numerical scheme

fuzzy closure operators closure operators and closure systems play a significant role in both pure and applied mathematics in the framework of fuzzy set theory several particular examples of closure operators and systems have been considered e g so called fuzzy subalgebras fuzzy congruences fuzzy topology etc recently fuzzy closure operators and fuzzy closure systems themselves i e operators which map fuzzy sets to fuzzy sets and the corresponding systems of closed fuzzy sets have been studied by gerla et al see e g 3 4 6 7 as a matter of fact a fuzzy set a is usually defined as a mapping from a universe set x into the real interval 0 1 in the above mentioned works therefore the structure of truth values of the logic behind is fixed to 0 1 equipped usually with minimum as the operation corresponding to logical conjunction as it appeared recently in the investigations of fuzzy logic in narrow sense 9 10 i e fuzzy logic as a many valued logical calculus there are several logical calculi formalizing the intuitive idea of fuzzy reasoning which are complete with respect to the semantics over special structures of truth values among these structures the most general one is that of a residuated lattice it is worth noticing that residuated lattices introduced originally in 12 as an abstraction in the study of ideal systems of rings have been proposed as a suitable structure of truth values by goguen in 8 from this point of view the need for a general notion of a fuzzy closure concept becomes apparent the aim of this paper is to outline a general theory of fuzzy closure operators and fuzzy closure systems in the next section we introduce the necessary concepts in section 3 fuzzy closure operators and systems are

probability like functionals and fuzzy logic abstract the aim of this paper is to show that fuzzy logic is a suitable tool to manage several types of probability like functionals namely we show that the superadditive functions the necessities the upper and lower probabilities and the envelopes can be considered theories of suitable fuzzy logics some general results about the compactness in fuzzy logic are also obtained

the fixed mesh ale approach applied to solid mechanics and fluid structure interaction problems in this paper we propose a method to solve solid mechanics and fluid structure interaction problems using always a fixed background mesh for the spatial discretization the main feature of the method is that it properly accounts for the advection of information as the domain boundary evolves to achieve this we use an arbitrary lagrangian eulerian ale framework the distinctive characteristic being that at each time step results are projected onto a fixed background mesh for solid mechanics problems subject to large strains the fixed mesh fm ale method avoids the element stretching found in fully lagrangian approaches for fsi problems fm ale allows for the use of a single background mesh to solve both the fluid and the structure copyright 2009 john wiley sons ltd

closure systems and l subalgebras abstract let x be a set and l a class of l subsets of x l is a closure system if it is closed with respect to greatest lower bounds if is an l subset then the g l b tf of g l g is said to be generated by we examine closure systems of l subalgebras and propose formulas for the l subalgebra of a required type generated by a given l subset

an eulerian lagrangian method for fluid structure interaction based on level sets abstract we describe a method for fluid structure interaction with the interface and free surfaces defined by level sets the fluid is treated by an eulerian mesh whereas the solid or structure by a lagrangian mesh the level set method provides a compact framework for writing the weak form and for developing and computing the discretized equations lagrange multiplier methods and penalty methods are used to couple the fluid and structure results are presented for a few compressible fluid problems representative of high pressure waves

an adaptive fixed mesh ale method for free surface flows in this work we present a fixed mesh ale method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain this mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required some of the main ingredients of the formulation are the use of an arbitrary lagrangian eulerian formulation for computing temporal derivatives the use of stabilization terms for stabilizing convection stabilizing the lack of compatibility between velocity and pressure interpolation spaces and stabilizing the ill conditioning introduced by the cuts on the background finite element mesh and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved the method is tested in several numerical examples the expected convergence rates both in space and time are observed smooth solution fields for both velocity and pressure are obtained as a result of the contribution of the stabilization terms finally a good agreement between the numerical results and the reference experimental data is obtained

normality and congruence in fuzzy subgroups abstract it is proved that normal fuzzy subgroups and fuzzy congruence relations determine each other in a group theoretic situation this is analogous to the crisp set theoretic case of groups

extension principles for closure operators on fuzzy sets and cuts abstract we investigate closure operators defined on various partly ordered sets of fuzzy objects including sets of all fuzzy sets with values in a complete residuated lattice and sets of all cuts systems defined in crisp sets and sets with similarity relations respectively we proved several extension theorems under which a closure operator defined on one universe can be extended to a closure operator defined on another universe we also investigate relationships between continuity of pairs of maps with respect to different closure operators

an arbitrary lagrangian eulerian finite element method for finite strain plasticity this paper presents a new arbitrary lagrangian eulerian ale finite element formulation for finite strain plasticity in non linear solid mechanics we consider the models of finite strain plasticity defined by the multiplicative decomposition of the deformation gradient in an elastic and a plastic part f fefp with the stresses given by a hyperelastic relation in contrast with more classical ale approaches based on plastic models of the hypoelastic type the ale formulation presented herein considers the direct interpolation of the motion of the material with respect to the reference mesh together with the motion of the spatial mesh with respect to this same reference mesh this aspect is shown to be crucial for a simple treatment of the advection of the plastic internal variables and dynamic variables in fact this advection is carried out exactly through a particle tracking in the reference mesh a calculation that can be accomplished very efficiently with the use of the connectivity graph of the fixed reference mesh a staggered scheme defined by three steps the smoothing the advection and the lagrangian steps leads to an efficient method for the solution of the resulting equations we present several representative numerical simulations that illustrate the performance of the newly proposed methods both quasi static and dynamic conditions are considered in these model examples copyright 2003 john wiley sons ltd