failure detection framework for stochastic discrete event systems with guaranteed error bounds this paper studies the online fault detection for stochastic discrete event systems dess under partial observability of events prior works have only studied the verification of the stochastic diagnosability s diagnosability property to the best of our knowledge this is a first paper that investigates the online detection schemes and also introduces the notions of their missed detections mds and false alarms fas due to the probabilistic nature of the problem mds and fas are possible even for s diagnosable systems and we establish that s diagnosability is a necessary and sufficient condition for achieving any desired levels of md and fa rates we also provide a detection scheme that can achieve the specified md and fa rates based on comparing a suitable detection statistic that we define with a suitable detection threshold that we algorithmically compute we also algorithmically compute the corresponding detection delay bound the detection scheme also works for non s diagnosable systems with the difference that in this case there exists a lower bound for achievable md rate that increases as the fa rate requirement is made more stringent by decreasing it

a current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number part i on a rectangular collocated grid system a consistent conservative and accurate scheme has been designed to calculate the current density and the lorentz force by solving the electrical potential equation for magnetohydrodynamics mhd at low magnetic reynolds numbers and high hartmann numbers on a finite volume structured collocated grid in this collocated grid velocity u pressure p and electrical potential f are located in the grid center while current fluxes are located on the cell faces the calculation of current fluxes on the cell faces is conducted using a conservative scheme which is consistent with the discretization scheme for the solution of electrical potential poisson equation a conservative interpolation is used to get the current density at the cell center which is used to conduct the calculation of lorentz force at the cell center for momentum equations we will show that both conservative and consistent are important properties of the scheme to get an accurate result for high hartmann number mhd flows with a strongly non uniform mesh employed to resolve the hartmann layers and side layers of hunt s conductive walls and shercliff s insulated walls a general second order projection method has been developed for the incompressible navier stokes equations with the lorentz force included this projection method can accurately balance the pressure term and the lorentz force for a fully developed core flow this method can also simplify the pressure boundary conditions for mhd flows

a polynomial algorithm for testing diagnosability of discrete event systems failure diagnosis in large and complex systems is a critical task in the realm of discrete event systems sampath et al 1995 proposed a language based failure diagnosis approach they introduced the diagnosability for discrete event systems and gave a method for testing the diagnosability by first constructing a diagnoser for the system the complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types we give an algorithm for testing diagnosability that does not construct a diagnoser for the system and its complexity is of fourth order in the number of states of the system and linear in the number of the failure types

polynomial time verification of diagnosability of partially observed discrete event systems the problem of verifying the properties of diagnosability and i diagnosability is considered we present new polynomial time algorithms for deciding diagnosability and i diagnosability these algorithms are based on the construction of a nondeterministic automaton called a verifier

existence and instability of steady states for a triangular cross diffusion system a computer assisted proof abstract in this paper we present and apply a computer assisted method to study steady states of a triangular cross diffusion system our approach consist in an a posteriori validation procedure that is based on using a fixed point argument around a numerically computed solution in the spirit of the newton kantorovich theorem it allows to prove the existence of various non homogeneous steady states for different parameter values in some situations we obtain as many as 13 coexisting steady states we also apply the a posteriori validation procedure to study the linear stability of the obtained steady states proving that many of them are in fact unstable

some unexpected results on the brillouin singular equation fold bifurcation of periodic solutions abstract in this paper we find some new patterns regarding the periodic solvability of the brillouin electron beam focusing equation x 1 cos t x 1 x in particular we prove that there exists 0 248 for which a 2 periodic solution exists for every 0 and the bifurcation diagram with respect to displays a fold for this result significantly contributes to the discussion about the well known conjecture asserting that the brillouin equation admits a periodic solution for every 0 1 4 leading to doubt about its truthfulness for the first time moreover we prove multiplicity of periodic solutions for a range of values of near the technique used relies on rigorous computation and can be extended to some generalizations of the brillouin equation with right hand side equal to 1 x p we briefly discuss the cases p 2 and p 3

efficient rigorous numerics for higher dimensional pdes via one dimensional estimates we present an efficient rigorous computational method which is an extension of the work analytic estimates and rigorous continuation for equilibria of higher dimensional pdes m gameiro and j p lessard j differential equations 249 2010 pp 2237 2268 the idea is to generate sharp one dimensional estimates using interval arithmetic which are then used to produce high dimensional estimates these estimates are used to construct the radii polynomials which provide an efficient way of determining a domain on which the contraction mapping theorem is applicable computing the equilibria using a finite dimensional projection the method verifies that the numerically produced equilibrium for the projection can be used to explicitly define a set which contains a unique equilibrium for the pde a new construction of the polynomials is presented where the nonlinearities are bounded by products of one dimensional estimates as opposed to using fft with large inputs it is demonstrated that with this approac

diagnosability of stochastic discrete event systems we investigate diagnosability of stochastic discrete event systems we define the notions of a and aa diagnosability for stochastic automata these notions are weaker than the corresponding notion of diagnosability for logical automata introduced by sampath et al through the construction of a stochastic diagnoser we determine offline conditions necessary and sufficient to guarantee a diagnosability and sufficient to guarantee aa diagnosability we also show how the stochastic diagnoser can be used for on line diagnosis of failure events we illustrate the results through two examples from hvac systems

diagnosability of fuzzy discrete event systems a fuzzy approach in order to more effectively cope with the real world problems of vagueness fuzzy discrete event systems fdess were proposed by lin and ying recently then we and cao and ying investigated the supervisory control of fdess independently in this paper we are concerned with another important issue of fdess the failure diagnosis more specifically 1 we propose a ldquofuzzy diagnosabilityrdquo approach by introducing a fuzzy diagnosability function to characterize the diagnosability degree which takes values in the interval 0 1 rather than 0 1 2 based on the observability of events we formalize the construction of the diagnosers that are used to perform fuzzy diagnosis 3 a number of basic properties of the diagnosers are investigated in particular we present a necessary and sufficient condition for failure diagnosis of fdess our results generalize the important consequences of the diagnosability for crisp discrete event systems dess introduced by sampath et al the newly proposed approach allows us to deal with the problem of diagnosability for both crisp dess and fdess 4 in addition a method for checking the fuzzy diagnosability for fdess is proposed also some examples are provided to illustrate the application of the diagnosability of fdess

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

a numerical verification method for solutions of boundary value problems with local uniqueness by banach s fixed point theorem in this paper we propose a method to prove the existence and the local uniqueness of solutions to infinite dimensional fixed point equations using computers choosing a set which possibly includes a solution we transform it by an approximate linearization of the operator appearing in the equation then we calculate the radii of the transformed set in order to check sufficient conditions for banach s fixed point theorem this method is applied to elliptic problems and numerical examples are given

an alternative approach to norm bound computation for inverses of linear operators in hilbert spaces abstract in the present paper we propose a computer assisted procedure to prove the invertibility of a linear operator in a hilbert space and to compute a verified norm bound of its inverse a number of the authors have previously proposed two verification approaches that are based on projection and constructive a priori error estimates the approach of the present paper is expected to bridge the gap between the two previous procedures in actual numerical verifications several verification examples that confirm the actual effectiveness of the proposed procedure are reported

bifuzzy discrete event systems and their supervisory control theory it is well known that type 1 fuzzy sets t1 fss have limited capabilities to handle some data uncertainties directly and type 2 fuzzy sets t2 fss can cover the shortcoming of t1 fss to a certain extent fuzzy discrete event systems fdess were proposed based on t1 fss theory hence fdes may not be a satisfactory model to characterize some high uncertainty systems in this paper we propose a new model called as bifuzzy discrete event systems bfdess by combining classical dess theory and t2 fss theory then we consider the supervisory control problem of bfdess the bifuzzy controllability theorem and nonblocking bifuzzy controllability theorem are demonstrated in addition an algorithm for checking the bifuzzy controllability condition is presented in addition two controllable approximations to an uncontrollable language are investigated in detail an illustrative example is provided to show the applicability and the advantages of the bfdes model

a cartesian grid finite volume method for the advection diffusion equation in irregular geometries we present a fully conservative high resolution finite volume algorithm for advection diffusion equations in irregular geometries the algorithm uses a cartesian grid in which some cells are cut by the embedded boundary a novel feature is the use of a capacity function to model the fact that some cells are only partially available to the fluid the advection portion then uses the explicit wave propagation methods implemented in clawpack and is stable for courant numbers up to 1 diffusion is modelled with an implicit finite volume algorithm results are shown for several geometries convergence is verified and the 1 norm order of accuracy is found to between 1 2 and 2 depending on the geometry and peclet number software is available on the web

rigorous computation of smooth branches of equilibria for the three dimensional cahn hilliard equation in this paper we propose a new general method to compute rigorously global smooth branches of equilibria of higher dimensional partial differential equations the theoretical framework is based on a combination of the theory introduced in global smooth solution curves using rigorous branch following van den berg et al math comput 79 271 1565 1584 2010 and in analytic estimates and rigorous continuation for equilibria of higher dimensional pdes gameiro and lessard j diff equ 249 9 2237 2268 2010 using this method one can obtain proofs of existence of global smooth solution curves of equilibria for large continuous parameter ranges and about local uniqueness of the solutions on the curve as an application we compute several smooth branches of equilibria for the three dimensional cahn hilliard equation

computational fixed point theory for differential delay equations with multiple time lags abstract we introduce a general computational fixed point method to prove existence of periodic solutions of differential delay equations with multiple time lags the idea of such a method is to compute numerical approximations of periodic solutions using newton s method applied on a finite dimensional projection to derive a set of analytic estimates to bound the truncation error term and finally to use this explicit information to verify computationally the hypotheses of a contraction mapping theorem in a given banach space the fixed point so obtained gives us the desired periodic solution we provide two applications the first one is a proof of coexistence of three periodic solutions for a given delay equation with two time lags and the second one provides rigorous computations of several nontrivial periodic solutions for a delay equation with three time lags

traveling wave oscillatory patterns in a signed kuramoto sivashinsky equation with absorption abstract in this paper a proof of a part of a conjecture raised in galaktionov and svirshchevskii 2007 concerning existence and global uniqueness of an asymptotically stable periodic orbit in a fourth order piecewise linear ordinary differential equation is presented the fourth order equation comes from the study of traveling wave patterns in a signed kuramoto sivashinsky equation with absorption the proof is twofold first the problem of solving for the periodic orbit is transformed into a zero finding problem on r 4 which is solved with a computer assisted proof based on newton s method and the contraction mapping theorem second the rigorous bounds about the periodic orbit in phase space are combined with the theory of discontinuous dynamical systems to prove that the orbit is asymptotically stable

orbital stability investigations for travelling waves in a nonlinearly supported beam abstract we consider the fourth order wave equation t t x x x x f 0 x t r r with a nonlinearity f vanishing at 0 travelling waves x t u x c t satisfy the ode u c 2 u f u 0 on r and for the case f u e u 1 the existence of at least 36 solitary travelling waves was proved in 4 by computer assisted means we investigate the orbital stability of these solutions via computation of their morse indices and using results from 11 and 12 in order to achieve our results we make use of both analytical and computer assisted techniques

existence of secondary bifurcations or isolas for pdes abstract in this paper we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations the technique combines the global bifurcation theorem knowledge about the non existence of nontrivial steady state solutions at the zero parameter value and explicit information about the coexistence of multiple nontrivial steady states at a positive parameter value we apply the method to the two dimensional swift hohenberg equation

a method of verified computations for solutions to semilinear parabolic equations using semigroup theory this paper presents a numerical method for verifying the existence and local uniqueness of a solution for an initial boundary value problem of semilinear parabolic equations the main theorem of this paper provides a sufficient condition for a unique solution to be enclosed within a neighborhood of a numerical solution in the formulation used in this paper the initial boundary value problem is transformed into a fixed point form using an analytic semigroup the sufficient condition is derived from banach s fixed point theorem this paper also introduces a recursive scheme to extend a time interval in which the validity of the solution can be verified as an application of this method the existence of a global in time solution is demonstrated for a certain semilinear parabolic equation

automatic differentiation for fourier series and the radii polynomial approach abstract in this work we develop a computer assisted technique for proving existence of periodic solutions of nonlinear differential equations with non polynomial nonlinearities we exploit ideas from the theory of automatic differentiation in order to formulate an augmented polynomial system we compute a numerical fourier expansion of the periodic orbit for the augmented system and prove the existence of a true solution nearby using an a posteriori validation scheme the radii polynomial approach the problems considered here are given in terms of locally analytic vector fields i e the field is analytic in a neighborhood of the periodic orbit hence the computer assisted proofs are formulated in a banach space of sequences satisfying a geometric decay condition in order to illustrate the use and utility of these ideas we implement a number of computer assisted existence proofs for periodic orbits of the planar circular restricted three body problem pcrtbp

a consistent and conservative scheme for mhd flows with complex boundaries on an unstructured cartesian adaptive system the numerical simulation of magnetohydrodynamics mhd flows with complex boundaries has been a topic of great interest in the development of a fusion reactor blanket for the difficulty to accurately simulate the hartmann layers and side layers along arbitrary geometries an adaptive version of a consistent and conservative scheme has been developed for simulating the mhd flows besides the present study forms the first attempt to apply the cut cell approach for irregular wall bounded mhd flows which is more flexible and conveniently implemented under adaptive mesh refinement amr technique it employs a volume of fluid vof approach to represent the fluid conducting wall interface that makes it possible to solve the fluid solid coupling magnetic problems emphasizing at how electric field solver is implemented when conductivity is discontinuous in cut cell for the irregular cut cells the conservative interpolation technique is applied to calculate the lorentz force at cell center on the other hand it will be shown how consistent and conservative scheme is implemented on fine coarse mesh boundaries when using amr technique then the applied numerical schemes are validated by five test simulations and excellent agreement was obtained for all the cases considered simultaneously showed good consistency and conservative properties

analytic estimates and rigorous continuation for equilibria of higher dimensional pdes abstract in this paper we extend the ideas of the so called validated continuation technique to the context of rigorously proving the existence of equilibria for partial differential equations defined on higher dimensional spatial domains for that effect we present a new set of general analytic estimates these estimates are valid for any dimension and are used together with rigorous computations to construct a finite number of radii polynomials these polynomials provide a computationally efficient method to prove via a contraction argument the existence and local uniqueness of solutions for a rather large class of nonlinear problems we apply this technique to prove existence and local uniqueness of equilibrium solutions for the cahn hilliard and the swift hohenberg equations defined on two and three dimensional spatial domains

reconstructing volume tracking a new algorithm for the volume tracking of interfaces in two dimensions is presented the algorithm is based upon a well defined second order geometric solution of a volume evolution equation the method utilizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology a linearity preserving piecewise linear interface geometry approximation ensures that solutions generated retain second order spatial accuracy second order temporal accuracy is achieved by virtue of a multidimensional unsplit time integration scheme we detail our geometrically based solution method in which material volume fluxes are computed systematically with a set of simple geometric tasks we then interrogate the method by testing its ability to track interfaces through large controlled topology changes whereby an initially simple interface configuration is subjected to vortical flows numerical results for these strenuous test problems provide evidence for the algorithm s improved solution quality and accuracy

a proof of wright s conjecture abstract wright s conjecture states that the origin is the global attractor for the delay differential equation y t y t 1 1 y t for all 0 2 when y t 1 this has been proven to be true for a subset of parameter values we extend the result to the full parameter range 0 2 and thus prove wright s conjecture to be true our approach relies on a careful investigation of the neighborhood of the hopf bifurcation occurring at 2 this analysis fills the gap left by complementary work on wright s conjecture which covers parameter values further away from the bifurcation point furthermore we show that the branch of slowly oscillating periodic orbits originating from this hopf bifurcation does not have any subsequent bifurcations and in particular no folds for 2 2 6 830 10 3 when combined with other results this proves that the branch of slowly oscillating solutions that originates from the hopf bifurcation at 2 is globally parametrized by 2

immersed boundary method for the mhd flows of liquid metals wall bounded magnetohydrodynamic mhd hereafter flows are of great theoretical and practical interest even for laminar cases mhd simulations are associated with very high computational cost due to the resolution requirements for the hartmann and side layers developing in the presence of solid obstacles in the presence of turbulence these difficulties are further compounded thus mhd simulations in complex geometries are currently a challenge the immersed boundary ib hereafter method is a reliable numerical tool for efficient hydrodynamic field simulations in arbitrarily geometries but it has not yet been extended for mhd simulations the present study forms the first attempt to apply the ib methodology for the computation of both the hydrodynamic and mhd fields a consistent numerical methodology is presented that is appropriate for efficient 3d mhd simulations in geometrically complicated domains using cartesian flow solvers for that purpose a projection scheme for the electric current density is presented based on an electric potential correction algorithm a suitable forcing scheme for electric density currents in the vicinity of non conducting immersed surfaces is also proposed the proposed methodology has been first extensively tested for hartmann layers in fully developed and developing channel and duct flows at hartmann numbers ha 500 2000 in order to demonstrate the potential of the method the three dimensional mhd flow around a circular cylinder at reynolds number re 200 is also presented the effects of grid resolution and variable arrangement on the simulation accuracy and consistency were examined when compared with existing numerical or analytic solutions excellent agreement was found for all the cases considered the proposed projection and forcing schemes for current densities were found capable of satisfying the charge conservation law in the presence of immersed non conducting boundaries finally we show how the proposed methodology can be used to extend the applicability of existing flow solvers that use the ib concept with a staggered variable arrangement

recent advances about the uniqueness of the slowly oscillating periodic solutions of wright s equation abstract an old conjecture in delay equations states that wright s equation y t y t 1 1 y t r has a unique slowly oscillating periodic solution sops for every parameter value 2 we reformulate this conjecture and we use a method called validated continuation to rigorously compute a global continuous branch of sops of wright s equation using this method we show that a part of this branch does not have any fold point partially answering the new reformulated conjecture

rigorous numerical verification of uniqueness and smoothness in a surface growth model abstract based on numerical data and a posteriori analysis we verify rigorously the uniqueness and smoothness of global solutions to a scalar surface growth model with striking similarities to the 3d navier stokes equations for certain initial data for which analytical approaches fail the key point is the derivation of a scalar ode controlling the norm of the solution whose coefficients depend on the numerical data instead of solving this ode explicitly we explore three different numerical methods that provide rigorous upper bounds for its solution

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

state based decentralized diagnosis of bi fuzzy discrete event systems recently we have introduced bi fuzzy discrete event systems bfdess and established their supervisory control theory under full observations and partial observations respectively compared with the models of discrete event systems and fuzzy discrete event systems bfdess are more satisfactory models to characterize some high uncertainty systems in this paper we study the fault diagnosis problems of bfdess first the framework of state based decentralized diagnosis is introduced then the notion of state based codiagnosability is defined and a necessary and sufficient condition for state based codiagnosability is provided in particular a polynomial time algorithm for state based codiagnosability verification and an online decentralized diagnosis method are presented in addition a compact state based decentralized diagnosis framework is introduced and the notion of state based jointly diagnosability and its verification algorithm are proposed finally the implication relationships between the two diagnosabilities are investigated

polynomial time verification of decentralized diagnosability of discrete event systems the first step in the diagnosis of failure occurrences in discrete event systems is the verification of the system diagnosability several works have addressed this problem using either diagnosers or verifiers for both centralized and decentralized architectures in this technical note we propose a new algorithm to verify decentralized diagnosability of discrete event systems the proposed algorithm requires polynomial time in the number of states and events of the system and has lower computational complexity than all other methods found in the literature in addition it can also be applied to the centralized case

constructive a priori error estimates for a full discrete approximation of the heat equation in this paper we consider the constructive a priori error estimates for a full discrete numerical solution of the heat equation our method is based on the finite element galerkin method with an interpolation in time that uses the fundamental solution for semidiscretization in space the present estimates play an essential role in the numerical verification method of exact solutions for the nonlinear parabolic equations this implies that by utilizing the present results we could get the guaranteed a posteriori error estimates for various kinds of nonlinear evolutional problems our results can also be considered as an explicit optimal estimate with the limited regularity of solutions which should be unknown up to the present

rigorous numerics for nonlinear differential equations using chebyshev series a computational method based on chebyshev series to rigorously compute solutions of initial and boundary value problems of analytic nonlinear vector fields is proposed the idea is to recast solutions as fixed points of an operator defined on a banach space of rapidly decaying chebyshev coefficients and to use the so called radii polynomials to show the existence of a unique fixed point near an approximate solution as applications solutions of initial value problems in the lorenz equations and symmetric connecting orbits in the gray scott equation are rigorously computed the symmetric connecting orbits are obtained by solving a boundary value problem with one of the boundary values in the stable manifold

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

global smooth solution curves using rigorous branch following in this paper we present a new method for rigorously computing smooth branches of zeros of nonlinear operators f l 1 b 1 l 2 b 2 where b 1 and b 2 are banach spaces the method is first introduced for parameter continuation and then generalized to pseudo arclength continuation examples in the context of ordinary partial and delay differential equations are given

safe diagnosability of fuzzy discrete event systems and a polynomial time verification since fuzzy discrete event systems fdess were significantly brought forward the study of fdess has received increasing attention recently this paper addresses the safe diagnosability under the framework of fdess the contributions are threefold first the notion of safe diagnosability for fuzzy systems is formalized a safe diagnosable fdes means that not only each failure can be detected in terms of fuzziness as well as the detection must be completed before any unsafe operation is executed then a necessary and sufficient condition of safe diagnosability of fdess is proposed by constructing the safe diagnoser finally we present an algorithm for verifying the safe diagnosability of fdess based on a constructive nondeterministic automaton namely verifier it is worth noting that both constructing the verifier and verifying the safe diagnosability of fdess can be realized with a polynomial complexity

a posteriori existence in numerical computations a typical a posteriori error analysis for numerical methods for differential equations consists of two elements the stability of the continuous problem and an a posteriori computed residual estimate if the problem is nonlinear then this is possible only if it is strongly monotone in this paper we will estimate the stability constant a posteriori as well in order to apply the inverse function theorem to derive the existence of solutions from the numerical computation and thus obtain rigorous a posteriori error estimates for nonmonotone equations

blow up profile for solutions of a fourth order nonlinear equation abstract it is well known that the nontrivial solutions of the equation u r u r f u r 0 blow up in finite time under suitable hypotheses on the initial data and f these solutions blow up with large oscillations knowledge of the blow up profile of these solutions is of great importance for instance in studying the dynamics of suspension bridges the equation is also commonly referred to as extended fisher kolmogorov equation or swift hohenberg equation in this paper we provide details of the blow up profile the key idea is to relate this blow up profile to the existence of periodic solutions for an auxiliary equation

a cartesian grid projection method for the incompressible euler equations in complex geometries many problems in fluid dynamics require the representation of complicated internal or external boundaries of the flow here we present a method for calculating time dependent incompressible inviscid flow which combines a projection method with a cartesian grid approach for representing geometry in this approach the body is represented as an interface embedded in a regular cartesian mesh the advection step is based on a cartesian grid algorithm for compressible flow in which the discretization of the body near the flow uses a volume of fluid representation a redistribution procedure is used to eliminate time step restrictions due to small cells where the boundary intersects the mesh the projection step uses an approximate projection based on a cartesian grid method for potential flow the method incorporates knowledge of the body through volume and area fractions along with certain other integrals over the mixed cells convergence results are given for the projection itself and for the time dependent algorithm in two dimensions the method is also demonstrated on flow past a half cylinder with vortex shedding

induced electric current based formulation in computations of low magnetic reynolds number magnetohydrodynamic flows we use the induced electric current as the main electromagnetic variable to compute low magnetic reynolds number magnetohydrodynamic mhd flows the equation for the induced electric current is derived by taking the curl of the induction equation and using ampere s law boundary conditions on the induced electric current are derived at the interface between the liquid and the thin conducting wall by considering the current loop closing in the wall and the adjacent liquid these boundary conditions at the liquid solid interface include the robin boundary condition for the wall normal component of the current and an additional equation for the wall potential to compute the tangential current component the suggested formulation denominated j formulation is applied to three common types of mhd wall bounded flows by implementing the finite difference technique i high hartmann number fully developed flows in a rectangular duct with conducting walls ii quasi two dimensional duct flow in the entry into a magnet and iii flow past a magnetic obstacle comparisons have been performed against the traditional formulation based on the induced magnetic field b formulation demonstrating very good agreement

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 factorized l fuzzy automaton and its l fuzzy topological characterization abstract this paper is towards the study of l fuzzy automata via theory of factorizations where l is a complete residuated lattice we study the concept of factorization of l fuzzy sets and factorization of collection of l fuzzy sets such factorizations are used i to study the concept of minimal l fuzzy automaton and ii to introduce l fuzzy topologies for the study of concepts associated with an l fuzzy automaton specifically we introduce the notion of factorized l fuzzy automaton corresponding to a given l fuzzy automaton and study the minimality of such automaton further we associate l fuzzy topologies for factorized l fuzzy automaton and use these to characterize some algebraic concepts

operations on type 2 fuzzy sets in this paper we discuss set operations on type 2 fuzzy sets including join and meet under minimum product t norm algebraic operations properties of membership grades of type 2 sets and type 2 relations and their compositions all this is needed to implement a type 2 fuzzy logic system fls

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

safe diagnosability of stochastic discrete event systems recently safe diagnosability of discrete event systems dess was investigated by paoli and lafortune which was viewed as the first necessary step of fault tolerant supervision in this paper we consider the problem of safe diagnosability in the framework of stochastic discrete event systems sdess we define the notion of safe diagnosability for stochastic automata in which fault detection occurs before any given forbidden string in the failed mode of system is executed the relationship between diagnosability and safe diagnosability for sdess is analyzed in particular a necessary and sufficient condition for safe diagnosability of sdess is presented by constructing the recognizer of illegal language and the safe diagnoser some examples are described to illustrate the results

gerris a tree based adaptive solver for the incompressible euler equations in complex geometries an adaptive mesh projection method for the time dependent incompressible euler equations is presented the domain is spatially discretised using quad octrees and a multilevel poisson solver is used to obtain the pressure complex solid boundaries are represented using a volume of fluid approach second order convergence in space and time is demonstrated on regular statically and dynamically refined grids the quad octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features the source code of the method implementation is freely available

a boundary condition capturing method for poisson s equation on irregular domains interfaces have a variety of boundary conditions or jump conditions that need to be enforced the ghost fluid method gfm was developed to capture the boundary conditions at a contact discontinuity in the inviscid euler equations and has been extended to treat more general discontinuities such as shocks detonations and deflagrations and compressible viscous flows in this paper a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous this new method is robust and easy to implement even in three spatial dimensions furthermore the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient poisson equation in the absence of interfaces allowing for straightforward application of standard black box solvers

rigorous numerics for ill posed pdes periodic orbits in the boussinesq equation in this paper we develop computer assisted techniques for the analysis of periodic orbits of ill posed partial differential equations as a case study our proposed method is applied to the boussinesq equation which has been investigated extensively because of its role in the theory of shallow water waves the idea is to use the symmetry of the solutions and a newton kantorovich type argument the radii polynomial approach to obtain rigorous proofs of existence of the periodic orbits in a weighted l1 banach space of space time fourier coefficients with exponential decay we present several computer assisted proofs of the existence of periodic orbits at different parameter values

fault diagnosis in discrete event systems framework and model reduction a state based approach for online passive fault diagnosis in systems modeled as finite state automata is presented in this framework the system and the diagnoser the fault detection system do not have to be initialized at the same time furthermore no information about the state or even the condition failure status of the system before the initiation of diagnosis is required the design of the fault detection system in the worst case has exponential complexity a model reduction scheme with polynomial time complexity is introduced to reduce the computational complexity of the design diagnosability of failures is studied and necessary and sufficient conditions for failure diagnosability are derived

validated continuation for equilibria of pdes one of the most efficient methods for determining the equilibria of a continuous parameterized family of differential equations is to use predictor corrector continuation techniques in the case of partial differential equations this procedure must be applied to some finite dimensional approximation which of course raises the question of the validity of the output we introduce a new technique that combines the information obtained from the predictor corrector steps with ideas from rigorous computations and verifies that the numerically produced equilibrium for the finite dimensional system can be used to explicitly define a set which contains a unique equilibrium for the infinite dimensional partial differential equation using the cahn hilliard and swift hohenberg equations as models we demonstrate that the cost of this new validated continuation is less than twice the cost of the standard continuation method alone

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

a current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number part ii on an arbitrary collocated mesh a conservative formulation of the lorentz force is given here for magnetohydrodynamic mhd flows at a low magnetic reynolds number with the current density calculated based on ohm s law and the electrical potential formula this conservative formula shows that the total momentum contributed from the lorentz force is conservative when the applied magnetic field is constant for the case with a non constant applied magnetic field the lorentz force has been divided into two parts a strong globally conservative part and a weak locally conservative part the conservative formula has been employed to develop a conservative scheme for the calculation of the lorentz force on an unstructured collocated mesh only the current density fluxes on the cell faces which are calculated using a consistent scheme with good conservation are needed for the calculation of the lorentz force meanwhile a conservative interpolation technique is designed to get the current density at the cell center from the current density fluxes on the cell faces this conservative interpolation can keep the current density at the cell center conservative which can be used to calculate the lorentz force at the cell center with good accuracy the lorentz force calculated from the conservative current at the cell center is equivalent to the lorentz force from the conservative formula when the applied magnetic field is constant which can conserve the total momentum we will further prove that the simple interpolation scheme used in the part i m j ni r munipalli n b morley p y huang m abdou a current density conservative scheme for mhd flows at a low magnetic reynolds number part i on a rectangular collocated grid system journal of computational physics in press doi 10 1016 j jcp 2007 07 025 of this series of papers is conservative on a rectangular grid and can keep the total momentum conservative in a rectangular grid

fuzzy discrete event systems under fuzzy observability and a test algorithm in order to more effectively cope with the real world problems of vagueness impreciseness and subjectivity fuzzy discrete event systems fdess were proposed recently notably fdess have been applied to biomedical control for human immunodeficiency virus hiv acquired immune deficiency syndrome aids treatment planning and sensory information processing for robotic control qiu independently developed supervisory control theory of fdess we note that the controllability of events in qiu s work is fuzzy but the observability of events is crisp and the observability of events in cao and ying s work is also crisp although the controllability is not completely crisp since the controllable events can be disabled with any degrees motivated by the necessity to consider the situation that the events may be observed or controlled with some membership degrees in this paper we establish the supervisory control theory of fdess with partial observations in which both the observability and controllability of events are fuzzy instead we formalize the notions of fuzzy controllability condition and fuzzy observability condition in addition controllability and observability theorem of fdess is set up in a more generic framework in particular we present a detailed computing flow to verify whether the controllability and observability conditions hold thus this result can decide the existence of supervisors also we use this computing method to check the existence of supervisors in the controllability and observability theorem of classical discrete event systems dess which is a new method and different from classical case a number of examples are elaborated on to illustrate the presented results

fuzzy discrete event systems for multiobjective control framework and application to mobile robot navigation fuzzy discrete event systems fdess have been introduced in recent years to model systems whose discrete states or discrete state transitions can be uncertain and are hence determined by a possibility degree this paper develops an fdes framework for the control of sampled data systems that have to fulfill multiple objectives the choice of a fuzzy system representation is justified by the assumption of a controller realization that depends on various potentially imprecise sensor measurements the proposed framework consists of three basic steps that are performed at each sampling instant first the current fuzzy state of the system is determined by a sensor evaluation second the fuzzy state in the future sampling instant is predicted for all possible control actions of the system finally an original multiobjective weighting strategy is proposed to determine the control action to be applied in the current sampling instant the features of the proposed approach are demonstrated by a detailed mobile robot example which includes a simulation study

supervisory control of fuzzy discrete event systems for simulation equivalence the supervisory control theory of fuzzy discrete event systems fdess for fuzzy language equivalence has been developed however in a way language equivalence has limited expressiveness therefore if the given specification can not be expressed by language equivalence then the control for language equivalence does not work in this paper we further establish the supervisory control theory of fdess for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence first we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two fdess then we present a method for deciding whether there is a fuzzy simulation or not in addition we also show several basic properties of fuzzy simulation relations afterward we put forward the notion of fuzzy simulation based controllability and in particular show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of fdess moreover we study the range control problem of fdess some examples are given to illustrate the main results obtained

observability and decentralized control of fuzzy discrete event systems fuzzy discrete event systems as a generalization of crisp discrete event systems have been introduced in order that it is possible to effectively represent uncertainty imprecision and vagueness arising from the dynamic of systems a fuzzy discrete event system has been modeled by a fuzzy automaton its behavior is described in terms of the fuzzy language generated by the automaton in this paper we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation observability normality and co observability of crisp languages are extended to fuzzy languages it is shown that the observability together with controllability of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor when a decentralized solution is desired it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co observable moreover the infimal controllable and observable fuzzy superlanguage and the supremal controllable and normal fuzzy sublanguage are also discussed simple examples are provided to illustrate the theoretical development

a projection method for locally refined grids a numerical method for the solution of the two dimensional euler equatons for incompressible flow on locally refined grids is presented the method is a second order godunov projection method adapted from bell colella and glaz second order accuracy of the numerical method in time and space is established through numerical experiments the main contributions of this work concern the formulation and implementation of a projection for refined grids a discussion of the adjointness relation between gradient and divergence operators for a refined grid mac projection is presented and a refined grid approximate projection is developed an efficient multigrid method which exactly solves the projection is developed and a method for casting certain approximate projections as mac projections on refined grids is presented

monotone scheme and boundary conditions for finite volume simulation of magnetohydrodynamic internal flows at high hartmann number a monotone scheme for finite volume simulation of magnetohydrodynamic internal flows at high hartmann number is presented the numerical stability is analysed with respect to the electromagnetic force standard central finite differences applied to finite volumes can only be numerically stable if the vector products involved in this force are computed with a scheme using a fully staggered grid the electromagnetic quantities electric currents and electric potential must be shifted by half the grid size from the mechanical ones velocity and pressure an integral treatment of the boundary layers is used in conjunction with boundary conditions for electrically conducting walls the simulations are performed with inhomogeneous electrical conductivities of the walls and reach high hartmann numbers in three dimensional simulations even though a non adaptive grid is used

continuation of homoclinic orbits in the suspension bridge equation a computer assisted proof abstract in this paper we prove existence of symmetric homoclinic orbits for the suspension bridge equation u u e u 1 0 for all parameter values 0 5 1 9 for each a parameterization of the stable manifold is computed and the symmetric homoclinic orbits are obtained by solving a projected boundary value problem using chebyshev series the proof is computer assisted and combines the uniform contraction theorem and the radii polynomial approach which provides an efficient means of determining a set centered at a numerical approximation of a solution on which a newton like operator is a contraction

regular article generation of short and long range temporal correlated noises we present the implementation of an algorithm to generate gaussian random noises with prescribed time correlations that can be either long or short ranged examples of langevin dynamics with short and long range noises are presented and discussed