local discontinuous galerkin methods for the stokes system in this paper we introduce and analyze local discontinuous galerkin methods for the stokes system for a class of shape regular meshes with hanging nodes we derive a priori estimates for the l2 norm of the errors in the velocities and the pressure we show that optimal order estimates are obtained when polynomials of degree k are used for each component of the velocity and polynomials of degree k 1 for the pressure for any k ge1 we also consider the case in which all the unknowns are approximated with polynomials of degree k and show that although the orders of convergence remain the same the method is more efficient numerical experiments verifying these facts are displayed

coupling stokes darcy flow with transport a mathematical and numerical model describing chemical transport in a stokes darcy flow system is discussed the flow equations are solved through domain decomposition using classical finite element methods in the stokes region and mixed finite element methods in the darcy region the local discontinuous galerkin ldg method is used to solve the transport equation models dealing with coupling between stokes and darcy equations have been extensively discussed in the literature this paper focuses on the approximation of the transport equation stability of the ldg scheme is analyzed and an a priori error estimate is proved several numerical examples verifying the theory and illustrating the capabilities of the method are presented

algebraic multigrid amg experiences and comparisons algebraic multigrid methods are designed for the solution of sparse linear systems of equations using multigrid principles in contrast to standard multigrid methods amg does not take advantage of the origin of a particular system of equations at hand nor does it exploit any underlying geometrical situation fully automatically and based solely on algebraic information contained in the given matrix amg constructs a sequence of grids and corresponding operators a special amg algorithm will be presented for a wide range of problems including certain problems which do not have a continuous background this algorithm yields an iterative method which exhibits a convergence behavior typical for multigrid methods

indirect adaptive fuzzy control for a nonholonomic underactuated wheeled inverted pendulum vehicle based on a data driven trajectory planner in this study we investigate an error data based trajectory planner and indirect adaptive fuzzy control for a class of wheeled inverted pendulum vehicle systems based on the error dynamics the closed loop trajectory planner can generate the desired velocity values using the virtual acceleration input for the tilt angle subsystem composite control for the rotational and longitudinal subsystems can be constructed via indirect adaptive fuzzy and sliding mode control approaches to achieve simultaneous velocity tracking and tilt angle stabilization we rigorously prove the system stability and convergence of the tracking error signals using the lyapunov theory and lasalle s invariance theorem the results of our numerical simulations demonstrated the efficiency of the proposed control strategies and the implementations of the algorithms

discontinuous galerkin method based on peridynamic theory for linear elasticity modeling of discontinuities shock waves crack surfaces etc in solid mechanics is one of the major research areas in modeling the mechanical behavior of materials among the numerical methods the discontinuous galerkin method dgm poses some advantages in solving these problems in this study a novel formulation for dgm is derived for elastostatics based on the peridynamic theory derivation of the proposed formulation is presented numerical analyses are performed for different problems and the numerical results are compared to that of the known exact solutions of the problems the proposed weak formulation is stable and coercive peridynamic discontinuous galerkin formulation is found to be robust and successful in modeling elastostatic problems copyright 2011 john wiley sons ltd

the generalized riemann problem for reactive flows abstract a generalized riemann problem is introduced for the equations of reactive non viscous compressible flow in one space dimension initial data are assumed to be linearly distributed on both sides of a jump discontinuity the resolution of the singularity is studied and the first order variation in time of flow variables is given in exact form

on 2d elliptic discontinuous galerkin methods we discuss the discretization using discontinuous galerkin dg formulation of an elliptic poisson problem two commonly used dg schemes are investigated the original average flux proposed by bassi and rebay j comput phys 1997 131 267 and the local discontinuous galerkin ldg siam j numer anal 1998 35 2440 2463 scheme in this paper we expand on previous expositions discontinuous galerkin methods theory computation and applications springer berlin 2000 135 146 siam j sci comput 2002 24 2 524 547 int j numer meth engng 2003 58 2 1119 1148 by adopting a matrix based notation with a view to highlighting the steps required in a numerical implementation of the dg method through consideration of standard c0 type expansion bases as opposed to elementally orthogonal expansions with the matrix formulation we are able to apply static condensation techniques to improve efficiency of the direct solver when high order expansions are adopted the use of c0 type expansions also permits the direct enforcement of dirichlet boundary conditions through a lifting approach where the ldg flux does not require further stabilization in our construction we also adopt a formulation of the continuous dg fluxes that permits a more general interpretation of their numerical implementation in particular it allows us to determine the conditions under which the ldg method provides a near local stencil finally a study of the conditioning and the size of the null space of the matrix systems resulting from the dg discretization of the elliptic problem is undertaken copyright 2005 john wiley sons ltd

coupling fluid flow with porous media flow the transport of substances back and forth between surface water and groundwater is a very serious problem we study herein the mathematical model of this setting consisting of the stokes equations in the fluid region coupled with the darcy equations in the porous medium coupled across the interface by the beavers joseph saffman conditions we prove existence of weak solutions and give a complete analysis of a finite element scheme which allows a simulation of the coupled problem to be uncoupled into steps involving porous media and fluid flow subproblems this is important because there are many legacy codes available which have been optimized for uncoupled porous media and fluid flow

a second order godunov type scheme for compressible fluid dynamics abstract a second order accurate scheme for the integration in time of the conservation laws of compressible fluid dynamics is presented two related versions are proposed one lagrangian and the second direct eulerian they both share the common ingredient which is a full analytic solution for the time derivatives of flow quantities at a jump discontinuity assuming initial nonvanishing slopes on both sides while this solution is an extension of the solution to the classical riemann problem the resulting schemes are second order extensions of godunov s methods in both cases they are very simple to implement in computer codes several numerical examples are shown where the only additional mechanism is a simple monotonicity algorithm

selective monostability in multi stable systems we propose a robust method that allows a periodic or a chaotic multi stable system to be transformed to a monostable system at an orbit with dominant frequency of any of the coexisting attractors our approach implies the selection of a particular attractor by periodic external modulation with frequency close to the dominant frequency in the power spectrum of a desired orbit and simultaneous annihilation of all other coexisting states by positive feedback both applied to one of the system parameters the method does not require any preliminary knowledge of the system dynamics and the phase space structure the efficiency of the method is demonstrated in both a non autonomous multi stable laser with coexisting periodic orbits and an autonomous rossler like oscillator with coexisting chaotic attractors the experiments with an erbium doped fibre laser provide evidence for the robustness of the proposed method in making the system monostable at an orbit with dominant frequency of any preselected attractor

a finite element method by patch reconstruction for the stokes problem using mixed formulations abstract in this paper we develop a patch reconstruction finite element method for the stokes problem the weak formulation of the interior penalty discontinuous galerkin is employed the proposed method has a great flexibility in velocity pressure space pairs whose stability properties are confirmed by the inf sup tests numerical examples show the applicability and efficiency of the proposed method

implementation of the grp scheme for computing radially symmetric compressible fluid flows the study of radially symmetric compressible fluid flows is interesting both from the theoretical and numerical points of view spherical explosion and implosion in air water and other media are well known problems in application typical difficulties lie in the treatment of singularity in the geometrical source and the imposition of boundary conditions at the symmetric center in addition to the resolution of classical discontinuities shocks and contact discontinuities in the present paper we present the implementation of direct generalized riemann problem grp scheme to resolve this issue the scheme is obtained directly by the time integration of the fluid flows our new contribution is to show rigorously that the singularity is removable and derive the updating formulae for mass and energy at the center together with the vanishing of the momentum we obtain new numerical boundary conditions at the center which are then incorporated into the grp scheme the main ingredient is the passage from the cartesian coordinates to the radially symmetric coordinates

the numerical solution of diffusion problems in strongly heterogeneous non isotropic materials a new second order finite difference algorithm for the numerical solution of diffusion problems in strongly heterogeneous and non isotropic media is constructed on problems with rough coefficients or highly nonuniform grids the new algorithm is superior to all other algorithms we have compared it with for problems with smooth coefficients on smooth grids the method is comparable with other second order methods the new algorithm is formulated for logically rectangular grids and is derived using thesupport operators method a key idea in deriving the method was to replace the usual inner product of vector functions by an inner product weighted by the inverse of the material properties tensor and to use the flux operator defined as the material properties tensor times the gradient rather than the gradient as one of the basic first order operators in the support operators method the discrete analog of the flux operator must also be the negative adjoint of the discrete divergence in an inner product that is a discrete analog of the continuum inner product the resulting method is conservative and the discrete analog of the variable coefficient laplacian is symmetric and negative definite on nonuniform grids in addition on any grid the discrete divergence is zero on constant vectors the null space for the gradient is the constant functions and when the material properties are piecewise constant the discrete flux operator is exact for piecewise linear functions we compare the methods on some of the most difficult examples to be found in the literature

on discontinuous galerkin methods discontinuous galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present several alternatives for treating the diffusion and advective fluxes have been introduced this report summarizes some of the methods that have been proposed several numerical examples are included in the paper these present discontinuous galerkin solutions of one dimensional problems with a scalar variable results are presented for diffusion reaction problems and advection diffusion problems we discuss the performance of various formulations with respect to accuracy as well as stability of the method copyright 2003 john wiley sons ltd

superconvergence of the velocity in mimetic finite difference methods on quadrilaterals superconvergence of the velocity is established for mimetic finite difference approximations of second order elliptic problems over h 2 uniform quadrilateral meshes the superconvergence result holds for a full tensor coefficient the analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar product in the velocity space the theoretical results are confirmed by numerical experiments

approximation of boundary conditions for mimetic finite difference methods abstract the numerical solution of partial differential equations solved with finite difference approximations that mimic the symmetry properties of the continuum differential operators and satisfy discrete versions of the appropriate integral identities are more likely to produce physically faithful results furthermore those properties are often needed when using the energy method to prove convergence and stability of a particular difference approximation unless special care is taken mimetic difference approximations derived for the interior grid points will fail to preserve the symmetries and identities between the gradient curl and divergence operators at the computational boundary in this paper we describe how to incorporate boundary conditions into finite difference methods so the resulting approximations mimic the identities for the differential operators of vector and tensor calculus the approach is valid for a wide class of partial differential equations of mathematical physics and will be described for poisson s equation with dirichlet neumann and robin boundary conditions we prove that the resulting difference approximation is symmetric and positive definite for each of these boundary conditions

a discontinuous hp finite element method for diffusion problems 1 d analysis abstract this paper presents the mathematical analysis of a new variant of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems not requiring auxiliary variables such as those used in mixed methods the focus of this study is on a class of linear second order boundary value problems for which we prove stability and a priori error estimates in both the finite and infinite dimensional spaces

controlling transient chaos in deterministic flows with applications to electrical power systems and ecology transient chaos is a common phenomenon in nonlinear dynamics of many physical biological and engineering systems in applications it is often desirable to maintain sustained chaos even in parameter regimes of transient chaos we address how to sustain transient chaos in deterministic flows we utilize a simple and practical method based on extracting the fundamental dynamics from time series to maintain chaos the method can result in control of trajectories from almost all initial conditions in the original basin of the chaotic attractor from which transient chaos is created we apply our method to three problems 1 voltage collapse in electrical power systems 2 species preservation in ecology and 3 elimination of undesirable bursting behavior in a chemical reaction system s1063 651x 99 04902 8 pacs number s 05 45 2a transient chaos is a ubiquitous phenomenon in nonlinear dynamical systems in such a case a trajectory typically behaves chaotically for a finite amount of time before settling into a final usually nonchaotic state the dynamical origin of transient chaos is known it is due to nonattracting chaotic saddles in phase space 1 4 a chaotic saddle is a bounded set and it has fractal structures in both stable and unstable directions in contrast to a chaotic attractor which exhibits a fractal structure only in the stable direction due to the fractal structure in the unstable direction an infinite number of gaps of all sizes exists along the unstable manifold of the chaotic saddle an initial condition is typically attracted toward the chaotic saddle along the stable direction stays in its vicinity for a finite amount of time and then leaves the chaotic saddle through one of the gaps in the unstable direction it is known that chaotic saddles and transient chaos are responsible for important physical phenomena such as chaotic

exploring partial control of chaotic systems in this paper we make a thorough exploration of the technique of partial control of chaotic systems this control technique allows one to keep the trajectories of a dynamical system close to a chaotic saddle even if the control applied is smaller than the effects of environmental noise in the system provided that the chaotic saddle is due to the existence of a horseshoelike mapping in phase space we state this here in a mathematically precise way using the conley moser conditions and we prove that they imply that our partial control strategy can be applied we also give an upper bound of the control noise ratio needed to achieve this goal and we describe how this technique can be applied for large noise values finally we study in detail the effect of imperfect targeting in our control technique all these results are illustrated numerically with the paradigmatic henon map

mortar multiscale finite element methods for stokes darcy flows we investigate mortar multiscale numerical methods for coupled stokes and darcy flows with the beavers joseph saffman interface condition the domain is decomposed into a series of subdomains coarse grid of either stokes or darcy type the subdomains are discretized by appropriate stokes or darcy finite elements the solution is resolved locally in each coarse element on a fine scale allowing for non matching grids across subdomain interfaces coarse scale mortar finite elements are introduced on the interfaces to approximate the normal stress and impose weakly continuity of the normal velocity stability and a priori error estimates in terms of the fine subdomain scale h h and the coarse mortar scale h h are established for fairly general grid configurations assuming that the mortar space satisfies a certain inf sup condition several examples of such spaces in two and three dimensions are given numerical experiments are presented in confirmation of the theory

korn s inequalities for piecewise h 1 vector fields korn s inequalities for piecewise h 1 vector fields are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

a triangulated vortex method for the axisymmetric euler equations a new method is presented for the prediction of unsteady axisymmetric inviscid flows by combining a triangulated vortex approach with a novel evaluation technique for the biot savart integrals a lagrangian vortex method is developed which eliminates the singularities usually present in axisymmetric methods without recourse to normalizations or other approximations furthermore the computational effort scales as the number of control points n and in the large n limit depends only on the order of quadrature employed the accuracy and computational effort are assessed by comparison with the velocity field of a gaussian core vortex ring and the use of the technique is illustrated by computation of the motion of norbury rings and of vortex ring pairing

adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small gain approach this paper considers the adaptive fuzzy robust control problem for a class of single input and single output siso stochastic nonlinear systems in strict feedback form the systems under study possess unstructured uncertainties unknown dead zone uncertain dynamics and unknown gain functions in the controller design fuzzy logic systems are adopted to approximate the unknown functions and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics by combining the backstepping technique with the stochastic small gain approach a novel adaptive fuzzy robust control scheme is developed it is shown that the proposed control approach can guarantee that the closed loop system is input state practically stable isps in probability and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters simulation results are provided to illustrate the effectiveness of the proposed control approach

a stochastic particle mesh scheme for uncertainty propagation in vortical flows abstract a new mesh particle scheme is constructed for uncertainty propagation in vortical flow the scheme is based on the incorporation of polynomial chaos pc expansions into a lagrangian particle approximation of the navier stokes equations the main idea of the method is to use a unique set of particles to transport the stochastic modes of the solution the particles are transported by the mean velocity field while their stochastic strengths are updated to account for diffusive and convective effects induced by the coupling between stochastic modes an integral treatment is used for the evaluation of the coupled stochastic terms following the framework of the particle strength exchange pse methods which yields a conservative algorithm it is also shown that it is possible to apply solution algorithms used in deterministic setting including particle mesh techniques and particle remeshing thus the method combines the advantages of particles discretizations with the efficiency of pc representations validation of the method on uncertain diffusion and convection problems is first performed an example is then presented of natural convection of a hot patch of fluid in infinite domain and the computations are used to illustrate the effectiveness of the approach for both large number of particles and high order pc expansions

adaptive neural output feedback controller design with reduced order observer for a class of uncertain nonlinear siso systems an adaptive output feedback control is studied for uncertain nonlinear single input single output systems with partial unmeasured states in the scheme a reduced order observer roo is designed to estimate those unmeasured states by employing radial basis function neural networks and incorporating the roo into a new backstepping design an adaptive output feedback controller is constructively developed a prominent advantage is its ability to balance the control action between the state feedback and the output feedback in addition the scheme can be still implemented when all the states are not available the stability of the closed loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set a simulation example is given to validate the effectiveness of the proposed scheme

the generalized riemann problems for compressible fluid flows towards high order the generalized riemann problems grp for nonlinear hyperbolic systems of balance laws in one space dimension are now well known and can be formulated as follows given initial data which are smooth on two sides of a discontinuity determine the time evolution of the solution near the discontinuity in particular the grp of k 1 th order high resolution is based on an analytical evaluation of time derivatives up to kth order which turns out to be dependent only on the spatial derivatives up to kth order while the classical riemann problem serves as a primary building block in the construction of many numerical schemes most notably the godunov scheme the analytic study of grp will lead to an array of grp schemes which extend the godunov scheme currently there are extensive studies on the second order grp scheme which proves to be robust and is capable of resolving complex multidimensional fluid dynamic problems ben artzi and falcovitz 2003 4 in this paper we provide a new approach for solving the grp for the compressible flow system towards high order accuracy the derivation of second order grp solver is more concise compared to those in previous works and the third order grp or quadratic grp is resolved for the first time the latter is shown to be necessary through numerical experiments with strong discontinuities our method relies heavily on the new treatment of rarefaction waves indeed as a main technical step the propagation of singularities argument for the rarefaction fan is simplified by deriving the linear ode systems for the evolution of characteristic derivatives in the x t coordinates for generalized riemann invariants the case of sonic point is incorporated into a general treatment the accuracy of the derived grp solvers is justified and numerical examples are presented for the performance of the resulting schemes

an adaptive grp scheme for compressible fluid flows this paper presents a second order accurate adaptive generalized riemann problem grp scheme for one and two dimensional compressible fluid flows the current scheme consists of two independent parts mesh redistribution and pde evolution the first part is an iterative procedure in each iteration mesh points are first redistributed and then a conservative interpolation formula is used to calculate the cell averages and the slopes of conservative variables on the resulting new mesh the second part is to evolve the compressible fluid flows on a fixed nonuniform mesh with the eulerian grp scheme which is directly extended to two dimensional arbitrary quadrilateral meshes several numerical examples show that the current adaptive grp scheme does not only improve the resolution as well as accuracy of numerical solutions with a few mesh points but also reduces possible errors or oscillations effectively

synthesized design of a fuzzy logic controller for an underactuated unicycle in this paper we propose synthesized design of a fuzzy logic controller flc for control of an underactuated unicycle system the flc objective is velocity control of the wheel while keeping the pendulum upright which is an unstable equilibrium the synthesized design consists of three phases first the flc structures including the number of rules membership functions inference and parametric relations are chosen based on heuristic knowledge about the unicycle second on the basis of a linearized model and linear feedback the flc output parameters are determined quantitatively for stabilization of the unicycle third the flc output parameters are tuned using an iterative learning tuning ilt algorithm which minimizes an objective function that specifies the desired unicycle performance the rationale for the synthesized flc design is full utilization of the available information which is achieved by combining model based and model free designs and hence improves the flc performance we minimize the number of flc rules and fuzzy labels six rules are used for regulation or setpoint tasks whereas 10 rules are used with extra integral control to eliminate steady state errors induced by system uncertainties and disturbances only two fuzzy labels are adopted for each fuzzy variable the ilt process consists of two phases exploration for stabilization and exploitation for better performance the effectiveness of the proposed flc is validated using intensive simulations and comparisons

optimal layout design of three dimensional geometrically non linear structures using the element connectivity parameterization method the topology design optimization of three dimensional geometrically non linear continuum structures is still difficult not only because of the size of the problem but also because of the unstable continuum finite elements that arise during the optimization to overcome these difficulties the element connectivity parameterization ecp method with two implementation formulations is proposed in ecp structural layouts are represented by inter element connectivity which is controlled by the stiffness of element connecting zero length links depending on the link location ecp may be classified as an external ecp e ecp or an internal ecp i ecp in this paper i ecp is newly developed to substantially enhance computational efficiency the main idea in i ecp is to reduce system matrix size by eliminating some internal degrees of freedom associated with the links at voxel level as for ecp implementation with commercial software e ecp developed earlier for two dimensional problems is easier to use even for three dimensional problems because it requires only numerical analysis results for design sensitivity calculation the characteristics of the i ecp and e ecp methods are compared and these methods are validated with numerical examples copyright 2006 john wiley sons ltd

support operator finite difference algorithms for general elliptic problems abstract an algorithm is developed for discretizing boundary value problems given by a general linear elliptic second order partial differential equation with general mixed or robin boundary conditions in general logically rectangular grids the continuum problem can be written as an operator equation where the operator is self adjoint and positive definite the discrete approximations have the same property consequently the matrices for the discrete problem are symmetric and positive definite also the scheme has a nearest neighbor stencil consequently the most powerful linear solvers can be applied in smooth grids the algorithm produces second order accurate solutions it is the generality of the problem general matrix coefficients general boundary conditions general logically rectangular grids that makes finding such an algorithm difficult the algorithm which is a combination of the method of support operators and the mapping method overcomes certain difficulties of the individual methods producing a high quality algorithm for solving general elliptic problems

fuzzy adaptive output feedback control of mimo nonlinear systems with partial tracking errors constrained in this paper a partial tracking error constrained fuzzy output feedback dynamic surface control dsc scheme is proposed for a class of uncertain multi input and multi output mimo nonlinear systems the considered mimo nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design with the help of fuzzy logic systems identifying the mimo unknown nonlinear systems a fuzzy adaptive observer is established to estimate the unmeasured states by transforming the tracking errors into new virtual error variables and based on the dsc backstepping recursive design technique a new adaptive fuzzy output feedback control method is developed it is proved that the proposed control approach can guarantee that all the signals of the resulting closed loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds the simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme

efficient dg like formulation equipped with curved boundary edges for solving elasto acoustic scattering problems summary a discontinuous galerkin dg based approach is proposed for computing the scattered field from an elastic bounded object immersed in an infinite homogeneous fluid medium the proposed method possesses two distinctive features first it employs higher order polynomial shape functions needed to address the high frequency propagation regime second it is equipped with curved boundary edges to provide an accurate representation of the fluid structure interface the most salient benefits resulting from the latter feature as demonstrated by the numerical investigation are the following i an improvement by at least two orders of magnitude on the relative error and ii the disappearance of spurious resonance frequencies in the surrounding fluid medium in addition the reported numerical results reveal that when using cubic polynomials with less than three elements per wavelength the proposed dg method computes the scattered field with a relative error below 1 for an elastic scatterer of about 30 wavelengths this observation highlights the potential of the proposed solution methodology for efficiently solving mid frequency to high frequency elasto acoustic scattering problems copyright 2014 john wiley sons ltd

convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes the stability and convergence properties of the mimetic finite difference method for diffusion type problems on polyhedral meshes are analyzed the optimal convergence rates for the scalar and vector variables in the mixed formulation of the problem are proved

an element wise locally conservative galerkin lcg method for solving diffusion and convection diffusion problems an element wise locally conservative galerkin lcg method is employed to solve the conservation equations of diffusion and convection diffusion this approach allows the system of simultaneous equations to be solved over each element thus the traditional assembly of elemental contributions into a global matrix system is avoided this simplifies the calculation procedure over the standard global continuous galerkin method in addition to explicitly establishing element wise flux conservation in the lcg method elements are treated as sub domains with weakly imposed neumann boundary conditions the lcg method obtains a continuous and unique nodal solution from the surrounding element contributions via averaging it is also shown in this paper that the proposed lcg method is identical to the standard global galerkin gg method at both steady and unsteady states for an inside node thus the method has all the advantages of the standard gg method while explicitly conserving fluxes over each element several problems of diffusion and convection diffusion are solved on both structured and unstructured grids to demonstrate the accuracy and robustness of the lcg method both linear and quadratic elements are used in the calculations for convection dominated problems petrov galerkin weighting and high order characteristic based temporal schemes have been implemented into the lcg formulation

controlling dynamics in spatially extended systems spatially extended systems exhibit a variety of spatiotemporal dynamics from stable to chaotic these dynamics can change under pathological conditions and impair normal functions thus having the ability to control the altered dynamics for improved functioning has the potential for wide ranging applications in real and artificial systems here we propose a simple and general method that can be used to target the spatiotemporal dynamics both globally and in spatially localized regions in either direction i e towards the stable or unstable manifold by simply changing the strength and the sign of an externally applied perturbation or pinning the method is applicable to both chaotic and nonchaotic systems with discrete and continuous local dynamics and for different topologies of interactions we also apply it to simulate an experiment on epileptogenic neuronal activity in rat hippocampal tissue b j gluckman et al j neurophys 76 6202 1996 this unified approach for differential targeting of global and local dynamics promises to be useful for systems spanning large spatial scales and having structural and functional heterogeneity

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

a direct eulerian grp scheme for compressible fluid flows a direct eulerian generalized riemann problem grp scheme is derived for compressible fluid flows riemann invariants are introduced as the main ingredient to resolve the generalized riemann problem grp directly for the eulerian formulation the crucial auxiliary lagrangian scheme in the original grp scheme is not necessary in the present framework the delicate sonic cases can be easily treated and the extension to multidimensional cases is obtained using the dimensional splitting technique

solution of the generalized riemann problem for advection reaction equations we present a method for solving the generalized riemann problem for partial differential equations of the advection reaction type the generalization of the riemann problem here is twofold firstly the governing equations include nonlinear advection as well as reaction terms and secondly the initial condition consists of two arbitrary but infinitely differentiable functions an assumption that is consistent with piecewise smooth solutions of hyperbolic conservation laws the solution procedure local and valid for sufficiently small times reduces the solution of the generalized riemann problem of the inhomogeneous nonlinear equations to that of solving a sequence of conventional riemann problems for homogeneous advection equations for spatial derivatives of the initial conditions we illustrate the approach via the model advection reaction equation the inhomogeneous burgers equation and the nonlinear shallow water equations with variable bed elevation

adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead zone inputs this paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with both unknown nonsymmetric dead zone inputs and immeasurable states in this research fuzzy logic systems are utilized to evaluate the unknown nonlinear functions and a fuzzy adaptive state observer is established to estimate the unmeasured states based on the information of the bounds of the dead zone slopes as well as treating the time varying inputs coefficients as a system uncertainty a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique it is shown that the proposed control approach can assure that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded it is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters simulation examples are also provided to illustrate the effectiveness of the proposed approach

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

pulse wave propagation in a model human arterial network assessment of 1 d visco elastic simulations against in vitro measurements a numerical model based on the nonlinear one dimensional 1 d equations of pressure and flow wave propagation in conduit arteries is tested against a well defined experimental 1 1 replica of the human arterial tree the tree consists of 37 silicone branches representing the largest central systemic arteries in the human including the aorta carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs the set up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow terminal branches end in simple resistance models consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure the parameters required by the numerical algorithm are directly measured in the in vitro set up and no data fitting is involved comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1 d time domain formulation to capture the main features of pulse wave propagation measured throughout the system test as a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation the experimental set up generates waveforms at terminal branches with additional non physiological oscillations the frequencies of these oscillations are well captured by the 1 d model even though amplitudes are overestimated adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect suggesting that wall visco elasticity might play an important role in the experimental results nevertheless average relative root mean square errors between simulations and experimental waveforms are smaller than 4 for pressure and 19 for the flow at all 70 locations studied

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

local flux mimetic finite difference methods we develop a local flux mimetic finite difference method for second order elliptic equations with full tensor coefficients on polyhedral meshes to approximate the velocity vector variable the method uses two degrees of freedom per element edge in two dimensions and n degrees of freedom per n gonal mesh face in three dimensions to approximate the pressure scalar variable the method uses one degree of freedom per element a specially chosen quadrature rule for the l 2 product of vector functions allows for a local flux elimination and reduction of the method to a cell centered finite difference scheme for the pressure unknowns under certain assumptions first order convergence is proved for both variables and second order convergence is proved for the pressure the assumptions are verified on simplicial meshes for a particular quadrature rule that leads to a symmetric method for general polyhedral meshes non symmetric methods are constructed based on quadrature rules that are shown to satisfy some of the assumptions numerical results confirm the theory

general scaling law in the saddle node bifurcation a complex phase space study saddle node bifurcations have been described in a multitude of nonlinear dynamical systems modeling physical chemical as well as biological systems typically this type of bifurcation involves the transition of a given set of fixed points from the real to the complex phase space after the bifurcation a saddle remnant can continue influencing the flows and generically for non degenerate saddle node bifurcations the time the flows spend in the bottleneck region of the ghost follows the inverse square root scaling law here we analytically derive this scaling law for a general one dimensional analytical autonomous dynamical system undergoing a not necessarily non degenerate saddle node bifurcation in terms of the degree of degeneracy by using complex variable techniques we then compare the analytic calculations with a one dimensional equation modeling the dynamics of an autocatalytic replicator the numerical results are in agreement with the analytical solution

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

numerical simulation of axisymmetric viscous flows by means of a particle method a vortex particle method for the simulation of axisymmetric viscous flow is presented the flow is assumed to be laminar and incompressible the navier stokes equations are expressed in an integral velocity vorticity formulation the inviscid scheme is based on nitsche s method for axisymmetric vortex sheets meanwhile two techniques are proposed for dealing with the viscous term the first uses an integral green s function method while the second is based on a diffusion velocity approach both are obtained by extension of existing methods for 2d flows the problem of satisfying boundary conditions along the axis of symmetry is specifically addressed the problem is solved by using cut off functions that are derived from the green s function of the axisymmetric diffusion equation the scheme is applied to simulate the evolution of vortex rings at intermediate reynolds number the processes of entrainment and wake formation are evident in the calculations as well as the extension of the support of vorticity due to viscous diffusion

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

remark on the generalized riemann problem method for compressible fluid flows the generalized riemann problem grp method was proposed for compressible fluid flows based on the lagrangian formulation m ben artzi j falcovitz a second order godunov type scheme for compressible fluid dynamics j comput phys 55 1 1984 1 32 and a direct eulerian version was developed in m ben artzi j li g warnecke a direct eulerian grp scheme for compressible fluid flows j comput phys 28 2006 19 43 by using the concept of riemann invariants the central feature of the grp method is the resolution of centered rarefaction waves in this note we show how to use the concept of riemann invariants in order to resolve the rarefaction waves in the lagrangian coordinate system and result in the grp scheme

a priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems we analyze three discontinuous galerkin approximations for solving elliptic problems in two or three dimensions in each one the basic bilinear form is nonsymmetric the first one has a penalty term on edges the second has one constraint per edge and the third is totally unconstrained for each of them we prove hp error estimates in the h1 norm optimal with respect to h the mesh size and nearly optimal with respect to p the degree of polynomial approximation we establish these results for general elements in two and three dimensions for the unconstrained method we establish a new approximation result valid on simplicial elements l2 estimates are also derived for the three methods

discontinuous galerkin finite element in time for solving periodic differential equations the dynamics of rotating systems can be modeled by ordinary differential equations with periodic time varying coefficients and forcing discontinuous galerkin dg methods which are known to be higher order accurate a stable and locally conservative are used to solve such equations in this work dg methods are shown to find the steady state periodic solution of a constant coefficient structural dynamics problem with periodic forcing and b helicopter rotor rigid blade flapping equation which is a parametric ordinary differential equation with periodic time varying coefficients and periodic forcing convergence of the numerical solution obtained is studied for both the above equations while h and p are refined separately it is found that the dg method works well for these problems and allows the development of an element level error estimate which can be used to monitor convergence and hence develop adaptive schemes it is clear from the results that even though higher order polynomials result in much faster convergence with reduced computational effort it also results in deterioration of the numerical performance for p 12 two adaptive strategies based on the element level displacement jump norm i e h and hp refinement are proposed and demonstrated on problems with higher harmonic forcing primary controls and parametric variations

a discontinuous galerkin method with nonoverlapping domain decomposition for the stokes and navier stokes problems a family of discontinuous galerkin finite element methods is formulated and analyzed for stokes and navier stokes problems an inf sup condition is established as well as optimal energy estimates for the velocity and l 2 estimates for the pressure in addition it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces

on godunov type methods near low densities abstract when the energy of a flow is largely kinetic many conservative differencing schemes may fail by predicting non physical states with negative density or internal energy we describe as positively conservative the subclass of schemes that by contrast always generate physical solutions from physical data and show that the godunov method is positively conservative it is also shown that no scheme whose interface flux derives from a linearised riemann solution can be positively conservative classes of data that will bring about the failure of such schemes are described however the harten lax van leer hlle scheme is positively conservative under certain conditions on the numerical wavespeeds and this observation allows the linearised schemes to be rescued by modifying the wavespeeds employed

partial control of chaotic systems in a region in phase space where there is a chaotic saddle all initial conditions will escape from it after a transient with the exception of a set of points of zero lebesgue measure the action of an external noise makes all trajectories escape faster attempting to avoid those escapes by applying a control smaller than noise seems to be an impossible task here we show however that this goal is indeed possible based on a geometrical property found typically in this situation the existence of a horseshoe the horseshoe implies that there exist what we call safe sets which assures that there is a general strategy that allows one to keep trajectories inside that region with control smaller than noise we call this type of control partial control of chaos

thermodynamical effects and high resolution methods for compressible fluid flows one of the fundamental differences of compressible fluid flows from incompressible fluid flows is the involvement of thermodynamics this difference should be manifested in the design of numerical schemes unfortunately the role of entropy expressing irreversibility is often neglected even though the entropy inequality as a conceptual derivative is verified for some first order schemes in this paper we refine the grp solver to illustrate how the thermodynamical variation is integrated into the design of high resolution methods for compressible fluid flows and demonstrate numerically the importance of thermodynamic effects in the resolution of strong waves as a by product we show that the grp solver works for generic equations of state and is independent of technical arguments

nonconforming finite elements for the stokes problem on obtient un nouveau resultat de stabilite pour l approximation du probleme de stokes stationnaire avec des elements finis non conformes

a spacetime discontinuous galerkin method for hyperbolic heat conduction non fourier conduction models remedy the paradox of infinite signal speed in the traditional parabolic heat equation for applications involving very short length or time scales hyperbolic conduction models better represent the physical thermal transport processes this paper reviews the maxwell cattaneo vernotte modification of the fourier conduction law and describes its implementation within a spacetime discontinuous galerkin sdg finite element method that admits jumps in the primary variables across element boundaries with arbitrary orientation in space and time a causal advancing front meshing procedure enables a patch wise solution procedure with linear complexity in the number of spacetime elements an h adaptive scheme and a special sdg shock capturing operator accurately resolve sharp solution features in both space and time numerical results for one spatial dimension demonstrate the convergence properties of the sdg method as well as the effectiveness of the shock capturing method simulations in two spatial dimensions demonstrate the proposed method s ability to accurately resolve continuous and discontinuous thermal waves in problems where rapid and localized heating of the conducting medium takes place

analysis of chaotic saddles in low dimensional dynamical systems the derivative nonlinear schrodinger equation abstract in this paper we present a computational study of nonattracting chaotic sets known as chaotic saddles in a low dimensional dynamical system describing stationary solutions of the derivative nonlinear schrodinger equation a driven dissipative model for alfven waves these chaotic saddles have gaps which are filled at chaotic transitions such as a saddle node bifurcation and an interior crisis we give a detailed explanation of how to numerically determine the chaotic saddles and describe how a chaotic attractor after an interior crisis point can be decomposed into two chaotic saddles dynamically connected by a set of coupling unstable periodic orbits created by a gap filling explosion after the crisis this coupling between two chaotic saddles is responsible for the intermittent dynamics displayed by the chaotic system after the interior crisis

observer based adaptive fuzzy tracking control of mimo stochastic nonlinear systems with unknown control directions and unknown dead zones in this paper an adaptive fuzzy backstepping output feedback tracking control approach is proposed for a class of multi input and multi output mimo stochastic nonlinear systems the mimo stochastic nonlinear systems under study are assumed to possess unstructured uncertainties unknown dead zones and unknown control directions by using a linear state transformation the unknown control coefficients and the unknown slopes characteristic of the dead zones are lumped together and the original system is transformed to a new system on which the control design becomes feasible fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by introducing a special nussbaum gain function into the backstepping control design a stable adaptive fuzzy output feedback tracking control scheme is developed the main features of the proposed adaptive control approach are that it can guarantee the stability of the closed loop system and the tracking errors converge to a small neighborhood of zero moreover it can solve the problems of unknown control direction unknown dead zone and unmeasured states simultaneously two simulation examples are provided to show the effectiveness of the proposed approach

mimetic finite difference method for the stokes problem on polygonal meshes various approaches to extend finite element methods to non traditional elements general polygons pyramids polyhedra etc have been developed over the last decade the construction of basis functions for such elements is a challenging task and may require extensive geometrical analysis the mimetic finite difference mfd method works on general polygonal meshes and has many similarities with low order finite element methods both schemes try to preserve the fundamental properties of the underlying physical and mathematical models the essential difference between the two schemes is that the mfd method uses only the surface representation of discrete unknowns to build the stiffness and mass matrices since no extension of basis functions inside the mesh elements is required practical implementation of the mfd method is simple for polygonal meshes that may include degenerate and non convex elements in this article we present a new mfd method for the stokes problem on arbitrary polygonal meshes and analyze its stability the method is developed for the general case of tensor coefficients which allows us to apply it to a linear elasticity problem as well numerical experiments show for the velocity variable second order convergence in a discrete l 2 norm and first order convergence in a discrete h 1 norm for the pressure variable first order convergence is shown in the l 2 norm

regular article a discontinuous galerkin ale method for compressible viscous flows in moving domains we present a matrix free discontinuous galerkin method for simulating compressible viscous flows in two and three dimensional moving domains to this end we solve the navier stokes equations in an arbitrary lagrangian eulerian ale framework spatial discretization is based on standard structured and unstructured grids but using an orthogonal hierarchical spectral basis the method is third order accurate in time and converges exponentially fast in space for smooth solutions a novelty of the method is the use of a force directed algorithm from graph theory that requires no matrix inversion to efficiently update the grid while minimizing distortions we present several simulations using the new method including validation with published results from a pitching airfoil and new results for flow past a three dimensional wing subject to large flapping insect like motion

a robust finite element method for darcy stokes flow finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed the system is approximately a linear stokes problem when the perturbation parameter is large while it degenerates to a mixed formulation of poisson s equation as the perturbation parameter tends to zero it is established basically by numerical experiments that most of the proposed finite element methods for stokes problem or the mixed poisson s system are not well behaved uniformly in the perturbation parameter this is used as the motivation for introducing a new robust finite element which exhibits this property

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

the generalized riemann problem method for the shallow water equations with bottom topography this paper extends the generalized riemann problem method grp to the system of shallow water equations with bottom topography the main contribution is that the generalized riemann problem method j comput phys 1984 55 1 1 32 is used to evaluate the midpoint values of solutions at each cell interface so that the bottom topography effect is included in numerical fluxes and at the same step the source term is discretized with an interface method in which only mid point values are plugged in this scheme is well balanced between the flux gradient and bottom topography when incorporating the surface gradient method sgm j comput phys 2001 168 1 1 25 into data reconstruction step and it is also suitable for both steady and unsteady flow simulations we illustrate the accuracy of this scheme by several 1 d and 2 d numerical experiments copyright 2005 john wiley sons ltd

numerical analysis of growing crack problems using particle discretization scheme this paper presents the particle discretization scheme pds to analyze brittle failure of solids the scheme uses characteristic functions of voronoi and delaunay tessellations to discretize a function and its derivatives respectively a discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks without making any extra computation to accommodate new displacement discontinuities when the scheme is implemented to a finite element method fem the resulting stiffness matrix coincides with the one that is obtained by using linear elements the accuracy of computing a stress intensity factor at a crack tip is examined it is shown that the accuracy is better than that of a fem with linear elements when the rotational degree of freedom is included in discretizing displacement functions three three dimensional growing crack problems are solved by means of the pds and the results are presented copyright 2009 john wiley sons ltd

a mimetic discretization of the stokes problem with selected edge bubbles a new mimetic finite difference method for the stokes problem is proposed and analyzed the mimetic discretization methodology can be understood as a generalization of the finite element method to meshes with general polygons polyhedrons in this paper the mimetic generalization of the unstable p 1 p 0 and the conditionally stable q1 p0 finite element is shown to be fully stable when applied to a large range of polygonal meshes moreover we show how to stabilize the remaining cases by adding a small number of bubble functions to selected mesh edges a simple strategy for selecting such edges is proposed and verified with numerical experiments

a two grid method of a mixed stokes darcy model for coupling fluid flow with porous media flow we study numerical methods for solving a coupled stokes darcy problem in porous media flow applications a two grid method is proposed for decoupling the mixed model by a coarse grid approximation to the interface coupling conditions error estimates are derived for the proposed method both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two grid approach for solving multimodeling problems potential extensions and future directions are discussed

nonlinear dynamics of iterative decoding systems analysis and applications iterative decoding algorithms may be viewed as high dimensional nonlinear dynamical systems depending on a large number of parameters in this work we introduce a simplified description of several iterative decoding algorithms in terms of the a posteriori average entropy and study them as a function of a single parameter that closely approximates the signal to noise ratio snr using this approach we show that virtually all the iterative decoding schemes in use today exhibit similar qualitative dynamics in particular a whole range of phenomena known to occur in nonlinear systems such as existence of multiple fixed points oscillatory behavior bifurcations chaos and transient chaos are found in iterative decoding algorithms as an application we develop an adaptive technique to control transient chaos in the turbo decoding algorithm leading to a substantial improvement in performance we also propose a new stopping criterion for turbo codes that achieves the same performance with considerably fewer iterations

the local discontinuous galerkin method for the oseen equations we introduce and analyze the local discontinuous galerkin method for the oseen equations of incompressible fluid flow for a class of shape regular meshes with hanging nodes we derive optimal a priori estimates for the errors in the velocity and the pressure in l 2 and negative order norms numerical experiments are presented which verify these theoretical results and show that the method performs well for a wide range of reynolds numbers

discontinuous galerkin and mimetic finite difference methods for coupled stokes darcy flows on polygonal and polyhedral grids we study locally mass conservative approximations of coupled darcy and stokes flows on polygonal and polyhedral meshes the discontinuous galerkin dg finite element method is used in the stokes region and the mimetic finite difference method is used in the darcy region dg finite element spaces are defined on polygonal and polyhedral grids by introducing lifting operators mapping mimetic degrees of freedom to functional spaces optimal convergence estimates for the numerical scheme are derived results from computational experiments supporting the theory are presented

arbitrary high order discontinuous galerkin schemes based on the grp method for compressible euler equations combined with the discontinuous galerkin dg framework the generalized riemann problem grp method is applied to design a grp dg scheme with high order accuracy for compressible euler equations since numerical fluxes with second order accuracy in time are derived by the grp method the reconstruction steps for physical variables in the new scheme are halved compared with the traditional runge kutta discontinuous galerkin rk dg scheme the numerical results are also improved due to more introduced physical information several numerical examples verify the validity of the proposed schemes

brief paper robust adaptive motion force control for wheeled inverted pendulums previous works for wheeled inverted pendulums usually eliminate nonholonomic constraint force in order to make the control design easier under the assumption that the friction force from the ground is as large as needed nevertheless such an assumption is unfeasible in practical applications in this paper adaptive robust motion force control for wheeled inverted pendulums is investigated with parametric and functional uncertainties the proposed robust adaptive controls based on physical properties of wheeled inverted pendulums make use of online adaptation mechanism to cancel the unmodelled dynamics based on lyapunov synthesis the proposed controls ensure that the system outputs track the given bounded reference signals within a small neighborhood of zero and guarantee the semi global uniform boundedness of all closed loop signals the effectiveness of the proposed controls is verified through extensive simulations

a general discontinuous galerkin method for finite hyperelasticity formulation and numerical applications a discontinuous galerkin formulation of the boundary value problem of finite deformation elasticity is presented the primary purpose is to establish a discontinuous galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the dg concept can show its superiority compared to the continuous formulation the method is based on a general hu washizu de veubeke functional allowing for displacement and stress discontinuities in the domain interior it is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation the consistency and linearized stability of the method in the non linear range as well as its convergence rate are proven an implementation in three dimensions is developed showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner in order to demonstrate the versatility accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided copyright 2006 john wiley sons ltd

locally conservative coupling of stokes and darcy flows a locally conservative numerical method for solving the coupled stokes and darcy flows problem is formulated and analyzed the approach employs the mixed finite element method for the darcy region and the discontinuous galerkin method for the stokes region a discrete inf sup condition and optimal error estimates are derived

adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums in this paper adaptive fuzzy logic control of dynamic balance and motion is investigated for wheeled inverted pendulums with parametric and functional uncertainties the proposed adaptive fuzzy logic control based on physical properties of wheeled inverted pendulums makes use of a fuzzy logic engine and a systematic online adaptation mechanism to approximate the unknown dynamics based on lyapunov synthesis the fuzzy control ensures that the system outputs track the given bounded reference signals to within a small neighborhood of zero and guarantees semi global uniform boundedness of all closed loop signals the effectiveness of the proposed control is verified through extensive simulations

a conley index study of the evolution of the lorenz strange set abstract in this paper we study the lorenz equations using the perspective of the conley index theory more specifically we examine the evolution of the strange set that these equations posses throughout the different values of the parameter we also analyze some natural morse decompositions of the global attractor of the system and the role of the strange set in these decompositions we calculate the corresponding morse equations and study their change along the successive bifurcations we see how the main features of the evolution of the lorenz system are explained by properties of the dynamics of the global attractor in addition we formulate and prove some theorems which are applicable in more general situations these theorems refer to poincare andronov hopf bifurcations of arbitrary codimension bifurcations with two homoclinic loops and a study of the role of the traveling repellers in the transformation of repeller attractor pairs into attractor repeller ones