continuous dependence and convergence results for brinkman and forchheimer models with variable viscosity the equations for convective fluid motion in a porous medium of brinkman or forchheimer type are analysed when the viscosity varies with either temperature or a salt concentration mundane situations such as salinization require models which incorporate strong viscosity variation therefore we establish rigorous a priori bounds with coefficients which depend only on boundary data initial data and the geometry of the problem which demonstrate continuous dependence of the solution on changes in the viscosity a convergence result is established for the darcy equations when the variable viscosity is allowed to tend to a constant viscosity

structure generating mechanisms in agent based models abstract the emergence of dynamical structures in multi agent systems is analysed three different mechanisms are identified namely 1 sensitive dependence in the agent dynamics and convex coupling 2 sensitive dependence and extremal dynamics and 3 interaction through a collectively generated field the dynamical origin of the emergent structures is traced back either to a modification by interaction of the lyapunov spectrum or to multistable dynamics

spatiotemporal recurrences of sandpile avalanches abstract we study the space and time properties of avalanches in a continuous sandpile model by constructing a temporally directed network linking together the recurrent avalanche events based on their spatial separation we use two different criteria for network construction a later event is connected to a previous one if it is either nearest or farthest from it among all the later events with this we observe scale free regimes emerge as characterized by the following power law exponents a 1 7 for the avalanche size distributions b f 2 1 in the in degree distribution of farthest recurrences c 1 for the separation distances and d 1 for the temporal separations of recurrences our results agree with earlier observations that describe the sandpile avalanches as repulsive events i e the next avalanche is more likely to be physically separated from an earlier one these observations which are not captured by usual interoccurrence statistics and by random connection mechanisms suggest an underlying spatiotemporal organization in the sandpile that makes it useful for modeling real world systems

simple deterministic self organized critical system we introduce a continuous cellular automaton that presents self organized criticality it is one dimensional totally deterministic without any embedded randomness not even in the initial conditions this system is in the same universality class as the oslo rice pile boundary driven interface depinning and the train model for earthquakes although the system is chaotic in the thermodynamic limit chaos occurs only in a microscopic level

optimal design of frame structures using multivariate spline approximation the objective of this work is to demonstrate the efficiency and applicability of the optimization algorithm using a multivariate spline approximation in the present algorithm based on the function values and first order derivatives of the constraints available at the intermediate points of optimization an explicit approximation of constraint functions is created by using the least squares spline algorithm the nonlinearity of the function is adaptively updated using feedback information from the previous two iterations for finding the order of spline approximation in addition constraint deletion and design variable linking concepts are employed in solving the approximate problem by using the quasianalytical sequential quadratic programming and dual methods the behavior constraints include stresses displacements and local buckling in the optimum design of frame structures to demonstrate the broad applicability of the optimization algorithm the cross sectional dimensions are directly selected as the design variables for frame problems having thin walled rectangular and tube cross sectional members and the cross sectional areas are selected as design variables for an section problem

higher order failure probability calculation using nonlinear approximations use of approximations for calculating the structural failure probability under uncertainties is a necessary aspect but efficient use of suitable approximations at different stages of reliability prediction and design makes this valuable tool practical for many large scale structures the objective of this paper is to address the modern approximation concepts and their utility in structural reliability estimation emphasis is placed on building the higher order approximations using intervening variables to closely represent the nonlinear limit state functions the most probable failure point mpp search can be carried either in x space or u space for a wide variety of random variable distributions several test problems with highly nonlinear performance functions are used to demonstrate the accuracy of the proposed method

power spectrum of mass and activity fluctuations in a sandpile we consider a directed abelian sandpile on a strip of size 2 ifmmode times else texttimes fi n driven by adding a grain randomly at the left boundary after every t timesteps we establish the exact equivalence of the problem of mass fluctuations in the steady state and the number of zeros in the ternary base representation of the position of a random walker on a ring of size 3 n we find that while the fluctuations of mass have a power spectrum that varies as 1 f for frequencies in the range 3 ensuremath 2n ensuremath ll f ensuremath ll 1 t the activity fluctuations in the same frequency range have a power spectrum that is linear in f

improved decay estimates in time dependent stokes flow abstract this paper investigates the time dependent stokes flow of a viscous fluid in a channel with nonzero net entry flow assuming the fluid to be initially at rest with entry flow at the finite end of a semi infinite channel energy bounds for the flow are derived it is shown that the flow decays exponentially in energy norm to a transient poiseuille flow as the distance from the finite end tends to infinity the problem was previously investigated by lin saacm 2 1992 249 264 for the case in which the net entry flow was zero our methods are patterned after those of lin but a somewhat better choice of arbitrary constants yields an improved decay rate for lin s problem

continuous transforming the btw to the manna model abstract in this paper we define some stochastic perturbations of the btw model which make it into manna model these models have a continuous parameter p where p 0 and 1 correspond to the btw and manna models respectively we have investigated the properties of the statistical observables of the waves of avalanches for various values of p our data supports the expectation of a crossover in such systems at large scales manna model is dominant therefore we find strong evidence in favor of the universality classes being distinct also it is observed that the btw fixed point is unstable when manna type perturbation is added to the model

spatial decay bounds for double diffusive convection in brinkman flow abstract this paper examines the time dependent double diffusive convection in brinkman flow in a semi infinite cylinder under appropriate initial and boundary conditions the authors establish exponential decay of solutions in energy norm with distance from the finite end of the cylinder

dissipative sandpile models with universal exponents we consider a dissipative variant of the stochastic abelian sandpile model on a two dimensional lattice the boundaries are closed and the dissipation is due to the fact that each toppled grain is removed from the lattice with probability epsilon it is shown that the scaling properties of this model are in the universality class of the stochastic abelian models with conservative dynamics and open boundaries in particular the dissipation rate epsilon can be adjusted according to a suitable function epsilon f l such that the avalanche size distribution will coincide with that of the conservative model on a finite lattice of size l

stochastic porous media equations and self organized criticality the existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and wiener forcing term is proven the finite time extinction of solutions with high probability is also proven in 1 d the results are relevant for self organized criticality behavior of stochastic nonlinear diffusion equations with critical states

on inequalities of korn friedrichs and babuska aziz korn s inequalities for integrals of quadratic functionals subject to certain side conditions have played a fundamental role in the development of elasticity theory see e g i 14 the korn inequalities are essential in establishing coerciveness of the differential operators of linear elastostatics and thus form the basis for existence results in that theory 9 among other areas in elasticity where consideration of korn s inequalities arise we cite for example fundamental studies on the mathematical foundations of finite elements 15 17 stability theory 11 and qualitative analyses of solution behavior such as those involved in the investigation of saint venant s principle 18 20 in the latter two areas of application in particular information on the optimal constants appearing in the inequalities the korn constants is of importance thus several investigations have been concerned with evaluating the korn constants for specific domains and with obtaining bounds for these constants 4 6 8 12 13 our purpose in this paper is to draw attention to an equivalence for two dimensional simply connected domains between korn s inequality in the second case see w 2 here and two other inequalities for quadratic functionals which have received comparatively little attention in the literature the first of these is an inequality due apparently to k o frmorichs 2 between the real and imaginary parts of an analytic function or equivalently between a harmonic function and its conjugate defined on a two dimensional domain r thus if w z f ig z xl ix2 is analytic on r friedrichs inequality reads

dynamics and entropy in the zhang model of self organized criticality we give a detailed study of dynamical properties of the zhang model including evaluation of topological entropy and estimates for the lyapunov exponents and the dimension of the attractor in the thermodynamic limit the entropy goes to zero and the lyapunov spectrum collapses

explicit constraint approximation forms in structural optimization part 1 analyses and projections abstract an analytical study of several alternative forms of constraint approximation relevant to problems in structural design is presented limitations of the existing forms of the constraint approximations are stated and methods are outlined to improve them a new generalized form of constraint approximation is proposed for optimal design problems with and without design variable linking a power form of constraint approximation is derived for bending types of finite elements having nonlinear size stiffness relationships a detailed analysis to determine the relative effectiveness of the various forms is included a rating guideline is proposed to quantify the characteristics of chosen approximations or family of approximations on grounds of accuracy and of conservatism of remaining feasible

emergence of quasiunits in the one dimensional zhang model we study the zhang model of sandpile on a one dimensional chain of length l where a random amount of energy is added at a randomly chosen site at each time step we show that in spite of this randomness in the input energy the probability distribution function of energy at a site in the steady state is sharply peaked and the width of the peak decreases as l 1 2 for large l we discuss how the energy added at one time is distributed among different sites by topplings with time we relate this distribution to the time dependent probability distribution of the position of a marked grain in the one dimensional abelian model with discrete heights we argue that in the large l limit the variance of energy at site x has a scaling form l 1 g x l where g xi varies as ln 1 xi for small xi which agrees very well with the results from numerical simulations

high quality approximation of eigenvalues in structural optimization a new function for approximating natural frequency constraints during structural optimization is presented the rayleigh quotient approximation rqa presented here icreases the quality of the approximate frequency constraint by approximating the modal strain and kinetic energies instead of the frequency eigenvalue itself

a univariate approximation at most probable point for higher order reliability analysis this paper presents a new univariate method employing the most probable point as the reference point for predicting failure probability of structural and mechanical systems subject to random loads material properties and geometry the method involves novel decomposition at the most probable point that facilitates a univariate approximation of a general multivariate function response surface generation of the univariate function and monte carlo simulation in addition to the effort of identifying the most probable point the method requires a small number of exact or numerical evaluations of the performance function at selected input results of four numerical examples involving elementary mathematical functions and structural solid mechanics problems indicate that the proposed method provides accurate and computationally efficient estimates of probability of failure finally the fatigue failure of lever arm in a wheel loader has been evaluated demonstrating the ability of the new method in solving industrial scale fatigue reliability problems

asymptotic behavior and synchronizability characteristics of a class of recurrent neural networks we propose an approach to the analysis of the influence of the topology of a neural network on its synchronizability in the sense of equal output activity rates given by a particular neural network model the model we introduce is a variation of the zhang model we investigate the time asymptotic behavior of the corresponding dynamical system in particular the conditions for the existence of an invariant compact asymptotic set and apply the results of the synchronizability analysis on a class of random scale free networks and to the classical random networks with poisson connectivity distribution

characteristics of deterministic and stochastic sandpile models in a rotational sandpile model rotational constraint representing a local external bias generally has a nontrivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena in order to study the effect of rotational bias in an out of equilibrium situation like self organized criticality a two state quasideterministic rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains an extended set of critical exponents are estimated to characterize the avalanche properties at the nonequilibrium steady state of the model the probability distribution functions are found to obey usual finite size scaling supported by negative time autocorrelation between the toppling waves the model exhibits characteristics of both deterministic and stochastic sandpile models

the btw mechanism on a self similar image of a square a path to unexpected exponents abstract we define the btw mechanism on a two dimensional heterogeneous self similar lattice our model exhibits the power distribution of avalanches with the exponent 2 2 where is the similarity exponent of the lattice the inequality 1 for the first time detected in this paper inside a broad class of sand piles is ensured by random loading uniformly distributed over the lattice

structural reliability optimization using an efficient safety index calculation procedure the objective of this paper is to conduct reliability based structural optimization in a multidisciplinary environment an efficient reliability analysis is developed by expanding the limit functions in terms of intermediate design variables the design constraints are approximated using multivariate splines in searching for the optimum the reduction in computational cost realized in safety index calculation and optimization are demonstrated through several structural problems this paper presents safety index computation analytical sensitivity analysis of reliability constraints and optimization using truss frame and plate examples

convergence and continuous dependence results for the brinkman equations the brinkman equations governing the flow of fluid in double diffusive convection are investigated in this paper and the structural stability results for the coefficients are obtained

large scale simulations of the zhang sandpile model we consider the non abelian sandpile model introduced by y c zhang on a two dimensional square lattice the static and dynamical properties of the model are investigated and compared to the abelian sandpile model of bak tang and wiesenfeld a detailed analysis which takes the finite size effects into account yields that the exponents of the avalanche probability distribution are the same as in the abelian model

new adaptive move limit management strategy for approximate optimization part 2 approximations play an important role in multidisciplinary design optimization by offering system behavior information at a relatively low cost most approximate optimization strategies are sequential in which an optimization of an approximate problem subject to design variable move limits is iteratively repeated until convergence the move limits are imposed to restrict the optimization to regions of the design space in which the approximations provide meaningful information to ensure convergence of the sequence of approximate optimizations to a karush kuhn tucker solution a move limit management strategy is required in a companion paper issues of move limit management are reviewed and a new adaptive strategy for move limit management is developed wujek b a and renaud j e new adaptive move limit management strategy for approximate optimization part 1 aiaa journal vol 36 no 10 1998 pp 1911 1921 with its basis in the provably convergent trust region methodology the trust region ratio approximation method tram strategy utilizes available gradient information and employs a backtracking process using various two point approximation techniques to provide a flexible move limit adjustment factor the tram strategy is successfully implemented in application to several multidisciplinary design optimization test problems in addition a comprehensive study comparing the performance of the tram strategy to existing move limit strategies is conducted results indicate that application of the tram strategy results in increased efficiency for approximate optimization processes these implementation studies highlight the ability of the tram strategy to control the amount of approximation error and efficiently manage the convergence to a karush kuhn tucker solution

a new three point approximation approach for design optimization problems in this paper a newly developed three point approximation scheme is proposed the expression of this scheme consists of a linear combination of the direct and reciprocal linear taylor expansions as well as of the lumped diagonal terms of the second order direct and inverse terms the unknown parameters of the expression are computed on the basis of the function and gradient values at three points in the design space based on this approach the accuracy of the existing constraint approximation methods can be improved the e ectiveness of the proposed approach is demonstrated on a number of numerical examples the numerical results are also compared with those of the previously published work copyright 2001 john wiley sons ltd

spatial decay bounds for the channel flow of the boussinesq equations in this paper we consider the boussinesq equations in a semi infinite channel we show that under appropriate restrictions on the data if the fluid velocity initially is small the solution will tend exponentially to a transient laminar flow as the distance from the entry section tends to infinity we also derive the explicit decay bounds

on the nonstationary linearized navier stokes problem in domains with cylindrical outlets to infinity the nonstationary linearized navier stokes system is studied in the domain with cylindrical outlets to infinity in weighted function spaces with an exponential weight function it is proved that under natural compatibility conditions there exists a unique solution with prescribed fluxes over the sections of outlets to infinity that exponentially tends in each outlet to the corresponding nonstationary poiseuille flow

phragmen lindelof alternative results for the shallow water equations for transient compressible viscous flow abstract in this paper the spatial behavior of the viscous shallow water equations in a two dimensional channel domain is studied a differential inequality for suitable energy associated with the solutions of the viscous shallow water equations in a semi infinite channel is derived from which we show the phragmen lindelof alternative results the main tool used is the energy method our results can be viewed as a version of saint venant s principle to the transient compressible viscous flow

decay estimates for homogeneous boussinesq equations in a semi infinite pipe abstract in this paper we establish the spatial decay bounds for homogeneous boussinesq equations in a semi infinite pipe flow assuming that the entrance velocity and magnetic field data are restricted appropriately and it converges to laminar flow as the distance down the pipe tends to infinity we derive a second order differential inequality that leads to an exponential decay estimate for the energy e z t defined in 27 we also indicate how to establish the explicit bound for the total energy

sandpile models and random walkers on finite lattices abelian sandpile models both deterministic such as the bak tang wiesenfeld btw model p bak c tang and k wiesenfeld phys rev lett 59 381 1987 and stochastic such as the manna model s s manna j phys a 24 l363 1991 are studied on finite square lattices with open boundaries the avalanche size distribution p l n is calculated for a range of system sizes l the first few moments of this distribution are evaluated numerically and their dependence on the system size is examined the sandpile models are conservative in the sense that grains are conserved in the bulk and can leave the system only through the boundaries it is shown that the conservation law provides an interesting connection between the sandpile models and random walk models using this connection it is shown that the average avalanche sizes l for the btw and manna models are equal to each other and both are equal to the average path length of a random walker starting from a random initial site on the same lattice of size l this is in spite of the fact that the sandpile models with deterministic btw and stochastic manna toppling rules exhibit different critical exponents indicating that they belong to different universality classes

lyapunov exponents and transport in the zhang model of self organized criticality we discuss the role played by lyapunov exponents in the dynamics of zhang s model of self organized criticality we show that a large part of the spectrum the slowest modes is associated with energy transport in the lattice in particular we give bounds on the first negative lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time we then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites we use a finite size scaling ansatz for the lyapunov spectrum and relate the scaling exponent to the scaling of quantities such as avalanche size duration density of active sites etc

dynamical properties of the zhang model of self organized criticality critical exponents of the infinitely slowly driven zhang model of self organized criticality are computed for d52 and 3 with particular emphasis devoted to the various roughening exponents besides confirming recent estimates of some exponents new quantities are monitored and their critical exponents computed among other results it is shown that the three dimensional exponents do not coincide with the bak tang wiesenfeld phys rev lett 59 381 1987 phys rev a 38 364 1988 abelian model and that the dynamical exponent as computed from the correlation length and from the roughness of the energy profile do not necessarily coincide as is usually implicitly assumed an explanation for this is provided the possibility of comparing these results with those obtained from renormalization group arguments is also briefly addressed s1063 651x 98 06107 8 pacs number s 64 60 lx

high dimensional model representation method for fuzzy structural dynamics abstract uncertainty propagation in multi parameter complex structures possess significant computational challenges this paper investigates the possibility of using the high dimensional model representation hdmr approach when uncertain system parameters are modeled using fuzzy variables in particular the application of hdmr is proposed for fuzzy finite element analysis of linear dynamical systems the hdmr expansion is an efficient formulation for high dimensional mapping in complex systems if the higher order variable correlations are weak thereby permitting the input output relationship behavior to be captured by the terms of low order the computational effort to determine the expansion functions using the cut method scales polynomically with the number of variables rather than exponentially this logic is based on the fundamental assumption underlying the hdmr representation that only low order correlations among the input variables are likely to have significant impacts upon the outputs for most high dimensional complex systems the proposed method is first illustrated for multi parameter nonlinear mathematical test functions with fuzzy variables the method is then integrated with a commercial finite element software adina modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach in the numerical examples triangular membership functions have been used and the results have been validated against direct monte carlo simulations it is shown that using the proposed hdmr approach the number of finite element function calls can be reduced without significantly compromising the accuracy

spatial decay estimates in time dependent double diffusive darcy plane flow this paper considers the time dependent double diffusive convective darcy flow in a semi infinite channel an exponential decay estimate in terms of the distance from the finite end of the channel is obtained from a second order differential inequality for a weighted energy integral the paper also indicates how to bound the total weighted energy

hybrid high dimensional model representation for reliability analysis abstract this paper presents a new probabilistic method based on hybrid high dimensional model representation hhdmr for predicting the failure probability of structural and mechanical systems subject to random loads material properties and geometry high dimensional model representation hdmr is a general set of quantitative model assessment and analysis tools for capturing the high dimensional relationships between sets of input and output model variables it is a very efficient formulation of the system response if higher order variable cooperative effects are weak and if the response function is dominantly of additive nature allowing the physical model to be captured by the first few lower order terms but if multiplicative nature of the response function is dominant then all right hand side components of hdmr must be used to be able to obtain the best result however if hdmr requires all components which means 2 n number of components to get a desired accuracy making the method very expensive in practice then factorized hdmr fhdmr can be used but in most cases the limit state performance function has neither additive nor multiplicative nature rather it has an intermediate nature this paper presents a new hhdmr based approximation for the limit state performance functions having an intermediate nature the proposed approximation of an implicit limit state performance function includes both hdmr and fhdmr expansions through a hybridity parameter as an alternative to the conventional methods for reliability analysis which are very computationally demanding when applied in conjunction with complex finite element models this study aims to assess how accurately and efficiently hhdmr technique can capture complex model output uncertainty once the approximate form of the original implicit limit state performance function is defined the failure probability can be obtained by statistical simulation results of six numerical examples involving mathematical functions and structural solid mechanics problems indicate that the failure probability obtained using hhdmr based approximation of an implicit limit state performance function provides significant accuracy when compared with the conventional monte carlo method while requiring fewer original model simulations

what can one learn about self organized criticality from dynamical systems theory we develop a dynamical system approach for the zhang model of self organized criticality for which the dynamics can be described either in terms of iterated function systems or as a piecewise hyperbolic dynamical system of skew product type in this setting we describe the soc attractor and discuss its fractal structure we show how the lyapunov exponents the haussdorf dimensions and the system size are related to the probability distribution of the avalanche size via the ledrappier young formula

flooding transition in the topography of toppling surfaces of stochastic and rotational sandpile models a continuous phase transition occurs in the topography of toppling surfaces of stochastic and rotational sandpile models when they are flooded with liquid say water the toppling surfaces are extracted from the sandpile avalanches that appear due to sudden burst of toppling activity in the steady state of these sandpile models though a wide distribution of critical flooding heights exists a critical point is defined by merging the flooding thresholds of all the toppling surfaces the criticality of the transition is characterized by power law distributionofislandareainthecriticalregime afinitesizescalingtheoryisdevelopedandverifiedbycalculating several new critical exponents the flooding transition is found to be an interesting phase transition and does not belong to the percolation universality class the universality class of this transition is found to depend on the degree of self affinity of the toppling surfaces characterized by the hurst exponent h and the fractal dimension df of critical spanning islands the toppling surfaces of different stochastic sandpile models are found to have a single hurst exponent whereas those of different rotational sandpile models have another hurst exponent as a consequence the universality class of different sandpile models remains preserved within the same symmetry of the models

finite time extinction for stochastic sign fast diffusion and self organized criticality we prove finite time extinction for stochastic sign fast diffusion equations driven by linear multiplicative space time noise corresponding to the bak tang wiesenfeld model for self organized criticality this solves a problem posed and left open in several works barbu methods appl sci 36 1726 1733 2013 rockner and wang j lond math soc 2 87 545 560 2013 barbu et al j math anal appl 389 147 164 2012 barbu and rockner comm math phys 311 539 555 2012 barbu et al comm math phys 285 901 923 2009 c r math acad sci paris 347 1 2 81 84 2009 the highly singular degenerate nature of the drift in interplay with the stochastic perturbation causes the need for new methods in the analysis of mass diffusion and several new estimates and techniques are introduced

improved two point function approximations for design optimization two point approximations are developed by utilizing both the function and gradient information of two data points the objective of this work is to build a high quality approximation to realize computational savings in solving complex optimization and reliability analysis problems two developments are proposed in the new twopoint approximations 1 calculation of a correction term by matching with the previous known function value and supplementing it to the first order approximation for including the effects of higher order terms and 2 development of a second order approximation without the actual calculation of second order derivatives by using an approximate hessian matrix several highly nonlinear functions and structural examples are used for demonstrating the new two point approximations that improved the accuracy of existing first order methods evelopmentof new and improved constraint approximations has been an active area of research in the mathematical optimization community over the last two decades 1 3 more accurate function approximations reduce the finite element analysis cost and increase the search domain in each iteration of an optimization run recent developments in constraint approximations addressed methods for eigenvalues dynamic response static forces structural reliability etc some of the typical methods are summarized in the following kirsch4 developed a scaling factor for a stiffness matrix and approximated the displacements stresses and forces with respect to sizing and topology variables vanderplaats and salajegheh5 used two levels of approximations for discrete sizing and shape design of structures first for solving the continuous problem and next the discrete one using a dual theory canfield6 developed an approach for eigenvalues by approximating the modal strain and kinetic energies independently thomas et al 7 presented an approximation for the frequency response of damped structures by using the concept of ref 6 a multivariate spline approximation was developed by wang and grandhi8 making use of the previously generated exact finite element analyses similarly a hermite approximation for n dimensional problems used several data points and had the property of reproducing the function and gradient values at the known data points 9 canfield10 used multipoint data in building an approximate hessian matrix and constructed a second order approximation for improving the accuracy toropov et al 11 approximated functions as a linear combination or products of variables and the coefficients of the polynomial were computed by applying a least squared approach on multiple data points fadel et al 12 considered intermediate variables in terms of exponentials and they were computed by matching the approximate function gradients with the previous point s exact values this approach did not compare the function values of the previous point wang and grandhi13 used a single exponential for all of the variables and calculated it by matching the approximate function with the previous point exact value and the gradient information of the previous point was not utilized the proposed paper develops an improved two point approximation utilizing both function and gradient information of two data points in the new two point approximation two developments are proposed 1 calculation of a correction term based on two function values and

a spectral approach for fuzzy uncertainty propagation in finite element analysis abstract uncertainty propagation in complex engineering systems with fuzzy variables constitutes a significant challenge this paper proposes a polynomial chaos type spectral approach based on orthogonal function expansion a fuzzy variable is represented as a set of interval variables via the membership function the interval variables are further transformed into the standard interval 1 1 smooth nonlinear functions of standard interval variables are projected in the basis of legendre polynomials by exploiting its orthogonal properties over the interval 1 1 the coefficients associated with the basis functions are obtained by a galerkin type of error minimisation the method is first illustrated using scalar functions of multiple fuzzy variables later the method is proposed for elliptic type finite element problems where the technique is extended to vector valued functions with multiple fuzzy variables the response of such systems can be expressed in the complete basis of multivariate legendre polynomials the coefficients obtained by galerkin type of error minimisation can be calculated from the solution of an extended set of linear algebraic equations an eigenfunction based model reduction technique is proposed to obtain the coefficient vectors in an efficient way a numerical example of axial deformation of a rod with fuzzy axial stiffness is considered to illustrate the proposed methods linear and nonlinear membership functions are used and the results are compared with direct numerical simulation results

continuous dependence on the soret coefficient for double diffusive convection in darcy flow in this paper the darcy model is used to describe the double diffusive flow of a fluid containing a solute continuous dependence of the solution on the soret coefficient is established

accelerated engineering design optimization using successive matrix inversion method in a design optimization procedure many repeated system analyses are conducted to evaluate certain performances of successively modified structural designs to alleviate the high computational cost of structural reanalysis an augmented preconditioner is introduced by using the successive matrix inversion smi method the smi method as an exact matrix solver is successively applied to an iterative procedure to accelerate the solution convergence by improving the numerical condition of the reanalysis system in this work a new iterative technique the binomial series iterative bsi method is developed from the binomial series expansion by using the same concept as smi as a combined iterative ci method smi is incorporated in the procedure of bsi the ci method combined with smi shows sufficient efficiency and robustness through a stable iterative behaviour due to simple and straightforward computations in the iterative procedure published in 2005 by john wiley sons ltd

spatial decay bounds in time dependent pipe flow of an incompressible viscous fluid in this paper the authors investigate the flow of an incompressible viscous fluid in a semi infinite cylindrical pipe if the net entrance flow is nonzero then the fluid velocity will not tend to zero as the distance from the entrance end tends to infinity when the fluid adheres at the cylinder wall and the fluid is initially at rest assuming that the entrance velocity data are small enough and that the fluid flow converges to a laminar flow as the distance down the pipe tends to infinity it is shown that the convergence in energy measure is at least exponential

self organized criticality in a bulk driven one dimensional deterministic system abstract we introduce a deterministic self organized critical system that is one dimensional and bulk driven we find that there is no unique universality class associated with the system that is the critical exponents change as the parameters of the system are changed this is in contrast with the boundary driven version of the model phys rev e 61 2000 6056 in which the exponents are unique this model can be seen as a discretized version of the conservative limit of the burridge knopoff model for earthquakes

spatial decay in a double diffusive convection problem in darcy flow this paper deals with a model of time dependent double diffusive convection in darcy flow in particular it is concerned with the spatial decay of solutions when the flow is confined to a semi infinite cylinder decay bounds for an energy expression are derived

structural stability for the brinkman equations of flow in double diffusive convection abstract this paper continues the investigation of structural stability for the brinkman equations modeling the double diffusive convection for flow in a porous medium it supplements earlier results of straughan and hutter b straughan k hutter a priori bounds and structural stability for double diffusive convection incorporating the soret effect proc r soc lond ser a 455 1999 767 777

exponential decay estimates for solutions of the von karman equations on a semi infinite strip this paper is concerned with the analysis of saint venant edge effects for nonlinear elastic plates the model used is based on the von karman plate equations a coupled system of two nonlinear elliptic partial differential equations with the biharmonic operator as the principal part energy methods are used to establish a nonlinear integro differential inequality for a quadratic functional arguments based on comparison theorems are then used to establish exponential decay of end effects