fractal reinforcement of elastic membranes we describe a homogenization model of an elastic membrane reinforced by the inclusion of a fractal string we follow a variational approach consisting in proving the convergence of certain energy functionals this leads to the spectral convergence of a sequence of weighted second order elliptic partial differential operators to a singular elliptic operator with a fractal term

spectral triples for the sierpinski gasket abstract we construct a family of spectral triples for the sierpinski gasket k for suitable values of the parameters we determine the dimensional spectrum and recover the hausdorff measure of k in terms of the residue of the volume functional a tr a d s at its abscissa of convergence d d which coincides with the hausdorff dimension d h of the fractal we determine the associated connes distance showing that it is bi lipschitz equivalent to the distance on k induced by the euclidean metric of the plane and show that the pairing of the associated fredholm module with odd k theory is non trivial when the parameters belong to a suitable range the abscissa of convergence d of the energy functional a tr d s 2 d a 2 d s 2 takes the value d e log 12 5 log 2 which we call energy dimension and the corresponding residue gives the standard dirichlet form on k

backstepping with bounded feedbacks for time varying systems a family of time varying nonlinear systems is globally uniformly asymptotically stabilized by bounded feedbacks constructed through a new extension of the backstepping approach explicit expressions of control laws and lyapunov functions are given

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

new control design for bounded backstepping under input delays we provide a new backstepping result for time varying systems with input delays the novelty of our work is in the bounds on the controls and the facts that i one does not need to compute any lie derivatives to apply our controls ii the controls have no distributed terms and iii we do not require any differentiability conditions on the available controls for the subsystems

input output feedback linearization of time delay systems in this note the input output linearization problem iolp for a class of single input single output nonlinear systems with multiple delays in the input the output and the state is studied the problem is solved by means of various static or dynamic compensators including state and output feedback the mathematical setting is based on some noncommutative algebraic tools and the introduction of a nonlinear version of the so called roesser models for this class of systems these are claimed to be the cornerstones for studying nonlinear time delay systems necessary and sufficient conditions are given for the existence of a static or pure shift output feedback which solves the iolp sufficient conditions for the existence of a dynamic state feedback solution are included as well

a further result on global stabilization of oscillators with bounded delayed input this note revisits the problem of globally stabilizing an oscillator with a bounded delayed input it establishes that an oscillator with input saturation can be globally asymptotically stabilized by a linear state feedback even in the presence of an arbitrarily large delay in the input this result strengthens a recent result in the literature which shows that such an oscillator can be globally asymptotically stabilized with a sufficiently small control input and the magnitude of the control input goes to zero as the delay increases to infinity the controller constructed in this note thus improves the efficiency of the closed loop system by fully utilizing the actuator capacity

global stabilization of multiple integrators with bounded controls this paper deals with the global stabilization of a chain of integrators by means of bounded feedback two nonlinear control laws made of summation of saturation of the state are proposed the first one extends that of sussmann sontag and yang 1994 ieee transactions on automatic control 39 12 2411 2425 and the second proposes variable saturation level to improve the performance both remain very simple and significantly improve the efficiency of the approach which is very competitive with respect to the other existing methods especially for its performance complexity ratio the robustness with respect to measurement delay and model uncertainty is numerically tested

a trace theorem for dirichlet forms on fractals abstract we consider a trace theorem for self similar dirichlet forms on self similar sets to self similar subsets in particular we characterize the trace of the domains of dirichlet forms on sierpinski gaskets and sierpinski carpets to their boundaries where the boundaries are represented by triangles and squares that confine the gaskets and the carpets as an application we construct diffusion processes on a collection of fractals called fractal fields these processes behave as an appropriate fractal diffusion within each fractal component of the field

adaptive control scheme for uncertain time delay systems the paper exposes some of the potential of a recently introduced backstepping transformation for linear uncertain time delay systems to address the classic problems of equilibrium regulation under partial measurements disturbance rejection parameter or delay adaptation for each of these problems an implementable control strategy is proposed it is analyzed through a convergence analysis of infinite dimensional dynamics based on a transport partial differential equation representation of the estimated input delay and the mentioned backstepping transformation the considered controllers contain this representation of the system under the form of a distributed parameter system and use it to determine relevant adaptation strategies an illustration example is proposed

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

integrals and potentials of differential 1 forms on the sierpinski gasket abstract we provide a definition of the integral along paths in the sierpinski gasket k for differential smooth 1 forms associated to the standard dirichlet form e on k we show how this tool can be used to study the potential theory on k in particular we prove i a de rham reconstruction of a 1 form from its periods around lacunas in k ii a hodge decomposition of 1 forms with respect to the hilbertian energy norm iii the existence of potentials of smooth 1 forms on a suitable covering space of k we finally show that this framework provides versions of the de rham duality theorem for the fractal k

brownian motion penetrating fractals an application of the trace theorem of besov spaces abstract for a closed connected set f in rn assume that there is a local regular dirichlet form a symmetric diffusion process on f whose domain is included in a lipschitz space or a besov space on f under some condition for the order of the space and the newtonian 1 capacity of f we prove that there exists a symmetric diffusion process on rn which moves like the process on f and like brownian motion on rn outside f as an application we will show that when f is a nested fractal or a sierpinski carpet whose hausdorff dimension is greater than n 2 we can construct brownian motion penetrating the fractal for the proof we apply the technique developed in the theory of besov spaces

on the stability of linear systems with uncertain delay this paper focuses on the stability of some class of delay systems including uncertainty in the delays more precisely we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system if the delay perturbation is constant necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some finite dimensional constant matrix pencil if the delay perturbation is time varying some sufficient stability conditions are derived using exact lyapunov krasovskii functionals illustrative examples are also included

truncation error analysis of lattice boltzmann methods a truncation error analysis is performed for models based on the lattice boltzmann lb equation this analysis involves two steps the recursive application of the lb equation and a taylor series expansion unlike previous analytical studies of lb methods the present work does not assume an asymptotic relationship between the temporal and spatial discretization parameters or between the probability distribution function f and its equilibrium distribution feq effective finite difference stencils are derived for both the distribution function and the primitive variables i e density and velocity the governing partial differential equations are also recovered the associated truncation errors are derived and the results are validated by numerical simulation of analytic flows analysis of the truncation errors elucidates the roles of the kinetic theory relaxation parameter and the discretization parameters x and t the effects of initial and boundary conditions are also addressed and are shown to significantly affect the overall accuracy of the method

asymptotic stabilization of an input delayed chain of integrators with nonlinearity in this paper we consider a stabilization problem of an input delayed chain of integrators with nonlinearity in this system the nonlinear part cannot be directly canceled by the input due to time delay we design a stabilizing controller and show that the system stability is determined by the types of nonlinear functions

a fractional step thermal lattice boltzmann model for high peclet number flow as a promising approach in hydrodynamics and thermodynamics modeling the lattice boltzmann method lbm still suffers severe numerical instability when the temperature field of the flow is convection dominant high peclet number despite a lot of research devoted to solve this problem worldwide to simulate high peclet number thermal flow at comparably few computational cost is still a hard work making it inefficient in practical use in this paper we combine the lbm and the fractional step method to propose a novel and stable thermal lattice boltzmann scheme for high peclet number flow without refining the lattice by numerical tests of thermal poiseuille flow and couette flow we quantify second order accuracy of the proposed model and through several cases of peclet number from low to high the superior stability and efficiency compared with existing thermal lattice boltzmann model

a trace theorem for the dirichlet form on the sierpinski gasket in connection with the theory for brownian motion on fractals a corresponding dirichlet form has been defined we consider here the fractal known as the sierpinski gasket and characterize the tra

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

lattice boltzmann method for 3 d flows with curved boundary in this work we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice boltzmann equation lbe 1 computational stability and accuracy of different lattice boltzmann models and 2 the treatment of the boundary conditions on curved solid boundaries and their 3 d implementations three athermal 3 d lbe models q15d3 q19d3 and q27d3 are studied and compared in terms of efficiency accuracy and robustness the boundary treatment recently developed by filippova and hanel 1998 j comp phys 147 219 and mei et al 1999 j comp phys 155 307 in 2 d is extended to and implemented for 3 d the convergence stability and computational efficiency of the 3 d lbe models with the boundary treatment for curved boundaries were tested in simulations of four 3 d flows 1 fully developed flows in a square duct 2 flow in a 3 d lid driven cavity 3 fully developed flows in a circular pipe and 4 a uniform flow over a sphere we found that while the 15 velocity 3 d q15d3 model is more prone to numerical instability and the q27d3 is more computationally intensive the q19d3 model provides a balance between computational reliability and efficiency through numerical simulations we demonstrated that the boundary treatment for 3 d arbitrary curved geometry has second order accuracy and possesses satisfactory stability characteristics

optimal relaxation collisions for lattice boltzmann methods the optimal relaxation time of about 0 8090 has been proposed to balance the efficiency stability and accuracy at a given lattice size of numerical simulations with lattice boltzmann methods the optimal lattice size for a desired reynolds number can be refined by reducing the mach number for incompressible flows the functioned polylogarithm polynomials are defined and used to express the lattice boltzmann equations at different time scales and to analyze the impact of relaxation times and lattice sizes on truncation errors smaller truncation errors can be achieved when relaxation times are greater than 0 5 and less than 1 0 the steady state lid driven cavity flow was chosen to validate the code of lattice boltzmann procedures the applications of the optimal relaxation parameters numerically balance the stability efficiency and accuracy through hartmann flow the optimal relaxation time can also be used to select the initial lattice size for the channel flow over a square cylinder with a given mach number

exact spectrum of the laplacian on a domain in the sierpinski gasket abstract for a certain domain in the sierpinski gasket sg whose boundary is a line segment a complete description of the eigenvalues of the laplacian with an exact count of dimensions of eigenspaces under the dirichlet and neumann boundary conditions is presented the method developed in this paper is a weak version of the spectral decimation method due to fukushima and shima since for a lot of bad eigenvalues the spectral decimation method can not be used directly let 0 x x be the eigenvalue counting functions of the laplacian associated to sg and respectively we prove a comparison between 0 x and x says that 0 0 x x c x log 2 log 5 log x for sufficiently large x for some positive constant c as a consequence x g log x x log 3 log 5 o x log 2 log 5 log x as x for some right continuous discontinuous log 5 periodic function g r r with 0 inf r g sup r g moreover we explain that the asymptotic expansion of x should admit a second term of the order log 2 log 5 that becomes apparent from the experimental data this is very analogous to the conjectures of weyl and berry

connections between razumikhin type theorems and the iss nonlinear small gain theorem a razumikhin type theorem that guarantees input to state stability for functional differential equations with disturbances is established using the nonlinear small gain theorem the result is used to show that input to state stabilizability for nonlinear finite dimensional control systems is robust in an appropriate sense to small time delays at the input also relaxed razumikhin type conditions guaranteeing global asymptotic stability for differential difference equations are given

technical communique robust stabilization of uncertain input delayed systems using reduction method this paper concerns a robust stabilization problem that arises when applying the so called reduction method to multiple input delayed systems with parametric uncertainties a robust stabilizing controller that can be constructed easily by solving convex problems in terms of linear matrix inequalities is presented numerical examples are provided to show that in many cases the proposed controller is less conservative and easier to obtain than the existing controllers

backstepping for nonlinear systems with delay in the input revisited in this paper a new solution to the problem of globally asymptotically stabilizing a nonlinear system in feedback form with a known pointwise delay in the input is proposed the result covers a family of systems wider than those studied in the literature and endows with control laws with a single delay in contrast to those given in previous works which include two distinct pointwise delays or distributed delays the strategy of design is based on the construction of an appropriate lyapunov krasovskii functional an illustrative example ends the paper