simulating the dynamics of inextensible vesicles by the penalty immersed boundary method in this paper we develop an immersed boundary ib method to simulate the dynamics of inextensible vesicles interacting with an incompressible fluid in order to take into account the inextensibility constraint of the vesicle the penalty immersed boundary pib method is used to virtually decouple the fluid and vesicle dynamics as numerical tests of our current pib method the dynamics of single and multiple inextensible vesicles under shear flows have been extensively explored and compared with the previous literature the method is also validated by a series of convergence study which confirms its consistent first order accuracy on the velocity field the vesicle configuration the vesicle area and the perimeter errors in addition the method is also applied to study a binary component vesicle problem

a unified view of the ipa sf and lr gradient estimation techniques we study the links between the likelihood ratio lr gradient estimation technique sometimes called the score function sf method and infinitesimal perturbation analysis ipa we show how ipa can be viewed as a degenerate special case of the lr and sf techniques by selecting an appropriate representation of the underlying sample space for a given simulation experiment we also show how different definitions of the sample space yield different variants of the lr method some of them mixing ipa with more straightforward lr we illustrate this by many examples we also give sufficient conditions under which the gradient estimators are unbiased

extended immersed boundary method using fem and rkpm abstract the proposed extended immersed boundary method eibm has several distinct features in comparison with the immersed boundary ib method in the ib method the interaction between the immersed elastic boundary and the surrounding viscous fluid is replaced with an equivalent body force distribution within the fluid domain the key ingredient of the ib method is the enforcement of the energy input from the equivalent body force into the fluid domain to be the same at all time as that of the elastic forces within the ib in eibm instead of the volumeless immersed elastic boundary we consider the submerged elastic solid which occupies a finite volume within the fluid domain in particular we replace the kinematic and dynamic matching of the fluid solid interface and the effect of the submerged solid with a judiciously chosen collection of equivalent nodal forces calculated in the context of finite element formulations the employment of the finite element representation enables a realistic stress analysis for the submerged solid subject to large deformations finally in eibm we also replace the discretized delta function commonly used in the ib method with the kernel functions in meshless reproducing kernel particle method rkpm with this improvement using the same finite support domain we could improve the discretized delta function from c 1 to c n continuity where n is chosen according to the required smoothness and resolution of such functions and more importantly enables the use of non uniform meshing in the fluid domain these extensions may eventually open doors to the modelling of complex biological fluid involving molecular cellular and flexible vessel flow interactions

on actor critic algorithms in this article we propose and analyze a class of actor critic algorithms these are two time scale algorithms in which the critic uses temporal difference learning with a linearly parameterized approximation architecture and the actor is updated in an approximate gradient direction based on information provided by the critic we show that the features for the critic should ideally span a subspace prescribed by the choice of parameterization of the actor we study actor critic algorithms for markov decision processes with polish state and action spaces we state and prove two results regarding their convergence

a boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d we present a new method for the evolution of inextensible vesicles immersed in a stokesian fluid we use a boundary integral formulation for the fluid that results in a set of nonlinear integro differential equations for the vesicle dynamics the motion of the vesicles is determined by balancing the non local hydrodynamic forces with the elastic forces due to bending and tension numerical simulations of such vesicle motions are quite challenging on one hand explicit time stepping schemes suffer from a severe stability constraint due to the stiffness related to high order spatial derivatives and a milder constraint due to a transport like stability condition on the other hand an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step we present two semi implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme we discretize the equations by using a spectral method in space and a multistep third order accurate scheme in time we use the fast multipole method fmm to efficiently compute vesicle vesicle interaction forces in a suspension with a large number of vesicles we report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme

a hierarchy of near optimal policies for multistage adaptive optimization in this paper we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty applicable to multistage robust optimization and stochastic programming we introduce a hierarchy of near optimal polynomial disturbance feedback control policies and show how these can be computed by solving a single semidefinite programming problem the approach yields a hierarchy parameterized by a single variable the degree of the polynomial policies which controls the trade off between the optimality gap and the computational requirements we evaluate our framework in the context of three classical applications two in inventory management and one in robust regulation of an active suspension system in which very strong numerical performance is exhibited at relatively modest computational expense

a reinforcement learning adaptive fuzzy controller for robots in this paper a new reinforcement learning scheme is developed for a class of serial link robot arms traditional reinforcement learning is the problem faced by an agent that must learn behavior through trial and error interactions with a dynamic environment in the proposed reinforcement learning scheme an agent is employed to collect signals from a fixed gain controller an adaptive critic element and a fuzzy action generating element the action generating element is a fuzzy approximator with a set of tunable parameters and the performance measurement mechanism sends an error metric to the adaptive critic element for generating and transferring a reinforcement learning signal to the agent moreover a tuning algorithm of the proposed scheme that can guarantee both tracking performance and stability is derived from the lyapunov stability theory therefore a combination of adaptive fuzzy control and reinforcement learning scheme is also concerned with algorithms for eliminating a sequence of decisions from experience simulations of the proposed reinforcement adaptive fuzzy control scheme on the cart pole balancing problem and a two degree of freedom 2dof manipulator scara robot arm verify the effectiveness of our approach

coupling of finite element and boundary integral methods for a capsule in a stokes flow we introduce a new numerical method to model the fluid structure interaction between a microcapsule and an external flow an explicit finite element method is used to model the large deformation of the capsule wall which is treated as a bidimensional hyperelastic membrane it is coupled with a boundary integral method to solve for the internal and external stokes flows our results are compared with previous studies in two classical test cases a capsule in a simple shear flow and in a planar hyperbolic flow the method is found to be numerically stable even when the membrane undergoes in plane compression which had been shown to be a destabilizing factor for other methods the results are in very good agreement with the literature when the viscous forces are increased with respect to the membrane elastic forces three regimes are found for both flow cases our method allows a precise characterization of the critical parameters governing the transitions copyright 2010 john wiley sons ltd

general results on the convergence of stochastic algorithms a deterministic approach is proposed for proving the convergence of stochastic algorithms of the most general form under necessary conditions on the input noise and reasonable conditions on the nonnecessarily continuous mean field emphasis is placed on the case where more than one stationary point exists we also use this approach to prove the convergence of a stochastic algorithm with markovian dynamics

importance sampling for stochastic simulations importance sampling is one of the classical variance reduction techniques for increasing the efficiency of monte carlo algorithms for estimating integrals the basic idea is to replace the original random mechanism in the simulation by a new one and at the same time modify the function being integrated in this paper the idea is extended to problems arising in the simulation of stochastic systems discrete time markov chains continuous time markov chains and generalized semi markov processes are covered applications are given to a gi g 1 queueing problem and response surface estimation computation of the theoretical moments arising in importance sampling is discussed and some numerical examples given

event based optimization of markov systems recent research indicates that markov decision processes mdps and perturbation analysis pa based optimization can be derived easily from two fundamental performance sensitivity formulas with this sensitivity point of view an event based optimization approach including event based sensitivity analysis and event based policy iteration was proposed via an example by x r cao discrete event dyn syst theory appl vol 15 pp 169 197 2005 this approach utilizes the special feature of a system and illustrates how the potentials can be aggregated using the special feature the approach applies to many practical problems that do not fit well the standard mdp formulation this note provides a mathematical formulation and proves the main results for this approach

a basic formula for online policy gradient algorithms this note presents a new basic formula for sample path based estimates for performance gradients for markov systems called policy gradients in reinforcement learning literature with this basic formula many policy gradient algorithms including those that have previously appeared in the literature can be easily developed the formula follows naturally from a sensitivity equation in perturbation analysis new research direction is discussed

decentralized delay optimal control for interference networks with limited renewable energy storage in this paper we consider delay minimization for interference networks with renewable energy source where the transmission power of a node comes from both the conventional utility power ac power and the renewable energy source we assume the transmission power of each node is a function of the local channel state local data queue state and local energy queue state only we consider two delay optimization formulations namely the decentralized partially observable markov decision process dec pomdp and noncooperative partially observable stochastic game posg in dec pomdp formulation we derive a decentralized online learning algorithm to determine the control actions and lagrangian multipliers lms simultaneously based on the policy gradient approach under some mild technical conditions the proposed decentralized policy gradient algorithm converges almost surely to a local optimal solution in the noncooperative posg formulation the transmitter nodes are noncooperative we extend the decentralized policy gradient solution and establish the technical proof for almost sure convergence of the learning algorithms in both cases the solutions are very robust to model variations

validation of an immersed thick boundary method for simulating fluid structure interactions of deformable membranes this paper constitutes an extension of the work of mendez et al 2014 36 for three dimensional simulations of deformable membranes under flow an immersed thick boundary method is used combining the immersed boundary method with a three dimensional modeling of the structural part the immersed boundary method is adapted to unstructured grids for the fluid resolution using the reproducing kernel particle method an unstructured finite volume flow solver for the incompressible navier stokes equations is coupled with a finite element solver for the structure the validation process relying on a number of test cases proves the efficiency of the method and its robustness is illustrated when computing the dynamics of a tri leaflet aortic valve the proposed immersed thick boundary method is able to tackle applications involving both thin and thick membranes closed and open membranes in significantly high reynolds number flows and highly complex geometries

simulation based optimization of markov reward processes this paper proposes a simulation based algorithm for optimizing the average reward in a finite state markov reward process that depends on a set of parameters as a special case the method applies to markov decision processes where optimization takes place within a parametrized set of policies the algorithm relies on the regenerative structure of finite state markov processes involves the simulation of a single sample path and can be implemented online a convergence result with probability 1 is provided

an immersed interface method for incompressible navier stokes equations the method developed in this paper is motivated by peskin s immersed boundary ib method and allows one to model the motion of flexible membranes or other structures immersed in viscous incompressible fluid using a fluid solver on a fixed cartesian grid the ib method uses a set of discrete delta functions to spread the entire singular force exerted by the immersed boundary to the nearby fluid grid points our method instead incorporates part of this force into jump conditions for the pressure avoiding discrete dipole terms that adversely affect the accuracy near the immersed boundary this has been implemented for the two dimensional incompressible navier stokes equations using a high resolution finite volume method for the advective terms and a projection method to enforce incompressibility in the projection step the correct jump in pressure is imposed in the course of solving the poisson problem this gives sharp resolution of the pressure across the interface and also gives better volume conservation than the traditional ib method comparisons between this method and the ib method are presented for several test problems numerical studies of the convergence and order of accuracy are included

a modification of the delves lyness method for locating the zeros of analytic functions abstract a new formula is proposed for the calculation of the integrals involved in the application of the delves lyness method for locating the zeros of analytic functions inside an arbitrary simple smooth contour this formula does not contain the derivative of the analytic function whose zeros are sought and moreover is free from multivaluedness problems for the integrand

immersed finite element method abstract in this paper the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models in ifem a lagrangian solid mesh moves on top of a background eulerian fluid mesh which spans over the entire computational domain hence the mesh generation is greatly simplified moreover both fluid and solid domains are modeled with the finite element methods and the continuity between the fluid and solid sub domains are enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method rkpm delta function in comparison with the immersed boundary ib method the higher ordered rkpm delta function enables the fluid domain to have nonuniform spatial meshes with arbitrary geometries and boundary conditions the use of such kernel functions may eventually open doors to multi scale and multi resolution modelings of complex fluid structure interaction problems rigid and deformable spheres dropping in channels are simulated to demonstrate the unique capabilities of the proposed method the results compare well with the experimental data to the authors knowledge these are the first solutions that deal with particulate flows with very flexible solids

a spectral boundary integral method for flowing blood cells a spectral boundary integral method for simulating large numbers of blood cells flowing in complex geometries is developed and demonstrated the blood cells are modeled as finite deformation elastic membranes containing a higher viscosity fluid than the surrounding plasma but the solver itself is independent of the particular constitutive model employed for the cell membranes the surface integrals developed for solving the viscous flow and thereby the motion of the massless membrane are evaluated using an o nlogn particle mesh ewald pme approach the cell shapes which can become highly distorted under physiologic conditions are discretized with spherical harmonics the resolution of these global basis functions is of course excellent but more importantly they facilitate an approximate de aliasing procedure that stabilizes the simulations without adding any numerical dissipation or further restricting the permissible numerical time step complex geometry no slip boundaries are included using a constraint method that is coupled into an implicit system that is solved as part of the time advancement routine the implementation is verified against solutions for axisymmetric flows reported in the literature and its accuracy is demonstrated by comparison against exact solutions for relaxing surface deformations it is also used to simulate flow of blood cells at 30 volume fraction in tubes between 4 9 and email protected in diameter for these it is shown to reproduce the well known non monotonic dependence of the effective viscosity on the tube diameter

a generalization of the siewert burniston method for the determination of zeros of analytic functions the siewert burniston method for the derivation of closed form formulas for the zeros of sectionally analytic functions with a discontinuity interval along the real axis based on the riemann hilbert boundary value problem in complex analysis is generalized to apply to the determination of the zeros of analytic functions without discontinuity intervals inside or outside simple smooth contours an application of this method to the closed form solution of the transcendental equation zez beb appearing in the theory of neutron moderation in nuclear reactors is also made

determination of poles of sectionally meromorphic functions abstract the numerical methods of abd ellal delves and reid for locating poles of meromorphic functions inside smooth closed contours c in the complex plane are generalized to apply to sectionally meromorphic functions satisfying a homogeneous or nonhomogeneous riemann hilbert boundary value problem on the simple closed contours of their discontinuity which may intersect c in the first case the zeros of the meromorphic functions can be determined as well two simple illustrations of the present generalization are also presented

stochastic optimization of regenerative systems using infinitesimal perturbation analysis we consider the problem of optimizing the steady state mean of a controlled regenerative process using a stochastic optimization algorithm driven by infinitesimal perturbation analysis ipa derivative estimates we derive ipa derivative estimates for our problem and prove almost sure convergence of the algorithm the generality of our formulation should encompass a wide variety of practical systems we illustrate our framework and results via several examples

finding optimal observation based policies for constrained pomdps under the expected average reward criterion in this technical note constrained partially observable markov decision processes with discrete state and action spaces under the average reward criterion are studied from a sensitivity point of view by analyzing the derivatives of performance criteria we develop a simulation based optimization algorithm to find the optimal observation based policy on the basis of a single sample path this algorithm does not need any overly strict assumption and can be applied to the general ergodic markov systems with the imperfect state information the performance is proved to converge to the optimum with probability 1 one numerical example is provided to illustrate the applicability of the algorithm

semi markov decision problems and performance sensitivity analysis recent research indicates that markov decision processes mdps can be viewed from a sensitivity point of view and the perturbation analysis pa mdps and reinforcement learning rl are three closely related areas in optimization of discrete event dynamic systems that can be modeled as markov processes the goal of this paper is two fold first we develop the pa theory for semi markov processes smps and then we extend the aforementioned results about the relation among pa mdp and rl to smps in particular we show that performance sensitivity formulas and policy iteration algorithms of semi markov decision processes can be derived based on the performance potential and realization matrix both the long run average and discounted cost problems are considered this approach provides a unified framework for both problems and the long run average problem corresponds to the discounted factor being zero the results indicate that performance sensitivities and optimization depend only on first order statistics single sample path based implementations are discussed

a unified approach to markov decision problems and performance sensitivity analysis with discounted and average criteria multichain cases we propose a unified framework to markov decision problems and performance sensitivity analysis for multichain markov processes with both discounted and average cost performance criteria with the fundamental concept of performance potentials we derive both performance gradient and performance difference formulas which play the central role in performance optimization the standard policy iteration algorithms for both discounted and average reward mdps can be established using the performance difference formulas in a simple and intuitive way and the performance gradient formulas together with stochastic approximation may lead to new optimization schemes this sensitivity based point of view of performance optimization provides some insights that link perturbation analysis markov decision processes and reinforcement learning together the research is an extension of the previous work on ergodic markov chains cao automatica 36 2000 771

an immersed interface method for viscous incompressible flows involving rigid and flexible boundaries we present an immersed interface method for the incompressible navier stokes equations capable of handling both rigid and flexible boundaries the immersed boundaries are represented by a number of lagrangian control points in order to ensure that the no slip condition on the rigid boundary is satisfied singular forces are applied on the fluid the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity and are interpolated using cubic splines the strength of the singular forces at the rigid boundary is determined by solving a small system of equations at each timestep for flexible boundaries the forces that the boundary exerts on the fluid are computed from the constitutive relation of the flexible boundary and are applied to the fluid through the jump conditions the position of the flexible boundary is updated implicitly using a quasi newton method bfgs within each timestep the navier stokes equations are discretized on a staggered cartesian grid by a second order accurate projection method for pressure and velocity and the overall scheme is second order accurate

3d vesicle dynamics simulations with a linearly triangulated surface simulations of biomembranes have gained an increasing interest in the past years specificities of these membranes propose new challenges for the numerics in particular vesicle dynamics are governed by bending forces as well as a surface incompressibility constraint a method to compute the bending force density resultant onto piecewise linearly triangulated surface meshes is described this method is coupled with a boundary element method solver for inner and outer fluids to compute vesicle dynamics under external flows the surface incompressibility constraint is satisfied by the construction of a projection operator

the potential structure of sample paths and performance sensitivities of markov systems we study the structure of sample paths of markov systems by using performance potentials as the fundamental units with a sample path based approach we show that performance sensitivity formulas performance gradients and performance differences of markov systems can be constructed intuitively by first principles with performance potentials or equivalently perturbation realization factors as building blocks in particular we derive sensitivity formulas for two markov chains with possibly different state spaces the proposed approach can be used to obtain flexibly the sensitivity formulas for a wide range of problems including those with partial information these formulas are the basis for performance optimization of discrete event dynamic systems including perturbation analysis markov decision processes and reinforcement learning the approach thus provides insight on on line learning and performance optimization and opens up new research directions sample path based algorithms can be developed

natural actor critic algorithms we present four new reinforcement learning algorithms based on actor critic natural gradient and function approximation ideas and we provide their convergence proofs actor critic reinforcement learning methods are online approximations to policy iteration in which the value function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent methods based on policy gradients in this way are of special interest because of their compatibility with function approximation methods which are needed to handle large or infinite state spaces the use of temporal difference learning in this way is of special interest because in many applications it dramatically reduces the variance of the gradient estimates the use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further reduce variance in some cases our results extend prior two timescale convergence results for actor critic methods by konda and tsitsiklis by using temporal difference learning in the actor and by incorporating natural gradients our results extend prior empirical studies of natural actor critic methods by peters vijayakumar and schaal by providing the first convergence proofs and the first fully incremental algorithms

immersed boundary methods for general finite difference and finite volume navier stokes solvers we present an immersed boundary algorithm for incompressible flows with complex boundaries suitable for cartesian or curvilinear grid system the key stages of any immersed boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary a line in 2d a surface in 3d and the spreading of a force field from the immersed boundary to the neighboring mesh points to enforce the desired boundary conditions on the immersed boundary points we propose a technique that uses the reproducing kernel particle method w k liu s jun y f zhang reproducing kernel particle methods int j numer methods fluids 20 8 1995 1081 1106 for the interpolation and spreading unlike other methods presented in the literature the one proposed here has the property that the integrals of the force field and of its moment on the grid are conserved independent of the grid topology uniform or non uniform cartesian or curvilinear the technique is easy to implement and is able to maintain the order of the original underlying spatial discretization applications to two and three dimensional flows in cartesian and non cartesian grid system with uniform and non uniform meshes are presented

actor critic type learning algorithms for markov decision processes algorithms for learning the optimal policy of a markov decision process mdp based on simulated transitions are formulated and analyzed these are variants of the well known actor critic or adaptive critic algorithm in the artificial intelligence literature distributed asynchronous implementations are considered the analysis involves two time scale stochastic approximations

perturbation realization potentials and sensitivity analysis of markov processes two fundamental concepts and quantities realization factors and performance potentials are introduced for markov processes the relations among these two quantities and the group inverse of the infinitesimal generator are studied it is shown that the sensitivity of the steady state performance with respect to the change of the infinitesimal generator can be easily calculated by using either of these three quantities and that these quantities can be estimated by analyzing a single sample path of a markov process based on these results algorithms for estimating performance sensitivities on a single sample path of a markov process can be proposed the potentials in this paper are defined through realization factors and are shown to be the same as those defined by poisson equations the results provide a uniform framework of perturbation realization for infinitesimal perturbation analysis ipa and non ipa approaches to the sensitivity analysis of steady state performance they also provide a theoretical background for the pa algorithms developed in recent years

a level set projection model of lipid vesicles in general flows a new numerical method to model the dynamic behavior of lipid vesicles under general flows is presented a gradient augmented level set method is used to model the membrane motion to enforce the volume and surface incompressibility constraints a four step projection method is developed to integrate the full navier stokes equations this scheme is implemented on an adaptive non graded cartesian grid convergence results are presented along with sample two dimensional results of vesicles under various flow conditions

non body fitted fluid structure interaction divergence conforming b splines fully implicit dynamics and variational formulation abstract immersed boundary ib methods deal with incompressible visco elastic solids interacting with incompressible viscous fluids a long standing issue of ib methods is the challenge of accurately imposing the incompressibility constraint at the discrete level we present the divergence conforming immersed boundary dcib method to tackle this issue the dcib method leads to completely negligible incompressibility errors at the eulerian level and various orders of magnitude of increased accuracy at the lagrangian level compared to other ib methods furthermore second order convergence of the incompressibility error at the lagrangian level is obtained as the discretization is refined in the dcib method the eulerian velocity pressure pair is discretized using divergence conforming b splines leading to inf sup stable and pointwise divergence free eulerian solutions the lagrangian displacement is discretized using non uniform rational b splines which enables to robustly handle large mesh distortions the data transfer needed between the eulerian and lagrangian descriptions is performed at the quadrature level using the same spline basis functions that define the computational meshes this conduces to a fully variational formulation sharp treatment of the fluid solid interface and a 0 5 increase in the convergence rate of the eulerian velocity and the lagrangian displacement measured in l 2 norm in comparison with using discretized dirac delta functions for the data transfer by combining the generalized method and a block iterative solution strategy the dcib method results in a fully implicit discretization which enables to take larger time steps various two and three dimensional problems are solved to show all the aforementioned properties of the dcib method along with mesh independence studies verification of the numerical method by comparison with the literature and measurement of convergence rates

a three dimensional computational analysis of fluid structure interaction in the aortic valve numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle moreover the fluid structure interaction in the aortic valve system is most frequently ignored in numerical modelling the effect of this interaction on the valve s behaviour during systolic functioning is investigated the large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood valve interaction modelling this has impeded numerical analyses of valves operating under physiological conditions a numerical method known as the lagrange multiplier based fictitious domain method is used to describe the large leaflet motion within the computational fluid domain this method is applied to a three dimensional finite element model of a stented aortic valve the model provides both the mechanical behaviour of the valve and the blood flow through it results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion

a sensitivity formula for risk sensitive cost and the actor critic algorithm abstract we propose for risk sensitive control of finite markov chains a counterpart of the popular actor critic algorithm for classical markov decision processes the algorithm is based on a sensitivity formula for the risk sensitive cost and is shown to converge with probability one to the desired solution the proof technique is an adaptation of the ordinary differential equations approach for the analysis of two time scale stochastic approximation algorithms

a basic formula for performance gradient estimation of semi markov decision processes abstract this paper presents a basic formula for performance gradient estimation of semi markov decision processes smdps under average reward criterion this formula directly follows from a sensitivity equation in perturbation analysis with this formula we develop three sample path based gradient estimation algorithms by using a single sample path these algorithms naturally extend many gradient estimation algorithms for discrete time markov systems to continuous time semi markov models in particular they require less storage than the algorithm in the literature

locating a crack of arbitrary but known shape by the method of path independent integrals abstract the solution of a crack problem of an arbitrary but known shape inside an infinite plane isotropic elastic medium can be achieved in general by the method of complex singular integral equations and their numerical solution by using the gauss or the lobatto chebyshev methods in a few special cases like straight or circular arc shaped cracks this solution is available in closed form in this paper we will not contribute to the above methods of solution of crack problems but we will propose a method for the determination of the exact position of such a crack inside a closed contour in the elastic medium by gathering and using information along this contour only by experimental techniques and applying the method of complex path independent integrals for the location of the crack this paper constitutes a nontrivial generalization of relevant previous results by the author and it is of quite general applicability in fracture mechanics for nondestructive testing numerical results for the particular case of a straight crack are displayed for the illustration of the efficiency of the method the generalization of the present results to the determination of additional geometric and loading parameters of the crack is also suggested very briefly and related numerical results concerning the length of the crack and the pressure distribution on it in the aforementioned numerical application are also presented

remarks on rate constitutive equations for finite deformation problems computational implications it is explicitly shown that if the spatial elasticity tensor of an elastic material is taken as isotropic for all possible configurations then its coefficients cannot be constants they must depend nontrivially on the jacobian determinant of the deformation gradient moreover the assumption typically made for computational purposes that its coefficients remain constant for all possible configurations is incompatible with elasticity it is further shown that an assumption widely used in the computational literature in the context of finite deformation plasticity namely relating an objective stress rate to the rate of deformation tensor through a fourth rank constant isotropic tensor is also incompatible with elasticity thus furnishing an example of an hypoelastic material which is not elastic

potential based online policy iteration algorithms for markov decision processes performance potentials play a crucial role in performance sensitivity analysis and policy iteration of markov decision processes the potentials can be estimated on a single sample path of a markov process in this paper we propose two potential based online policy iteration algorithms for performance optimization of markov systems the algorithms are based on online estimation of potentials and stochastic approximation we prove that with these two algorithms the optimal policy can be attained after a finite number of iterations a simulation example is given to illustrate the main ideas and the convergence rates of the algorithms