variable order fractional discrete time recurrent neural networks abstract discrete fractional calculus is suggested to describe neural networks with memory effects fractional discrete time recurrent neural network is proposed on an isolated time scale stability results are investigated via banach fixed point technique the attractive solution space is constructed and stability conditions are provided furthermore short memory and variable order fractional neural networks are given according to the stability conditions two and three dimensional numerical examples are used to demonstrate the theoretical results

lyapunov functions for riemann liouville like fractional difference equations abstract discrete memory effects are introduced by fractional difference operators asymptotic stabilities of nonlinear fractional difference equations are investigated in this paper a linear scalar fractional difference equality is utilized lyapunov second direct method is proposed for nonlinear discrete fractional systems asymptotic stability conditions are provided and some examples are given

optimal design for non newtonian flows using a topology optimization approach we study non newtonian effects on the layout and geometry of flow channels using a material distribution based topology optimization approach the flow is modeled with the single relaxation hydrodynamic lattice boltzmann method and the shear dependence of viscosity is included through the carreau yasuda model for non newtonian fluids to represent the viscosity of blood in this model we use non newtonian similarity further we introduce a scaling to decrease the effects of the non newtonian model in porous regions in order to stabilize the coupling of the lbm porosity and non newtonian flow models for the resulting flow model we derive the non newtonian sensitivity analysis for steady state conditions and illustrate the non newtonian effect on channel layouts for a 2d dual pipe design problem at different reynolds numbers

detecting shocks outliers and breaks in time series abstract a single outlier in a regression model can be detected by the effect of its deletion on the residual sum of squares an equivalent procedure is the simple intervention in which an extra parameter is added for the mean of the observation in question similarly for unobserved components or structural time series models the effect of elaborations of the model on inferences can be investigated by the use of interventions involving a single parameter such as trend or level changes because such time series models contain more than one variance the effect of the intervention is measured by the change in individual variances we examine the effect on the estimated parameters of moving various kinds of intervention along the series the horrendous computational problems involved are overcome by the use of score statistics combined with recent developments in filtering and smoothing interpretation of the resulting time series plots of diagnostics is aided by simulation envelopes our procedures illustrated with four example permit keen insights into the fragility of inferences to specific shocks such as outliers and level breaks although the emphasis is mostly on parameter estimation forecast are also considered possible extensions include seasonal adjustment and detrending of series

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

chaos synchronization of fractional chaotic maps based on the stability condition abstract in the fractional calculus one of the main challenges is to find suitable models which are properly described by discrete derivatives with memory fractional logistic map and fractional lorenz maps of riemann liouville type are proposed in this paper the general chaotic behaviors are investigated in comparison with the caputo one chaos synchronization is designed according to the stability results the numerical results show the method s effectiveness and fractional chaotic map s potential role for secure communication

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

topology optimization for turbulent flow with spalart allmaras model abstract in this research a new finite element fe based topology optimization to for turbulent flow was developed using the spalart allmaras s a equation which is one of the reynolds averaged navier stokes rans equations despite many innovative works on the subject of fluidic to it is rare to consider the influence of turbulent flow in to to consider the effect of complex turbulent fluid motion this research considered the s a model developed mainly for aerodynamic flows for a successful to one primary issue is modification of the s a turbulent model to account for topological evolution during the optimization process to address this issue we proposed the addition of penalization terms to the original governing equations to show the validity of the present approach and the effect of turbulent flow on optimal layouts some two dimensional benchmark designs studied for laminar flow were reconsidered by considering the effect of turbulent flow the eddy viscosity values were increased at some local regions due to the boussinesq hypothesis and naturally optimal layouts affected by the spatially varying viscosity were obtained in turbulent flow it was also found that the balance between the inertia force and the viscosity force plays an important role in topological designs

diagnosing shocks in time series abstract efficient means of modeling aberrant behavior in times series are developed our methods are based on state space forms and allow test statistics for various interventions to be computed from a single run of the kalman filter smoother the approach encompasses existing detection methodologies departures commonly observed in practice such as outlying values level shifts and switches are readily dealt with new diagnostic statistics are proposed implications for structural models autoregressive integrated moving average models and models with explanatory variables are given

topology optimization of the shear thinning non newtonian fluidic systems for minimizing wall shear stress this paper suggests the topology optimization process to minimize wall shear stress by considering shear thinning non newtonian fluid effects in the systematic design of fluidic systems dealing with blood topology optimization was originally developed for mechanical design problems and within the last decade the method has been extended to a range of fluidic applications in this paper the carreau yasuda constitutive equation model is used for shear thinning non newtonian fluid modeling the fundamental idea is that the material density of each element or grid point is a design variable thus the geometry is parameterized in a pixel like pattern then material interpolation functions for inverse permeability and dynamic viscosity are used to ensure convergence of the solution and resolve non linearity in order to define wall shear stress on implicit boundary between solid and fluid i e blood occurring in fluidic topology optimization the relaxation method of wall shear stress is first proposed in this study we then apply the proposed fluidic topology optimization to actual fluidic systems dealing with blood e g a femoral bypass graft these design examples validate the efficiency of the proposed approach and show that topology optimization can be used for the initial conceptual design of various fluidic systems

algorithms for the fractional calculus a selection of numerical methods many recently developed models in areas like viscoelasticity electrochemistry diffusion processes etc are formulated in terms of derivatives and integrals of fractional non integer order in this paper we present a collection of numerical algorithms for the solution of the various problems arising in this context we believe that this will give the engineer the necessary tools required to work with fractional models in an efficient way

combination of topology optimization and optimal control method this paper presents the combination of topology optimization and optimal control method to find the optimal match between the material topology and control in the presented method the material topology is determined using the simp solid isotropic material with penalization method which has been popularly used in topology optimization in the simp method the design variable is relaxed and bounded in the interval 0 1 and the evolution of the design variable is usually implemented by the method of moving asymptotes mma which can be used to deal with optimization problem with multiple integral constraints and bound constraint of the design variable in the combination of topology optimization and optimal control method the control variable appears along with the design variable in order to evolve the control variable and design variable using mma simultaneously the control variable is regularized using a bound constraint and the corresponding bound constraint is projected onto the interval 0 1 which is the same as the bound constraint of the design variable the optimization problem is analyzed using the adjoint method to obtain the adjoint sensitivity during the optimization procedure the design and control variables are filtered by the helmholtz filters to ensure the smoothness of the distribution to ensure the minimum scale length and remove the gray area in the material topology the filtered design variable is projected by the threshold method the feasibility and robustness of the combination of these two methods are demonstrated by several test problems including heat transfer fluid flow and compliance minimization

topology optimization of unsteady incompressible navier stokes flows this paper discusses the topology optimization of unsteady incompressible navier stokes flows an optimization problem is formulated by adding the artificial darcy frictional force into the incompressible navier stokes equations the optimization procedure is implemented using the continuous adjoint method and the finite element method the effects of dynamic inflow reynolds number and target flux on specified boundaries for the optimal topology of unsteady navier stokes flows are presented numerical examples demonstrate the feasibility and necessity of this topology optimization method for unsteady navier stokes flows

topology optimization based on a two dimensional swirl flow model of tesla type pump devices abstract tesla pumps are composed of rotating disks without blades and are based on the boundary layer effect i e viscous friction forces acting on the fluid and coand effect the tesla pump has various applications however the efficiency of its operation is quite low which makes room for the optimization of its design this way novel configurations of devices based on this working principle can be developed thus in this work a topology optimization formulation is proposed to optimize the rotor of a tesla type pump device by using a 2d swirl flow model which is a specific model that presents an axisymmetric flow with or without flow rotation around the axisymmetric axis the 2d swirl laminar fluid flow modeling is solved by using the finite element method a traditional material model is adopted by considering nodal design variables and is extended to take into account the fact that the optimization is performed in a rotating reference frame and the relative tangential velocity behaves differently than the other velocity components since the 2d swirl flow model is axisymmetric a multi objective function is defined in order to minimize energy dissipation and vorticity an extra term is proposed to the vorticity function to reduce the generation of grayscale results an interior point optimization algorithm ipopt is applied to solve the optimization problem numerical results taking into account different aspects of the design of the rotor of a tesla type device are presented

topology optimization of creeping fluid flows using a darcy stokes finite element a new methodology is proposed for the topology optimization of fluid in stokes flow the binary design variable and no slip condition along the solid fluid interface are regularized to allow for the use of continuous mathematical programming techniques the regularization is achieved by treating the solid phase of the topology as a porous medium with flow governed by darcy s law fluid flow throughout the design domain is then expressed as a single system of equations created by combining and scaling the stokes and darcy equations the mixed formulation of the new darcy stokes system is solved numerically using existing stabilized finite element methods for the individual flow problems convergence to the no slip condition is demonstrated by assigning a low permeability to solid phase and results suggest that auxiliary boundary conditions along the solid fluid interface are not needed the optimization objective considered is to minimize dissipated power and the technique is used to solve examples previously examined in literature the advantages of the darcy stokes approach include that it uses existing stabilization techniques to solve the finite element problem it produces 0 1 void solid topologies i e there are no regions of artificial material and that it can potentially be used to optimize the layout of a microscopically porous material copyright 2005 john wiley sons ltd

an adjoint based lattice boltzmann method for noise control problems in this paper optimal control of acoustic problems is addressed within the lattice boltzmann method framework to this end an adjoint based lattice boltzmann method is proposed to solve the adjoint problem the adjoint state provides an easy access to the optimization gradients the line search step in newton s descent method is performed through a combination of complex differentiation and adjoint problem in the lattice boltzmann method the implementation of an active noise reduction method for two dimensional weakly compressible low mach number flows is discussed and the applicability of the method is assessed

lattice boltzmann method for simulating the viscous flow in large distensible blood vessels a lattice boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries the mass conservation for the boundary condition is tested in detail the viscous flow in elastic vessels is simulated with a pressure radius relationship similar to that of the pulmonary blood vessels the numerical results for steady flow agree with the analytical prediction to very high accuracy and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally the model is expected to find many applications for studying blood flows in large distensible arteries especially in those suffering from atherosclerosis stenosis aneurysm etc

level set based topology optimization of transient flow using lattice boltzmann method considering an oscillating flow condition abstract topology optimization is widely applied to various design problems in both structure and fluid dynamics engineering specifically the development of energy dissipation devices with vibration control remains a key consideration the aim of this study is to improve devices that maximize the absorption or dissipation of the vibration of an oscillating object and propose an approach in which the level set based topology optimization of transient flow using the lattice boltzmann method is simultaneously applied to forward and reverse direction flows to deal with oscillating flows in real world engineering designs although several studies have examined topology optimization to minimize dissipated kinetic energy this study introduces an objective function for maximizing the dissipated kinetic energy in time varying fluid flows via velocity gradients

topology optimization using the lattice boltzmann method incorporating level set boundary expressions this paper presents a topology optimization method for fluid dynamics problems based on the level set method and using the lattice boltzmann method lbm in this optimization method the optimization problems are formulated based on the original boltzmann equation and the design sensitivities are precisely obtained without the time consuming numerical operations encountered when dealing with a large scale asymmetric matrix in contrast to previous research in which the lbm uses the lattice boltzmann equation lbe for the formulations of optimization problems and the derivation of their adjoint equations that is we newly derive sensitivity formulations from the original boltzmann equation not the lbe that can be said to be an approximated equation and these formulations yield strictly correct sensitivities that are error free based on the above formulations we construct a level set based topology optimization method incorporating a fictitious interface energy for the design of a fluid channel that minimizes flow friction furthermore two and three dimensional numerical examples are provided to confirm the validity and utility of the presented method

existence and uniqueness theorem for a class of delay differential equations with left and right caputo fractional derivatives the existence and uniqueness theorems for functional right left delay and left right advanced fractional functional differential equations with bounded delay and advance respectively are proved the continuity with respect to the initial function for these equations is also proved under some lipschitz kind conditions the q operator is used to transform the delay type equation to an advanced one and vice versa an example is given to clarify the results

lattice fractional diffusion equation in terms of a riesz caputo difference abstract a fractional difference is defined by the use of the right and the left caputo fractional differences the definition is a two sided operator of riesz type and introduces back and forward memory effects in space difference then a fractional difference equation method is suggested for anomalous diffusion in discrete finite domains a lattice fractional diffusion equation is proposed and the numerical simulation of the diffusion process is discussed for various difference orders the result shows that the riesz difference model is particularly suitable for modeling complicated dynamical behaviors on discrete media

on riemann and caputo fractional differences in this paper we define left and right caputo fractional sums and differences study some of their properties and then relate them to riemann liouville ones studied before by miller k s and ross b atici f m and eloe p w abdeljawad t and baleanu d and a few others also the discrete version of the q operator is used to relate the left and right caputo fractional differences a caputo fractional difference equation is solved the solution proposes discrete versions of mittag leffler functions

a discrete fractional order cournot duopoly game abstract this paper focuses on associating the cournot duopoly problem with long memory effects first of all we generate a discrete fractional order cournot duopoly game by introducing the caputo fractional order difference calculus to the classical duopoly theory in the fractional order game participants can make their decisions by taking full advantage of their historical information then we discuss both nash equilibria and local stability of the game by employing the linear approximation theory at last we numerically validate the main results by using bifurcation diagrams phase portraits the largest lyapunov exponent and the 0 1 test algorithms

a predictive view of the detection and characterization of influential observations in regression analysis abstract assuming a set of observations is available from the general linear model and assuming prior information about parameters we propose a method of assessing the influence of specified subsets of the data when the goal is to predict future observations

assessing the predictive influence of cases in a state space process an important inferential objective in state space modelling is to recover unobserved states using fixed interval smoothing thus the identification of cases which have a substantial influence on the smoothers is a relevant practical problem to facilitate this identification we propose a case deletion diagnostic which can be easily computed using the outputs of the standard filtering and smoothing algorithms our diagnostic is defined as the kullback leibler directed divergence between two versions of the conditional density which determines the smoothers one based on all the data the other based on all the data except for the case or cases in question we investigate the detection performance of the diagnostic in a practical application

option pricing beyond black scholes based on double fractional diffusion abstract we show how the prices of options can be determined with the help of double fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops than the use of options whose prices were fixed by the black scholes formula

lattice boltzmann method for non newtonian power law fluids we study an ad hoc extension of the lattice boltzmann method that allows the simulation of non newtonian fluids described by generalized newtonian models we extensively test the accuracy of the method for the case of shear thinning and shear thickening truncated power law fluids in the parallel plate geometry and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution finally we also tested the method in the reentrant flow geometry in which the shear rate is no longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points in this geometry we also found excellent agreement with the solutions obtained by standard finite element methods and the agreement improves with higher lattice resolution

dynamic linear model diagnostics summary in time series analysis using dynamic linear models retrospective analysis involves the calculation of filtered or smoothed distributions for state parameters in the past we develop and illustrate novel results that are useful in retrospective assessment of the influence of individual observations on such distributions in particular new and computationally simple filtering equations are derived for past state parameters based on leaving out one observation at a time providing dynamic model based versions of methods currently used in standard static regression diagnostics