An adaptive, hanging-node, discontinuous isogeometric analysis method for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation

In this paper a discontinuous, hanging-node, isogeometric analysis (IGA) method is developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation in two-dimensional space. The complexities involved in upwinding across curved element boundaries that contain hanging-nodes have been addressed to ensure that the scheme remains conservative. A robust algorithm for cycle-breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction. The convergence rate of the scheme has been verified using the method of manufactured solutions (MMS) with a smooth solution. Heuristic error indicators have been used to drive an adaptive mesh refinement (AMR) algorithm to take advantage of the hanging-node discretisation. The effectiveness of this method is demonstrated for three test cases. The first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source. The second test case is a radiation shielding problem and the third is a 3×3 “supercell” featuring a burnable absorber. In the final test case, comparisons are made to the discontinuous Galerkin finite element method (DGFEM) using both straight-sided and curved quadratic finite elements

Modeling and Verification of Agent based Adaptive Traffic Signal using Symbolic Model Verifier

This paper addresses the issue of modeling and verification of a Multi Agent System (MAS) scenario. We have considered an agent based adaptive traffic signal system. The system monitors the smooth flow of traffic at intersection of two road segment. After describing how the adaptive traffic signal system can efficiently be used and showing its advantages over traffic signals with predetermined periods, we have shown how we can transform this scenario into Finite State Machine (FSM). Once the system is transformed into a FSM, we have verified the specifications specified in Computational Tree Logic(CTL) using NuSMV as a model checking tool. Simulation results obtained from NuSMV showed us whether the system satisfied the specifications or not. It has also showed us the state where the system specification does not hold. Using which we traced back our system to find the source, leading to the specification violation. Finally, we again verified the modified system with NuSMV for its specifications.Comment: 13 pages, 6 figures, Submitted to International Journal of Computer Application (IJCA

A stochastic behavior analysis of stochastic restricted-gradient descent algorithm in reproducing kernel Hilbert spaces

This paper presents a stochastic behavior analysis of a kernel-based stochastic restricted-gradient descent method. The restricted gradient gives a steepest ascent direction within the so-called dictionary subspace. The analysis provides the transient and steady state performance in the mean squared error criterion. It also includes stability conditions in the mean and mean-square sense. The present study is based on the analysis of the kernel normalized least mean square (KNLMS) algorithm initially proposed by Chen et al. Simulation results validate the analysis

Goal-based h-adaptivity of the 1-D diamond difference discrete ordinate method.

The quantity of interest (QoI) associated with a solution of a partial differential equation (PDE) is not, in general, the solution itself, but a functional of the solution. Dual weighted residual (DWR) error estimators are one way of providing an estimate of the error in the QoI resulting from the discretisation of the PDE. This paper aims to provide an estimate of the error in the QoI due to the spatial discretisation, where the discretisation scheme being used is the diamond difference (DD) method in space and discrete ordinate (SNSN) method in angle. The QoI are reaction rates in detectors and the value of the eigenvalue (Keff)(Keff) for 1-D fixed source and eigenvalue (KeffKeff criticality) neutron transport problems respectively. Local values of the DWR over individual cells are used as error indicators for goal-based mesh refinement, which aims to give an optimal mesh for a given QoI

History-based action selection bias in posterior parietal cortex.

Making decisions based on choice-outcome history is a crucial, adaptive ability in life. However, the neural circuit mechanisms underlying history-dependent decision-making are poorly understood. In particular, history-related signals have been found in many brain areas during various decision-making tasks, but the causal involvement of these signals in guiding behavior is unclear. Here we addressed this issue utilizing behavioral modeling, two-photon calcium imaging, and optogenetic inactivation in mice. We report that a subset of neurons in the posterior parietal cortex (PPC) closely reflect the choice-outcome history and history-dependent decision biases, and PPC inactivation diminishes the history dependency of choice. Specifically, many PPC neurons show history- and bias-tuning during the inter-trial intervals (ITI), and history dependency of choice is affected by PPC inactivation during ITI and not during trial. These results indicate that PPC is a critical region mediating the subjective use of history in biasing action selection

A Simple Algebraic Grid Adaptation Scheme with Applications to Two- and Three-dimensional Flow Problems

An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented. The scheme locally adjusts the grid density based on gradients of selected flow variables from either finite difference or finite volume calculations. A user-prescribed grid stretching can be specified such that control of the grid spacing can be maintained in areas of known flowfield behavior. For example, the grid can be clustered near a wall for boundary layer resolution and made coarse near the outer boundary of an external flow. A grid smoothing technique is incorporated into the adaptive grid routine, which is found to be more robust and efficient than the weight function filtering technique employed by other researchers. Since the present algebraic scheme requires no iteration or solution of differential equations, the computer time needed for grid adaptation is trivial, making the scheme useful for three-dimensional flow problems. Applications to two- and three-dimensional flow problems show that a considerable improvement in flowfield resolution can be achieved by using the proposed adaptive grid scheme. Although the scheme was developed with steady flow in mind, it is a good candidate for unsteady flow computations because of its efficiency