Preconditioning the solution of the time-dependent neutron diffusion equation by recycling Krylov subspaces

Spectral preconditioners are based on the fact that the convergence rate of the Krylov subspace methods is improved if the eigenvalues of the smallest magnitude of the system matrix are ‘removed’. In this paper, two preconditioning strategies are studied to solve a set of linear systems associated with the numerical integration of the time-dependent neutron diffusion equation. Both strategies can be implemented using the matrix–vector product as the main operation and succeed at reducing the total number of iterations needed to solve the set of systems.     

Methodology to resolve the transport equation with the discrete ordinates code TORT into the IPEN/MB-01 reactor

Resolution of the steady-state Neutron Transport Equation in a nuclear pool reactor is usually achieved by means of two different numerical methods: Monte Carlo (stochastic) and Discrete Ordinates (deterministic). The Discrete Ordinates method solves the Neutron Transport Equation for a set of selected directions, obtaining a set of directional equations and solutions for each equation which are the angular flux. In order to deal with the energy dependence, an energy multi-group approximation is commonly performed, obtaining a set of equations depending on the number of energy groups. In addition, spatial discretization is also required and the problem is solved by sweeping the geometry mesh. However, special cross-sections are required due to the energy and directional discretization, thus a methodology based on NJOY99 code capabilities has been used. Finally, in order to demonstrate the capability of this method, the 3D discrete ordinates code TORT has been applied to resolve the IPEN/MB-01 reactor.     

Underactuated fingers controlled by robust and adaptive trajectory following methods

Choosing an appropriate control scheme to alleviate nonlinearities and uncertainties is not a trivial task, especially when models are not easily available and practical evaluation provides the only means for actual performance assessment. Various factors can contribute to these nonlinearities and uncertainties, such as friction and stiction. Thus, this article investigates four different control schemes, namely PID, adaptive, conventional sliding mode control (SMC) and integral sliding mode control (ISMC) which are implemented in the Bristol Elumotion Robot Hand (BERUL) to analyse and overcome the aforementioned problems. The hand has five fingers with 16 joints and all fingers are underactuated. The implementation of the proposed control schemes are challenging since the BERUL fingers have significant friction, stiction and unknown parameters. The fingers are light in weight and fragile. Comparative performance characteristics have shown that the ISMC is the most suitable candidate to provide good experimental trajectory following and positioning control for underactuated BERUL fingers.     

Explicit solution of relative entropy weighted control

We consider the minimization over probability measures of the expected value of a random variable, regularized by relative entropy with respect to a given probability distribution. In the general setting we provide a complete characterization of the situations in which a finite optimal value exists and the situations in which a minimizing probability distribution exists. Specializing to the case where the underlying probability distribution is Wiener measure, we characterize finite relative entropy changes of measure in terms of square integrability of the corresponding change of drift. For the optimal change of measure for the relative entropy weighted optimization, an expression involving the Malliavin derivative of the cost random variable is derived. The theory is illustrated by its application to several examples, including the case where the cost variable is the maximum of a standard Brownian motion over a finite time horizon. For this example we obtain an exact optimal drift, as well as an approximation of the optimal drift through a Monte-Carlo algorithm.     

Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term

We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small.     

On solutions to fuzzy stochastic differential equations with local martingales

This paper deals with a class of fuzzy stochastic differential equations (FSDEs) driven by a continuous local martingale under the Lipschitzian condition. Such equations can be useful in modeling hybrid systems, where the phenomena are simultaneously subjected to two kinds of uncertainties: randomness and fuzziness. The solutions of the FSDEs are the fuzzy stochastic processes, and their uniqueness is considered to be in a strong sense. Thus, the existence and uniqueness of solutions to the FSDEs under the Lipschitzian condition is first proven. Moreover, some asymptotic properties of the solutions to the FSDEs are investigated. Finally, an illustrating example on the interest term model is provided.     

Bubble temperature data for phenol-alcohol systems: Phenol-I-Amyl alcohol and phenol-n-Amyl alcohol systems

In order to supplement the literature data on VLE, isobaric bubble temperature data were collected for the binary systems phenol-i-amyl alcohol and phenol-n-amyl alcohol over the entire composition range by indirect method using a standard Swietoslawski type ebulliometer. The measurements were made at three sub-atmospheric pressures. The experimental t-x data were correlated with both equation of state method and gamma-phi methods. In the former approach, the Soave equation of state is used, whereas in the latter case Wilson, NRTL and UNIQUAC equations are used.     

On the Design of Observer for Nonlinear Time‐Delay Systems

This paper suggests a new method to design observers in a class of nonlinear time‐delay systems with delays in system states. The method is based on an extension of the well‐known state‐dependent Riccati equation (SDRE) technique. The conditions for locally asymptotic stability of the proposed observer are investigated. Some numerical simulations are provided to show the design procedure and the flexibility of the proposed observer.     

基于时滞分割法的区间变时滞不确定系统鲁棒稳定新判据

针对一类存在泛数有界不确性的区间变时滞线性系统, 利用Lyapunov-Krasovskii (L-K) 泛函方法并结合线性矩阵不等式(LMI) 技术建立一种新的保守性更低的鲁棒稳定性判据. 首先基于时滞分割方法将时滞区间均分成N 等分, 针对不同的子区间构造合适的L-K 泛函; 然后在各自的分割区间采用保守性较小的积分不等式处理泛函沿时间的导数, 基于凸组合技术建立了LMI 形式的时滞相关稳定性新判据; 最后通过数值实例验证了结论的有效性.