Chebyshev model arithmetic for factorable functions

This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

X-Ray Diffraction From Ion Implanted Zones

Measurements of x-ray profiles and diffuse scattering from (111), (100) single crystal Niobium films implanted with Nitrogen to average levels of 5 and 0.5 atomic percent are discussed. Theoretical analysis of the asymmetric profiles are used to determine the strain profile in the implanted films. The measured strain profile results from two factors: (1) depth distribution of implants and knock-on damage and (2) elastic constraints. Residual elastic strains develop due to the constraints imposed by a sapphire substrate. Comparison of the diffraction results with theoretical predictions of TRIM indicates the presence of measurable knock-on damage in the films. Huang and Stokes-Wilson scattering measurements made using synchrotron radiation at the ORNL beamline, Brookhaven National Laboratory, were used to reveal the identity of defects formed during the knock-on process

Initiatives to reduce energy use in cold stores

The cold chain is believed to be responsible for approximately 2.5% of global greenhouse gas emissions through direct and indirect (energy consumption) effects. Cold storage rooms consume considerable amounts of energy. Within cold storage facilities 60-70% of the electrical energy can be used for refrigeration. Therefore cold store users have considerable incentive to reduce energy consumption

Voluntary wheel running access produces opposite effects in male and female rats on both palatable diet consumption and associated ventral striatal opioid- and dopamine-related gene expression

The relationship between physical activity levels and feeding behaviors has been a focus of preclinical research for decades, yet this interaction has only recently been explored for potential sex differences. The aim of the present study was to isolate sex-dependent effects of voluntary wheel running (RUN) vs. sedentary locked wheel (SED) home cage conditions on palatability-driven feeding behavior using a 2-diet choice task between standard chow and a high-fat diet. The sex-dependent effects of physical activity on feeding behavior were examined following a within-subject novel reversal design of physical activity conditions (i.e., RUN > SED > RUN), to assess temporal sensitivity of the interaction. Following the final 2 weeks of reestablished and sustained RUN vs. SED conditions in separate groups of both males and females, reward-related opioid and dopamine gene expression within the nucleus accumbens (Acb) brain region were analyzed. Results demonstrated that the initial RUN > SED transition led to sex-dependent effects of SED condition, as males increased, and females decreased their high fat consumption, compared to their respective high fat consumption during previous RUN condition phase. Following reintroduction to the RUN condition, males decreased, and females increased their high fat consumption, compared to their separate SED control group. Last, sex-dependent shifts in ventral striatal opioid- and dopamine-related gene expression were observed to parallel the behavioral effects. The major findings of the study reveal that SED and RUN home cage conditions shift palatability-driven feeding in the opposite direction for males and females, these effects are sensitive to reversal, and these sex-dependent feeding behaviors track sex-dependent changes to critical reward-related gene expression patterns in the Acb. Considering the present high rates of sedentary behavior and obesity, furthering our understanding of the interaction between physical activity (or lack thereof) and feeding behavior should be a priority, especially in the context of these divergent sex-dependent outcomes

A Set-Theoretic Method for Verifying Feasibility of a Fast Explicit Nonlinear Model Predictive Controller

In this chapter an algorithm for nonlinear explicit model predictive control is presented. A low complexity receding horizon control law is obtained by approximating the optimal control law using multiscale basis function approximation. Simultaneously, feasibility and stability of the approximate control law is ensured through the computation of a capture basin (region of attraction) for the closed-loop system. In a previous work, interval methods were used to construct the capture basin (feasible region), yet this approach suffered due to slow computation times and high grid complexity. In this chapter, we suggest an alternative to interval analysis based on zonotopes. The suggested method significantly reduces the complexity of the combined function approximation and verification procedure through the use of DC (difference of convex) programming, and recursive splitting. The result is a multiscale function approximation method with improved computational efficiency for fast nonlinear explicit model predictive control with guaranteed stability and constraint satisfaction