Critical Objective Size and Calmness Modulus in Linear Programming

This paper introduces the concept of critical objective size associated with a linear program in order to provide operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping under uniqueness of nominal optimal solution and perturbations of all coefficients. Our starting point is an upper bound on this modulus given in Cánovas et al. (4). In this paper we prove that this upper bound is attained if and only if the norm of the objective function coefficient vector is less than or equal to the critical objective size. This concept also allows us to obtain operative lower bounds on the calmness modulus. We analyze in detail an illustrative example in order to explore some strategies that can improve the referred upper and lower bounds.     

Use of a graphite–polyurethane composite electrode for electroanalytical determination of indole-3-acetic acid in soil samples

A new electroanalytical methodology was developed for the quantification of the phytohormone indole-3-acetic acid (IAA), using a graphite–polyurethane composite electrode (GPU) and the square wave voltammetry (SWV), in 0.1 mol L^− 1 phosphoric acid solution (pH 1.6). Analytical curves were constructed under optimized conditions (f = 100 s^− 1, a = 50 mV, E_i = 5 mV) and the reached detection and quantification limits were 26 μg L^− 1 and 0.2 mg L^− 1, respectively. The developed methodology is simple and accurate for the routine determination of IAA. In order to verify the application of the electroanalytical methodology in fortified soil samples without previous treatment, an IAA assay was performed without serious interferences of the soil constituents.     

A Monge–Kantorovich mass transport problem for a discrete distance

This paper is concerned with a Monge-Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to transport the involved mass from its origin to its destination. For this problem we construct special Kantorovich potentials, and optimal transport plans via a nonlocal version of the PDE formulation given by Evans and Gangbo for the classical case with the Euclidean distance. We also study how these problems, when rescaling the step distance, approximate the classical problem. In particular we obtain, taking limits in the rescaled nonlocal formulation, the PDE formulation given by Evans-Gangbo for the classical problem.     

Half-quantum vortices in exciton–polariton condensates in applied magnetic field

We study the behavior of half-quantum vortices (HQVs) in exciton–polariton condensates in planar semiconductor microcavities in applied magnetic field. Below the critical magnetic field, that is defined by the polariton–polariton interaction constant, the condensate is elliptically polarized and there are two types of HQVs, deep and shallow. They correspond to singularities in majority and minority circular components of the condensate wave function, respectively. The core radius (healing length) of the deep HQVs decreases and the core radius of the shallow HQVs increases with increase of magnetic field. The shallow HQVs disappear and the deep HQVs transform into the integer vortices in the circularly polarized condensate when the applied magnetic field exceeds the critical one.     

Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part I—computer optimization techniques

In recent years, numerical and experimental investigations on the draft tube performance have confirmed the importance of the inlet swirling flow created by the runner vanes. The results indicate that it is still a challenge to get the optimal flow distribution at the draft tube inlet which gives the best machine performance over a range of operation points. Consequently, there is a need to adjust the runner-draft tube coupling to minimize the losses arising from the inlet flow distribution. This paper focus on establishing an optimization methodology for maximizing the draft tube performance as a function of the inlet velocity profile. The overall work is divides into two parts: The part one establish the inlet velocity parametrization, the numerical optimization set-up and the objective function definition. The part two validate the numerical CFD draft tube model. These steps are represented by the coupling of the commercial softwares MATLAB, FLUENT and iSIGHT. It is considered that this proved methodology will help to find a inlet velocity profile shape which will be able to suppress or mitigate the undesirable draft tube flow characteristics.     

The limit as <Emphasis Type="Italic">p</Emphasis> → ∞ in a nonlocal <Emphasis Type="Italic">p</Emphasis>-Laplacian evolution equation: a nonlocal approximation of a model for sandpiles

In this paper, we study the nonlocal ∞-Laplacian type diffusion equation obtained as the limit as p → ∞ to the nonlocal analogous to the p-Laplacian evolution,

The heavy ion beam diagnostic for the tokamak ISTTOK

In this paper we describe the heavy ion beam diagnostic for the tokamak ISTTOK, which has been designed to determine the temporal evolution of the plasma density, poloidal magnetic field and plasma potential profiles. This diagnostic makes use of a new type of high density caesium plasma source, a multiple cell detector and a fast data acquisition system. We describe the numerical code for trajectory and beam attenuation simulations, a method for the experimental determination of the poloidal field profile, the ion gun and the detection, control and data acquisition systems. Calibration tests and the first experimental results are presented