A Convergent Approximation of the Pareto Optimal Set for Finite Horizon Multiobjective Optimal Control Problems (MOC) Using Viability Theory

The objective of this paper is to provide a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems for which the objective space is not necessarily convex. Our approach is based on Viability Theory. We first introduce the set-valued return function V and show that the epigraph of V is equal to the viability kernel of a properly chosen closed set for a properly chosen dynamics. We then introduce an approximate set-valued return function with finite set-values as the solution of a multiobjective dynamic programming equation. The epigraph of this approximate set-valued return function is shown to be equal to the finite discrete viability kernel resulting from the convergent numerical approximation of the viability kernel proposed in [4, 5]. As a result, the epigraph of the approximate set-valued return function converges towards the epigraph of V. The approximate set-valued return function finally provides the proposed numerical approximation of the Pareto optimal set for every initial time and state. Several numerical examples are provided

Frequency shifts and relaxation rates for spin 1/2 particles moving in electromagnetic fields

We discuss the behaviour of the Larmor frequency shift and the longitudinal relaxation rate due to non-uniform electromagnetic fields on an assembly of spin 1/2 particles, in adiabatic and nonadiabatic regimes. We also show some general relations between the various frequency shifts and between the frequency shifts and relaxation rates. The remarkable feature of all our results is that they were obtained without any specific assumptions on the explicit form of the correlation functions of the fields. Hence, we expect that our results are valid both for diffusive and ballistic regime of motion and arbitrary cell shapes and surface scattering. These results can then be applied to a wide variety of realistic systems

Set-Valued Return Function and Generalized Solutions for Multiobjective Optimal Control Problems (MOC)

In this paper, we consider a multiobjective optimal control problem where the preference relation in the objective space is defined in terms of a pointed convex cone containing the origin, which defines generalized Pareto optimality. For this problem, we introduce the set-valued return function V and provide a unique characterization for V in terms of contingent derivative and coderivative for set-valued maps, which extends two previously introduced notions of generalized solution to the Hamilton-Jacobi equation for single objective optimal control problems.Comment: 29 pages, submitted to SICO

Constraining short-range spin-dependent forces with polarized helium 3 at the Laue-Langevin Institute

We have searched for a short-range spin-dependent interaction mediated by a hypothetical light scalar boson with CP-violating couplings to the neutron using the spin relaxation of hyperpolarized $^3$He. The walls of the $^3$He cell would generate a depolarizing pseudomagnetic field.Comment: Twelfth Conference on the Intersections of Particle and Nuclear Physics (CIPANP2015), Vail Marriott Mountain Resort, Vail, Colorado, US

Continuous approximate synthesis of planar function-generators minimising the design error

It has been observed in the literature that as the cardinality of the prescribed discrete input-output data set increases, the corresponding four-bar linkages that minimise the Euclidean norm of the design and structural errors tend to converge to the same linkage. The important implication is that minimising the Euclidean norm, or any p-norm, of the structural error, which leads to a nonlinear least-squares problem requiring iterative solutions, can be accomplished implicitly by minimising that of the design error, which leads to a linear least-squares problem that can be solved directly. Apropos, the goal of this paper is to take the first step towards proving that as the cardinality of the data set tends towards infinity the observation is indeed true. In this paper we will integrate the synthesis equations in the range between minimum and maximum input values, thereby reposing the discrete approximate synthesis problem as a continuous one. Moreover, we will prove that a lower bound of the Euclidean norm, and indeed of any p-norm, of the design error for planar RRRR function-generating linkages exists and is attained with continuous approximate synthesis

Re-entrant spin glass and magnetoresistance in Co_{0.2}Zn_{0.8}Fe_{1.6}Ti_{0.4}O_4 spinel oxide

We have investigated the static and dynamic response of magnetic clusters in Co_{0.2}Zn_{0.8}Fe_{1.6}Ti_{0.4}O_4 spinel oxide, where a sequence of magnetic phase transitions, i.e., paramagnetic (PM) to ferromagnetic at T_{C} $\leq$ 270K and ferromagnetic to canted spin glass state at T_f$$\leq$ 125K is observed

A discrete dynamic programming approximation to the multiobjective deterministic finite horizon optimal control problem

This paper addresses the problem of finding an approximation to the minimal element set of the objective space for the class of multiobjective deterministic finite horizon optimal control problems. The objective space is assumed to be partially ordered by a pointed convex cone containing the origin. The approximation procedure consists of a two-step discretization in time and state space. Following the first-order time discretization, the dynamic programming principle is used to find the multiobjective discrete dynamic programming equation equivalent to the resulting discrete multiobjective optimal control problem. The multiobjective discrete dynamic programming equation is finally discretized in the state space. The convergence of the approximation for both discretization steps is discussed

Project 8 Phase III Design Concept

We present a working concept for Phase III of the Project 8 experiment, aiming to achieve a neutrino mass sensitivity of $2~\mathrm{eV}$ ($90~\%$ C.L.) using a large volume of molecular tritium and a phased antenna array. The detection system is discussed in detail.Comment: 3 pages, 3 figures, Proceedings of Neutrino 2016, XXVII International Conference on Neutrino Physics and Astrophysics, 4-9 July 2016, London, U

Results from the Project 8 phase-1 cyclotron radiation emission spectroscopy detector

The Project 8 collaboration seeks to measure the absolute neutrino mass scale by means of precision spectroscopy of the beta decay of tritium. Our technique, cyclotron radiation emission spectroscopy, measures the frequency of the radiation emitted by electrons produced by decays in an ambient magnetic field. Because the cyclotron frequency is inversely proportional to the electron's Lorentz factor, this is also a measurement of the electron's energy. In order to demonstrate the viability of this technique, we have assembled and successfully operated a prototype system, which uses a rectangular waveguide to collect the cyclotron radiation from internal conversion electrons emitted from a gaseous $^{83m}$Kr source. Here we present the main design aspects of the first phase prototype, which was operated during parts of 2014 and 2015. We will also discuss the procedures used to analyze these data, along with the features which have been observed and the performance achieved to date.Comment: 3 pages; 2 figures; Proceedings of Neutrino 2016, XXVII International Conference on Neutrino Physics and Astrophysics, 4-9 July 2016, London, U