Delta-Nabla Optimal Control Problems

We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results in the literature obtained as particular cases. As an application of the results of the paper we give necessary and sufficient Pareto optimality conditions for delta-nabla bi-objective optimal control problems.Comment: Preprint version of an article submitted 28-Nov-2009; revised 02-Jul-2010; accepted 20-Jul-2010; for publication in Journal of Vibration and Contro

The relationship between meat disgust and meat avoidance—A chicken-and-egg problem

This is the final version. Available from Frontiers Media via the DOI in this record. Data availability statement: The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: https://osf.io/ vkcef/?view_only=aea15b1ad2e44e899191e2699161894b.Feelings of disgust toward meat have been researched for at least 30 years, but so far the causal relationship that may link meat disgust and meat consumption has remained elusive. Two possible pathways have been proposed in previous literature: the more common pathway seems to be that meat disgust is developed after a transition to vegetarianism, potentially via the process of moralization and recruitment of (moral) disgust. Other accounts suggest the existence of a second pathway in which disgust initiates the avoidance of meat and this can be explained by existing theories of disgust functioning as a pathogen avoidance mechanism and meat serving as a pathogen cue. However, the evidence base for either relationship remains thin and to our knowledge no research has examined whether temporary meat abstention can lead to increases in meat disgust, as the first pathway suggests. We measured meat disgust and meat intake in n = 40 meat eaters before and after attempting a meat-free diet for 1 month (while taking part in the annual vegan campaign Veganuary). Although most participants lapsed to eating meat during this period, we found that reductions in meat intake during the month were predictive of increases in meat disgust afterwards. This supports the view that meat disgust is expressed as a result of meat avoidance in meat eaters. Implications for theoretical understanding of the relationship between meat disgust and meat avoidance, as well as the development of disgust based interventions are discussed.University of Exete

Effect of uniaxial stress on ferroelectric behavior of (Bi1/2Na1/2)TiO3-based lead-free piezoelectric ceramics

Prior studies have shown that a field-induced ferroelectricity in ceramics with general chemical formula (1-x-y) (Bi1/2 Na1/2) TiO3 -x BaTiO3 -y (K0.5 Na0.5) NbO3 and a very low remanent strain can produce very large piezoelectric strains. Here we show that both the longitudinal and transverse strains gradually change with applied electric fields even during the transition from the nonferroelectric to the ferroelectric state, in contrast to known Pb-containing antiferroelectrics. Hence, the volume change and, in turn, the phase transition can be affected using uniaxial compressive stresses, and the effect on ferroelectricity can thus be assessed. It is found that the 0.94 (Bi1/2 Na1/2) TiO3 -0.05 BaTiO3 -0.01 (K0.5 Na0.5) NbO3 ceramic (largely ferroelectric), with a rhombohedral R3c symmetry, displays large ferroelectric domains, significant ferroelastic deformation, and large remanent electrical polarizations even at a 250 MPa compressive stress. In comparison, the 0.91 (Bi1/2 Na1/2) TiO3 -0.07 BaTiO3 -0.02 (K0.5 Na0.5) NbO3 ceramic (largely nonferroelectric) possesses characteristics of a relaxor ferroelectric ceramic, including a pseudocubic structure, limited ferroelastic deformation, and low remanent polarization. The results are discussed with respect of the proposed antiferroelectric nature of the nonferroelectric state.open291

Electric-field-induced antiferroelectric to ferroelectric phase transition in mechanically confined Pb0.99Nb0.02[(Zr0.57Sn0.43)(0.94)Ti-0.06](0.98)O-3

The electric-field-induced phase transition was investigated under mechanical confinements in bulk samples of an antiferroelectric perovskite oxide at room temperature. Profound impacts of mechanical confinements on the phase transition are observed due to the interplay of ferroelasticity and the volume expansion at the transition. The uniaxial compressive prestress delays while the radial compressive prestress suppresses it. The difference is rationalized with a phenomenological model of the phase transition accounting for the mechanical confinement.open241

On Max-Stable Processes and the Functional D-Norm

We introduce a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence. The distribution function G of a continuous max-stable process on [0,1] is introduced and it is shown that G can be represented via a norm on functional space, called D-norm. This is in complete accordance with the multivariate case and leads to the definition of functional generalized Pareto distributions (GPD) W. These satisfy W=1+log(G) in their upper tails, again in complete accordance with the uni- or multivariate case. Applying this framework to copula processes we derive characterizations of the domain of attraction condition for copula processes in terms of tail equivalence with a functional GPD. \delta-neighborhoods of a functional GPD are introduced and it is shown that these are characterized by a polynomial rate of convergence of functional extremes, which is well-known in the multivariate case.Comment: 22 page

Correlation function of weakly interacting bosons in a disordered lattice

One of the most important issues in disordered systems is the interplay of the disorder and repulsive interactions. Several recent experimental advances on this topic have been made with ultracold atoms, in particular the observation of Anderson localization, and the realization of the disordered Bose-Hubbard model. There are however still questions as to how to differentiate the complex insulating phases resulting from this interplay, and how to measure the size of the superfluid fragments that these phases entail. It has been suggested that the correlation function of such a system can give new insights, but so far little experimental investigation has been performed. Here, we show the first experimental analysis of the correlation function for a weakly interacting, bosonic system in a quasiperiodic lattice. We observe an increase in the correlation length as well as a change in shape of the correlation function in the delocalization crossover from Anderson glass to coherent, extended state. In between, the experiment indicates the formation of progressively larger coherent fragments, consistent with a fragmented BEC, or Bose glass.Comment: 16 pages, 8 figure

Euler-Lagrange equations for composition functionals in calculus of variations on time scales

In this paper we consider the problem of the calculus of variations for a functional which is the composition of a certain scalar function $H$ with the delta integral of a vector valued field $f$, i.e., of the form $H(\int_{a}^{b}f(t,x^{\sigma}(t),x^{\Delta}(t))\Delta t)$. Euler-Lagrange equations, natural boundary conditions for such problems as well as a necessary optimality condition for isoperimetric problems, on a general time scale, are given. A number of corollaries are obtained, and several examples illustrating the new results are discussed in detail.Comment: Submitted 10-May-2009 to Discrete and Continuous Dynamical Systems (DCDS-B); revised 10-March-2010; accepted 04-July-201

Domain switching energies: Mechanical versus electrical loading in La-doped bismuth ferrite-lead titanate

The mechanical stress-induced domain switching and energy dissipation in morphotropic phase boundary (1 - x)(Bi(1-y)La(y))FeO(3)-xPbTiO(3) during uniaxial compressive loading have been investigated at three different temperatures. The strain obtained was found to decrease with increasing lanthanum content, although a sharp increase in strain was observed for compositions doped with 7.5 and 10 at. % La. Increased domain switching was found in compositions with decreased tetragonality. This is discussed in terms of the competing influences of the amount of domain switching and the spontaneous strain on the macroscopic behavior under external fields. Comparison of the mechanically and electrically dissipated energy showed significant differences, discussed in terms of the different microscopic interactions of electric field and stress.open10

Focusing and Compression of Ultrashort Pulses through Scattering Media

Light scattering in inhomogeneous media induces wavefront distortions which pose an inherent limitation in many optical applications. Examples range from microscopy and nanosurgery to astronomy. In recent years, ongoing efforts have made the correction of spatial distortions possible by wavefront shaping techniques. However, when ultrashort pulses are employed scattering induces temporal distortions which hinder their use in nonlinear processes such as in multiphoton microscopy and quantum control experiments. Here we show that correction of both spatial and temporal distortions can be attained by manipulating only the spatial degrees of freedom of the incident wavefront. Moreover, by optimizing a nonlinear signal the refocused pulse can be shorter than the input pulse. We demonstrate focusing of 100fs pulses through a 1mm thick brain tissue, and 1000-fold enhancement of a localized two-photon fluorescence signal. Our results open up new possibilities for optical manipulation and nonlinear imaging in scattering media

The maximally entangled symmetric state in terms of the geometric measure

The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination of analytical and numerical results, the most entangled symmetric states for up to 12 qubits are explored and discussed. The optimization problem on the sphere presented here is then compared with two classical optimization problems on the S^2 sphere, namely Toth's problem and Thomson's problem, and it is observed that, in general, they are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and reference