A note on the realignment criterion

For a quantum state in a bipartite system represented as a density matrix, researchers used the realignment matrix and functions on its singular values to study the separability of the quantum state. We obtain bounds for elementary symmetric functions of singular values of realignment matrices. This answers some open problems proposed by Lupo, Aniello, and Scardicchio. As a consequence, we show that the proposed scheme by these authors for testing separability would not work if the two subsystems of the bipartite system have the same dimension.Comment: 11 pages, to appear in Journal of Physics A: Mathematical and Theoretica

Daphnias: from the individual based model to the large population equation

The class of deterministic 'Daphnia' models treated by Diekmann et al. (J Math Biol 61: 277-318, 2010) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23: 114-135, 1983) and Diekmann et al. (Nieuw Archief voor Wiskunde 4: 82-109, 1984). In this note, we formulate the individual based models (IBM) supposedly underlying those deterministic models. The models treat the interaction between a general size-structured consumer population ('Daphnia') and an unstructured resource ('algae'). The discrete, size and age-structured Daphnia population changes through births and deaths of its individuals and throught their aging and growth. The birth and death rates depend on the sizes of the individuals and on the concentration of the algae. The latter is supposed to be a continuous variable with a deterministic dynamics that depends on the Daphnia population. In this model setting we prove that when the Daphnia population is large, the stochastic differential equation describing the IBM can be approximated by the delay equation featured in (Diekmann et al., l.c.)

Direct evidence of a zigzag spin chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation on single crystal Na2IrO3\rm Na_2IrO_3

We have combined single crystal neutron and x-ray diffractions to investigate the magnetic and crystal structures of the honeycomb lattice $\rm Na_2IrO_3$. The system orders magnetically below $18.1(2)$ K with Ir$^{4+}$ ions forming zigzag spin chains within the layered honeycomb network with ordered moment of $\rm 0.22(1) \mu_B$/Ir site. Such a configuration sharply contrasts the N{\'{e}}el or stripe states proposed in the Kitaev-Heisenberg model. The structure refinement reveals that the Ir atoms form nearly ideal 2D honeycomb lattice while the $\rm IrO_6$ octahedra experience a trigonal distortion that is critical to the ground state. The results of this study provide much-needed experimental insights into the magnetic and crystal structure crucial to the understanding of the exotic magnetic order and possible topological characteristics in the 5$d$-electron based honeycomb lattice.Comment: Revised version as that to appear in PR

Direct strain and elastic energy evaluation in rolled-up semiconductor tubes by x-ray micro-diffraction

We depict the use of x-ray diffraction as a tool to directly probe the strain status in rolled-up semiconductor tubes. By employing continuum elasticity theory and a simple model we are able to simulate quantitatively the strain relaxation in perfect crystalline III-V semiconductor bi- and multilayers as well as in rolled-up layers with dislocations. The reduction in the local elastic energy is evaluated for each case. Limitations of the technique and theoretical model are discussed in detail.Comment: 32 pages (single column), 9 figures, 39 reference

Radiometric force in dusty plasmas

A radiofrequency glow discharge plasma, which is polluted with a certain number of dusty grains, is studied. In addition to various dusty plasma phenomena, several specific colloidal effects should be considered. We focus on radiometric forces, which are caused by inhomogeneous temperature distribution. Aside from thermophoresis, the role of temperature distribution in dusty plasmas is an open question. It is shown that inhomogeneous heating of the grain by ion flows results in a new photophoresis like force, which is specific for dusty discharges. This radiometric force can be observable under conditions of recent microgravity experiments.Comment: 4 pages, amsmat

Asteroid lightcurves from the Palomar Transient Factory survey: Rotation periods and phase functions from sparse photometry

We fit 54,296 sparsely-sampled asteroid lightcurves in the Palomar Transient Factory to a combined rotation plus phase-function model. Each lightcurve consists of 20+ observations acquired in a single opposition. Using 805 asteroids in our sample that have reference periods in the literature, we find the reliability of our fitted periods is a complicated function of the period, amplitude, apparent magnitude and other attributes. Using the 805-asteroid ground-truth sample, we train an automated classifier to estimate (along with manual inspection) the validity of the remaining 53,000 fitted periods. By this method we find 9,033 of our lightcurves (of 8,300 unique asteroids) have reliable periods. Subsequent consideration of asteroids with multiple lightcurve fits indicate 4% contamination in these reliable periods. For 3,902 lightcurves with sufficient phase-angle coverage and either a reliably-fit period or low amplitude, we examine the distribution of several phase-function parameters, none of which are bimodal though all correlate with the bond albedo and with visible-band colors. Comparing the theoretical maximal spin rate of a fluid body with our amplitude versus spin-rate distribution suggests that, if held together only by self-gravity, most asteroids are in general less dense than 2 g/cm$^3$, while C types have a lower limit of between 1 and 2 g/cm$^3$, in agreement with previous density estimates. For 5-20km diameters, S types rotate faster and have lower amplitudes than C types. If both populations share the same angular momentum, this may indicate the two types' differing ability to deform under rotational stress. Lastly, we compare our absolute magnitudes and apparent-magnitude residuals to those of the Minor Planet Center's nominal $G=0.15$, rotation-neglecting model; our phase-function plus Fourier-series fitting reduces asteroid photometric RMS scatter by a factor of 3.Comment: 35 pages, 29 figures. Accepted 15-Apr-2015 to The Astronomical Journal (AJ). Supplementary material including ASCII data tables will be available through the publishing journal's websit

Analytic Controllability of Time-Dependent Quantum Control Systems

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrodinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert space -- and thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time-independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrodinger control problem. The applicability of the resulting theorem is illustrated with selected examples.Comment: 13 page

Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds

Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of order 3; they are not timelike Jordan Osserman. They are k-spacelike higher order Jordan Osserman for $2\le k\le s$; they are k-timelike higher order Jordan Osserman for $s+2\le k\le 2s$, and they are not k timelike higher order Jordan Osserman for $2\le s\le s+1$.Comment: Update bibliography, fix minor misprint

Stronger computational modelling of signalling pathways using both continuous and discrete-state methods

Starting from a biochemical signalling pathway model expresses in a process algebra enriched with quantitative information, we automatically derive both continuous-space and discrete-space representations suitable for numerical evaluation. We compare results obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results