Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility

We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$ could be either a set of saddle (exit) points of the well, or a set of further (meta)stable configurations. Three types of results are reported: (1) A general theory is developed, based on the path-wise approach to metastability, which has three important attributes. First, it is general in that it does not assume reversibility of the process, does not focus only on hitting times to rare events and does not assume a particular starting measure. Second, it relies only on the natural hypothesis that the mean hitting time to $G$ is asymptotically longer than the mean recurrence time to $x_0$ or $G$. Third, despite its mathematical simplicity, the approach yields precise and explicit bounds on the corrections to exponentiality. (2) We compare and relate different metastability conditions proposed in the literature so to eliminate potential sources of confusion. This is specially relevant for evolutions of infinite-volume systems, whose treatment depends on whether and how relevant parameters (temperature, fields) are adjusted. (3) We introduce the notion of early asymptotic exponential behavior to control time scales asymptotically smaller than the mean-time scale. This control is particularly relevant for systems with unbounded state space where nucleations leading to exit from metastability can happen anywhere in the volume. We provide natural sufficient conditions on recurrence times for this early exponentiality to hold and show that it leads to estimations of probability density functions

Finite-element modeling of liquid-crystal hydrodynamics with a variable degree of order

A finite-element model of liquid-crystal hydrodynamics based on the Qian and Sheng formulation has been developed. This formulation is a generalization of the Ericksen-Leslie theory to include variations in the order parameter, allowing for a proper description of disclinations. The present implementation is well suited to treat properly the various length scales necessary to model large regions yet resolve the rapid variations in the order parameter in proximity to disclinations

Modeling of weak anisotropic anchoring of nematic liquid crystals in the Landau-de Gennes theory

The anisotropic anchoring effect of a treated solid surface on a nematic liquid crystal is described in the Landau-de Gennes theory using a power expansion on the tensor-order parameter and two mutually orthogonal unit vectors. The expression has three degrees of freedom, allowing for independent assignment of polar and azimuthal anchoring strengths and a preferred value of the surface-order parameter. It is shown that in the limit for a uniaxial constant-order parameter, the expression simplifies to the anisotropic generalization of the Rapini-Papoular anchoring energy density proposed by Zhao et al. Experimentally measurable values with a physical meaning in the Oseen-Frank theory can be scaled and assigned to the scalar coefficients of the tensor-order-parameter expansion. Results of numerical experiments comparing the anchoring according to the study of Zhao et al. in the Oseen-Frank theory and the power expansion in the Landau-de Gennes theory are presented and shown to agree well

Impact of Power Allocation and Antenna Directivity in the Capacity of a Multiuser Cognitive Ad Hoc Network

This paper studies the benefits that power control and antenna directivity can bring to the capacity of a multiuser cognitive radio network. The main objective is to optimize the secondary network sum rate under the capacity constraint of the primary network. Exploiting location awareness, antenna directivity, and the power control capability, the cognitive radio ad hoc network can broaden its coverage and improve capacity. Computer simulations show that by employing the proposed method the system performance is significantly enhanced compared to conventional fixed power allocation

Nonleptonic B→D(∗)DsJ(∗)B \to D^{(*)}D_{sJ}^{(*)} decays and the nature of the orbitally excited charmed-strange mesons

The Belle Collaboration has recently reported a study of the decays $B \to D_{s1}(2536)^{+}\bar{D}^{(\ast)}$ and has given also estimates of relevant ratios between branching fractions of decays $B \to D^{(\ast)}D_{sJ}^{(\ast)}$ providing important information to check the structure of the $D_{s0}^{\ast}(2317)$, $D_{s1}(2460)$ and $D_{s1}(2536)$ mesons. The disagreement between experimental data and Heavy Quark Symmetry has been used as an indication that $D_{s0}^{\ast}(2317)$ and $D_{s1}(2460)$ mesons could have a more complex structure than the canonical $c\bar{s}$ one. We analyze these ratios within the framework of a constituent quark model, which allows us to incorporate the effects given by finite $c$-quark mass corrections. Our findings are that while the $D_{s1}(2460)$ meson could have a sizable non-$q\bar{q}$ component, the $D_{s0}^{\ast}(2317)$ and $D_{s1}(2536)$ mesons seem to be well described by a pure $q\bar{q}$ structure.Comment: 13 pages, 1 figur

Algal culture studies related to a Closed Ecological Life Support System (CELSS)

Studies with algal cultures which relate to closed ecological life support systems (CELSS) are discussed. A description of a constant cell density apparatus for continuous culture of algae is included. Excretion of algal by-products, and nitrogen utilization and excretion are discussed

ROBOSIM: An intelligent simulator for robotic systems

The purpose of this paper is to present an update of an intelligent robotics simulator package, ROBOSIM, first introduced at Technology 2000 in 1990. ROBOSIM is used for three-dimensional geometrical modeling of robot manipulators and various objects in their workspace, and for the simulation of action sequences performed by the manipulators. Geometric modeling of robot manipulators has an expanding area of interest because it can aid the design and usage of robots in a number of ways, including: design and testing of manipulators, robot action planning, on-line control of robot manipulators, telerobotic user interface, and training and education. NASA developed ROBOSIM between 1985-88 to facilitate the development of robotics, and used the package to develop robotics for welding, coating, and space operations. ROBOSIM has been further developed for academic use by its co-developer Vanderbilt University, and has been in both classroom and laboratory environments for teaching complex robotic concepts. Plans are being formulated to make ROBOSIM available to all U.S. engineering/engineering technology schools (over three hundred total with an estimated 10,000+ users per year)