Maximum group velocity in a one-dimensional model with a sinusoidally varying staggered potential

We use Floquet theory to study the maximum value of the stroboscopic group velocity in a one-dimensional tight-binding model subjected to an on-site staggered potential varying sinusoidally in time. The results obtained by numerically diagonalizing the Floquet operator are analyzed using a variety of analytical schemes. In the low-frequency limit we use adiabatic theory, while in the high-frequency limit the Magnus expansion of the Floquet Hamiltonian turns out to be appropriate. When the magnitude of the staggered potential is much greater or much less than the hopping, we use degenerate Floquet perturbation theory; we find that dynamical localization occurs in the former case when the maximum group velocity vanishes. Finally, starting from an ``engineered'' initial state where the particles (taken to be hard-core bosons) are localized in one part of the chain, we demonstrate that the existence of a maximum stroboscopic group velocity manifests in a light-cone-like spreading of the particles in real space.

Distribution, relative abundance, and conservation status of Asian elephants in Karnataka, southern India

Karnataka state in southern India supports a globally significant and the country's largest population of the Asian elephant Elephas maximus. A reliable map of Asian elephant distribution and measures of spatial variation in their abundance, both vital needs for conservation and management action, are unavailable not only in Karnataka, but across its global range. Here, we use various data gathered between 2000 and 2015 to map the distribution of elephants in Karnataka at the scale of the smallest forest management unit, the `beat', while also presenting data on elephant dung density for a subset of `elephant beats.' Elephants occurred in 972 out of 2855 forest beats of Karnataka. Sixty percent of these 972 beats and 55% of the forest habitat lay outside notified protected areas (PM), and included lands designated for agricultural production and human dwelling. While median elephant dung density inside protected areas was nearly thrice as much as outside, elephants routinely occurred in or used habitats outside PM where human density, land fraction under cultivation, and the interface between human-dominated areas and forests were greater. Based on our data, it is clear that India's framework for elephant conservation which legally protects the species wherever it occurs, but protects only some of its habitats while being appropriate in furthering their conservation within PM, seriously falters in situations where elephants reside in and/or seasonally use areas outside PAs. Attempts to further elephant conservation in production and dwelling areas have extracted high costs in human, elephant, material and monetary terms in Karnataka. In such settings, conservation planning exercises are necessary to determine where the needs of elephants or humans must take priority over the other, and to achieve that in a manner that is based not only on reliable scientific data but also on a process of public reasoning. (C) 2015 Elsevier Ltd. All rights reserved.

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

Minimization Problems Based on Relative alpha-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted I-alpha) were studied. Such minimizers were called forward I-alpha-projections. Here, a complementary class of minimization problems leading to the so-called reverse I-alpha-projections are studied. Reverse I-alpha-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (alpha > 1) and in constrained compression settings (alpha < 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse I-alpha-projection into a forward I-alpha-projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

Fusing the Navigation Information of Dual Foot-Mounted Zero-Velocity-Update-Aided Inertial Navigation Systems

A range constraint method viz. centroid method is proposed to fuse the navigation information of dual (right and left) foot-mounted Zero-velocity-UPdaTe (ZUPT)-aided Inertial Navigation Systems (INSs). Here, the range constraint means that the distance of separation between the position estimates of right and left foot ZUPT-aided INSs cannot be greater than a quantity known as foot-to-foot maximum separation. We present the experimental results which illustrate the applicability of the proposed method. The results show that the proposed method significantly enhances the accuracy of the navigation solution when compared to using two uncoupled foot-mounted ZUPT-aided INSs. Also, we compare the performance of the proposed method with the existing data fusion methods.

Relative stabilities of condensed face sharing mono- and di-carboranes: CB20H18 and C2B19H18+

The relative energies of triangular face sharing condensed macro polyhedral carboranes: CB20H18 and C2B19H18+ derived from mono- and di-substitution of carbons in (4) B21H18- is calculated at B3LYP/6-31G* level. The relative energies, H center dot center dot center dot H non-bonding distances, NICS values, topological charge analysis and orbital overlap compatibility connotes the face sharing condensed macro polyhedral mono-carboranes, 8 (4-CB20H18) to be the lowest energy isomer. The di-carba- derivative, (36) 4,4'a-C2B19H18+ with carbons substituted in a different B-12 cage in (4) B21H18- in anti-fashion is the most stable isomer among 28 possibilities. This structure has less non-bonding H center dot center dot center dot H interaction and is in agreement with orbital-overlap compatibility, and these two have the pivotal role in deciding the stability of these clusters. An estimate of the inherent stability of these carboranes is made using near-isodesmic equations which show that CB20H18 (8) is in the realm of the possible. (C) 2015 Elsevier B.V. All rights reserved.

Position-dependent velocity of an effective temperature point for the estimation of the thermal diffusivity of solids

A new approach is proposed to estimate the thermal diffusivity of optically transparent solids at ambient temperature based on the velocity of an effective temperature point (ETP), and by using a two-beam interferometer the proposed concept is corroborated. 1D unsteady heat flow via step-temperature excitation is interpreted as a `micro-scale rectilinear translatory motion' of an ETP. The velocity dependent function is extracted by revisiting the Fourier heat diffusion equation. The relationship between the velocity of the ETP with thermal diffusivity is modeled using a standard solution. Under optimized thermal excitation, the product of the `velocity of the ETP' and the distance is a new constitutive equation for the thermal diffusivity of the solid. The experimental approach involves the establishment of a 1D unsteady heat flow inside the sample through step-temperature excitation. In the moving isothermal surfaces, the ETP is identified using a two-beam interferometer. The arrival-time of the ETP to reach a fixed distance away from heat source is measured, and its velocity is calculated. The velocity of the ETP and a given distance is sufficient to estimate the thermal diffusivity of a solid. The proposed method is experimentally verified for BK7 glass samples and the measured results are found to match closely with the reported value.