Classical integrability in the BTZ black hole

Using the fact the BTZ black hole is a quotient of AdS(3) we show that classical string propagation in the BTZ background is integrable. We construct the flat connection and its monodromy matrix which generates the non-local charges. From examining the general behaviour of the eigen values of the monodromy matrix we determine the set of integral equations which constrain them. These equations imply that each classical solution is characterized by a density function in the complex plane. For classical solutions which correspond to geodesics and winding strings we solve for the eigen values of the monodromy matrix explicitly and show that geodesics correspond to zero density in the complex plane. We solve the integral equations for BMN and magnon like solutions and obtain their dispersion relation. We show that the set of integral equations which constrain the eigen values of the monodromy matrix can be identified with the continuum limit of the Bethe equations of a twisted SL(2, R) spin chain at one loop. The Landau-Lifshitz equations from the spin chain can also be identified with the sigma model equations of motion.

Regional Flood Frequency Analysis using Two-level Clustering Approach

Clustering techniques are used in regional flood frequency analysis (RFFA) to partition watersheds into natural groups or regions with similar hydrologic responses. The linear Kohonen's self‐organizing feature map (SOFM) has been applied as a clustering technique for RFFA in several recent studies. However, it is seldom possible to interpret clusters from the output of an SOFM, irrespective of its size and dimensionality. In this study, we demonstrate that SOFMs may, however, serve as a useful precursor to clustering algorithms. We present a two‐level. SOFM‐based clustering approach to form regions for FFA. In the first level, the SOFM is used to form a two‐dimensional feature map. In the second level, the output nodes of SOFM are clustered using Fuzzy c‐means algorithm to form regions. The optimal number of regions is based on fuzzy cluster validation measures. Effectiveness of the proposed approach in forming homogeneous regions for FFA is illustrated through application to data from watersheds in Indiana, USA. Results show that the performance of the proposed approach to form regions is better than that based on classical SOFM.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

Optimizing Delay in Sequential Change Detection on Ad Hoc Wireless Sensor Networks

We consider the classical problem of sequential detection of change in a distribution (from hypothesis 0 to hypothesis 1), where the fusion centre receives vectors of periodic measurements, with the measurements being i.i.d. over time and across the vector components, under each of the two hypotheses. In our problem, the sensor devices ("motes") that generate the measurements constitute an ad hoc wireless network. The motes contend using a random access protocol (such as CSMA/CA) to transmit their measurement packets to the fusion centre. The fusion centre waits for vectors of measurements to accumulate before taking decisions. We formulate the optimal detection problem, taking into account the network delay experienced by the vectors of measurements, and find that, under periodic sampling, the detection delay decouples into network delay and decision delay. We obtain a lower bound on the network delay, and propose a censoring scheme, where lagging sensors drop their delayed observations in order to mitigate network delay. We show that this scheme can achieve the lower bound. This approach is explored via simulation. We also use numerical evaluation and simulation to study issues such as: the optimal sampling rate for a given number of sensors, and the optimal number of sensors for a given measurement rate

Spectral Finite Element Formulation for Nanorods via Nonlocal Continuum Mechanics

In this article, the Eringen's nonlocal elasticity theory has been incorporated into classical/local Bernoulli-Euler rod model to capture unique properties of the nanorods under the umbrella of continuum mechanics theory. The spectral finite element (SFE) formulation of nanorods is performed. SFE formulation is carried out and the exact shape functions (frequency dependent) and dynamic stiffness matrix are obtained as function of nonlocal scale parameter. It has been found that the small scale affects the exact shape functions and the elements of the dynamic stiffness matrix. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave dispersion properties of carbon nanotubes.

Modeling of active fiber composite for delamination sensing

In order to demonstrate the feasibility of Active Fiber Composites (AFC) as sensors for detecting damage, a pretwisted strip made of AFC with symmetric free-edge delamination is considered in this paper. The strain developed on the top/bottom of the strip is measured to detect and assess delamination. Variational Asymptotic Method (VAM) is used in the development of a non-classical non-linear cross sectional model of the strip. The original three dimensional (3D) problem is simplified by the decomposition into two simpler problems: a two-dimensional (2D) problem, which provides in a compact form the cross-sectional properties using VAM, and a non-linear one-dimensional (1D) problem along the length of the beam. This procedure gives the non-linear stiffnesses, which are very sensitive to damage, at any given cross-section of the strip. The developed model is used to study a special case of cantilevered laminated strip with antisymmetric layup, loaded only by an axial force at the tip. The charge generated in the AFC lamina is derived in closed form in terms of the 1D strain measures. It is observed that delamination length and location have a definite influence on the charge developed in the AFC lamina. Also, sensor voltage output distribution along the length of the beam is obtained using evenly distributed electrode strip. These data could in turn be used to detect the presence of damage.

Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state

Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the ``fully frustrated'' Bose-Hubbard model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time-reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.

Adsorption on Edge-Functionalized Bilayer Graphene Nanoribbons: Assessing the Role of Functional Groups in Methane Uptake

A combination of ab initio and classical Monte Carlo simulations is used to investigate the effects of functional groups on methane binding. Using Moller-Plesset (MP2) calculations, we obtain the binding energies for benzene functionalized with NH2, OH, CH3, COOH, and H2PO3 and identify the methane binding sites. In all cases, the preferred binding sites are located above the benzene plane in the vicinity of the benzene carbon atom attached to the functional group. Functional groups enhance methane binding relative to benzene (-6.39 kJ/mol), with the largest enhancement observed for H2PO3 (-8.37 kJ/mol) followed by COOH and CH3 (-7.77 kJ/mol). Adsorption isotherms are obtained for edge-functionalized bilayer graphene nanoribbons using grand canonical Monte Carlo simulations with a five-site methane model. Adsorbed excess and heats of adsorption for pressures up to 40 bar and 298 K are obtained with functional group concentrations ranging from 3.125 to 6.25 mol 96 for graphene edges functionalized with OH, NH2, and COOH. The functional groups are found to act as preferred adsorption sites, and in the case of COOH the local methane density in the vicinity of the functional group is found to exceed that of bare graphene. The largest enhancement of 44.5% in the methane excess adsorbed is observed for COOH-functionalized nanoribbons when compared to H terminated ribbons. The corresponding enhancements for OH- and NH2-functionalized ribbons are 10.5% and 3.7%, respectively. The excess adsorption across functional groups reflects the trends observed in the binding energies from MP2 calculations. Our study reveals that specific site functionalization can have a significant effect on the local adsorption characteristics and can be used as a design strategy to tailor materials with enhanced methane storage capacity.

Wheeler-Feynman absorber revisited: a useful technique to calculate decay rates and lifetimes in small scale optical systems

The Wheeler-Feynman (WF) absorber theory of radiation though no more of interest in explaining self interaction of an electron, can be very useful in today's research in small scale optical systems. The significance of the WF absorber is the use of time-symmetrical solution of Maxwell's equations as opposed to only the retarded solution. The radiative coupling of emitters to nano wires in the near field and change in their lifetimes due to small mode volume enclosures have been elucidated with the retarded solutions before. These solutions have also been shown to agree with quantum electrodynamics, thus allowing for classical electromagnetic approaches in such problems. It is here assumed that the radiative coupling of the emitter with a body is in proportion to its contribution to the classical force of radiative reaction as derived in the WF absorber theory. Representing such nano structures as a partial WF absorber acting on the emitter makes the computations considerably easier than conventional electromagnetic solutions for full boundary conditions.

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N vertical bar N = 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal W-3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N - 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N >= 4, the sl(N|N - 1) theory admits smooth supersymmetric conical defects.

Bismuth carboxylates with Brucite- and Fluorite-related structures: synthesis structure and properties

Three new compounds of bismuth, C4N2H10]center dotBi(C7H4NO4)(C7H3NO4)]center dot H2O, I, Bi(C5H3N2O4) (C5H2N2O4)], II, and Bi(mu(2)-OH)(C7H3NO4)], III, have been prepared by the reaction between bismuth nitrate and heterocyclic aromatic dicarboxylic acids, 2,6-pyridinedicarboxylic acid, 4,5-imidazoledicarboxylic acid, and 3,4-pyridinedicarboxylic acid, respectively, under hydrothermal conditions. The structures of all the compounds have linkages between Bi2O2 and the corresponding dicarboxylate forming a simple molecular unit in I, a bilayer arrangement in II, and a three-dimensional extended structure in III. The topological arrangement of the nodal building units in the structures indicates that a brucite-related layer (II) and fluorite-related arrangement (III) can be realized in these structures. By utilizing the secondary interactions, one can correlate the structure of III to a Kagome-related one. The observation of such classical inorganic related structures in the bismuth carboxylates is noteworthy. Lewis acid catalytic studies on the formation of ketal suggest the possible participatory role of the lone pair of electrons. All the compounds are characterized employing elemental analysis, IR, UV-vis, and thermal studies.

Violation of entropic Leggett-Garg inequality in nuclear spins

We report an experimental study of recently formulated entropic Leggett-Garg inequality (ELGI) by Usha Devi et al. Phys. Rev. A 87, 052103 (2013)]. This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior. Here we study ELGI using a two-qubit nuclear magnetic resonance system. To perform the noninvasive measurements required for the ELGI study, we prepare the system qubit in a maximally mixed state as well as use the ``ideal negative result measurement'' procedure with the help of an ancilla qubit. The experimental results show a clear violation of ELGI by over four standard deviations. These results agree with the predictions of quantum theory. The violation of ELGI is attributed to the fact that certain joint probabilities are not legitimate in the quantum scenario, in the sense they do not reproduce all the marginal probabilities. Using a three-qubit system, we also demonstrate that three-time joint probabilities do not reproduce certain two-time marginal probabilities.