THREE-LAYER FLUID FLOW OVER A SMALL OBSTRUCTION ON THE BOTTOM OF A CHANNEL

Many boundary value problems occur in a natural way while studying fluid flow problems in a channel. The solutions of two such boundary value problems are obtained and analysed in the context of flow problems involving three layers of fluids of different constant densities in a channel, associated with an impermeable bottom that has a small undulation. The top surface of the channel is either bounded by a rigid lid or free to the atmosphere. The fluid in each layer is assumed to be inviscid and incompressible, and the flow is irrotational and two-dimensional. Only waves that are stationary with respect to the bottom profile are considered in this paper. The effect of surface tension is neglected. In the process of obtaining solutions for both the problems, regular perturbation analysis along with a Fourier transform technique is employed to derive the first-order corrections of some important physical quantities. Two types of bottom topography, such as concave and convex, are considered to derive the profiles of the interfaces. We observe that the profiles are oscillatory in nature, representing waves of variable amplitude with distinct wave numbers propagating downstream and with no wave upstream. The observations are presented in tabular and graphical forms.

NMR relaxation studies in doped poly-3-methylthiophene

NMR relaxation rates (1/T-1), magnetic susceptibility, and electrical conductivity studies in doped poly-3-methylthiophene are reported in this paper. The magnetic susceptibility data show the contributions from both Pauli and Curie spins, with the size of the Pauli term depending strongly on the doping level. Proton and fluorine NMR relaxation rates have been studied as a function of temperature (3-300 K) and field (for protons at 0.9, 9.0, 16.4, and 23.4 T, and for fluorine at 9.0 T). The temperature dependence of T-1 is classified into three regimes: (a) For T < (g mu(B) B/2k(B)), the relaxation mechanism follows a modified Korringa relation due to electron-electron interactions and disorder. H-1-T-1 is due to the electron-nuclear dipolar interaction in addition to the contact term. (b) For the intermediate temperature range (g mu(B) B/2k(B)) < T < T-BPP (the temperature where the contribution from the reorientation motion to the T-1 is insignificant) the relaxation mechanism is via spin diffusion to the paramagnetic centers. (c) In the high-temperature regime and at low Larmor frequency the relaxation follows the modified Bloembergen, Purcell, and Pound model. T-1 data analysis has been carried out in light of these models depending upon the temperature and frequency range of study. Fluorine relaxation data have been analyzed and attributed to the PF6 reorientation. The cross relaxation among the H-1 and F-19 nuclei has been observed in the entire temperature range suggesting the role of magnetic dipolar interaction modulated by the reorientation of the symmetric molecular subgroups. The data analysis shows that the enhancement in the Korringa ratio is greater in a less conducting sample. Intra-and interchain hopping of charge carriers is found to be a dominant relaxation mechanism at low temperature. Frequency dependence of T-1(-1) on temperature shows that at low temperature T < (g mu(B) B/2k(B))] the system shows three dimensions and changes to quasi one dimension at high temperature. Moreover, a good correlation between electrical conductivity, magnetic susceptibility, and NMR T-1 data has been observed.

Comparative study of magnetic ordering in bulk and nanoparticles of Sm0.65Ca0.35MnO3: Magnetization and electron magnetic resonance measurements

To explore the effect of size reduction to nanoscale on the hole doped Sm0.65Ca0.35MnO3 compound, dc magnetic measurements and electron magnetic resonance (EMR) were done on bulk and nanoparticle samples in the temperature range 10 <= T <= 300 K. Magnetization measurement showed that the bulk sample undergoes a charge ordering transition at 240K and shows a mixed magnetic phase at low temperature. However, the nanosample underwent a ferromagnetic transition at 75 K, and the charge ordered state was destabilized on size reduction down to nanoscale. The low-temperature ferromagnetic component is found to be enhanced in nanoparticles as compared to their bulk counterpart. Interestingly around room temperature, bulk particles show higher magnetization where as at low temperature nanoparticles show higher magnetization. Ferromagnetism in the bulk is due to super exchange where as ferromagnetism in nanoparticles is due to uncompensated spins of the surface layer. Temperature variation of EMR parameters correlates well with the results of magnetic measurements. The magnetic behaviour of the nanoparticles is understood in terms of the core shell scenario. (C) 2015 AIP Publishing LLC.

Spin-reorientation and weak ferromagnetism in antiferromagnetic TbMn0.5Fe0.5O3

Orthorhombic single crystals of TbMn0.5Fe0.5O3 are found to exhibit spin-reorientation, magnetization reversal, and weak ferromagnetism. Strong anisotropy effects are evident in the temperature dependent magnetization measurements along the three crystallographic axes a, b, and c. A broad magnetic transition is visible at T-N(Fe/Mn) = 286K due to paramagnetic to A(x)G(y)C(z) ordering. A sharp transition is observed at T-SR(Fe/Mn) = 28 K, which is pronounced along c axis in the form of a sharp jump in magnetization where the spins reorient to G(x)A(y)F(z) configuration. The negative magnetization observed below T-SR(Fe/Mn) along c axis is explained in terms of domain wall pinning. A component of weak ferromagnetism is observed in field-scans along c-axis but below 28 K. Field-induced steps-like transitions are observed in hysteresis measurement along b axis below 28 K. It is noted that no sign of Tb-order is discernible down to 2K. TbMn0.5Fe0.5O3 could be highlighted as a potential candidate to evaluate its magneto-dielectric effects across the magnetic transitions. (C) 2015 AIP Publishing LLC.

On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties

We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan in Discrete Math. 55:221-232, 1985), while for example the problems of finding a minimum s-t separator that induces a connected graph or forms an independent set are fixed-parameter tractable when parameterized by the size of the separator (Marx et al. in ACM Trans. Algorithms 9(4): 30, 2013). Motivated by these results, we study properties that generalize cliques, independent sets, and connected graphs, and determine the complexity of finding separators satisfying these properties. We investigate these problems also on bounded-degree graphs. Our results are as follows: Finding a minimum c-connected s-t separator is FPT for c=2 and W1]-hard for any ca parts per thousand yen3. Finding a minimum s-t separator with diameter at most d is W1]-hard for any da parts per thousand yen2. Finding a minimum r-regular s-t separator is W1]-hard for any ra parts per thousand yen1. For any decidable graph property, finding a minimum s-t separator with this property is FPT parameterized jointly by the size of the separator and the maximum degree. Finding a connected s-t separator of minimum size does not have a polynomial kernel, even when restricted to graphs of maximum degree at most 3, unless .

Structural-modulation-driven spin canting and reentrant glassy magnetic phase in ferromagnetic Lu2MnNiO6

Unusual behavior of reentrant spin-glass (RSG) compound Lu2MnNiO6 has been investigated by magnetometry and neutron diffraction. The system possesses a ferromagnetic (FM) ordering below 40 K and undergoes a RSG transition at 20 K. Additionally, Lu2MnNiO6 retains memory effect above the glassy transition till spins sustain ordering. A novel critical behavior with unusual critical exponents (beta =similar to 0.241 and gamma similar to 1.142) is observed that indicates a canting in the spin structure below the ferromagnetic transition (T-C). A comprehensive analysis of temperature-dependent neutron diffraction data and first-principles calculations divulge that a structural distortion induced by an octahedral tilting results in a canted spin structure below T-C.

Algorithm for Autonomous Reorganization of Mobile Wireless Camera Sensor Networks to Improve Coverage

In this paper, sensing coverage by wireless camera-embedded sensor networks (WCSNs), a class of directional sensors is studied. The proposed work facilitates the autonomous tuning of orientation parameters and displacement of camera-sensor nodes in the bounded field of interest (FoI), where the network coverage in terms of every point in the FoI is important. The proposed work is first of its kind to study the problem of maximizing coverage of randomly deployed mobile WCSNs which exploits their mobility. We propose an algorithm uncovered region exploration algorithm (UREA-CS) that can be executed in centralized and distributed modes. Further, the work is extended for two special scenarios: 1) to suit autonomous combing operations after initial random WCSN deployments and 2) to improve the network coverage with occlusions in the FoI. The extensive simulation results show that the performance of UREA-CS is consistent, robust, and versatile to achieve maximum coverage, both in centralized and distributed modes. The centralized and distributed modes are further analyzed with respect to the computational and communicational overheads.

Nonvanishing of Koecher-Maass series attached to Siegel cusp forms

We prove a nonvanishing result for Koecher-Maass series attached to Siegel cusp forms of weight k and degree n in certain strips on the complex plane. When n = 2, we prove such a result for forms orthogonal to the space of the Saito-Kurokawa lifts `up to finitely many exceptions', in bounded regions. (C) 2015 Elsevier Inc. All rights reserved.

Origin of room temperature weak-ferromagnetism in antiferromagnetic Pb(Fe2/3W1/3)O-3 ceramic

We report the origin of room temperature weak ferromagnetic behavior of polycrystalline Pb(Fe2/3W1/3)O-3 (PFW) powder. The structure and magnetic properties of the ceramic powder prepared by a Columbite method were characterized by X-ray and neutron diffraction, Mossbauer spectroscopy and magnetization measurements. Rietveld analysis of diffraction data confirm the formation of single phase PFW, without traces of any parasitic pyrochlore phase. PFW was found to crystallize in the cubic structure at room temperature. The Rietveld refinement of neutron diffraction data measured at room temperature confirmed the G-type antiferromagnetic structure of PFW in our sample. However, along with the antiferromagnetic (AFM) ordering of the Fe spins, we have observed the existence of weak ferromagnetism at room temperature through: (i) a clear opening of hysteresis (M-H) loop, (ii) bifurcation of the field cooled and zero-field cooled susceptibility; supported by Mossbauer spectroscopy results. The P-E loop measurements showed a non-linear slim hysteresis loop at room temperature due to the electronic conduction through the local inhomogeneities in the PFW crystallites and the inter-particle regions. By corroborating all the magnetic measurements, especially the spin glass nature of the sample, with the conduction behavior of the sample, we report here that the observed ferromagnetism originates at these local inhomogeneous regions in the sample, where the Fe-spins are not perfectly aligned antiferromagnetically due to the compositional disordering. (C) 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

An approximation to the QoS aware throughput region of a tree network under IEEE 802.15.4 CSMA/CA with application to wireless sensor network design

In the context of wireless sensor networks, we are motivated by the design of a tree network spanning a set of source nodes that generate packets, a set of additional relay nodes that only forward packets from the sources, and a data sink. We assume that the paths from the sources to the sink have bounded hop count, that the nodes use the IEEE 802.15.4 CSMA/CA for medium access control, and that there are no hidden terminals. In this setting, starting with a set of simple fixed point equations, we derive explicit conditions on the packet generation rates at the sources, so that the tree network approximately provides certain quality of service (QoS) such as end-to-end delivery probability and mean delay. The structures of our conditions provide insight on the dependence of the network performance on the arrival rate vector, and the topological properties of the tree network. Our numerical experiments suggest that our approximations are able to capture a significant part of the QoS aware throughput region (of a tree network), that is adequate for many sensor network applications. Furthermore, for the special case of equal arrival rates, default backoff parameters, and for a range of values of target QoS, we show that among all path-length-bounded trees (spanning a given set of sources and the data sink) that meet the conditions derived in the paper, a shortest path tree achieves the maximum throughput. (C) 2015 Elsevier B.V. All rights reserved.

QoS Constrained Optimal Sink and Relay Placement in Planned Wireless Sensor Networks

We are given a set of sensors at given locations, a set of potential locations for placing base stations (BSs, or sinks), and another set of potential locations for placing wireless relay nodes. There is a cost for placing a BS and a cost for placing a relay. The problem we consider is to select a set of BS locations, a set of relay locations, and an association of sensor nodes with the selected BS locations, so that the number of hops in the path from each sensor to its BS is bounded by h(max), and among all such feasible networks, the cost of the selected network is the minimum. The hop count bound suffices to ensure a certain probability of the data being delivered to the BS within a given maximum delay under a light traffic model. We observe that the problem is NP-Hard, and is hard to even approximate within a constant factor. For this problem, we propose a polynomial time approximation algorithm (SmartSelect) based on a relay placement algorithm proposed in our earlier work, along with a modification of the greedy algorithm for weighted set cover. We have analyzed the worst case approximation guarantee for this algorithm. We have also proposed a polynomial time heuristic to improve upon the solution provided by SmartSelect. Our numerical results demonstrate that the algorithms provide good quality solutions using very little computation time in various randomly generated network scenarios.

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

Efficient density matrix renormalization group algorithm to study Y junctions with integer and half-integer spin

An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N = 3n + 1 approximate to 500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with N-A not equal N-B. The ground state (GS) and spin densities rho(r) = < S-r(z)> at site r are quite different for junctions with S = 1/2, 1, 3/2, and 2. The GS has finite total spin S-G = 2S(S) for even (odd) N and for M-G = S-G in the S-G spin manifold, rho(r) > 0(< 0) at sites of the larger (smaller) sublattice. S = 1/2 junctions have delocalized states and decreasing spin densities with increasing N. S = 1 junctions have four localized S-z = 1/2 states at the end of each arm and centered on the junction, consistent with localized states in S = 1 chains with finite Haldane gap. The GS of S = 3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S = 1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S = 3/2 or 2 junctions.

COMPLEX GEODESICS, THEIR BOUNDARY REGULARITY, AND A HARDY-LITTLEWOOD-TYPE LEMMA

We begin by giving an example of a smoothly bounded convex domain that has complex geodesics that do not extend continuously up to partial derivative D. This example suggests that continuity at the boundary of the complex geodesics of a convex domain Omega (sic) C-n, n >= 2, is affected by the extent to which partial derivative Omega curves or bends at each boundary point. We provide a sufficient condition to this effect (on C-1-smoothly bounded convex domains), which admits domains having boundary points at which the boundary is infinitely flat. Along the way, we establish a Hardy-Littlewood-type lemma that might be of independent interest.

Origin of the Spin-Orbital Liquid State in a Nearly J=0 Iridate Ba3ZnIr2O9

We show using detailed magnetic and thermodynamic studies and theoretical calculations that the ground state of Ba3ZnIr2O9 is a realization of a novel spin-orbital liquid state. Our results reveal that Ba3ZnIr2O9 with Ir5+ (5d(4)) ions and strong spin-orbit coupling (SOC) arrives very close to the elusive J = 0 state but each Ir ion still possesses a weak moment. Ab initio density functional calculations indicate that this moment is developed due to superexchange, mediated by a strong intradimer hopping mechanism. While the Ir spins within the structural Ir2O9 dimer are expected to form a spin-orbit singlet state (SOS) with no resultant moment, substantial frustration arising from interdimer exchange interactions induce quantum fluctuations in these possible SOS states favoring a spin-orbital liquid phase down to at least 100 mK.