Distributed Function Computation over Fields and Rings via Linear Compression of Sources

The setting considered in this paper is one of distributed function computation. More specifically, there is a collection of N sources possessing correlated information and a destination that would like to acquire a specific linear combination of the N sources. We address both the case when the common alphabet of the sources is a finite field and the case when it is a finite, commutative principal ideal ring with identity. The goal is to minimize the total amount of information needed to be transmitted by the N sources while enabling reliable recovery at the destination of the linear combination sought. One means of achieving this goal is for each of the sources to compress all the information it possesses and transmit this to the receiver. The Slepian-Wolf theorem of information theory governs the minimum rate at which each source must transmit while enabling all data to be reliably recovered at the receiver. However, recovering all the data at the destination is often wasteful of resources since the destination is only interested in computing a specific linear combination. An alternative explored here is one in which each source is compressed using a common linear mapping and then transmitted to the destination which then proceeds to use linearity to directly recover the needed linear combination. The article is part review and presents in part, new results. The portion of the paper that deals with finite fields is previously known material, while that dealing with rings is mostly new.Attempting to find the best linear map that will enable function computation forces us to consider the linear compression of source. While in the finite field case, it is known that a source can be linearly compressed down to its entropy, it turns out that the same does not hold in the case of rings. An explanation for this curious interplay between algebra and information theory is also provided in this paper.

Control technique for non-linear and unbalance compensation of an integrated magnetics-based three-phase series-shunt-compensated uninterruptible power supply

Handling unbalanced and non-linear loads in a three-phase AC power supply has always been a difficult issue. This has been addressed in the literature by either using fast controllers in the fundamental rotating reference frame or using separate controllers in reference frames specific to the harmonics. In the former case, the controller needs to be fast and in the latter case, besides the need for many controllers, negative-sequence components need to be extracted from the measured signal. This study proposes a control scheme for harmonic and unbalance compensation of a three-phase uninterruptible power supply wherein the problems mentioned above are addressed. The control takes place in the fundamental positive-sequence reference frame using only a set of feedback and feed-forward compensators. The harmonic components are extracted by a process of frame transformations and used as feed-forward compensation terms in the positive-sequence fundamental reference frame. This study uses a method wherein the measured signal itself is used for fundamental negative-sequence compensation. As the feed-forward compensator handles the high-bandwidth components, the feedback compensator can be a simple low-bandwidth one. This control algorithm is explained and validated experimentally.

Control technique for non-linear and unbalance compensation of an integrated magnetics-based three-phase series-shunt-compensated uninterruptible power supply

Handling unbalanced and non-linear loads in a three-phase AC power supply has always been a difficult issue. This has been addressed in the literature by either using fast controllers in the fundamental rotating reference frame or using separate controllers in reference frames specific to the harmonics. In the former case, the controller needs to be fast and in the lattercase, besides the need for many controllers, negative-sequence components need to be extracted from the measured signal.This study proposes a control scheme for harmonic and unbalance compensation of a three-phase uninterruptible power supply wherein the problems mentioned above are addressed. The control takes place in the fundamental positive-sequence reference frame using only a set of feedback and feed-forward compensators. The harmonic components are extracted by process of frame transformations and used as feed-forward compensation terms in the positive-sequence fundamental reference frame. This study uses a method wherein the measured signal itself is used for fundamental negative-sequence compensation. As the feed-forward compensator handles the high-bandwidth components, the feedback compensator can be a simple low-bandwidth one. This control algorithm is explained and validated experimentally.

Two new 1D chains of Ni(2)Na(2) heterometallic double half-cubane building units: Synthesis, structures and variable temperature magnetic study

An equimolar mixture of Ni(NO(3))(2)center dot 6H(2)O and pyridine-2-aldehyde with two equivalents of NaN(3) in methanol in the presence of NaOMe resulted in the formation of light green precipitate which upon crystallization from dimethylformamide (DMF) yielded light green single crystals [{Ni(2)Na(2)(pic)(4)(N(3))(2)(H(2)O)(2)(MeOH)}center dot MeOH center dot 3H(2)O](n) (1) and [{Ni(2)Na(2)(pic)(4)(N(3))(2)(H(2)O)(4)}center dot 2DMF center dot H(2)O](n) (2) (pic = pyridine-2-carboxylate) at room temperature and high temperature (100 degrees C), respectively. Variable temperature magnetic studies revealed the existence of overall ferromagnetic behaviour with J approximate to + 10 cm(-1) and D approximate to -2 to -7 cm(-1) for 1 and 2, respectively. Negative D values as well as variation of D upon slight distortion of structure by varying reaction temperature were observed. The X-band Electron Paramagnetic Resonance (EPR) spectra of both 2 and 3 were recorded below 50 K. The structural distortion was also implicated from the EPR spectra. Density Functional Theory (DFT) calculations on both complexes were performed in two different ways to corroborate the magnetic results. Considering only Ni(2)(II) dimeric unit, results were J = + 20.65 cm(-1) and D = -3.16 cm(-1) for 1, and J = +24.56 cm(-1) and D = -4.67 cm(-1) for 2. However, considering Ni(2)(II)Na(2)(I) cubane as magnetic core the results were J = +16.35 cm(-1) (1), +19.54 cm(-1) (2); D = -3.05 cm(-1) (1), -4.25 cm(-1) (2).

Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory

This article presents the buckling analysis of orthotropic nanoplates such as graphene using the two-variable refined plate theory and nonlocal small-scale effects. The two-variable refined plate theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate, hence it is unnecessary to use shear correction factors. Nonlocal governing equations of motion for the monolayer graphene are derived from the principle of virtual displacements. The closed-form solution for buckling load of a simply supported rectangular orthotropic nanoplate subjected to in-plane loading has been obtained by using the Navier's method. Numerical results obtained by the present theory are compared with first-order shear deformation theory for various shear correction factors. It has been proven that the nondimensional buckling load of the orthotropic nanoplate is always smaller than that of the isotropic nanoplate. It is also shown that small-scale effects contribute significantly to the mechanical behavior of orthotropic graphene sheets and cannot be neglected. Further, buckling load decreases with the increase of the nonlocal scale parameter value. The effects of the mode number, compression ratio and aspect ratio on the buckling load of the orthotropic nanoplate are also captured and discussed in detail. The results presented in this work may provide useful guidance for design and development of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.

2.5PN linear momentum flux from inspiralling compact binaries in quasicircular orbits and associated recoil: Nonspinning case

Anisotropic emission of gravitational waves (GWs) from inspiralling compact binaries leads to the loss of linear momentum and hence gravitational recoil of the system. The loss rate of linear momentum in the far-zone of the source (a nonspinning binary system of black holes in quasicircular orbit) is investigated at the 2.5 post-Newtonian (PN) order and used to provide an analytical expression in harmonic coordinates for the 2.5PN accurate recoil velocity of the binary accumulated in the inspiral phase. The maximum recoil velocity of the binary system at the end of its inspiral phase (i.e at the innermost stable circular orbit (ISCO)) estimated by the 2.5PN formula is of the order of 4 km s(-1) which is smaller than the 2PN estimate of 22 km s(-1). Going beyond inspiral, we also provide an estimate of the more important contribution to the recoil velocity from the plunge phase. The maximum recoil velocity at the end of the plunge, involving contributions both from inspiral and plunge phase, for a binary with symmetric mass ratio nu = 0.2 is of the order of 182 km s(-1).

Non-linear electrical response of chalcogenide glasses: Memory state phenomena

Investigations on the switching behaviour of arsenic-tellurium glasses with Ge or Al additives, yield interesting information about the dependence of switching on network rigidity, co-ordination of the constituents, glass transition & ambient temperature and glass forming ability.

A novel variable resolution global spectral method on the sphere

A variable resolution global spectral method is created on the sphere using High resolution Tropical Belt Transformation (HTBT). HTBT belongs to a class of map called reparametrisation maps. HTBT parametrisation of the sphere generates a clustering of points in the entire tropical belt; the density of the grid point distribution decreases smoothly in the domain outside the tropics. This variable resolution method creates finer resolution in the tropics and coarser resolution at the poles. The use of FFT procedure and Gaussian quadrature for the spectral computations retains the numerical efficiency available with the standard global spectral method. Accuracy of the method for meteorological computations are demonstrated by solving Helmholtz equation and non-divergent barotropic vorticity equation on the sphere. (C) 2011 Elsevier Inc. All rights reserved.

Structural Transformations, Composition Anomalies and a Dramatic Collapse of Linear Polymer Chains in Dilute Ethanol-Water Mixtures

Water-ethanol mixtures exhibit many interesting anomalies, such as negative excess partial molar volume of ethanol, excess sound absorption coefficient at low concentrations, and positive deviation from Raoult's law for vapor pressure, to mention a few. These anomalies have been attributed to different, often contradictory origins, but a quantitative understanding is still lacking. We show by computer simulation and theoretical analyses that these anomalies arise from the sudden emergence of a bicontinuous phase that occurs at a relatively low ethanol concentration of x(eth) approximate to 0.06-0.10 (that amounts to a volume fraction of 0.17-0.26, which is a significant range!). The bicontinuous phase is formed by aggregation of ethanol molecules, resulting in a weak phase transition whose nature is elucidated. We find that the microheterogeneous structure of the mixture gives rise to a pronounced nonmonotonic composition dependence of local compressibility and nonmonotonic dependence in the peak value of the radial distribution function of ethyl groups. A multidimensional free energy surface of pair association is shown to provide a molecular explanation of the known negative excess partial volume of ethanol in terms of parallel orientation and hence better packing of the ethyl groups in the mixture due to hydrophobic interactions. The energy distribution of the ethanol molecules indicates additional energy decay channels that explain the excess sound attenuation coefficient in aqueous alcohol mixtures. We studied the dependence of the solvation of a linear polymer chain on the composition of the water-ethanol solvent. We find that there is a sudden collapse of the polymer at x(eth) approximate to 0.05-a phenomenon which we attribute to the formation of the microheterogeneous structures in the binary mixture at low ethanol concentrations. Together with recent single molecule pulling experiments, these results provide new insight into the behavior of polymer chain and foreign solutes, such as enzymes, in aqueous binary mixtures.

Relevance of local parallel theory to the linear stability of laminar separation bubbles

Laminar separation bubbles are thought to be highly non-parallel, and hence global stability studies start from this premise. However, experimentalists have always realized that the flow is more parallel than is commonly believed, for pressure-gradient-induced bubbles, and this is why linear parallel stability theory has been successful in describing their early stages of transition. The present experimental/numerical study re-examines this important issue and finds that the base flow in such a separation bubble becomes nearly parallel due to a strong-interaction process between the separated boundary layer and the outer potential flow. The so-called dead-air region or the region of constant pressure is a simple consequence of this strong interaction. We use triple-deck theory to qualitatively explain these features. Next, the implications of global analysis for the linear stability of separation bubbles are considered. In particular we show that in the initial portion of the bubble, where the flow is nearly parallel, local stability analysis is sufficient to capture the essential physics. It appears that the real utility of the global analysis is perhaps in the rear portion of the bubble, where the flow is highly non-parallel, and where the secondary/nonlinear instability stages are likely to dominate the dynamics.

Fatigue de-bond growth in adhesively bonded single lap joints

The fatigue de-bond growth studies have been conducted on adhesively bonded lap joint specimens between aluminium and aluminium with Redux-319A adhesive with a pre-defined crack of 3 mm at the bond end. The correlations between fracture parameters and the de-bond growth data are established using both numerical and experimental techniques. In the numerical method, geometrically non-linear finite element analyses were carried out on adhesively bonded joint specimen for various de-bond lengths measured from the lap end along the mid-bond line of the adhesive. The finite element results were post processed to estimate the SERR components G (I) and G (II) using the Modified Virtual Crack Closure Integral (MVCCI) procedure. In experimental work, specimens were fabricated and fatigue de-bond growth tests were conducted at a stress ratio R = -1. The results obtained from both numerical analyses and testing have been used to generate de-bond growth curve and establish de-bond growth law in the Paris regime for such joints. The de-bond growth rate is primarily function of mode-I SERR component G (I) since the rate of growth in shear mode is relatively small. The value of Paris exponent m is found to be 6.55. The high value of de-bond growth exponent in Paris regime is expected, since the adhesive is less ductile than conventional metallic materials. This study is important for estimating the life of adhesively bonded joints under both constant and variable amplitude fatigue loads.

Radial infall of two compact objects: 2.5-post-Newtonian linear momentum flux and associated recoil

The loss rate of linear momentum from a binary system composed of compact objects (radially falling towards each other under mutual gravitational influence) has been investigated using the multipolar post-Minkowskian approach. The 2.5PN accurate analytical formula for the linear momentum flux is provided, in terms of the separation of the two objects, in harmonic coordinates, both for a finite and an infinite initial separation. The 2.5PN formulas for the linear momentum flux are finally used to estimate the recoil velocity accumulated during a premerger phase of the binary evolution.

Effect of magnetic field on Mott's variable-range hopping parameters in multiwall carbon nanotube mat

We report the temperature and magnetic field dependence of the conductivity of multiwall carbon nanotube mat in the temperature range 1.4-150 K and in magnetic fields up to 10 T. It is observed that charge transport in this system is governed by Mott's variable-range hopping of three-dimensional type in the higher temperature range and two-dimensional type in the lower temperature range. Mott's various parameters, such as localization length, hopping length, hopping energy and density of states at the Fermi level are deduced from the variable-range hopping fit. The resistance of the sample decreases with the magnetic field applied in the direction of tube axis of the nanotubes. The magnetic field gives rise to delocalization of states with the well-known consequence of a decrease in Mott's T-0 parameter in variable-range hopping. The application of magnetic field lowers the crossover temperature at which three-dimensional variable-range hopping turns to two-dimensional variable-range hopping. The conductivity on the lower temperature side is governed by the weak localization giving rise to positive magnetoconductance. Finally, a magnetic field-temperature diagram is proposed showing different regions for different kinds of transport mechanism.

Feasibility study of the measurement of Higgs pair creation at a photon linear collider

We studied the feasibility of the measurement of Higgs pair creation at a photon linear collider. From the sensitivity to the anomalous self-coupling of the Higgs boson, the optimum gamma gamma collision energy was found to be around 270 GeV for a Higgs mass of 120 GeV/c(2). We found that large backgrounds such as gamma gamma -> W+W-, ZZ, and b (b) over barb (b) over bar can be suppressed if correct assignment of tracks to parent partons is achieved and Higgs pair events can be observed with a statistical significance of similar to 5 sigma by operating the photon linear collider for 5 years.