Nonlinear conduction in charge-ordered Pr0.63Ca0.37MnO3: Effect of magnetic fields

Nonlinear conduction in a single crystal of charge-ordered Pr0.63Ca0.37MnO3 has bren investigated in an applied magnetic field. In zero field, the nonlinear conduction, which starts at T< T-CO, can give rise to a region of negative differential resistance (NDR) which shows up below the Neel temperature. Application of a magnetic field Inhibits the appearance of NDR and makes the nonlinear conduction strongly hysteritic on cycling of the bias current. This is most severe in the temperature range where the charge-ordered state melts in an applied magnetic field. Our experiment strongly suggests that application of a magnetic field in the charge-ordering regime causes a coexistence of two phases.

On Finding the Natural Number of Topics with Latent Dirichlet Allocation: Some Observations

It is important to identify the ``correct'' number of topics in mechanisms like Latent Dirichlet Allocation(LDA) as they determine the quality of features that are presented as features for classifiers like SVM. In this work we propose a measure to identify the correct number of topics and offer empirical evidence in its favor in terms of classification accuracy and the number of topics that are naturally present in the corpus. We show the merit of the measure by applying it on real-world as well as synthetic data sets(both text and images). In proposing this measure, we view LDA as a matrix factorization mechanism, wherein a given corpus C is split into two matrix factors M-1 and M-2 as given by C-d*w = M1(d*t) x Q(t*w).Where d is the number of documents present in the corpus anti w is the size of the vocabulary. The quality of the split depends on ``t'', the right number of topics chosen. The measure is computed in terms of symmetric KL-Divergence of salient distributions that are derived from these matrix factors. We observe that the divergence values are higher for non-optimal number of topics - this is shown by a `dip' at the right value for `t'.

Design of speaker identification schemes for large number of speakers (A)

Design of speaker identification schemes for a small number of speakers (around 10) with a high degree of accuracy in controlled environment is a practical proposition today. When the number of speakers is large (say 50–100), many of these schemes cannot be directly extended, as both recognition error and computation time increase monotonically with population size. The feature selection problem is also complex for such schemes. Though there were earlier attempts to rank order features based on statistical distance measures, it has been observed only recently that the best two independent measurements are not the same as the combination in two's for pattern classification. We propose here a systematic approach to the problem using the decision tree or hierarchical classifier with the following objectives: (1) Design of optimal policy at each node of the tree given the tree structure i.e., the tree skeleton and the features to be used at each node. (2) Determination of the optimal feature measurement and decision policy given only the tree skeleton. Applicability of optimization procedures such as dynamic programming in the design of such trees is studied. The experimental results deal with the design of a 50 speaker identification scheme based on this approach.

Weber-Fechner type nonlinear behavior in zigzag edge graphene nanoribbons

Using a continuum Dirac theory, we study the density and spin response of zigzag edge-terminated graphene ribbons subjected to edge potentials and Zeeman fields. Our analytical calculations of the density and spin responses of the closed system (fixed particle number) to the static edge fields, show a highly nonlinear Weber-Fechner type behavior where the response depends logarithmically on the edge potential. The dependence of the response on the size of the system (e.g., width of a nanoribbon) is also uncovered. Zigzag edge graphene nanoribbons, therefore, provide a realization of response of organs such as the eye and ear that obey Weber-Fechner law. We validate our analytical results with tight-binding calculations. These results are crucial in understanding important effects of electron-electron interactions in graphene nanoribbons such as edge magnetism, etc., and also suggest possibilities for device applications of graphene nanoribbons.

Potentiometric determination of activities in the two-phase fields of the system Na2O---(α)Al2O3

Three compounds have been found to be stable in the pseudobinary system Na2O---(α)Al2O3 between 825 and 1400 K; two nonstoichiometric phases, β-alumina and β″-alumina, and NaAlO2. The homogeneity of β-alumina ranges from 9.5 to 11 mol% Na2O, while that of β″-alumina from 13.3 to 15.9 mol% Na2O at 1173 K. The activity of Na2O in the two-phase fields has been determined by a solid-state potentiometric technique. Since both β- and β″-alumina are fast sodium ion conductors, biphasic solid electrolyte tubes were used in these electrochemical measurements. The open circuit emf of the following cells were measured from 790 to 980 K: [GRAPHICS] The partial molar Gibbs' energy of Na2O relative to gamma-Na2O in the two-phase regions can be represented as: DELTA-GBAR(Na2O)(alpha- + beta-alumina) = -270,900 + 24.03 T, DELTA-GBAR(Na2O)(beta- + beta"-alumina) = -232,700 + 56.19 T, and DELTA-GBAR(Na2O)(beta"-alumina + NaAlO2) = -13,100 - 4.51 T J mol-1. Similar galvanic cells using a Au-Na alloy and a mixture of Co + CoAl(2+2x)O4+3x + (alpha)Al2O3 as electrodes were used at 1400 K. Thermodynamic data obtained in these studies are used to evaluate phase relations and partial pressure of sodium in the Na2O-(alpha) Al2O3 system as a function of oxygen partial pressure, composition and temperature.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

Study of forging design using slip-line fields

The main purpose of forging design is to ensure cavity filling with minimum material wastage, minimum die load and minimum deformation energy. Given the desired shape of the component and the material to be forged, this goal is achieved by optimising the initial volume of the billet, the geometrical parameters of the die and the process parameters. It is general industrial practise to fix the initial billet volume and the die parameters using empirical relationships derived from practical experience. In this paper a basis for optimising some of the parameters for simple closed-die forging is proposed. Slip-line field solutions are used to predict the flow, the load and the energy in a simple two-dimensional closed-die forging operation. The influence of the design parameters; flash-land width, excess initial workpiece area and forged cross-sectional size; on complete cavity filling and efficient cavity filling are investigated. Using the latter as necessary requirements for forging, the levels of permissable design parameters are determined, the variation of these levels with the size of the cross-section then being examined.

Low reynolds number flow of a dilute suspension in slowly varying tubes

We have discussed here the flow of a dilute suspension of rigid particles in Newtonian fluid in slowly varying tubes characterized by a small parameter ε. Solutions are presented in the form of asymptotic expansions in powers of ε. The effect of the suspension on the fluid is described by two parameters β and γ which depend on the volume fraction of the particles which we assume to be small. It is found that the presence of the particles accelerate the process of eddy formation near the constriction and shifts the point of separation.

Cubicity of Interval Graphs and the Claw Number

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product l(1) x l(2) x ... x l(b), where each l(i) is a closed interval of unit length on the real line. The cub/city of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line-i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number psi(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least log(2) psi(G)]. In this article, we show that for an interval graph G log(2) psi(G)-]<= cub(G)<=log(2) psi(G)]+2. It is not clear whether the upper bound of log(2) psi(G)]+2 is tight: till now we are unable to find any interval graph with cub(G)> (log(2)psi(G)]. We also show that for an interval graph G, cub(G) <= log(2) alpha], where alpha is the independence number of G. Therefore, in the special case of psi(G)=alpha, cub(G) is exactly log(2) alpha(2)]. The concept of cubicity can be generalized by considering boxes instead of cubes. A b-dimensional box is a Cartesian product l(1) x l(2) x ... x l(b), where each I is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k-dimensional boxes. It is clear that box(G)<= cub(G). From the above result, it follows that for any graph G, cub(G) <= box(G)log(2) alpha]. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323-333, 2010

Signal characterization using fractal dimension

Fractal Dimensions (FD) are one of the popular measures used for characterizing signals. They have been used as complexity measures of signals in various fields including speech and biomedical applications. However, proper interpretation of such analyses has not been thoroughly addressed. In this paper, we study the effect of various signal properties on FD and interpret results in terms of classical signal processing concepts such as amplitude, frequency, number of harmonics, noise power and signal bandwidth. We have used Higuchi's method for estimating FDs. This study may help in gaining a better understanding of the FD complexity measure itself, and for interpreting changing structural complexity of signals in terms of FD. Our results indicate that FD is a useful measure in quantifying structural changes in signal properties.

Alfvén waves in inhomogeneous magnetic fields: An integrodifferential equation formulation

An integrodifferential formulation for the equation governing the Alfvén waves in inhomogeneous magnetic fields is shown to be similar to the polyvibrating equation of Mangeron. Exploiting this similarity, a time‐dependent solution for smooth initial conditions is constructed. The important feature of this solution is that it separates the parts giving the Alfvén wave oscillations of each layer of plasma and the interaction of these oscillations representing the phase mixing.