Two-temperature accretion around rotating black holes: a description of the general advective flow paradigm in the presence of various cooling processes to explain low to high luminous sources

We investigate viscous two-temperature accretion disc flows around rotating black holes. We describe the global solution of accretion flows with a sub-Keplerian angular momentum profile, by solving the underlying conservation equations including explicit cooling processes self-consistently. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. We focus on the set of solutions for sub-Eddington, Eddington and super-Eddington mass accretion rates around Schwarzschild and Kerr black holes with a Kerr parameter of 0.998. It is found that the flow, during its infall from the Keplerian to sub-Kepleria transition region to the black hole event horizon, passes through various phases of advection: the general advective paradigm to the radiatively inefficient phase, and vice versa. Hence, the flow governs a much lower electron temperature similar to 10(8)-10(9.5) K, in the range of accretion rate in Eddington units 0.01 less than or similar to (M) over dot less than or similar to 100, compared to the hot protons of temperature similar to 10(10.2)-10(11.8) K. Therefore, the solution may potentially explain the hard X-rays and gamma-rays emitted from active galactic nuclei (AGNs) and X-ray binaries. We then compare the solutions for two different regimes of viscosity. We conclude that a weakly viscous flow is expected to be cooling dominated, particularly at the inner region of the disc, compared to its highly viscous counterpart, which is radiatively inefficient. With all the solutions in hand, we finally reproduce the observed luminosities of the underfed AGNs and quasars (e. g. Sgr A*) to ultraluminous X-ray sources (e. g. SS433), at different combinations of input parameters, such as the mass accretion rate and the ratio of specific heats. The set of solutions also predicts appropriately the luminosity observed in highly luminous AGNs and ultraluminous quasars (e. g. PKS 0743-67).

Jet Engine Health Signal Denoising Using Optimally Weighted Recursive Median Filters

The removal of noise and outliers from health signals is an important problem in jet engine health monitoring. Typically, health signals are time series of damage indicators, which can be sensor measurements or features derived from such measurements. Sharp or sudden changes in health signals can represent abrupt faults and long term deterioration in the system is typical of gradual faults. Simple linear filters tend to smooth out the sharp trend shifts in jet engine signals and are also not good for outlier removal. We propose new optimally designed nonlinear weighted recursive median filters for noise removal from typical health signals of jet engines. Signals for abrupt and gradual faults and with transient data are considered. Numerical results are obtained for a jet engine and show that preprocessing of health signals using the proposed filter significantly removes Gaussian noise and outliers and could therefore greatly improve the accuracy of diagnostic systems. [DOI: 10.1115/1.3200907].

Acyclic edge coloring of subcubic graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and it is denoted by a′(G). From a result of Burnstein it follows that all subcubic graphs are acyclically edge colorable using five colors. This result is tight since there are 3-regular graphs which require five colors. In this paper we prove that any non-regular connected graph of maximum degree 3 is acyclically edge colorable using at most four colors. This result is tight since all edge maximal non-regular connected graphs of maximum degree 3 require four colors.

Analyzing information flow in brain networks with nonparametric Granger causality

Multielectrode neurophysiological recording and high-resolution neuroimaging generate multivariate data that are the basis for understanding the patterns of neural interactions. How to extract directions of information flow in brain networks from these data remains a key challenge. Research over the last few years has identified Granger causality as a statistically principled technique to furnish this capability. The estimation of Granger causality currently requires autoregressive modeling of neural data. Here, we propose a nonparametric approach based on widely used Fourier and wavelet transforms to estimate both pairwise and conditional measures of Granger causality, eliminating the need of explicit autoregressive data modeling. We demonstrate the effectiveness of this approach by applying it to synthetic data generated by network models with known connectivity and to local field potentials recorded from monkeys performing a sensorimotor task.

Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis

In recent years, spatial variability modeling of soil parameters using random field theory has gained distinct importance in geotechnical analysis. In the present Study, commercially available finite difference numerical code FLAC 5.0 is used for modeling the permeability parameter as spatially correlated log-normally distributed random variable and its influence on the steady state seepage flow and on the slope stability analysis are studied. Considering the case of a 5.0 m high cohesive-frictional soil slope of 30 degrees, a range of coefficients of variation (CoV%) from 60 to 90% in the permeability Values, and taking different values of correlation distance in the range of 0.5-15 m, parametric studies, using Monte Carlo simulations, are performed to study the following three aspects, i.e., (i) effect ostochastic soil permeability on the statistics of seepage flow in comparison to the analytic (Dupuit's) solution available for the uniformly constant permeability property; (ii) strain and deformation pattern, and (iii) stability of the given slope assessed in terms of factor of safety (FS). The results obtained in this study are useful to understand the role of permeability variations in slope stability analysis under different slope conditions and material properties. (C) 2009 Elsevier B.V. All rights reserved.

A note on the Hadwiger number of circular arc graphs

The intention of this note is to motivate the researchers to study Hadwiger's conjecture for circular arc graphs. Let η(G) denote the largest clique minor of a graph G, and let χ(G) denote its chromatic number. Hadwiger's conjecture states that η(G)greater-or-equal, slantedχ(G) and is one of the most important and difficult open problems in graph theory. From the point of view of researchers who are sceptical of the validity of the conjecture, it is interesting to study the conjecture for graph classes where η(G) is guaranteed not to grow too fast with respect to χ(G), since such classes of graphs are indeed a reasonable place to look for possible counterexamples. We show that in any circular arc graph G, η(G)less-than-or-equals, slant2χ(G)−1, and there is a family with equality. So, it makes sense to study Hadwiger's conjecture for this family.

Boundary-layer effects on internal flow choking in dual-thrust solid rocket motors

Theoretical studies have been carried out to examine internal flow choking in the inert simulators of a dual-thrust motor. Using a two-dimensional k-omega turbulence model, detailed parametric studies have been carried out to examine aerodynamic choking and the existence of a fluid throat at the transition region during the startup transient of dual-thrust motors. This code solves standard k-omega turbulence equations with shear flow corrections using a coupled second-order-implicit unsteady formulation. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-averaged, Navier-Stokes equations is employed. It was observed that, at the subsonic inflow conditions, there is a possibility of the occurrence of internal flow choking in dual-thrust motors due to the formation of a fluid throat at the beginning of the transition region induced by area blockage caused by boundary-layer-displacement thickness. It has been observed that a 55% increase in the upstream port area of the dual-thrust motor contributes to a 25% reduction in blockage factor at the transition region, which could negate the internal How choking and supplement with an early choking of the dual-thrust motor nozzle. If the height of the upstream port relative to the motor length is too small, the developing boundary layers from either side of the port can interact, leading to a choked,flow. On the other hand, if the developing boundary layers are far enough apart, then choking does not occur. The blockage factor is greater in magnitude for the choked case than for the unchoked case. More tangible explanations are presented in this paper for the boundary-layer blockage and the internal flow choking in dual-thrust motors, which hitherto has been unexplored.

Constitutive equation for elevated temperature flow behavior of plain carbon steels using dimensional analysis

Dimensional analysis using π-theorem is applied to the variables associated with plastic deformation. The dimensionless groups thus obtained are then related and rewritten to obtain the constitutive equation. The constants in the constitutive equation are obtained using published flow stress data for carbon steels. The validity of the constitutive equation is tested for steels with up to 1.54 wt%C at temperatures: 850–1200 °C and strain rates: 6 × 10−6–2 × 10−2 s−1. The calculated flow stress agrees favorably with experimental data.

On the Cubicity of AT-Free Graphs and Circular-Arc Graphs

A unit cube in k dimensions (k-cube) is defined as the Cartesian product R-1 x R-2 x ... x R-k where R-i (for 1 <= i <= k) is a closed interval of the form [a(i), a(i) + 1] on the real line. A graph G on n nodes is said to be representable as the intersection of k-cubes (cube representation in k dimensions) if each vertex of C can be mapped to a k-cube such that two vertices are adjacent in G if and only if their corresponding k-cubes have a non-empty intersection. The cubicity of G denoted as cub(G) is the minimum k for which G can be represented as the intersection of k-cubes. An interesting aspect about cubicity is that many problems known to be NP-complete for general graphs have polynomial time deterministic algorithms or have good approximation ratios in graphs of low cubicity. In most of these algorithms, computing a low dimensional cube representation of the given graph is usually the first step. We give an O(bw . n) algorithm to compute the cube representation of a general graph G in bw + 1 dimensions given a bandwidth ordering of the vertices of G, where bw is the bandwidth of G. As a consequence, we get O(Delta) upper bounds on the cubicity of many well-known graph classes such as AT-free graphs, circular-arc graphs and cocomparability graphs which have O(Delta) bandwidth. Thus we have: 1. cub(G) <= 3 Delta - 1, if G is an AT-free graph. 2. cub(G) <= 2 Delta + 1, if G is a circular-arc graph. 3. cub(G) <= 2 Delta, if G is a cocomparability graph. Also for these graph classes, there axe constant factor approximation algorithms for bandwidth computation that generate orderings of vertices with O(Delta) width. We can thus generate the cube representation of such graphs in O(Delta) dimensions in polynomial time.

d-Regular Graphs of Acyclic Chromatic Index at Least d+2

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). It was conjectured by Alon, Suclakov and Zaks (and earlier by Fiamcik) that a'(G) <= Delta+2, where Delta = Delta(G) denotes the maximum degree of the graph. Alon et al. also raised the question whether the complete graphs of even order are the only regular graphs which require Delta+2 colors to be acyclically edge colored. In this article, using a simple counting argument we observe not only that this is not true, but in fact all d-regular graphs with 2n vertices and d>n, requires at least d+2 colors. We also show that a'(K-n,K-n) >= n+2, when n is odd using a more non-trivial argument. (Here K-n,K-n denotes the complete bipartite graph with n vertices on each side.) This lower bound for Kn,n can be shown to be tight for some families of complete bipartite graphs and for small values of n. We also infer that for every d, n such that d >= 5, n >= 2d+3 and dn even, there exist d-regular graphs which require at least d+2-colors to be acyclically edge colored. (C) 2009 Wiley Periodicals, Inc. J Graph Theory 63: 226-230, 2010.

Continuous-Flow Surface Aeration Systems

An aeration process in ail activated sludge plant is a continuous-flow system. In this system, there is a steady input flow (flow from the primary clarifier or settling tank with some part from the secondary clarifier or secondary settling tank) and output flow connection to the secondary clarifier or settling tank. The experimental and numerical results obtained through batch systems can not be relied on and applied for the designing of a continuous aeration tank. In order to scale up laboratory results for field application, it is imperative to know the geometric parameters of a continuous system. Geometric parameters have a greater influence on the mass transfer process of surface aeration systems. The present work establishes the optimal geometric configuration of a continuous-flow surface aeration system. It is found that the maintenance of these optimal geometric parameters systems result in maximum aeration efficiency. By maintaining the obtained optimal geometric parameters, further experiments are conducted in continuous-flow surface aerators with three different sizes in order to develop design curves correlating the oxygen transfer coefficient and power number with the rotor speed. The design methodology to implement the presently developed optimal geometric parameters and correlation equations for field application is discussed.

Field Flow Sensitive Pointer and Escape Analysis for Java Using Heap Array SSA

Context sensitive pointer analyses based on Whaley and Lam’s bddbddb system have been shown to scale to large Java programs. We provide a technique to incorporate flow sensitivity for Java fields into one such analysis and obtain an escape analysis based on it. First, we express an intraprocedural field flow sensitive analysis, using Fink et al.’s Heap Array SSA form in Datalog. We then extend this analysis interprocedurally by introducing two new φ functions for Heap Array SSA Form and adding deduction rules corresponding to them. Adding a few more rules gives us an escape analysis. We describe two types of field flow sensitivity: partial (PFFS) and full (FFFS), the former without strong updates to fields and the latter with strong updates. We compare these analyses with two different (field flow insensitive) versions of Whaley-Lam analysis: one of which is flow sensitive for locals (FS) and the other, flow insensitive for locals (FIS). We have implemented this analysis on the bddbddb system while using the SOOT open source framework as a front end. We have run our analysis on a set of 15 Java programs. Our experimental results show that the time taken by our field flow sensitive analyses is comparable to that of the field flow insensitive versions while doing much better in some cases. Our PFFS analysis achieves average reductions of about 23% and 30% in the size of the points-to sets at load and store statements respectively and discovers 71% more “caller-captured” objects than FIS.

GMM based Bayesian approach to speech enhancement in signal transform domain

Considering a general linear model of signal degradation, by modeling the probability density function (PDF) of the clean signal using a Gaussian mixture model (GMM) and additive noise by a Gaussian PDF, we derive the minimum mean square error (MMSE) estimator. The derived MMSE estimator is non-linear and the linear MMSE estimator is shown to be a special case. For speech signal corrupted by independent additive noise, by modeling the joint PDF of time-domain speech samples of a speech frame using a GMM, we propose a speech enhancement method based on the derived MMSE estimator. We also show that the same estimator can be used for transform-domain speech enhancement.

Hadwiger Number and the Cartesian Product of Graphs

The Hadwiger number eta(G) of a graph G is the largest integer n for which the complete graph K-n on n vertices is a minor of G. Hadwiger conjectured that for every graph G, eta(G) >= chi(G), where chi(G) is the chromatic number of G. In this paper, we study the Hadwiger number of the Cartesian product G square H of graphs. As the main result of this paper, we prove that eta(G(1) square G(2)) >= h root 1 (1 - o(1)) for any two graphs G(1) and G(2) with eta(G(1)) = h and eta(G(2)) = l. We show that the above lower bound is asymptotically best possible when h >= l. This asymptotically settles a question of Z. Miller (1978). As consequences of our main result, we show the following: 1. Let G be a connected graph. Let G = G(1) square G(2) square ... square G(k) be the ( unique) prime factorization of G. Then G satisfies Hadwiger's conjecture if k >= 2 log log chi(G) + c', where c' is a constant. This improves the 2 log chi(G) + 3 bound in [2] 2. Let G(1) and G(2) be two graphs such that chi(G1) >= chi(G2) >= clog(1.5)(chi(G(1))), where c is a constant. Then G1 square G2 satisfies Hadwiger's conjecture. 3. Hadwiger's conjecture is true for G(d) (Cartesian product of G taken d times) for every graph G and every d >= 2. This settles a question by Chandran and Sivadasan [2]. ( They had shown that the Hadiwger's conjecture is true for G(d) if d >= 3).

Numerical Simulation of Groundwater Flow with Gradually Increasing Heterogeneity due to Clogging

Well injection replenishes depleting water levels in a well field. Observation well water levels some distance away from the injection well are the indicators of the success of a well injection program. Simulation of the observation well response, located a few tens of meters from the injection well, is likely to be affected by the effects of nonhomogeneous medium, inclined initial water table, and aquifer clogging. Existing algorithms, such as the U.S. Geological Survey groundwater flow software MODFLOW, are capable of handling the first two conditions, whereas time-dependent clogging effects are yet to be introduced in the groundwater flow models. Elsewhere, aquifer clogging is extensively researched in theory of filtration; scope for its application in a well field is a potential research problem. In the present paper, coupling of one such filtration theory to MODFLOW is introduced. Simulation of clogging effects during “Hansol” well recharge in the parts of western India is found to be encouraging.