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).

Investigating limitations of SURF approach for thermal imaging analysis and mapping

Wildlife conservation involves an understanding of a specific animal, its environment and the interaction within a local ecosystem. Unmanned Aerial Vehicles (UAVs) present cost effective, non-intrusive solution for detecting animals over large areas and the use thermal imaging cameras offer the ability detect animals that would otherwise be concealed to visible light cameras. This report examines some of limitations on using SURF for the development of large maps using multiple stills images extracted from the thermal imaging video camera which contain wildlife (eg. Koala in them).

Approximation of solutions to fractional integral equation

In this paper we shall study a fractional integral equation in an arbitrary Banach space X. We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem. We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also proved in a separable Hilbert space with some additional assumptions on the operator A. Finally we give an example to illustrate the applications of the abstract results.

Weibull modulus for diverse strength due to sample-specificity

By sample specificity it is meant that specimens with the same nominal material parameters and tested under the same environmental conditions may exhibit different behavior with diversified strength. Such an effect has been widely observed in the testing of material failure and is usually attributed to the heterogeneity of material at the mesoscopic level. The degree with which mesoscopic heterogeneity affects macroscopic failure is still not clear. Recently, the problem has been examined by making use of statistical ensemble evolution of dynamical system and the mesoscopic stress re-distribution model (SRD). Sample specificity was observed for non-global mean stress field models, such as the duster mean field model, stress concentration at tip of microdamage, etc. Certain heterogeneity of microdamage could be sensitive to particular SRD leading to domino type of coalescence. Such an effect could start from the microdamage heterogeneity and then be magnified to other scale levels. This trans-scale sensitivity is the origin of sample specificity. The sample specificity leads to a failure probability Phi (N) with a transitional region 0 < (N) < 1, so that globally stable and catastrophic modes could co-exist. It is found that the scatter in strength can fit the Weibull distribution very well. Hence, the Weibull modulus is indicative of sample specificity. Numerical results obtained from the SRD for different non-global mean stress fields show that Weibull modulus increases with increasing sample span and influence region of microdamage.

Perturbational finite volume scheme for the one-dimensional Navier-Stokes equations

Starting from the second-order finite volume scheme,though numerical value perturbation of the cell facial fluxes, the perturbational finite volume (PFV) scheme of the Navier-Stokes (NS) equations for compressible flow is developed in this paper. The central PFV scheme is used to compute the one-dimensional NS equations with shock wave.Numerical results show that the PFV scheme can obtain essentially non-oscillatory solution.

On the contact width in generalized plain strain JKR model for isotropic solids

Adhesive contact model between an elastic cylinder and an elastic half space is studied in the present paper, in which an external pulling force is acted on the above cylinder with an arbitrary direction and the contact width is assumed to be asymmetric with respect to the structure. Solutions to the asymmetric model are obtained and the effect of the asymmetric contact width on the whole pulling process is mainly discussed. It is found that the smaller the absolute value of Dundurs' parameter beta or the larger the pulling angle theta, the more reasonable the symmetric model would be to approximate the asymmetric one.

Eigenvalue problems associated with Korn's inequalities in the theory of elasticity

Interest in the possible applications of a priori inequalities in linear elasticity theory motivated the present investigation. Korn's inequality under various side conditions is considered, with emphasis on the Korn's constant. In the "second case" of Korn's inequality, a variational approach leads to an eigenvalue problem; it is shown that, for simply-connected two-dimensional regions, the problem of determining the spectrum of this eigenvalue problem is equivalent to finding the values of Poisson's ratio for which the displacement boundary-value problem of linear homogeneous isotropic elastostatics has a non-unique solution.

Previous work on the uniqueness and non-uniqueness issue for the latter problem is examined and the results applied to the spectrum of the Korn eigenvalue problem. In this way, further information on the Korn constant for general regions is obtained.

A generalization of the "main case" of Korn's inequality is introduced and the associated eigenvalue problem is a gain related to the displacement boundary-value problem of linear elastostatics in two dimensions.

Low-rank optimization for distance matrix completion

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks. © 2011 IEEE.

Climb-enabled discrete dislocation plasticity

A small strain two-dimensional discrete dislocation plasticity framework coupled to vacancy diffusion is developed wherein the motion of edge dislocations is by a combination of glide and climb. The dislocations are modelled as line defects in a linear elastic medium and the mechanical boundary value problem is solved by the superposition of the infinite medium elastic fields of the dislocations and a complimentary non-singular solution that enforces the boundary conditions. Similarly, the climbing dislocations are modelled as line sources/sinks of vacancies and the vacancy diffusion boundary value problem is also solved by a superposition of the fields of the line sources/sinks in an infinite medium and a complementary non-singular solution that enforces the boundary conditions. The vacancy concentration field along with the stress field provides the climb rate of the dislocations. Other short-range interactions of the dislocations are incorporated via a set of constitutive rules. We first employ this formulation to investigate the climb of a single edge dislocation in an infinite medium and illustrate the existence of diffusion-limited and sink-limited climb regimes. Next, results are presented for the pure bending and uniaxial tension of single crystals oriented for single slip. These calculations show that plasticity size effects are reduced when dislocation climb is permitted. Finally, we contrast predictions of this coupled framework with an ad hoc model in which dislocation climb is modelled by a drag-type relation based on a quasi steady-state solution. © 2013 Elsevier Ltd. All rights reserved.

Low-rank optimization with trace norm penalty

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges superlinearly to the global solution while maintaining complexity that is linear in the number of rows and columns of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. © 2013 Society for Industrial and Applied Mathematics.

Extraction kinetics of Sc(III), Y(III), La(III) and Gd(III) from chloride medium by Cyanex 302 in heptane using the constant interfacial cell with laminar flow

The extraction kinetics of Sc, Y, La and Gd(III) from the hydrochloric acid medium using Cyanex 302 (hereafter HL) in heptane solution have been measured by the constant interfacial cell with laminar flow. Reaction regions are explored at liquid-liquid interface. Extraction regimes are deduced to be diffusion-controlled for Sc(Ill) and mixed controlled for Y, La and Gd(Ill). Extraction mechanisms are discussed according to the dimeric model of Cyanex 302 in non-polar solution. From the temperature dependence of rate measurement, the values of E-a, Delta H-+/-, Delta S-+/- and Delta G(300)(+/-) are calculated and it is found that the absolute values of these parameters keep crescent trend for Sc, Y, La and Gd(III). At the same time, it is found that it can easily achieve the mutual separation among the Sc, Y and La(III) with kinetics extraction methods.

电阻率测井反演方法应用研究

Formation resistivity is one of the most important parameters to be evaluated in the evaluation of reservoir. In order to acquire the true value of virginal formation, various types of resistivity logging tools have been developed. However, with the increment of the proved reserves, the thickness of interest pay zone is becoming thinner and thinner, especially in the terrestrial deposit oilfield, so that electrical logging tools, limited by the contradictory requirements of resolution and investigation depth of this kinds of tools, can not provide the true value of the formation resistivity. Therefore, resitivity inversion techniques have been popular in the determination of true formation resistivity based on the improving logging data from new tools. In geophysical inverse problems, non-unique solution is inevitable due to the noisy data and deficient measurement information. I address this problem in my dissertation from three aspects, data acquisition, data processing/inversion and applications of the results/ uncertainty evaluation of the non-unique solution. Some other problems in the traditional inversion methods such as slowness speed of the convergence and the initial-correlation results. Firstly, I deal with the uncertainties in the data to be processed. The combination of micro-spherically focused log (MSFL) and dual laterolog(DLL) is the standard program to determine formation resistivity. During the inversion, the readings of MSFL are regarded as the resistivity of invasion zone of the formation after being corrected. However, the errors can be as large as 30 percent due to mud cake influence even if the rugose borehole effects on the readings of MSFL can be ignored. Furthermore, there still are argues about whether the two logs can be quantitatively used to determine formation resisitivities due to the different measurement principles. Thus, anew type of laterolog tool is designed theoretically. The new tool can provide three curves with different investigation depths and the nearly same resolution. The resolution is about 0.4meter. Secondly, because the popular iterative inversion method based on the least-square estimation can not solve problems more than two parameters simultaneously and the new laterolog logging tool is not applied to practice, my work is focused on two parameters inversion (radius of the invasion and the resistivty of virgin information ) of traditional dual laterolog logging data. An unequal weighted damp factors- revised method is developed to instead of the parameter-revised techniques used in the traditional inversion method. In this new method, the parameter is revised not only dependency on the damp its self but also dependency on the difference between the measurement data and the fitting data in different layers. At least 2 iterative numbers are reduced than the older method, the computation cost of inversion is reduced. The damp least-squares inversion method is the realization of Tikhonov's tradeoff theory on the smooth solution and stability of inversion process. This method is realized through linearity of non-linear inversion problem which must lead to the dependency of solution on the initial value of parameters. Thus, severe debates on efficiency of this kinds of methods are getting popular with the developments of non-linear processing methods. The artificial neural net method is proposed in this dissertation. The database of tool's response to formation parameters is built through the modeling of the laterolog tool and then is used to training the neural nets. A unit model is put forward to simplify the dada space and an additional physical limitation is applied to optimize the net after the cross-validation method is done. Results show that the neural net inversion method could replace the traditional inversion method in a single formation and can be used a method to determine the initial value of the traditional method. No matter what method is developed, the non-uniqueness and uncertainties of the solution could be inevitable. Thus, it is wise to evaluate the non-uniqueness and uncertainties of the solution in the application of inversion results. Bayes theorem provides a way to solve such problems. This method is illustrately discussed in a single formation and achieve plausible results. In the end, the traditional least squares inversion method is used to process raw logging data, the calculated oil saturation increased 20 percent than that not be proceed compared to core analysis.

Rozproszone algorytmy aproksymacyjne dla grafów dyskowych

Wydział Matematyki i Informatyki: Zakład Matematyki Dyskretnej

Desenvolvimento de ferramentas de apoio multicritério à decisão em problemas de localização

Tese de doutoramento, Estatística e Investigação Operacional (Análise de Sistemas), Universidade de Lisboa, Faculdade de Ciências, 2014

Lor’s - Women personal rain protection solutions

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics