The Spectral Features of Disk and Corona with Mass Evaporation in the Low/Hard State

We investigate the spectral features of accretion flows composed of an outer cool, optically thick disk and inner hot, optically thin, advection dominated accretion flows (ADAF) within the framework of disk and corona with mass evaporation (Liu et al. 2002a). In this work, both the magnetic field and Compton scattering of soft photons from the disk by electrons in the corona are included to calculate the evaporation rates at different distances. The disk is truncated at the distance where the evaporation rate equals to the accretion rate ($\dot m_{\rm evap}(r_{\rm tr})=\dot m$). For a series of accretion rates, the corresponding truncation radii are calculated out, with which we are able to calculate the emergent spectra from the inner ADAF + outer disk + corona. At very low accretion rates, the spectra are similar to that of a pure ADAF because the disk is truncated at large distances. The disk component becomes important at high accretion rates since the truncation occurs at small distances. An anti-correlation between the Eddington ratio $\xi \equiv L_{\rm 0.5-25 \,keV}/L_{\rm Edd}$ and the hard X-ray photon index $\Gamma_{\rm 3-25 \,keV}$ at low/hard states is predicted by the model. Comparing the theoretical results with observations, we find that our model can reproduce the anti-correlation between the Eddington ratio $\xi$ and the hard X-ray photon index observed for the X-ray binary XTE J1118+480.Comment: 11 pages and 7 figures, published by PAS

Modelling of deep wells thermal modes

Purpose. Investigation of various heat-exchange conditions influence of the tower liquid on the deep wells thermal conditions. Methods. Methods of heat-exchange processes mathematical modeling are used. On the basis of the developed scheme for calculation, the thermal condition in a vertical well with a concentric arrangement of the drill-string was investigated. It was assumed that the walls of the well are properly insulated, and there is no flow or loss of fluid. The temperature distribution in the Newtonian (water) and non-Newtonian (clay mud) liquid along the borehole was simulated taking into account changes in the temperature regime of rocks with depth. To verify the calculation method and determine the reliability of the results, a comparative analysis of the calculated and experimental data to determine the temperature of the drilling liquid in the well was performed. Findings. A mathematical model for the study of temperature fields along the well depth was proposed and verified. A steady-state temperature distribution along the borehole is obtained for various types (Newtonian or non-Newtonian) tower liquid, with a linear law of change in rocks temperature with depth. It has been established that the temperature of the liquid flow at the face of hole and at the exit to the surface depends on the type of liquid used and the flow regime. It has been established that due to thermal insulation of drill pipe columns, heat-exchange between the downward and upward flow is reduced, which leads to a decrease in the temperature of the downward flow at the face of hole, providing a more favorable temperature at the face, which contributes to better destruction of the rock and cooling the tool during drilling. Originality. The nature of temperature distribution and changes along the borehole under the steady-state mode of heat-exchange in a turbulent and structural flow regime for both Newtonian and non-Newtonian circulating liquid are revealed. Practical implications. The proposed mathematical model and obtained results can be used to conduct estimates of the thermal conditions of wells and the development of recommendations for controlling the intensity of heat-exchange processes in the well, in accordance with the requirements of a specific technology.Мета. Дослідження впливу різних умов теплообміну циркулюючої рідини на тепловий режим глибоких свердловин. Методика. Використано методи математичного моделювання процесів теплообміну. На основі розробленої схеми до розрахунку досліджувався тепловий режим у вертикальній свердловині з концентричним розташуванням бурильної колони. Передбачалося, що стінки свердловини належним чином ізольовані, приплив і втрати рідини відсутні. Моделювався розподіл температур у потоках ньютонівської (води) та неньютонівської (глинистого розчину) рідин уздовж стовбура свердловини з урахуванням зміни температурного режиму гірських порід з глибиною. Для верифікації методики розрахунку і визначення достовірності результатів був виконаний порівняльний аналіз розрахункових та експериментальних даних з визначення температури промивної рідини у свердловині. Результати. Запропонована і верифіційована математична модель для дослідження температурних полів з глибиною свердловини. Отримано стаціонарний розподіл температур уздовж стовбура свердловини для різних типів (ньютонівських або неньютонівських) циркулюючих рідин при лінійному законі зміни температури гірських порід з глибиною. Виявлено, що температура потоку рідини на вибої свердловини і на виході на денну поверхню залежить від типу використовуваної рідини і режиму течії. Встановлено, що за рахунок термоізоляції колони бурильних труб знижується теплообмін між низхідним і висхідним потоками, що призводить до зниження температури низхідного потоку на вибої свердловини, забезпечуючи більш сприятливий температурний режим на вибої, який сприяє кращому руйнування породи та охолодженню інструменту при бурінні. Наукова новизна. Виявлено характер розподілу та зміни температури вздовж стовбура свердловин при стаціонарному режимі теплообміну в турбулентному і структурному режимах течії як для ньютонівських, так і неньютонівських циркулюючих рідин. Практична значимість. Запропонована математична модель і отримані результати можуть використовуватися для проведення оціночних розрахунків теплових режимів свердловин та розробки рекомендацій з управління інтенсивністю теплообмінних процесів у свердловині відповідно до вимог конкретної технології.Цель. Исследование влияния различных условий теплообмена циркулирующей жидкости на тепловой режим глубоких скважин. Методика. Использованы методы математического моделирования процессов теплообмена. На основе разработанной схемы к расчету исследовался тепловой режим в вертикальной скважине с концентрическим расположением бурильной колоны. Предполагалось, что стенки скважины надлежащим образом изолированы, приток и потери жидкости отсутствуют. Моделировалось распределение температур в потоках ньютоновской (воды) и неньютоновской (глинистого раствора) жидкостей вдоль ствола скважины с учетом изменения температурного режима горных пород с глубиной. Для верификации методики расчета и определения достоверности результатов был выполнен сравнительный анализ расчетных и экспериментальных данных по определению температуры промывочной жидкости в скважине. Результаты. Предложена и верифицирована математическая модель для исследования температурных полей по глубине скважины. Получено стационарное распределение температур вдоль ствола скважины для различных типов (ньютоновских или неньютоновских) циркулирующих жидкостей при линейном законе изменения температуры горных пород с глубиной. Выявлено, что температура потока жидкости на забое скважины и на выходе на дневную поверхность зависит от типа используемой жидкости и режима течения. Установлено, что за счет термоизоляции колоны бурильных труб снижается теплообмен между нисходящим и восходящим потоками, что приводит к снижению температуры нисходящего потока на забое скважины, обеспечивая более благоприятный температурный режим на забое, который способствует лучшему разрушению породы и охлаждению инструмента при бурении. Научная новизна. Выявлен характер распределения и изменения температуры вдоль ствола скважин при стационарном режиме теплообмена в турбулентном и структурном режимах течения как для ньютоновских, так и неньютоновских циркулирующих жидкостей. Практическая значимость. Предложенная математическая модель и полученные результаты могут использоваться для проведения оценочных расчетов тепловых режимов скважин и разработки рекомендаций по управлению интенсивностью теплообменных процессов в скважине в соответствии с требованиями конкретной технологии.The authors thank the Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine (Dnipro, Ukraine) for providing technical and informational support in this work

The Dependence of Spectral State Transition and Disk Truncation on Viscosity Parameter $\alpha

A wealth of Galactic accreting X-ray binaries have been observed both in low/hard state and high/soft state. The transition between these two states was often detected. Observation shows that the transition luminosity between these two states is different for different sources, ranging from 1% to 4% of the Eddington luminosity. Even for the same source the transition luminosity at different outbursts is also different. The transition can occur from 0.0069 to 0.15 Eddington luminosity. To investigate the underlying physics, we study the influence of viscosity parameter $\alpha$ on the transition luminosity on the basis of the disk-corona model for black holes. We calculate the mass evaporation rate for a wide range of viscosity parameter, $0.1\le \alpha\le 0.9$. By fitting the numerical results, we obtain fitting formulae for both the transition accretion rate and the corresponding radius as a function of $\alpha$. We find that the transition luminosity is very sensitive to the value of $\alpha$, $L/L_{\rm Edd}\propto\alpha^{2.34}$. For $0.1\le\alpha\le 0.6$, the transition luminosity varies by two orders of magnitude, from 0.001 to 0.2 Eddington luminosity. Comparing with observations we find that the transition luminosity can be fitted by adjusting the value of $\alpha$, and the model determined values of $\alpha$ are mostly in the range of observationally inferred value. Meanwhile we investigate the truncation of the disk in the low/hard state for some luminous sources. Our results are roughly in agreement with the observations.Comment: 8 pages, 3 figures,accepted by PAS

Confinement of matter fields in compact (2+1)-dimensional QED theory of high-TcT_{c} superconductors

We study confinement of matter fields in the effective compact (2+1)-dimensional QED theory of high-$T_{c}$ superconductors. It is shown that the monopole configurations do not affect the propagator of gauge potential $a_{\mu}$. Based on this result, we found that: chiral symmetry breaking and confinement take place simultaneously in the antiferromagnetic state; neither monopole effect nor Anderson-Higgs mechanism can cause confinement in the d-wave superconducting state.Comment: 5 pages, no figure

Sampled-data synchronization control of dynamical networks with stochastic sampling

Copyright @ 2012 IEEEThis technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61028008, 60974030, 61134009 and 61104125, the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany

Bounded H∞ synchronization and state estimation for discrete time-varying stochastic complex for discrete time-varying stochastic complex networks over a finite horizon

Copyright [2011] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, new synchronization and state estimation problems are considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon. A novel concept of bounded H∞ synchronization is proposed to handle the time-varying nature of the complex networks. Such a concept captures the transient behavior of the time-varying complex network over a finite horizon, where the degree of bounded synchronization is quantified in terms of the H∞-norm. A general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. By utilizing a timevarying real-valued function and the Kronecker product, criteria are established that ensure the bounded H∞ synchronization in terms of a set of recursive linear matrix inequalities (RLMIs), where the RLMIs can be computed recursively by employing available MATLAB toolboxes. The bounded H∞ state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that, over a finite horizon, the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level. Again, an RLMI approach is developed for the state estimation problem. Finally, two simulation examples are exploited to show the effectiveness of the results derived in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council of U.K. under Grant GR/S27658/01, the National Natural Science Foundation of China under Grant 61028008 and Grant 60974030, the National 973 Program of China under Grant 2009CB320600, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany