Hysteresis effects and diagnostics of the shock formation in low angular momentum axisymmetric accretion in the Kerr metric

The secular evolution of the purely general relativistic low angular momentum accretion flow around a spinning black hole is shown to exhibit hysteresis effects. This confirms that a stationary shock is an integral part of such an accretion disc in the Kerr metric. The equations describing the space gradient of the dynamical flow velocity of the accreting matter have been shown to be equivalent to a first order autonomous dynamical systems. Fixed point analysis ensures that such flow must be multi-transonic for certain astrophysically relevant initial boundary conditions. Contrary to the existing consensus in the literature, the critical points and the sonic points are proved not to be isomorphic in general. Homoclinic orbits for the flow flow possessing multiple critical points select the critical point with the higher entropy accretion rate, confirming that the entropy accretion rate is the degeneracy removing agent in the system. However, heteroclinic orbits are also observed for some special situation, where both the saddle type critical points of the flow configuration possesses identical entropy accretion rate. Topologies with heteroclinic orbits are thus the only allowed non removable degenerate solutions for accretion flow with multiple critical points, and are shown to be structurally unstable. Depending on suitable initial boundary conditions, a homoclinic trajectory can be combined with a standard non homoclinic orbit through an energy preserving Rankine-Hugoniot type of stationary shock. An effective Lyapunov index has been proposed to analytically confirm why certain class of transonic flow can not accommodate shock solutions even if it produces multiple critical points. (Abridged)Comment: mn2e.cls format. 24 pages. 4 figure

Evaluation of a Respiration Rate Sensor for Recording Tidal Volume in Calves under Field Conditions

In the assessment of pulmonary function in health and disease, both respiration rate (RR) and tidal volume (Vt) are fundamental parameters of spontaneous breathing. The aim of this study was to evaluate whether an RR sensor, which was previously developed for cattle, is suitable for additional measurements of Vt in calves. This new method would offer the opportunity to measure Vt continuously in freely moving animals. To measure Vt noninvasively, the application of a Lilly-type pneumotachograph implanted in the impulse oscillometry system (IOS) was used as the gold standard method. For this purpose, we applied both measuring devices in different orders successively, for 2 days on 10 healthy calves. However, the Vt equivalent (RR sensor) could not be converted into a true volume in mL or L. For a reliable recording of the Vt equivalent, a technical revision of the RR sensor excluding artifacts is required. In conclusion, converting the pressure signal of the RR sensor into a flow equivalent, and subsequently into a volume equivalent, by a comprehensive analysis, provides the basis for further improvement of the measuring system

CONVEYOR-TYPE SMALL HYDROPOWER PLANT FOR SHALLOW RIVER WATERS

This paper deals with the development of a small conveyor-type hydropower plant intended for operation in shallow river waters without construction of a dam. The proposed design offers a closed-shaped flattened conveyor equipped with flat-shaped blades. The conveyor is oriented perpendicular to the fluid flow. Several identical flat blades interacting with fluid flow are mounted on conveyor belt and move together with the belt in one straight line direction. Then after turning in the reversing mechanism, blades move in the opposite direction. The conveyor system has a built-in energy generator which drive shaft is connected with one of the reversing ends of the plant. Conveyor belt system dynamics analysis is performed on the base of equivalent model with one degree of freedom. The interaction of a moving conveyor flat blade in translation motion with fluid flow is studied by computer simulation with program Mathcad using a superposition principle. In accordance with this approach, a fast-chaotic motion of fluid particles (Brownian motion) is separated from the slow-directed flow motion, with the given average velocity. Optimization of system parameters (blade orientation angle to fluid flow, interaction constants of the braking generator) is performed, using a generated power as criterion. Simulation results confirm the serviceability and operational efficiency of the proposed hydropower plant in shallow river waters.

Improving Network Reductions for Power System Analysis

abstract: The power system is the largest man-made physical network in the world. Performing analysis of a large bulk system is computationally complex, especially when the study involves engineering, economic and environmental considerations. For instance, running a unit-commitment (UC) over a large system involves a huge number of constraints and integer variables. One way to reduce the computational expense is to perform the analysis on a small equivalent (reduced) model instead on the original (full) model. The research reported here focuses on improving the network reduction methods so that the calculated results obtained from the reduced model better approximate the performance of the original model. An optimization-based Ward reduction (OP-Ward) and two new generator placement methods in network reduction are introduced and numerical test results on large systems provide proof of concept. In addition to dc-type reductions (ignoring reactive power, resistance elements in the network, etc.), the new methods applicable to ac domain are introduced. For conventional reduction methods (Ward-type methods, REI-type methods), eliminating external generator buses (PV buses) is a tough problem, because it is difficult to accurately approximate the external reactive support in the reduced model. Recently, the holomorphic embedding (HE) based load-flow method (HELM) was proposed, which theoretically guarantees convergence given that the power flow equations are structure in accordance with Stahl’s theory requirements. In this work, a holomorphic embedding based network reduction (HE reduction) method is proposed which takes advantage of the HELM technique. Test results shows that the HE reduction method can approximate the original system performance very accurately even when the operating condition changes.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Liquid Clocks - Refinement Types for Time-Dependent Stream Functions

The concept of liquid clocks introduced in this paper is a significant step towards a more precise compile-time framework for the analysis of synchronous and polychromous languages. Compiling languages such as Lustre or SIGNAL indeed involves a number of static analyses of programs before they can be synthesized into executable code, e.g., synchronicity class characterization, clock assignment, static scheduling or causality analysis. These analyses are often equivalent to undecidable problems, necessitating abstracting such programs to provide sound yet incomplete analyses. Such abstractions unfortunately often lead to the rejection of programs that could very well be synthesized into deterministic code, provided abstraction refinement steps could be applied for more accurate analysis. To reduce the false negatives occurring during the compilation process, we leverage recent advances in type theory -- with the definition of decidable classes of value-dependent type systems -- and formal verification, linked to the development of efficient SAT/SMT solvers, to provide a type-theoretic approach that considers all the above analyses as type inference problems. In order to simplify the exposition of our new approach in this paper, we define a refinement type system for a minimalistic, synchronous, stream-processing language to concisely represent, analyse, and verify logical and quantitative properties of programs expressed as stream-processing data-flow networks. Our type system provides a new framework to represent logical time (clocks) and scheduling properties, and to describe their relations with stream values and, possibly, other quantas. We show how to analyze synchronous stream processing programs (à la Lustre, Signal) to enable previously described analyzes involved in compiling such programs. We also prove the soundness of our type system and elaborate on the adaptability of this core framework by outlining its extensibility to specific models of computations and other quantas

A method for calculating transient thrust and flow-rate levels for Mariner type attitude control nitrogen gas jets

The purpose of this report is to define and program the transient pneumatic flow equations necessary to determine, for a given set of conditions (geometry, pressures, temperatures, valve on time, etc.), the total nitrogen impulse and mass flow per pulse for the single pulsing of a Mariner type reaction control assembly valve. The rates of opening and closing of the valves are modeled, and electrical pulse durations from 20 to 100 ms are investigated. In developing the transient flow analysis, maximum use was made of the steady-state analysis. The impulse results are also compared to an equivalent square-wave impulse for both the Mariner Mars 1971 (MM'71) and Mariner Mars 1964 (MM'64) systems. It is demonstrated that, whereas in the MM'64 system, the actual impulse was as much as 56 percent higher than an assumed impulse (which is the product of the steady-state thrust and value on time i.e., the square wave), in the MM'71 system, these two values were in error in the same direction by only approximately 4 percent because of the larger nozzle areas and shorter valve stroke used

Design and Evaluation of Flow Mapping Systems for Heterogeneous Wireless Networks

Mobile wireless networks are always challenged by growing application demand. The increasing heterogeneity of both mobile device connection capability and wireless network coverage forms a general heterogeneous wireless network (HetNet). This type of HetNet contains sub-networks of different Radio Access Technologies. How to better coordinate the mappings of flows between Access Points (AP) and User Equipment (UE) inside this type of HetNet to improve system and user-level performance is an interesting research problem. The flow mapping systems used by off-the-shelf mobile devices make policy-based decisions from local information. Several global information based flow mapping systems that use Generalized Proportional Fairness (GPF) as the optimization objectives have been proposed to improve the system-level performance. However, they have not been compared with both the local-policy based approaches and the optimal solution under the same assumptions with variations of system parameters. Therefore, it is still unclear to the community whether it is worthwhile to construct a flow mapping system for HetNets composed by LTE and WiFi networks, even under a simplified assumption of only optimizing throughput related system performance metrics. In this dissertation, we evaluate three types of flow mapping systems: Global Information based Flow Mapping Systems (GIFMS), Local Information based Flow Mapping Systems (LIFMS), and Semi-GIFMS. We evaluate these systems with metrics related to both the spectrum efficiency and flow-level fairness under the following variations of system parameters: 1) topologies of UEs; 2) coverage of APs; 3) number of UEs; 4) number of non-participating UEs; 5) on-off session dynamics; 6) UE mobility. We also discuss options to implement each type of flow mapping systems and any relevant trade-offs. From the evaluations, we find that the currently-in-use WiFi preferred local greedy flow mapping system provides far poorer spectral efficiency and generalized proportional fairness than all the other tested flow mapping systems, including the local greedy flow mapping systems that give LTE and WiFi equal opportunities (local-greedy-equal-chance) in most settings. This finding indicates that the flow mapping system in use has much room for improvement in terms of GPF and aggregate throughput. The performance of local-greedy-equal-chance is close to that of the global and AP-level information based systems under some UE topologies. However, their performance is not as consistent as the global and AP-level based systems when UEs form clusters that produce AP load imbalance. We also derive the incremental evaluations of GPF for both proportional and max-min fair scheduled APs. Based on these derivations, we propose a design for AP-level information based flow mapping system or Semi-GIFMS. It is an event-triggered flow mapping system based on minimum AP-level metrics monitoring and dissemination. From our evaluation and analysis, this flow mapping system performs equivalent to or better than GIFMS in terms of both GPF and aggregate throughput in all the tested scenarios. It also owns the advantages of lower overhead and not requiring an additional scheduling server. We think it is the best choice for the next generation HetNets where APs can be modified to monitor and broadcast the minimum information identified. Furthermore, we find that the number of UEs, number of non-participating UEs, coverage of APs, bandwidth sharing types of APs, on-off session and UE mobility dynamics do not have a major impact on the relative performance difference among various flow mapping systems

An Equivalent Homogeneous Continuum Approach to Modeling Solute Transport and Water Flow in Regularly Structured Porous Media

Theoretical investigations and numerical and laboratory experiments were conducted to evaluate the feasibility and limitations of describing solute transport and water flow in regularly structured porous media with an equivalent homogeneous continuum approach. For the analysis of solute transport, it is shown that distinguishing between resident and flux concentration detection modes is of fundamental importance to obtain physically meaningful solutions of the governing equations in situations when large local variations in pore water velocities occur. Effects of using erroneous detection modes are demonstrated theoretically and experimentally for porous media with bimodal velocity distributions. Using a time moment method, relationships between diffusion-controlled or first-order kinetic type mobile-immobile transport models and an "equivalent" monocontinuum dispersion model are derived and criteria for the validity of the latter approach are obtained. A generalization of the moment analysis results is presented which relates the effective dispersivity tor the monocontinuum system with arbitrary bimodal structure to primary geometrical and physical properties of the system. Effects of local transverse mixing within zones of the bicontinuum are demonstrated experimentally to appreciably affect the validity of monocontinuum degeneration unless a time-dependent dispersion coefficient is adopted. The moment method is also used to evaluate constraints on the description of transport through layered media with flow transverse to the stratification as equivalent homogeneous porous media. Experimental results are employed to demonstrate the method. Finally an analysis at the feasibility of describing flow in variably saturated porous media with heterogeneities perpendicular to the mean flow field are investigated. Comparison of numerically simulated flow in a dual medium system with predictions based on analytically calculated average conductivity saturation-pressure relationships indicates that the averaging procedure may provide satisfactory results under a variety of imposed boundary conditions