41 research outputs found

    Sensitivity of Markov chains for wireless protocols

    Get PDF
    Network communication protocols such as the IEEE 802.11 wireless protocol are currently best modelled as Markov chains. In these situations we have some protocol parameters α\alpha, and a transition matrix P(α)P(\alpha) from which we can compute the steady state (equilibrium) distribution z(α)z(\alpha) and hence final desired quantities q(α)q(\alpha), which might be for example the throughput of the protocol. Typically the chain will have thousands of states, and a particular example of interest is the Bianchi chain defined later. Generally we want to optimise qq, perhaps subject to some constraints that also depend on the Markov chain. To do this efficiently we need the gradient of qq with respect to α\alpha, and therefore need the gradient of zz and other properties of the chain with respect to α\alpha. The matrix formulas available for this involve the so-called fundamental matrix, but are there approximate gradients available which are faster and still sufficiently accurate? In some cases BT would like to do the whole calculation in computer algebra, and get a series expansion of the equilibrium zz with respect to a parameter in PP. In addition to the steady state zz, the same questions arise for the mixing time and the mean hitting times. Two qualitative features that were brought to the Study Group’s attention were: * the transition matrix PP is large, but sparse. * the systems of linear equations to be solved are generally singular and need some additional normalisation condition, such as is provided by using the fundamental matrix. We also note a third highly important property regarding applications of numerical linear algebra: * the transition matrix PP is asymmetric. A realistic dimension for the matrix PP in the Bianchi model described below is 8064×8064, but on average there are only a few nonzero entries per column. Merely storing such a large matrix in dense form would require nearly 0.5GBytes using 64-bit floating point numbers, and computing its LU factorisation takes around 80 seconds on a modern microprocessor. It is thus highly desirable to employ specialised algorithms for sparse matrices. These algorithms are generally divided between those only applicable to symmetric matrices, the most prominent being the conjugate-gradient (CG) algorithm for solving linear equations, and those applicable to general matrices. A similar division is present in the literature on numerical eigenvalue problems

    Gas entrainment at a propagating slug front

    Get PDF

    An Investigation into the Physics of Blowing Polysilicon Fuses

    Get PDF
    The semi-conductor fuses in this research are fabricated on a submicron process. A voltage potential is applied across the fuse, in order to achieve a blow. This current peaks with a short pulse in the order of tens of milliamps which has a long decrease to zero current flow, resulting in a blown fuse. A fuse blows due to the pinching together of electrically insulating material which initially surrounds the conducting pathway. The pinch cuts across the conductor, and so halts the current flow. In small-geometry fuses a cavity also forms during the blowing process. The company wishes to understand the fuse blow process mathematically in order to develop a model that can accurately simulate the blowing of the fuses. This report records the thermal, electrical, solid and fluid mechanics of the blowing process that was discussed at the Study Group, with remarks on possible future research for modelling the process

    A magic two-relaxation-time lattice Boltzmann algorithm for magnetohydrodynamics

    Get PDF
    The two-relaxation-time collision operator in discrete kinetic theory models collisions between particles by grouping them into pairs with anti-parallel velocities. It prescribes a linear relaxation towards equilibrium with one rate for the even combination of distribution functions for each pair, and another rate for the odd combination. We reformulate this collision operator using relaxation rates for the forward-propagating and backward-propagating combinations instead. An optimal pair of relaxation rates sets the forward-propagating combination of each pair of distributions to equilibrium. Only the backward-propagating non-equilibrium distributions remain. Applying this result twice gives closed discrete equations for evolving the macroscopic variables alone across three time levels. We split the equivalent equations into a first-order system: a conservation law and a kinetic equation for the flux. All other quantities are evaluated at equilibrium. We apply this formalism to the magnetic field in a lattice Boltzmann scheme for magnetohydrodynamics. The antisymmetric part of the kinetic equation matches the Maxwell–Faraday equation and Ohm's law. The symmetric part matches the hyperbolic divergence cleaning model. The discrete divergence of the magnetic field remains zero, to within round-off error, when the initial magnetic field is the discrete curl of a vector potential. We have thus constructed a mimetic or constrained transport scheme for magnetohydrodynamics

    Arc Phenomena in low-voltage current limiting circuit breakers

    Get PDF
    Circuit breakers are an important safety feature in most electrical circuits, and they act to prevent excessive currents caused by short circuits, for example. Low-voltage current limiting circuit breakers are activated by a trip solenoid when a critical current is exceeded. The solenoid moves two contacts apart to break the circuit. However, as soon as the contacts are separated an electric arc forms between them, ionising the air in the gap, increasing the electrical conductivity of air to that of the hot plasma that forms, and current continues to flow. The currents involved may be as large as 80,000 amperes. Critical to the success of the circuit breaker is that it is designed to cause the arc to move away from the contacts, into a widening wedge-shaped region. This lengthens the arc, and then moves it onto a series of separator plates called an arc divider or splitter. The arc divider raises the voltage required to sustain the arcs across it, above the voltage that is provided across the breaker, so that the circuit is broken and the arcing dies away. This entire process occurs in milliseconds, and is usually associated with a sound like an explosion and a bright ash from the arc. Parts of the contacts and the arc divider may melt and/or vapourise. The question to be addressed by the Study Group was to mathematically model the arc motion and extinction, with the overall aim of an improved understanding that would help the design of a better circuit breaker. Further discussion indicated that two key mechanisms are believed to contribute to the movement of the arc away from the contacts, one being self-magnetism (where the magnetic field associated with the arc and surrounding circuitry acts to push it towards the arc divider), and the other being air flow (where expansion of air combined with the design of the chamber enclosing the arc causes gas flow towards the arc divider). Further discussion also indicated that a key aspect of circuit breaker design was that it is desirable to have as fast a quenching of the arc as possible, that is, the faster the circuit breaker can act to stop current flow, the better. The relative importance of magnetic and air pressure effects on quenching speed is of central interest to circuit design

    Accuracy of a video odometry system for trains

    Get PDF
    Reliable Data Systems is developing a video-based odometry system that enables trains to measure velocities and distances travelled without the need for trackside infrastructure. A camera is fixed in the cab, taking images of the track immediately ahead, at rates in the range 25–50 frames per second. The images in successive frames are ‘unwarped’ to provide a plan view of the track and then matched, to produce an ‘optical flow’ that measures the distance travelled. The Study Group was asked to investigate ways of putting bounds on the accuracy of such a system, and to suggest any improvements that might be made. The work performed in the week followed three strands: (a) an understanding of how deviations from the camera’s calibrated position lead to errors in the train’s calculated position and velocity; (b) development of models for the train suspension, designed to place bounds on these deviations; and (c) the performance of the associated image processing algorithms

    Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier-Maxwell slip boundary conditions

    Get PDF
    We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, and nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity and the pressure relative to asymptotic solutions of the compressible Navier–Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular and diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier–Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back and other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself

    Minimal information for studies of extracellular vesicles (MISEV2023): From basic to advanced approaches

    Get PDF
    Extracellular vesicles (EVs), through their complex cargo, can reflect the state of their cell of origin and change the functions and phenotypes of other cells. These features indicate strong biomarker and therapeutic potential and have generated broad interest, as evidenced by the steady year-on-year increase in the numbers of scientific publications about EVs. Important advances have been made in EV metrology and in understanding and applying EV biology. However, hurdles remain to realising the potential of EVs in domains ranging from basic biology to clinical applications due to challenges in EV nomenclature, separation from non-vesicular extracellular particles, characterisation and functional studies. To address the challenges and opportunities in this rapidly evolving field, the International Society for Extracellular Vesicles (ISEV) updates its 'Minimal Information for Studies of Extracellular Vesicles', which was first published in 2014 and then in 2018 as MISEV2014 and MISEV2018, respectively. The goal of the current document, MISEV2023, is to provide researchers with an updated snapshot of available approaches and their advantages and limitations for production, separation and characterisation of EVs from multiple sources, including cell culture, body fluids and solid tissues. In addition to presenting the latest state of the art in basic principles of EV research, this document also covers advanced techniques and approaches that are currently expanding the boundaries of the field. MISEV2023 also includes new sections on EV release and uptake and a brief discussion of in vivo approaches to study EVs. Compiling feedback from ISEV expert task forces and more than 1000 researchers, this document conveys the current state of EV research to facilitate robust scientific discoveries and move the field forward even more rapidly
    corecore