Vortex Trapping Cavity on Airfoil: High-Order Penalized Vortex Method Numerical Simulation and Water Tunnel Experimental Investigation

This paper presents a two-dimensional implementation of the high-order penalized vortex in cell method applied to solve the flow past an airfoil with a vortex trapping cavity operating under moderate Reynolds number. The purpose of this article is to investigate the fundamentals of the vortex trapping cavity. The first part of the paper treats with the numerical implementation of the method and high-order schemes incorporated into the algorithm. Poisson, stream-velocity, advection, and diffusion equations were solved. The derivation, finite difference formulation, Lagrangian particle remeshing procedure, and accuracy tests were shown. Flow past complex geometries was possible through the penalization method. A procedure description for preparing geometry data was included. The entire methodology was tested with flow past impulsively started cylinder for three Reynolds numbers: 550, 3000, 9500. Drag coefficient, streamlines, and vorticity contours were checked against results obtained by other authors. Afterwards, simulations and experimental results are presented for a standard airfoil and those equipped with a trapping vortex cavity. Airfoil with an optimized cavity shape was tested under three angles of attack: 3°, 6°, 9°. The Reynolds number is equal to Re = 2 × 104. Apart from performing flow analysis, drag and lift coefficients for different shapes were measured to assess the effect of vortex trapping cavity on aerodynamic performance. Flow patterns were compared against ultraviolet dye visualizations obtained from the water tunnel experiment.

Covert Cycle Stealing in a Single FIFO Server

Consider a setting where Willie generates a Poisson stream of jobs and routes them to a single server that follows the first-in first-out discipline. Suppose there is an adversary Alice, who desires to receive service without being detected. We ask the question: What is the number of jobs that she can receive covertly, i.e., without being detected by Willie? In the case where both Willie and Alice jobs have exponential service times with respective rates μ 1 and μ 2 , we demonstrate a phase-transition when Alice adopts the strategy of inserting a single job probabilistically when the server idles: over n busy periods, she can achieve a covert throughput, measured by the expected number of jobs covertly inserted, of O (√ n ) when μ 1 < 2 μ 2 , O (√ n log n ) when μ 1 = 2μ 2 , and O ( n μ 2 /μ 1 ) when μ 1 > 2μ 2 . When both Willie and Alice jobs have general service times, we establish an upper bound for the number of jobs Alice can execute covertly. This bound is related to the Fisher information. More general insertion policies are also discussed.

First Passage Time Distribution for Spiking Neuron with Delayed Excitatory Feedback

A class of spiking neuronal models with threshold 2 is considered. It is defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire (LIF) or the binding neuron model, and also for some artificial neurons. A neuron is stimulated with a Poisson stream of excitatory impulses. Each output impulse is conveyed through the feedback line to the neuron input after finite delay [Formula: see text]. This impulse is identical to those delivered from the input stream. We have obtained a general relation allowing calculating exactly the probability density function (PDF) [Formula: see text] for distribution of the first passage time of crossing the threshold, which is the distribution of output interspike intervals (ISI) values for this neuron. The calculation is based on known PDF [Formula: see text] for that same neuron without feedback, intensity of the input stream [Formula: see text] and properties of the feedback line. Also, we derive exact relation for calculating the moments of [Formula: see text] based on known moments of [Formula: see text]. The obtained general expression for [Formula: see text] is checked numerically using Monte Carlo simulation for the case of LIF model. The course of [Formula: see text] has a [Formula: see text]-function-type peculiarity. This fact contributes to the discussion about the possibility to model neuronal activity with Poisson process, supporting the “no” answer.

Relation Between Firing Statistics of Spiking Neuron with Instantaneous Feedback and Without Feedback

We consider a class of spiking neuron models, defined by a set of conditions which are typical for basic threshold-type models like leaky integrate-and-fire, or binding neuron model and also for some artificial neurons. A neuron is fed with a point renewal process. A relation between the three probability density functions (PDF): (i) PDF of input interspike intervals ISIs, (ii) PDF of output interspike intervals of a neuron with a feedback and (iii) PDF for that same neuron without feedback is derived. This allows to calculate any one of the three PDFs provided the remaining two are given. Similar relation between corresponding means and variances is derived. The relations are checked exactly for the binding neuron model stimulated with Poisson stream.

Transient solution of /G/1 with Second Optional Service Subject to Reneging during Vacation and Breakdown time

In this paper, we present a batch arrival non- Markovian queuing model with second optional service. Batches arrive in Poisson stream with mean arrival rate ?, such that all customers demand the first essential service, whereas only some of them demand the second "optional" service. We consider reneging to occur when the server is unavailable during the system breakdown or vacations periods. The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly.

The Analysis, Optimization, and Simulation of a Two-Stage Tandem Queueing Model with Hyperexponential Service Time at Second Stage

The aim of this paper is to analyze a tandem queueing model with two stages. The arrivals to the first stage are Poisson stream and the service time at this stage is exponential. There is no waiting room at first stage. The service time is hyperexponential and no waiting is allowed at second stage. The transition probabilities and loss probabilities of this model are obtained. In addition, the loss probability at second stage is optimized. Performance measures and the variance of the numbers of customers of this tandem queueing model are found. It is seen that the numbers of customers in first stage and second stage are dependent. Finally we have simulated this queueing model. For different values of parameters, exact values, simulated values, and optimal values of obtained performance measures of this model are numerically shown in tables and graphs.

Transient Solution of M[X]=G=1 With Second Optional Service, Bernoulli Schedule Server Vacation and Random Break Downs

In this model, we present a batch arrival non- Markovian queueingmodel with second optional service, subject to random break downs andBernoulli vacation. Batches arrive in Poisson stream with mean arrivalrate (> 0), such that all customers demand the rst `essential' ser-vice, wherein only some of them demand the second `optional' service.The service times of the both rst essential service and the second op-tional service are assumed to follow general (arbitrary) distribution withdistribution function B1(v) and B2(v) respectively. The server may un-dergo breakdowns which occur according to Poisson process with breakdown rate . Once the system encounter break downs it enters the re-pair process and the repair time is followed by exponential distributionwith repair rate . Also the sever may opt for a vacation accordingto Bernoulli schedule. The vacation time follows general (arbitrary)distribution with distribution function v(s). The time-dependent prob-ability generating functions have been obtained in terms of their Laplacetransforms and the corresponding steady state results have been derivedexplicitly. Also the mean queue length and the mean waiting time havebeen found explicitly.

Spiking Statistics of Excitatory Neuron with Feedback

Firing statistics of excitatory binding neuron (BN) is considered. The neuron is driven externally by a Poisson stream. Influence of feedback, which conveys every output impulse to the input with time delay , on the statistics of output spikes is studied. The resulting output stream is not Poissonian, and the authors obtain its inter-spike intervals (ISI) distribution for the case of BN, BN with instantaneous, , and delayed, , feedback. Output statistics of neuron with delayed feedback differs essentially from that found for the case of no feedback as well as from the case of instantaneous feedback. ISI distributions, found for delayed feedback, are characterized with jumps, derivative discontinuities and include -function type singularity. Also, for non-zero refractory time, the authors obtain multiple-ISI conditional probability density and prove, that delayed feedback presence results in non-Markovian statistics of neuronal firing. It is concluded, that delayed feedback presence can radically change neuronal firing statistics.

Output Stream of Binding Neuron with Feedback

The binding neuron (BN) output firing statistics is considered. The neuron is driven externally by the Poisson stream of intensity <img src="http://www.igi-global.com/Images/Symbols/m01.gif" />. The influence of the feedback, which conveys every output impulse to the input with time delay <img src="http://www.igi-global.com/Images/Symbols/m02.gif" />, on the statistics of BN's output spikes is considered. The resulting output stream is not Poissonian, and we look for its interspike intervals (ISI) distribution for the case of BN, BN with instantaneous, <img src="http://www.igi-global.com/Images/Symbols/m03.gif" />, and delayed, <img src="http://www.igi-global.com/Images/Symbols/m04.gif" />, feedback. For the BN with threshold 2 an exact mathematical expressions as functions of <img src="http://www.igi-global.com/Images/Symbols/m05.gif" />, <img src="http://www.igi-global.com/Images/Symbols/m06.gif" /> and BN's internal memory, <img src="http://www.igi-global.com/Images/Symbols/m07.gif" /> are derived for the ISI distribution, output intensity and ISI coefficient of variation. For higher thresholds these quantities are found numerically. The distributions found for the case of instantaneous feedback include jumps and derivative discontinuities and differ essentially from those obtained for BN without feedback. Statistics of a neuron with delayed feedback has remarkable peculiarities as compared to the case of <img src="http://www.igi-global.com/Images/Symbols/m08.gif" />. ISI distributions, found for delayed feedback, are characterized with jumps, derivative discontinuities and include singularity of Dirac's <img src="http://www.igi-global.com/Images/Symbols/m09.gif" />-function type. The obtained ISI coefficient of variation is a unimodal function of input intensity, with the maximum value considerably bigger than unity. It is concluded that delayed feedback presence can radically alter neuronal output firing statistics.