Time Distribution Function Research Articles

Continuous time random walk model for non-uniform bed-load transport with heavy-tailed hop distances and waiting times

Bed-load transport along widely graded river-beds typically exhibits anomalous dynamics, whose efficient characterization may require parsimonious stochastic models with pre-defined statistics involving the waiting time and hop distance distributions for sediment particles. This study employs a continuous time random walk (CTRW) model to characterize bed-load particle motions on a widely graded gravel-bed with cluster microforms built in our lab. Flume experiments guide the selection of the Mittag-Leffler (M-L) function as the waiting time distribution function, and the Lévy α-stable density for the hop distance distribution function in the CTRW model. Monte Carlo simulations show that the resulting CTRW model can well capture the observed flume experimental data (with either a continuous or an instantaneous source) with coexisting super- and sub-dispersion behaviors in the bed-load transport process. Analyses further discover the dual impact of clusters on the dynamics of fine sediment particles. Some particles are more likely to be blocked or trapped by clusters, while others have a high probability to be accelerated by the flow accelerating belt between the clusters. Therefore, with proper statistical distributions and relevant parameters for sediment waiting times and hop distances, the CTRW model may efficiently capture the complex dynamics in sediment transport.

Containment control of stochastic multiagent systems with semi‐Markovian switching topologies

SummaryThe containment control of stochastic multiagent systems with semi‐Markov switching topologies is investigated in this paper. The general case that the distribution function of the sojourn time is dependent on both the current system mode and the target mode is considered. Taking state multiplicative noise into account and using stochastic techniques, sufficient conditions to achieve the containment control in the asymptotic mean square sense are obtained in a form of linear matrix inequalities and the controller design condition is given. Finally, a simulation is given to demonstrate the effectiveness of the obtained theoretical results.

Household transmission and disease transmissibility of a large HAV outbreak in Lazio, Italy, 2016–2017

A major outbreak of Hepatitis A Virus (HAV) has swept through Europe between mid-2016 and 2017, mainly within the community of men who have sex with men (MSM). Over the same period, about 1000 outbreak-related cases of acute Hepatitis A (AHA) were recorded in Lazio region, Italy.We calibrated a Bayesian model to reconstruct likely transmission events within all 44 households where multiple infections were recorded, representing a total of 103 cases from the HAV outbreak in Lazio. Based on information on the observed times of symptom onset, we estimated the probability distribution function of the HAV generation time and used it to compute the effective and instantaneous reproduction numbers for the considered outbreak from the overall epidemic curve (N = 998 cases).We estimated a mean generation time of 30.2 days (95%CI: 25.2–33.0) and an effective reproduction number of about 1.63 (95% CI: 1.35–1.94). Transmissibility peaked in January 2017, shortly before targeted awareness and vaccination campaigns were put in place by health authorities; however, transmission remained above the epidemic threshold until June 2017. Within households, children (0–15) and young adults (16–30) infected preferentially individuals of the same age class, whereas transmission within older age groups was substantially homogeneous.These results suggest that the implemented interventions were able to slow down HAV transmission, but not to bring it rapidly to a halt. According to our estimates of the HAV transmissibility, about 50% of the at-risk persons should be immunized to prevent similar outbreaks in the future. Our results also indicate spillover from community transmission to household members, suggesting the opportunity of vaccinating household contacts of cases to prevent further spread of the epidemics.

Characterization and optimization of highly active and Ba-deficient BaCo0.4Fe0.4Zr0.1Y0.1O3--based cathode materials for protonic ceramics fuel cells

Highly active triple-conducting (proton-, oxygen-ion-, and electron-conducting) perovskite oxide BaCo 0.4 Fe 0.4 Zr 0.1 Y 0.1 O 3- δ need to further optimize the electrochemical performance and chemical stability in carbon dioxide and water containing atmospheres, greatly limiting its widespread use in protonic ceramics fuel cells (PCFCs). Here, Ba-site deficient Ba 0.9 Co 0.4 Fe 0.4 Zr 0.1 Y 0.1 O 3- δ (B9CFZY) was synthesized and investigated as a promising candidate concerning the chemical and structural stability, electrical conductivity and electrochemical performance. Anode-supported button cells with the prevalent BaZr 0.1 Ce 0.7 Y 0.2 O 3- δ (BZCY) as electrolyte using B9CFZY and B9CFZY-BZCY cathodes, respectively, were fabricated and then measured at 700-550 °C. The maximum power density of the cells with B9CFZY-based cathodes increase from 452 mW cm −2 to 537 mW cm −2 at 700 °C, however, the corresponding polarization loss decreases from 0.30 to 0.15 Ω cm 2 by adding proton-conducting BZCY. Importantly, to better explore the reasons for the improved electrochemical performance, the distribution function of relaxation time (DRT) is used to distinguish different electrode polarization processes of both cells. The results indicate the polarization peaks (P3) of cells with composite cathode resulting from oxygen gas adsorption and dissociation can be greatly accelerated as well as the polarization peaks (P2) resulting from oxygen species diffusion to three phase boundaries or active sites in the cathode. The dramatic improvements demonstrate Ba deficient B9CFZY-BZCY material can be a very competitive cathode material for PCFCs.

Probabilistic Analysis for Estimation of the Initiation Time of Corrosion

Abstract In this paper, a probabilistic study on durability concrete was carried out. In such a design, initiation time of corrosion must be expressed as a mathematical model using Fick’s second law and the statistical distributions properties of theirs parameters was included in this model. The scatter both in the environmental exposure conditions and structural properties was considered as random fields in the mathematical model with a probabilistic design. The main objective of this study is predicted initiation time of corrosion of concrete structures in chloride containing environments. This probabilistic study is developed using Monte Carlo simulation to determine the contribution of each input parameters and the statistical parameters of the random variables on the probability distribution functions of the initiation time of corrosion. Also, a comparison study was carried out to analyze the impact of the probability distribution on the response (the initiation time of corrosion).

On distribution of upper marginal records in bivariate random sequences

The theory of record values has been extensively studied in the statistical literature. However, there are not many papers devoted to the theory of records for bivariate and multivariate random sequences. This paper presents the marginal record values and record times in extended sequence of bivariate random vectors. The joint distributions of some upper marginal records are derived. Some results on joint probability mass function of upper record time vectors and distribution function of upper record value vectors are given via copula functions. Moreover, the numerical and graphical applications of considered upper records using flood data and prediction of rainfall variables such as intensity, depth, and duration are provided.

Analysis of queuing system with calls of various width

In this paper, we study the mathematical model of a multi-channel queuing system in which Poisson flows of voice and data calls are served. It is assumed that narrow-band voice calls require only one free channel to service, while at the same time, number of free channels that required to service broadband data calls is b, b>1. The system adopts a widely used in practice, fully accessible access strategy to the common channel pool, according to which there are no differences between different types of speech and data calls. If upon arrival of a voice call (data call) there is one free channel (b>1 free channels), then it occupies free channel(s) of the system; otherwise the call is lost. The distribution functions of channel occupation time by heterogeneous calls are exponential with different average values. It is shown that the mathematical model of the system is a certain two-dimensional Markov chain with a finite set of states. An algorithm is proposed for constructing the generating matrix of this chain and it is proved that from any state of this chain in a finite number of steps it is possible to go to any other state. Using the Kolmogorov theorem, it is proved that the constructed two-dimensional Markov chain is reversible, and therefore the stationary probability distribution of the states of this Markov chain has a multiplicative form. An explicit form of the multiplicative representation is obtained. Explicit formulas have been developed for calculating the probabilities of the states of the Markov chain under study, and using these probabilities of states, explicit formulas have been proposed for calculating the indicators of service quality — call probabilities of each type calls and channel utilization. The developed formulas allow us to conduct numerical experiments in order to study the behavior of indicators of the quality of service of the system relative to changes in its parameters, as well as solve the problems of their optimization with respect to the selected quality criterion for the functioning of the system.

Distribution of the time to buffer overflow in the M/G/1/N-type queueing model with batch arrivals and multiple vacation policy

A single-channel FIFO queueing model with finite buffer capacity and the multiple vacation policy is investigated, in which jobs arrive according to a compound Poisson process and are being processed individually with a general-type distribution function of the service time. A multiple vacation period, consisting of a number of independent generally-distributed server vacations, is being started each time when the system becomes empty. During this period, the processing of jobs is suspended. Successive server vacations are being initialised until at least one job is present in the buffer at the completion epoch of one of them. A compact formula for the Laplace transform of the distribution of the time to the first buffer overflow, conditioned by initial number of packets present in the buffer, is found. The analytical approach is based on the paradigm of embedded Markov chain, integral equations and Korolyuk’s potential idea. Numerical illustrating examples are attached as well.

Reduction tree to determine estimators from the multivariate interval censored data

In this paper methods for finding the nonparametric maximum likelihood estimator (NPMLE) of the distribution function of time to event data will be presented. The basic approach is to use graph theory (in particular reduction tree), to simplify the problem. The Multivariate interval censored data can be represented by its intersection graph. The idea behind the reduction tree approach is based on the fact that when censored data can be partitioned into several groups such that observations from different groups do not intersect, we may compute the NPMLE with the data in each group separately. Each group can be further simplified when sorne observations in the group intersect all other observations: with respect to the group, such observations have no incidence on the NPMLE computation. Once these observations are, in effect, removed from the group, the group may be further partitioned.The process can go on recursively, forming the reduction tree. In the three dimension, the support area intersection of beams, where X absis the time of infection, Y ordinat the time of onset and Z the time of death. The results obtained by the leaves from the reduction tree are not unique and are maximum cliques.

Characterization of Sr2Fe1.5Mo0.5O6-δ -Gd0.1Ce0.9O1.95 symmetrical electrode for reversible solid oxide cells

Development of reversible solid oxide cells (RSOCs) must face one major challenge of the poor reliability origination from the oxidization of Ni-based hydrogen electrode materials. In this work, Sr2Fe1.5Mo0.5O6-δ -Gd0.1Ce0.9O1.95 (SFM-GDC) symmetrical electrode working both air and hydrogen electrode is designed and investigated for RSOCs. Regardless of the redox condition, SFM shows excellent structural stability by the XRD analysis and HR-TEM observation. Meanwhile, XPS analysis obviously demonstrates the co-existence of Fe2+/Fe3+ and Mo5+/Mo6+ couples, of which both proportions increase with the reduce oxygen partial pressure. Applying SFM-GDC symmetrical electrode, the 300 μm-thick YSZ electrolyte-supported RSOCs with GDC buffer layers show acceptance electrochemical performance, and switch smoothly between power generation and electrolysis modes with no obvious degradation after 20 h short-term stability working under humidified (∼3%H2O) H2 and 3%H2O-air atmospheres, respectively. Besides, the impedance spectrum were further studied using a relaxation time distribution function (DRT), and two polarization peaks (P1, P2) observed in the power generation mode shifted to the left at low frequency with the reduced temperature, while one more new polarization peak (P3) corresponds to the reaction gas diffusion owing to the low concentration steam (∼3% H2O) in electrolysis mode. This research highlights that the stable and efficient SFM-GDC symmetrical electrode can be the potential RSOCs electrode candidates.

A theory of distribution functions of relaxation times for the deconvolution of immittance data

Deconvolution of immittance spectroscopy (IS) data into a not directly measurable distribution of uncorrelated relaxation times (DRT) of polarisation processes occurring in the measured system provides useful information on the system. It primarily regards the identification of the number of such processes through their relaxation time constants, τ. Upon changing the conditions of the measurement, it also covers the variation particularly of the position and intensity of the relaxation time in the DRT spectrum.These information revealed by numerical inversion commonly using constrained least squares (LS) minimisation or fast Fourier transformation (FFT), help to construct an equivalent electrical circuit (EEC) model, which subsequently allows complex nonlinear least squares (CNLS) fitting of the IS data to simulate system behaviour.The inverse problem of deconvolving IS data into DRT is based on the principle of superposition of the immittances of passive (lumped) elements, such as a resistor, R, an inductor, L and a capacitor, C combined in parallel or series and forming branches of RLC electrical circuit networks of different types (Kelvin-Voigt, Maxwell-Wagner, Cauer, Foster, etc.). In the limit of an infinite number of branches, the network immittance convolved with the DRT function is mathematically described by a Fredholm singular integral equation (SIE) equated with the immittance of the studied system.As a novelty, from a SIE of the second kind, we derive the hitherto concealed complex valuedness of the DRT using the Hilbert integral transform (HT) and DRT properties for Kelvin-Voigt type RLC networks. We emphasise the necessity and usefulness of complex valued DRT for its numerical estimation by the FFT method and LS minimisation. We also provide for the derivation of theoretical DRT from rational immittances known analytically in closed form, e.g. assuming their representation by a HT compliant EEC model.

Математическое моделирование процессов коалесценции и дробления капель и пузырей в изотропном турбулентном потоке (обзор)

Предложенный обзор посвящен теоретическому анализу, расчету и моделированию процессов слияния и дробления капель и пузырей в изотропном турбулентном потоке. Проанализирован ряд исследований, посвященных этим проблемам. Рассмотрены вопросы определения минимальных и максимальных размеров капель и пузырей, а также частот дробления и слияния, которые связаны с решением диффузионного уравнения массопереноса. Слияние капель рассматривается как результат утончения межфазной пленки, образованной между двумя каплями в результате их столкновения. Предложено математическое описание утончения межфазной пленки с учетом эффекта Марангони. Анализ множества исследований, в том числе и собственных, показал, что в зависимости от масштаба турбулентных пульсаций экстремальный размер, а также частоты коалесценции и дробления капель и пузырей зависят от удельной энергии диссипации в турбулентном потоке, от их размеров и физических свойств частиц и среды. Важными параметрами, обеспечивающими агрегативную устойчивость дисперсной среды типа «жидкость - жидкость» или «жидкость - газ» к дроблению, деформации и слиянию, являются коэффициент поверхностного натяжения и диссипация энергии, физические свойства среды и частиц, а в изотропном турбулентном потоке - отношение коэффициента поверхностного натяжения к удельной энергии диссипации. Рассмотрены также вопросы, связанные с эволюцией функции распределения частиц по времени и размерам в условиях изотропной турбулентности с использованием решений стохастического уравнения Фоккера-Планка для непрерывного изменения размеров капель и пузырей и интегро-дифференциального кинетического уравнения коалесценции и дробления для скачкообразного изменения размеров частиц. Предложено множество аналитических решений этих уравнений для частных случаев. Более глубокий анализ на основе математических закономерностей явлений переноса позволяет стандартным образом рассчитывать такие системы в некотором приближении как непрерывные с бесконечно малым скачком. Показано, что детерминированное описание этих явлений без учета их стохастической природы является неполным и может приводить к существенным отклонениям от истинной природы указанных выше процессов. Полученные результаты сравнены с существующими экспериментальными данными по коалесценции и дроблению капель и пузырей, что показало удовлетворительное соответствие расчетным значениям.

Research on TBF distribution model of circular tool magazine and ATC

Tool magazine and automatic tool changer (ATC) is one of the most important function units of a machining centre and its reliability directly influences the reliability of the machining centre. Failure analysis is the basic work in reliability study. So far, there are few studies on failure of the tool magazine and ATC. Based on the failure data obtained from the field tracing of a kind of circular tool magazine and ATC, the probability density function, the distribution function and failure function of time between failures (TBF) of the tool magazine and ATC are calculated. It is preliminarily assumed that the TBF of the circular tool magazine and ATC obey Weibull distribution. Parameter estimation and hypothesis testing of the Weibull distribution model are done. Finally, the effectiveness of the model is verified. The work can provide a reference for failure prediction of circular tool magazine and ATC.

Generating a stable primary schedule for an integrated surgical suite

Efficient utilisation of operating room (OR) is a common anxiety of surgical suit manager which necessitate an effective planning and scheduling of surgeries. In this paper we investigate predictive/reactive scheduling of an integrated surgical suite in the form of a two-stage hybrid flow shop scheduling problem (HFSP). The deterministic model comprises both assignment and sequencing decisions for elective surgeries. By further considering shared capacity between elective and emergency patients, a chance constrained programming model is extended for the first time to cope with uncertain disruption. It is shown that how a chance constrained model will reduce to just considering an augmented surgery which processing time depends on distribution function of emergency surgery processing time and confidence level of scheduler. Two new important measures in reactive scheduling literature, 'stability' and 'robustness' are taking into account in surgical suite scheduling for the first time. Computational results demonstrate the efficiency of primary schedule generated by extended chance constrained programming model as well as the effectiveness of new measures in hospitals. As the chance constrained model is NP-hard, a decomposition heuristic algorithm based on tabu search (TS) is proposed to cope with problems of real size.

Generating a stable primary schedule for an integrated surgical suite

Efficient utilisation of operating room (OR) is a common anxiety of surgical suit manager which necessitate an effective planning and scheduling of surgeries. In this paper we investigate predictive/reactive scheduling of an integrated surgical suite in the form of a two-stage hybrid flow shop scheduling problem (HFSP). The deterministic model comprises both assignment and sequencing decisions for elective surgeries. By further considering shared capacity between elective and emergency patients, a chance constrained programming model is extended for the first time to cope with uncertain disruption. It is shown that how a chance constrained model will reduce to just considering an augmented surgery which processing time depends on distribution function of emergency surgery processing time and confidence level of scheduler. Two new important measures in reactive scheduling literature, 'stability' and 'robustness' are taking into account in surgical suite scheduling for the first time. Computational results demonstrate the efficiency of primary schedule generated by extended chance constrained programming model as well as the effectiveness of new measures in hospitals. As the chance constrained model is NP-hard, a decomposition heuristic algorithm based on tabu search (TS) is proposed to cope with problems of real size.

Exponential change of measure for general piecewise deterministic Markov processes

We consider a general piecewise deterministic Markov process (PDMP) $X=\{X_t\}_{t\geqslant~0}$ with a measure-valued generator $\mathcal{A}$, for which the conditional distribution function of the inter-occurrence time is not necessarily absolutely continuous. A general form of the exponential martingales that are associated with $X$ is given by By considering this exponential martingale to be a likelihood-ratio process, we define a new probability measure and show that the process $X$ is still a general PDMP under the new probability measure. We additionally find the new measure-valued generator and its domain. To illustrate our results, we investigate the continuous-time compound binomial model.

Residence time distribution in a structured packing unit for monitoring aerosol emissions

Solvent absorption in a structured packed column has been demonstrated as a viable option for post-combustion carbon capture. Amine emissions in the form of aerosol particles pose a major challenge that severely impacts the separation efficiency of the packed column. The aerosol particles quickly achieve the motion of the gas flow. In this context, residence time distribution (RTD) of the gaseous phase will provide insights for managing aerosol particles, thereby controlling amine loss in the packed column. Computational fluid dynamics (CFD) modeling of such columns is a multiscale problem because of a wide range of disparity in length scales. Accordingly, three-dimensional CFD simulations in the representative elementary unit of a structured packing are conducted using OpenFOAM. The RTD is analyzed in terms of residence time distribution function, mean residence time and variance. Effects of the diffusivity and flow rates on RTD are extensively studied, and the dispersion coefficient is calculated using a one-dimensional axial dispersion model. RTDs computed in a smaller domain are extrapolated to a larger domain using the convolution integral. The CFD computed and corresponding CFD models derived from the convolution integral match well at different flow rates and domain sizes. A comparison of RTD among diff ;erent packing designs is presented at a fixed number of repeating units and different flow rates. The mean residence time is found to larger than the superficial time, which is a unique behavior of structure packing. For a fixed number of repeating units, a packed column having higher specific area showed broad dispersion and the axial Péclet number decreases.

Analysis of switching times statistical distributions for perpendicular magnetic memories

Abstract Magnetization switching by injected spin-polarized current or applied field pulses is considered for perpendicular magnetic nanosystems with uniaxial symmetry and subject to thermal fluctuations. Such systems can model both perpendicular spin-transfer-torque magnetic random access memories and magnetic grains for state-of-the-art perpendicular recording. It is shown that, in the limit of high energy barriers and large current/field amplitudes, the probability and cumulative distribution functions of switching times can be analytically computed as function of material, geometrical parameters and thermal noise level. The theoretical predictions are confirmed by macrospin and full micromagnetic simulations. By using the derived formulas, it is shown that analysis of Write-Error Rates (WERs) at typical levels of reliability required by magnetic recording technology can be easily performed.

Numerical analysis of mixing in block‐head mixing screws

The research reported here used 3D non‐Newtonian flow simulations to investigate the pumping and mixing capability of block‐head mixers. Block‐head mixers are distributive mixing screws that are widely used to homogenize the polymer melt and eliminate thermal gradients. The polymer‐processing industry employs a variety of block‐head mixers, with little consensus on design and distribution of screw flights and mixing blocks. This analysis addresses this issue based on a computational design study in which the influence of three geometrical parameters was examined: (1) the number of flights at a mixing block, (2) the number of blocks along the screw, and (3) the stagger angle between the blocks. To examine the flow behavior of the mixing screws, the pressure consumption and energy dissipation is evaluated. Distributive mixing is analyzed using residence time distribution functions, kinematic stretching parameters, and the scale of segregation. Dispersive mixing is assessed by means of the mixing index and the shear stress. The results of this design study increase the understanding of block‐head mixers and contribute to the design and optimization of such geometries. The findings can further be applied to mixing screws of similar geometry, including pin‐type and knob mixers. POLYM. ENG. SCI., 59:E88–E104, 2019. © 2018 The Authors. Polymer Engineering & Science published by Wiley Periodicals, Inc. on behalf of Society of Plastics Engineers.

Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration

A nonrenewable resource extraction game model is analyzed in a differential game theory framework with random duration. If the cumulative distribution function (c.d.f.) of the final time is discontinuous, the related subgames are differentiated based on the position of the initial instant with respect to the jump. We investigate properties of optimal trajectories and of imputation distribution procedures if the game is played cooperatively.