Salt Distribution in a Soil Irrigated by Subsurface Emitter

The best design of subsurface trickle irrigation systems requires knowledge of water and salt distribution patterns around the emitters that match the root extraction and minimize water losses. The transient distribution of water and salt in a two-dimensional homogeneous Iraqi soil domain under subsurface trickle irrigation with different settings of an emitter is investigated numerically using 2D-HYDRUS software. Three types of Iraqi soil were selected. The effect of altering different values of water application rate and initial soil water content was investigated in the developed model. The coefficient of correlation (R2) and the root-mean-square error (RMSE) was used to validate the predicted numerical result. This statistical analysis revealed that there was no much difference between the predicted numerical results, and the measured values. R2 varied from 0.75 to 0.93 and the (RMSE) from 0.079 to 0.116. The comparison confirms the accuracy of the developed model, and it shows that it can be used to simulate the front wetting patterns of water and salt distribution under subsurface trickle irrigation systems. The simulation outcome showed that as the distance from the emitter increased, soil salinity far from the emitter decreased. As expected, irrigation duration and amount affects the dimension of the solute distribution.

BROWNIAN MOTION MINUS THE INDEPENDENT INCREMENTS: REPRESENTATION AND QUEUING APPLICATION

This paper relaxes assumptions defining multivariate Brownian motion (BM) to construct processes with dependent increments as tractable models for problems in engineering and management science. We show that any Gaussian Markov process starting at zero and possessing stationary increments and a symmetric smooth kernel has a parametric kernel of a particular form, and we derive the unique unbiased, jointly sufficient, maximum-likelihood estimators of those parameters. As an application, we model a single-server queue driven by such a process and derive its transient distribution conditional on its history.

On Mautner-Type Probability of Capture of Intergalactic Meteor Particles by Habitable Exoplanets

Both macro and microprojectiles (e.g., interplanetary, interstellar and even intergalactic material)are seen as important vehicles for the exchange of potential (bio)material within our solar system as wellas between stellar systems in our Galaxy. Accordingly, this requires estimates of the impact probabilitiesfor different source populations of projectiles, including for intergalactic meteor particles which havereceived relatively little attention since considered as rare events (discrete occurrences that are statisticallyimprobable due to their very infrequent appearance). We employ the simple but yet comprehensivemodel of intergalactic microprojectile capture by the gravity of exoplanets which enables us to estimatethe map of collisional probabilities for an available sample of exoplanets in habitable zones around hoststars. The model includes a dynamical description of the capture adopted from Mautner model ofinterstellar exchange of microparticles and changed for our purposes. We use statistical and informationmetrics to calculate probability map of intergalactic meteorite particle capture. Moreover, by calculatingthe entropy index map we measure the concentration of these rare events. We further adopted a modelfrom immigration theory, to show that the transient distribution of birth/death/immigration of materialfor the simplest case has a high value.

On Mautner-Type Probability of Capture of Intergalactic Meteor Particles by Habitable Exoplanets

Both macro and microprojectiles (e.g., interplanetary, interstellar and even intergalactic material) are seen as an important vehicle for the exchange of (bio)material within our solar system as well as between stellar systems in our Galaxy. Accordingly, this requires estimates of the impact probabilities for different source populations of projectiles, specifically for intergalactic meteor particles which have received relatively little attention since considered as rare events (discrete occurrences that are statistically improbable due to their very infrequent appearance). We employ the simple but yet comprehensive model of intergalactic microprojectile capture by the gravity of exoplanets which enables us to estimate the map of collisional probabilities for an available sample of exoplanets in habitable zones around host stars. The model includes a dynamical description of the caption adopted from Mautner model of interstellar exchange of microparticles and changed for our purposes. We use statistical and information metrics to calculate probability map of intergalactic meteorite particle capture. Moreover, by calculating the entropy index map we measure the concentration of these rare events. By adopting a model from immigration theory, we show that the transient distribution of birth/death/immigration of material for the simplest case has a high value.

Fractional Queues with Catastrophes and Their Transient Behaviour

Starting from the definition of fractional M/M/1 queue given in the reference by Cahoy et al. in 2015 and M/M/1 queue with catastrophes given in the reference by Di Crescenzo et al. in 2003, we define and study a fractional M/M/1 queue with catastrophes. In particular, we focus our attention on the transient behaviour, in which the time-change plays a key role. We first specify the conditions for the global uniqueness of solutions of the corresponding linear fractional differential problem. Then, we provide an alternative expression for the transient distribution of the fractional M/M/1 model, the state probabilities for the fractional queue with catastrophes, the distributions of the busy period for fractional queues without and with catastrophes and, finally, the distribution of the time of the first occurrence of a catastrophe.

Transient heat transfer at fluid flow in a thick-walled pipeline

The work aims to determine the transient temperature distribution of the medium and the pipeline wall using the finite difference method. Time courses of the temperature of the flowing medium and pipeline walls caused by a step change in temperature of the medium at the pipeline inlet, obtained by the numerical method, were compared with the courses calculated using strict analytical formulas. The numerical method of determining the transient distribution of temperature of medium and pipeline wall can be used in the analysis of heating and cooling of heating or steam pipelines with any changes in time of mass flow rate of the flowing medium or temperature of the medium at the inlet to the pipeline.

Some asymptotic results for the transient distribution of the Halfin–Whitt diffusion process

We consider the Halfin–Whitt diffusion process Xd(t), which is used, for example, as an approximation to the m-server M/M/m queue. We use recently obtained integral representations for the transient density p(x,t) of this diffusion process, and obtain various asymptotic results for the density. The asymptotic limit assumes that a drift parameter β in the model is large, and the state variable x and the initial condition x0 (with Xd(0) = x0 > 0) are also large. We obtain some alternate representations for the density, which involve sums and/or contour integrals, and expand these using a combination of the saddle point method, Laplace method and singularity analysis. The results give some insight into how steady state is achieved, and how if x0 > 0 the probability mass migrates from Xd(t) > 0 to the range Xd(t) < 0, which is where it concentrates as t → ∞, in the limit we consider. We also discuss an alternate approach to the asymptotics, based on geometrical optics and singular perturbation techniques.