Search Results (59)

An $MAP/PH/N$-type queuing system functioning within a finite-state Markovian random environment is studied. The random environment’s state impacts the number of available servers, the underlying processes of customer arrivals and service, and the impatience rate of customers. The impact on the state space of the underlying processes of customer arrivals and of the more general, as compared to exponential, service time distribution defines the novelty of the model. The behavior of the system is described by a multidimensional Markov chain that belongs to the classes of the level-independent quasi-birth-and-death processes or asymptotically quasi-Toeplitz Markov chains, depending on whether or not the customers are absolutely patient in all states of the random environment or are impatient in at least one state of the random environment. Using the tools of the corresponding processes or chains, a stationary analysis of the system is implemented. In particular, it is shown that the system is always ergodic if customers are impatient in at least one state of the random environment. Expressions for the computation of the basic performance measures of the system are presented. Examples of their computation for the system with three states of the random environment are presented as 3-D surfaces. The results can be useful for the analysis of a variety of real-world systems with parameters that may randomly change during system operation. In particular, they can be used for optimally matching the number of active servers and the bandwidth used by the transmission channels to the current rate of arrivals, and vice versa. Full article

The motion of a copter with a suspended payload in a vertical plane is considered. The payload has a spherical shape and contains a concentric spherical cavity partially filled with ideal liquid. The system is subjected to horizontal stationary wind. The aerodynamic load on the payload is described within the framework of a quasi-steady approach. The dynamics of the liquid are simulated using the phenomenological pendulum model. The points of this study are the controllability and observability of a stationary flight of a copter with the payload. A control strategy is proposed, which aims to bring the system from a certain initial state to a certain final state, such that the center of mass of the copter moves along a given sufficiently smooth curve. The control is designed to ensure the suppression of oscillations of the payload and the liquid along the entire trajectory. Full article

In the present paper, a modification of the standard mean-field model is considered, allowing for the description of the formation of a dynamic equilibrium between infected and recovered persons in a population of constant size. The key point of this model is that it highlights two-infection transfer mechanisms depending on the physical nature of the contact between people. We separate the transfer mechanism related directly to the movement of people (the so-called transport processes) from the one occurring at zero relative speed of persons (the so-called social contacts). Under the framework of a physical chemical analogy, the dependencies for the infection transfer rate constants are proposed for both purely transport and social mechanisms of spread. These dependencies are used in discussing the formation of quasi-stationary states in the model, which can be interpreted as endemic equilibrium states. The stability of such endemic equilibria is studied by the method of Lyapunov function. Full article

In this paper, we create a framework for the uniform algorithmic analysis of queueing systems with the Markov arrival process and the simultaneous service of a restricted number of customers, described by a multidimensional Markov chain. This chain behaves as the finite-state quasi-death process between successive service-beginning epochs, with jumps occurring at these epochs. Such a description of the service process generalizes many known mechanisms of restricted resource sharing and is well suited for describing various future mechanisms. Scenarios involving customers who cannot enter service upon arrival, access via waiting in an infinite buffer, and access via retrials are considered. We compare the generators of the multidimensional Markov chains describing the operation of queueing systems with a buffer and with retrials and show that the sufficient conditions for the ergodicity of these systems coincide. The computation of the stationary distributions of these chains is briefly discussed. The results can be used for performance evaluation and capacity planning of various queueing models with the Markov arrival process and a variety of different service mechanisms that provide simultaneous service to many customers. Full article

To ensure the operational safety of the automatic couplers of a rolling stock subjected to cyclic loading, reliability and residual service life must be determined. This paper involved the prediction of the durability of the automatic coupler SA3 by analytical summation of cyclic damage. During the investigation, the cyclic characteristics and damage modes of the automatic coupler material that influence the accumulation of damage are determined. The stress and strain state assessment model was developed using a 3D finite element method for the automatic coupler housing as a geometrically complex component. A methodology was used to assess damage per load cycle that is applicable to any sequence of automatic coupler load cycles. For this purpose, the authors used low-cycle stationary load dependencies that account for quasi-static and low-cycle fatigue damage. The investigation showed that a coupler may develop a crack due to accumulated quasi-static and fatigue damage. For damage summation, the dependences of low-cycle stationary stress-controlled load accounting for low-cycle, quasi-static fatigue damage are proposed in view of the variation of the load on the automatic coupler during operation depending on the weight of the rolling stock, velocity, and railway relief. The proposed methodology is applicable to the calculation of other housings under similar loading conditions. Full article

Despite the current appreciation of pulque as a probiotic fermented beverage, pulque has been also regarded as a poor-quality product, particularly due to the lack of sanitary control during its elaboration. To address this problem, a semi-continuous fermentation system was established, emulating the artisanal production process. Microfiltration-sterilized aguamiel was employed as the substrate, whereas a good-quality pulque was used as the fermentation inoculum. During the fermentation, the physicochemical, microbiological (lactic acid and Leuconostoc-type bacteria and yeasts) and sensory characteristics of the must were monitored. The isolated microorganisms were identified by molecular biology and MALDI-MS techniques. The sterilization of aguamiel by microfiltration did not negatively affect its physicochemical attributes. After 6–8 days of operation of the semi-continuous bioreactor, the fermentation reached a quasi-stationary state considering most of the parameters monitored during the experiment. The final fermentation product presented similar physicochemical, microbial and sensory properties to those of the pulque inoculum. The genera identified were Leuconostoc, Lentilactobacillus, Lactobacillus, Liquorilactobacillus, Fructilactobacillus and Saccharomyces. The strains Lentilactobacillus diolivorans and Liquorilactobacillus capillatus and uvarum have not been previously isolated from pulque. In conclusion, the fermentation system developed in this work was effective to standardize the quality of pulque while preserving the positive attributes of the artisanal process, thus harnessing the probiotic properties of pulque. Full article

A recently proposed scalar forcing scheme that maintains the mixture fraction mean, root-mean-square and probability density function in the unburned gas can lead to a statistically quasi-stationary state in direct numerical simulations of turbulent stratified combustion when combined with velocity forcing. Scalar forcing alongside turbulence forcing leads to greater values of turbulent burning velocity and flame surface area in comparison to unforced simulations for globally fuel-lean mixtures. The sustained unburned gas mixture inhomogeneity changes the percentage shares of back- and front-supported flame elements in comparison to unforced simulations, and this effect is particularly apparent for high turbulence intensities. Scalar forcing does not significantly affect the heat release rates due to different modes of combustion and the micro-mixing rate within the flame characterised by scalar dissipation rate of the reaction progress variable. Thus, scalar forcing has a significant potential for enabling detailed parametric studies as well as providing well-converged time-averaged statistics for stratified-mixture combustion using Direct Numerical Simulations in canonical configurations. Full article

Polarization states define a fundamental property in optics. Consequently, polarization state characterization is essential in many areas of both field industrial applications and scientific research. However, a full identification of space-variant Stokes parameters faces great challenges, like multiple power measurements. In this contribution, we present a spatially resolved polarization measurement using artificial birefringent metallic elements, the so-called hollow waveguides. Differently oriented and space-variant hollow waveguide arrays, a stationary analyzer and a CMOS camera form the basis of the experimental setup for one single spatially resolved power measurement. From this power measurement, the Stokes parameters can be calculated in quasi-real-time, with a spatial resolution down to 50 μm in square. The dimensions of the individual hollow waveguides, which are less than or equal to the employed wavelength, determine the spectral range, here in the near infrared around $\mathsf{\lambda }$ = 1550 nm. This method allows for the rapid and compact determination of spatially resolved Stokes parameters, which is experimentally confirmed using defined wave plates, as well as an undefined injection-molded polymer substrate. Full article

We consider an irreducible positive-recurrent discrete-time Markov process on the state space $X={\mathbb{Z}}_{+}^M\times J$, where ${\mathbb{Z}}_{+}$ is the set of non-negative integers and $J=\{1,2,\dots ,n\}$. The number of states in $J$ may be either finite or infinite. We assume that the process is a homogeneous quasi-birth-and-death process (QBD). It means that the one-step transition probability between non-boundary states $(k,i)$ and $(n,j)$ may depend on $i,j$, and $n-k$ but not on the specific values of $k$ and $n$. It is shown that the stationary probability vector of the process is expressed through square matrices of order $n$, which are the minimal non-negative solutions to nonlinear matrix equations. Full article

This article considers a theoretical analysis of the influence of the main coupled effects and spacers on the transfer of salt ions in electromembrane systems (EMS) using a 2D mathematical model of the transfer process in a desalting channel with spacers based on boundary value problems for the coupled system of Nernst–Planck–Poisson and Navier–Stokes equations. The basic patterns of salt ion transport have been established, taking into account diffusion, electromigration, forced convection, electroconvection, dissociation/recombination reactions of water molecules, as well as spacers located inside the desalting channel. It has been shown that spacers and taking into account the dissociation/recombination reaction of water molecules significantly change both the formation and development of electroconvection. This article confirms the fact of the exaltation of the limiting current studied by Harkatz, where it is shown that the current (flux) of salt ions increases when the dissociation reaction begins by a certain value called the exaltation current, which is proportional to the flow of water dissociation products. A significant combined effect of electroconvection and dissociation/recombination reactions as well as the spacer system in the desalting channel on the transport of salt ions are shown. The complex, nonlinear, and non-stationary interaction of all the main effects of concentration polarization and spacers in the desalting channel are also considered in the work. Full article

Molecular switches based on functionalized graphene nanoribbons (GNRs) are of great interest in the development of nanoelectronics. In experiment, it was found that a significant difference in the conductance of an anthraquinone derivative can be achieved by altering the pH value of the environment. Building on this, in this work we investigate the underlying mechanism behind this effect and propose a general design principle for a pH based GNR-based switch. The electronic structure of the investigated systems is calculated using density functional theory and the transport properties at the quasi-stationary limit are described using nonequilibrium Green’s function and the Landauer formalism. This approach enables the examination of the local and the global transport through the system. The electrons are shown to flow along the edges of the GNRs. The central carbonyl groups allow for tunable transport through control of the oxidation state via the pH environment. Finally, we also test different types of GNRs (zigzag vs. armchair) to determine which platform provides the best transport switchability. Full article

The reliable and repeatable fabrication of complex geometries with predetermined homogeneous properties is still a major challenge in electron beam powder bed fusion (PBF-EB). Although previous research identified a variety of process parameter–property relationships, the underlying end-to-end approach, which directly relates process parameters to material properties, omits the underlying thermal conditions. Since the local properties are governed by the local thermal conditions of the melt pool, the end-to-end approach is insufficient to transfer predetermined properties to complex geometries and different processing conditions. This work utilizes high-throughput thermal simulation for the identification of fundamental relationships between process parameters, processing conditions, and the resulting melt pool geometry in the quasi-stationary state of line-based hatching strategies in PBF-EB. Through a comprehensive study of over 25,000 parameter combinations, including beam power, velocity, line offset, preheating temperature, and beam diameter, process parameter-melt pool relationships are established, processing boundaries are identified, and guidelines for the selection of process parameters to the achieve desired properties under different processing conditions are derived. Full article

The results of a tungsten–niobium alloy synthesis by the impact of pulsed compression plasma flows are presented. Tungsten plates with a 2 μm thin niobium coating were treated with dense compression plasma flows generated by a quasi-stationary plasma accelerator. The plasma flow with an absorbed energy density of 35–70 J/cm² and pulse duration of 100 μs melted the niobium coating and a part of the tungsten substrate, which caused liquid-phase mixing and WNb alloy synthesis. Simulation of the temperature distribution in the top layer of the tungsten after the plasma treatment proved the formation of the melted state. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) were used to determine the structure and phase composition. The thickness of the WNb alloy was 10–20 μm and a W(Nb) bcc solid solution was found. Full article

This work presents the potential for using pulsed gas injection to produce amorphous carbon films. In this experiment, the frequency of injecting small amounts of gas was used to control the pressure amplitudes, thus achieving the conditions of plasma generation from stationary, through quasi-stationary, to pulsed oscillations of pressure. In addition, we used various gases and their mixtures, an alternative to argon. In the experiment, we studied the energy state of the plasma. The films were examined for phase and chemical composition, surface morphology, and optical and mechanical properties. We determined low-frequency pulsed gas injections to be conditions favorable for $C\left({sp}^3\right)-C\left({sp}^3\right)$ bond formation. The plasma generated by gas injections is better ionized than that generated by static pressure. Pulsed conditions favor the plasma species to retain their kinetic energy, limiting the probability of intermolecular collision events. Since helium has a relatively high ionization energy, it is a practical addition to sputtering gas because of the increasing sp³ content in the films. The electrons created by helium ionization improve the plasma’s ionization degree. Full article

In the framework of quantum mechanics using quasi-Hermitian operators the standard unitary evolution of a non-stationary but still closed quantum system is only properly described in the non-Hermitian interaction picture (NIP). In this formulation of the theory both the states and the observables vary with time. A few aspects of implementation of this picture are illustrated via the “wrong-sign” quartic oscillators. It is shown that in contrast to the widespread belief, both of the related Schrödinger-equation generators $G\left(t\right)$ and the Heisenberg-equation generators $\Sigma \left(t\right)$ are just auxiliary concepts. Their spectra are phenomenologically irrelevant and, in general, complex. It is argued that only the sum $H\left(t\right)=G\left(t\right)+\Sigma \left(t\right)$ of the latter operators retains the standard physical meaning of the instantaneous energy of the unitary quantum system in question. Full article