Probability-theoretic Approach to Modeling a Respirator on Chemically Bound Oxygen

At present, the main prospects for improving the insulating means of respiratory protection are related to the chemical method of oxygen reservation. The arguments in favor of this choice are the high density of oxygen packaging and its self-regulating supply, depending on the physical activity of the person. Usually, the working process in devices on chemically bound oxygen is modeled using mathematical physics methods that solve the so-called sorption dynamics problem. As a result, under given boundary and initial conditions, the concentration of CO2 molecules in the regenerative cartridge turns out to be a deterministic function of time and coordinates. However, the coordinate of the elementary act of sorption is essentially a random variable. The law of its distribution evolves as the absorbing resource of the regenerative cartridge is consumed. Taking into account the above, a probability-theoretic approach to modeling the working process of an insulating breathing apparatus based on chemically bound oxygen was developed. The approach is based on the description by probability theory methods of the random coordinate of the elementary act of chemosorption of a CO2 molecule by potassium peroxide granules and the random lifetime of this molecule in the regenerative cartridge of the respiratory apparatus. The evolution of the initial and central statistical moments of these values is established. The symmetry of their probability density with respect to the permutation of dimensionless arguments is shown, which are the time and distance from the entrance to the regenerative cartridge to the considered layer of chemisorbent. The presence of symmetry increases the speed of numerical experiments by one or two orders of magnitude. Gaussian asymptotics of the process at long times and corrections to it by inverse degrees of dispersion due to asymmetries and excesses of different orders are revealed. This further increases the speed of numerical experiments in computer simulation of the working process of an insulating respirator on chemically bound oxygen.

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Optimization of the thermal regime of the insulating breathing apparatus on chemically bound oxygen

Proceedings of the National Academy of Sciences of Belarus Physical-Technical Series ◽

10.29235/1561-8358-2021-66-1-101-109 ◽

2021 ◽

Vol 66 (1) ◽

pp. 101-109

Author(s):

S. G. Ekhilevskiy ◽

E. P. Potapenko

Keyword(s):

Numerical Experiments ◽

Dead Layer ◽

Technical Solution ◽

Respiratory Protection ◽

Heat Sources ◽

Breathing Apparatus ◽

Air Stream ◽

Exhaled Air ◽

Flow Filtration ◽

Slow Filtration

It is proved that the main prospects for improving the insulating means of respiratory protection are related to the chemical method of oxygen reservation. To increase the efficiency of its use, it is necessary to use the resource of the dead layer of the chemosorbent and prevent the sintering of the granules of the oxygen-containing product under the action of exothermic heat. This is achieved by faster pulsed passage of exhaled air through the frontal layers of the chemosorbent and its slow filtration through the rest of the regenerative cartridge. To evaluate the effectiveness of such a technical solution, a mathematical model of air regeneration in an insulating breathing apparatus with an uneven rate of exhalation filtration through a regenerative cartridge is constructed. The dependencies on the time and coordinate of the concentration of CO2 molecules in the air stream and the share of the use of the protective resource of the regenerative cartridge are obtained. Using numerical experiments, the optimal coordinate of the air flow filtration rate jump was determined to prevent sintering of the granules. Depending on the amount of pressure damping on exhalation and inspiration for the RHS respirator, an increase in the protective effect of the device was determined and a decrease in the power of exothermic heat sources in the frontal layers of the oxygen-containing product was calculated. The results obtained confirm the effectiveness of the considered improvements of the design, which make it possible to increase the reliability of insulating breathing apparatus on chemically bound oxygen and to increase the efficiency of using their protective resource.

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The multitype continuous-time Markov branching process in a periodic environment

Advances in Applied Probability ◽

10.2307/1426495 ◽

1980 ◽

Vol 12 (1) ◽

pp. 81-93 ◽

Cited By ~ 10

Author(s):

B. Klein ◽

P. D. M. MacDonald

Keyword(s):

Continuous Time ◽

Branching Process ◽

Cell Kinetics ◽

Initial Conditions ◽

Random Variable ◽

Diurnal Rhythms ◽

Biological Applications ◽

Regular Case ◽

Markov Branching Process ◽

Periodic Environment

The multitype continuous-time Markov branching process has many biological applications where the environmental factors vary in a periodic manner. Circadian or diurnal rhythms in cell kinetics are an important example. It is shown that in the supercritical positively regular case the proportions of individuals of various types converge in probability to a non-random periodic vector, independent of the initial conditions, while the absolute numbers of individuals of various types converge in probability to that vector multiplied by a random variable whose distribution depends on the initial conditions. It is noted that the proofs are straightforward extensions of the well-known results for a constant environment.

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Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps

Izvestiya VUZ Applied Nonlinear Dynamics ◽

10.18500/0869-6632-2021-29-6-943-952 ◽

2021 ◽

Vol 29 (6) ◽

pp. 943-952

Author(s):

Vasiliy Nechaev ◽

◽

Elena Rybalova ◽

Galina Strelkova ◽

◽

...

Keyword(s):

Coupling Strength ◽

Noise Intensity ◽

Initial Conditions ◽

Random Variable ◽

Inhomogeneous Distribution ◽

Control Parameters ◽

Chimera States ◽

Intensity Parameters ◽

Different Characteristics ◽

Ring Elements

The aim of the research is to study the influence of inhomogeneity in a control parameter of all partial elements in a ring of nonlocally coupled chaotic maps on the possibility of observing chimera states in the system and to compare the changes in regions of chimera realization using different methods of introducing the inhomogeneity. Methods. In this paper, snapshots of the system dynamics are constructed for various values of the parameters, as well as spatial distributions of cross-correlation coefficient values, which enable us to determine the regime observed in the system for these parameters. To improve the accuracy of the obtained results, the numerical studies are carried out for fifty different realizations of initial conditions of the ring elements. Results. It is shown that a fixed inhomogeneous distribution of the control parameters with increasing noise intensity leads to an increase in the range of the coupling strength where chimera states are observed. With this, the boundary lying in the region of strong coupling changes more significantly as compared with the case of weak coupling strength. The opposite effect is provided when the control parameters are permanently affected by noise. In this case increasing the noise intensity leads to a decrease in the interval of existence of chimera states. Additionally, the nature of the random variable distribution (normal or uniform one) does not strongly influence the observed changes in the ring dynamics. The regions of existence of chimera states are constructed in the plane of «coupling strength – noise intensity» parameters. Conclusion. We have studied how the region of existence of chimeras changes when the coupling strength between the ring elements is varied and when different characteristics of the inhomogeneous distribution of the control parameters are used. It has been shown that in order to increase the region of observing chimera states, the control parameters of the elements must be distributed inhomogeneously over the entire ensemble. To reduce this region, a constant noise effect on the control parameters should be used.

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Simulation of a Breathing Apparatus on Chemically Bound Oxygen with a Circular Pendulum Circuit of the Air Duct Part

Occupational Safety in Industry ◽

10.24000/0409-2961-2021-1-46-52 ◽

2021 ◽

pp. 46-52

Author(s):

S.G. Ekhilevskiy ◽

◽

O.V. Golubeva ◽

E.P. Potapenko ◽

◽

...

Keyword(s):

Maximum Permissible Concentration ◽

Protective Action ◽

Dead Layer ◽

Respiratory Protection ◽

Sorbent Layer ◽

Breathing Resistance ◽

Breathing Apparatus ◽

Short Period ◽

The Dead ◽

Made In

At present, the main prospects for improving the insulating means of respiratory protection are associated with the chemical method of oxygen reservation. The arguments in favor of this choice are the high packing density of oxygen and its self-regulating supply, depending on the physical activity of a person. The main schemes of the air duct part of breathing apparatus on chemically bound oxygen are circular and pendulum. The attempt is made in the article to combine the advantages of the circular (small harmful space) and pendulum (small volume of the dead layer) schemes of breathing apparatus on chemically bound oxygen. For these purposes, the formalism method was developed, which allows mathematically and with the help of a computer to simulate the dynamic sorption activity of the regenerative cartridge of a breathing apparatus with a hybrid (circular-pendulum) scheme of the air duct part. The increase in the protective action of the apparatus is determined due to the use of the resource of the dead sorbent layer in the result of the air flow reverse in the pendulum part of the regenerative cartridge. Feasibility of using a hybrid scheme in the self-rescuers with a short period of protective action is shown. The optimal length of the pendulum part is determined, at which the breathing resistance decreases, and the harmful space occupied by the air returning for inhalation without contact with the unreacted layers of the oxygen-containing product is not increased. Its weak dependence on the total length of the regenerative cartridge and the maximum permissible concentration of carbon dioxide in the air returning to inhalation is shown, which makes the circular pendulum scheme realizable in practice.

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Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points

Mathematics ◽

10.3390/math8020230 ◽

2020 ◽

Vol 8 (2) ◽

pp. 230

Author(s):

Juan-Carlos Cortés ◽

Ana Navarro-Quiles ◽

José-Vicente Romero ◽

María-Dolores Roselló

Keyword(s):

Differential Equations ◽

Initial Conditions ◽

Random Variable ◽

Second Order ◽

Singular Points ◽

Linear Differential Equations ◽

Transformation Technique ◽

Order Linear ◽

Bessel Differential Equation ◽

Linear Differential

In this contribution, we construct approximations for the density associated with the solution of second-order linear differential equations whose coefficients are analytic stochastic processes about regular-singular points. Our analysis is based on the combination of a random Fröbenius technique together with the random variable transformation technique assuming mild probabilistic conditions on the initial conditions and coefficients. The new results complete the ones recently established by the authors for the same class of stochastic differential equations, but about regular points. In this way, this new contribution allows us to study, for example, the important randomized Bessel differential equation.

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Rotational Behavior of Cometary-type Bodies

Symposium - International Astronomical Union ◽

10.1017/s0074180900091294 ◽

1992 ◽

Vol 152 ◽

pp. 291-296

Author(s):

Eric Bois ◽

Pascal Oberti ◽

Claude Froeschlé

Keyword(s):

Qualitative Study ◽

Rotational Motion ◽

Numerical Experiments ◽

Initial Conditions ◽

Close Approach ◽

Rotational Behavior ◽

Comet Nucleus ◽

Gravitational Perturbation ◽

The Sun ◽

Sensitivity To Initial Conditions

The present paper deals with a general dynamical qualitative study of the rotational motion for cometary-type bodies submitted to gravitational torques. Numerical experiments of the evolution of comet nucleus attitude have been then performed, including the Sun and Jupiter's disturbing torques in the model. Results show small effects of the solar gravitational perturbation for Halley-type orbits. Only a very close-approach with Jupiter induces notable effects. The latter configuration presents some interesting sensitivity to initial conditions.

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PEDESTRIAN FLOW MODELS WITH SLOWDOWN INTERACTIONS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202513400083 ◽

2013 ◽

Vol 24 (02) ◽

pp. 249-275 ◽

Cited By ~ 20

Author(s):

ALINA CHERTOCK ◽

ALEXANDER KURGANOV ◽

ANTHONY POLIZZI ◽

ILYA TIMOFEYEV

Keyword(s):

Numerical Experiments ◽

Initial Conditions ◽

Coupled System ◽

Coarse Grained ◽

Order System ◽

Stochastic Cellular Automata ◽

Cellular Automata Model ◽

Flow Models ◽

Pedestrian Traffic ◽

Microscopic Stochastic Model

In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for pedestrians moving in two opposite directions. Coarse-grained mesoscopic and macroscopic analogs are derived leading to the coupled system of PDEs for the density of the pedestrian traffic. The obtained first-order system of conservation laws is only conditionally hyperbolic. We also derive higher-order nonlinear diffusive corrections resulting in a parabolic macroscopic PDE model. Numerical experiments comparing and contrasting the behavior of the microscopic stochastic model and the resulting coarse-grained PDEs for various parameter settings and initial conditions are performed. These numerical experiments demonstrate that the nonlinear diffusion is essential for reproducing the behavior of the stochastic system in the nonhyperbolic regime.

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The multitype continuous-time Markov branching process in a periodic environment

Advances in Applied Probability ◽

10.1017/s0001867800033395 ◽

1980 ◽

Vol 12 (01) ◽

pp. 81-93 ◽

Cited By ~ 1

Author(s):

B. Klein ◽

P. D. M. MacDonald

Keyword(s):

Continuous Time ◽

Branching Process ◽

Cell Kinetics ◽

Initial Conditions ◽

Random Variable ◽

Diurnal Rhythms ◽

Biological Applications ◽

Regular Case ◽

Markov Branching Process ◽

Periodic Environment

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Contact lines over random topographical substrates. Part 1. Statics

Journal of Fluid Mechanics ◽

10.1017/s0022112010005975 ◽

2011 ◽

Vol 672 ◽

pp. 358-383 ◽

Cited By ~ 22

Author(s):

NIKOS SAVVA ◽

GRIGORIOS A. PAVLIOTIS ◽

SERAFIM KALLIADASIS

Keyword(s):

Numerical Experiments ◽

Random Variable ◽

Contact Angles ◽

Contact Lines ◽

Substrate Roughness ◽

Random Functions ◽

Flat Substrate ◽

The Subject ◽

Influence Of Substrate ◽

Theoretical Results

We investigate theoretically the statistics of the equilibria of two-dimensional droplets over random topographical substrates. The substrates are appropriately represented as families of certain stationary random functions parametrized by a characteristic amplitude and wavenumber. In the limit of shallow topographies and small contact angles, a linearization about the flat-substrate equilibrium reveals that the droplet footprint is adequately approximated by a zero-mean, normally distributed random variable. The theoretical analysis of the statistics of droplet shift along the substrate is highly non-trivial. However, for weakly asymmetric substrates it can be shown analytically that the droplet shift approaches a Cauchy random variable; for fully asymmetric substrates its probability density is obtained via Padé approximants. Generalization to arbitrary stationary random functions does not change qualitatively the behaviour of the statistics with respect to the characteristic amplitude and wavenumber of the substrate. Our theoretical results are verified by numerical experiments, which also suggest that on average a random substrate neither enhances nor reduces droplet wetting. To address the question of the influence of substrate roughness on wetting, a stability analysis of the equilibria must be performed so that we can distinguish between stable and unstable equilibria, which in turn requires modelling the dynamics. This is the subject of Part 2 of this study.

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The coupling of regenerative processes

Advances in Applied Probability ◽

10.2307/1426618 ◽

1983 ◽

Vol 15 (3) ◽

pp. 531-561 ◽

Cited By ~ 49

Author(s):

Hermann Thorisson

Keyword(s):

Initial Conditions ◽

Random Variable ◽

Total Variation Norm ◽

Absolutely Continuous ◽

Moment Conditions ◽

Common Component ◽

General State Space ◽

Regeneration Times ◽

The Times ◽

Random Times

A distributional coupling concept is defined for continuous-time stochastic processes on a general state space and applied to processes having a certain non-time-homogeneous regeneration property: regeneration occurs at random times So, S1, · ·· forming an increasing Markov chain, the post-Sn process is conditionally independent of So, · ··, Sn–1 given Sn, and the conditional distribution is independent of n. The coupling problem is reduced to an investigation of the regeneration times So, S1, · ··, and a successful coupling is constructed under the condition that the recurrence times Xn+1 = Sn+1 – Sn given that , are stochastically dominated by an integrable random variable, and that the distributions , have a common component which is absolutely continuous with respect to Lebesgue measure (or aperiodic when the Sn's are lattice-valued). This yields results on the tendency to forget initial conditions as time tends to ∞. In particular, tendency towards equilibrium is obtained, provided the post-Sn process is independent of Sn. The ergodic results cover convergence and uniform convergence of distributions and mean measures in total variation norm. Rate results are also obtained under moment conditions on the Ps's and the times of the first regeneration.

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