Mathematical Model of Gas Dilution in Two Phases Flows of Fluid and Gas

The paper describes the flow of a suspension which is a mixture of two phases: liquid and solid granules. The continuum model with microstructure is introduced, which involves two independent kinematic quantities: the velocity vector and the micro-rotation vector. The physical analogy is based on the movement of the suspension between two coaxial cylinders. The inner cylinder is stationary and the outer one rotates with constant angular velocity. This physical analogy enabled a mathematical model in a form of two coupled differential equations with variable coefficients. The aim of the paper is to present the numerical aspect of the solution for this complex mathematical model. It is assumed that the solid granules are identically oriented and that under the influence of the fluid they move translationally or rotate around the symmetry axis but the direction of their symmetry axes does not change. The solution was obtained by the ordinary finite difference method, and then the corresponding sets of points (nodes) were routed by interpolation graphics.

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Mathematical model of transmission dynamics with mitigation and health measures for SARS-CoV-2 infection in European countries

10.21203/rs.3.rs-32248/v1 ◽

2020 ◽

Author(s):

Shweta Sankhwar ◽

Narender Kumar ◽

Ravins Dohare

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

European Countries ◽

Transmission Dynamics ◽

Second Phase ◽

Geographical Regions ◽

Two Phases ◽

Spread Of Infection ◽

And Control

Abstract The pandemic of Severe Acute Respiratory Syndrome Coronavirus (SARS-CoV-2) continue to pose a serious threat to global health resulting in disease COVID-19. No specific drug or vaccine is available against this infection. Therefore, the prevention is only way to reduce the spread of infection. The pandemic needs an enhanced mathematical model, therefore, we propose a SEIAJR compartmental mathematical model to estimate the basic reproduction number (R0 ) and the transmission dynamics of four European countries (Germany, United Kingdom, Switzerland and Spain). The proposed mathematical model incorporates mitigation and healthcare measures as recommended by ECDC (European Centre for Disease Prevention and Control). The simulation of proposed model is done in two phases. First-phase simulation estimates basic reproduction number and mitigation rate according to active infected cases in all four European countries. R0 estimate 2.82 - 3.3 for considered European countries. Second-phase simulation predicts the dynamics of infection on the estimated R0 with varying mitigation rate and constant healthcare rate. This study predicts that no more mitigation is required to invade the infection. The current mitigation and healthcare measures are enough to stop the propogation of infection, however, infection would last by end of July 2020. The developed mathematical model would also be applicable to portray the infection trasmission dynamics for other geographical regions with varying parameters.

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A Mathematical Model of Biological Purification in Aerated Activated Carbon Biofilters

Water Science & Technology ◽

10.2166/wst.1982.0128 ◽

1982 ◽

Vol 14 (6-7) ◽

pp. 599-618 ◽

Cited By ~ 6

Author(s):

G Martin ◽

A-Y Le Roux ◽

P Schulhof

Keyword(s):

Mathematical Model ◽

Biological Activity ◽

Activated Carbon ◽

Probable Mechanism ◽

Second Phase ◽

Adsorption Phenomenon ◽

Biological Purification ◽

Phase Development ◽

Two Phases ◽

Heavy Loads

On the basis of results obtained in the laboratory and in a semi-industrial pilot, this paper outlines the probable mechanism of biological purification on activated carbon. It shows that with small loads, the medium's porosity plays a permanent role in the treatment of a water. The biological activity which develops on the material acts in a complementary fashion, allowing for continuous regeneration of the activated carbon's pores. With heavy loads, there are two phases. During the first, adsorption and biological regeneration are complementary. This phase lasts three to four hours. During the second phase, development of the biomass obstructs the occurrence of the adsorption phenomenon. Substrate is removed on the surface. This second phase lasts from fifteen to twenty hours, until the filter is clogged. After washing, the first phase again enters into operation. A mathematical model is presented. It describes results obtained with small and heavy loads.

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Evolution of Individual Grains in 3d Microstructure Generated by Computational Simulation of Transformations Involving Two Phases

Materials Science Forum ◽

10.4028/www.scientific.net/msf.930.305 ◽

2018 ◽

Vol 930 ◽

pp. 305-310

Author(s):

André Luiz Moraes Alves ◽

Guilherme Dias da Fonseca ◽

Marcos Felipe Braga da Costa ◽

Weslley Luiz da Silva Assis ◽

Paulo Rangel Rios

Keyword(s):

Mathematical Model ◽

Solid State ◽

Phase Transformations ◽

Microstructure Evolution ◽

Initial Phase ◽

Computational Simulation ◽

3D Microstructure ◽

Phase Transform ◽

Two Phases ◽

Individual Grains

In the phase transformations of the solid state, situations can occur in which the initial phase transform forming two or more distinct phases. The exact mathematical model for situations where more than one transformation occurs simultaneously or sequentially was proposed by Rios and Villa. The computational simulation was used to study the evolution and visualization of the possible microstructures that these transformations may present. The causal cone methodology was adopted. The simulations were compared with the analytical model to ensure that they occur as expected. The growth of individual grains of each phase was monitored in 3D microstructure evolution. With this monitoring, was possible to extract useful data able to quantify the simulated 3D microstructure. Quantifying the simulated microstructures increase the possibility of the simulations give to the experimentalist insights about the transformations. In this paper, it is verified that each grain evolves in an individual way, as expected, however their growth is similar.

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Curvature-Induced Spatial Ordering of Composition in Lipid Membranes

Computational and Mathematical Methods in Medicine ◽

10.1155/2017/7275131 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11 ◽

Cited By ~ 5

Author(s):

Shimrit Katz ◽

Sefi Givli

Keyword(s):

Mathematical Model ◽

Phase Separation ◽

Lipid Membranes ◽

Phase Segregation ◽

Geometric Features ◽

Two Component ◽

Modulated Phase ◽

Spatial Ordering ◽

The Difference ◽

Two Phases

Phase segregation of membranal components, such as proteins, lipids, and cholesterols, leads to the formation of aggregates or domains that are rich in specific constituents. This process is important in the interaction of the cell with its surroundings and in determining the cell’s behavior and fate. Motivated by published experiments on curvature-modulated phase separation in lipid membranes, we formulate a mathematical model aiming at studying the spatial ordering of composition in a two-component biomembrane that is subjected to a prescribed (imposed) geometry. Based on this model, we identified key nondimensional quantities that govern the biomembrane response and performed numerical simulations to quantitatively explore their influence. We reproduce published experimental observations and extend them to surfaces with geometric features (imposed geometry) and lipid phases beyond those used in the experiments. In addition, we demonstrate the possibility for curvature-modulated phase separation above the critical temperature and propose a systematic procedure to determine which mechanism, the difference in bending stiffness or difference in spontaneous curvatures of the two phases, dominates the coupling between shape and composition.

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A Mathematical Model of Measles with Vaccination and Two Phases of Infectiousness

IOSR Journal of Mathematics ◽

10.9790/5728-101495105 ◽

2014 ◽

Vol 10 (1) ◽

pp. 95-105 ◽

Cited By ~ 7

Author(s):

Ochoche J. M. ◽

◽

Gweryina R. I.

Keyword(s):

Mathematical Model ◽

Two Phases

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Simulation of the Ductile Iron Solidification Using a Cellular Automaton

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.457.330 ◽

2010 ◽

Vol 457 ◽

pp. 330-336 ◽

Cited By ~ 7

Author(s):

Andriy A. Burbelko ◽

Edward Fraś ◽

Daniel Gurgul ◽

Wojciech Kapturkiewicz ◽

Jorge Antonio Sikora

Keyword(s):

Mathematical Model ◽

Cellular Automaton ◽

Ductile Iron ◽

Calculation Method ◽

Eutectic Composition ◽

Eutectic Solidification ◽

Proposed Model ◽

Two Phases ◽

The Mathematical Model ◽

Method Model

The mathematical model of the globular eutectic solidification in 2D was designed. Pro¬posed model is based on the Cellular Automaton Finite Differences (CA-FD) calculation method. Model has been used for studies of the primary and of globular eutectic grains growth during the ductile iron (DI) solidification. A hyper-eutectic composition has been analyzed but this model can be used in the solidification modeling of hypo- and eutectic DI. The proposed model makes possible to trace the unrestricted growth of primary grains of two phases from the liq¬uid, transition from free to cooperative solidification, and cooperative growth of globular eutectic.

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Mechanical Properties of Aluminum Foam-Polymer Multifunctional Hybrid Materials

Volume 14: Processing and Engineering Applications of Novel Materials ◽

10.1115/imece2009-12861 ◽

2009 ◽

Cited By ~ 1

Author(s):

James R. Hadley ◽

Nassif E. Rayess ◽

Nihad Dukhan ◽

Dan Q. Houston

Keyword(s):

Mechanical Properties ◽

Mathematical Model ◽

Injection Molding ◽

Relative Density ◽

Polymer Composite ◽

Hybrid Materials ◽

Hybrid Material ◽

Aluminum Foam ◽

Thermoplastic Polymer ◽

Two Phases

A hybrid material consisting of an interpenetrating phase composite of aluminum foam and thermoplastic polymer was made and tested for its basic tensile mechanical properties. The material was made by injection molding a polymer (two polypropylenes and an acetal were used) through a Duocell aluminum foam (10% relative density and 10, 20 and 40 pores per inch linear densities). The material is referred to as an Aluminum Foam Polymer Composite (AFPC) and involves the aluminum foam and the polymer occupying the same volume. The continuous, interconnected morphologies of the two phases (aluminum foam and polymer) sets this type of material apart from regular composites. The AFPC exhibited an increase in stiffness, a reduction in strength and less ductility than the parent polymer. A basic mathematical model and a discussion of the physics were used to shed some light on the behavior of this material.

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ANYLSIS OF PIPE MECHANISM LOCOMOTION

TECHNICAL SCIENCES AND TECHNOLOG IES ◽

10.25140/2411-5363-2019-4(18)-36-42 ◽

2019 ◽

pp. 36-42

Author(s):

Filip Filakovsky ◽

Ivan Virgala

Keyword(s):

Mathematical Model ◽

Target Setting ◽

Time Consumption ◽

Long Time ◽

Cooling Phase ◽

Two Phases ◽

Inspection Tasks ◽

Spring Mechanism ◽

Actual Target ◽

The Mathematical Model

Urgency of the research. Inspection tasks are frequently and very important from the view of safety. From this reason the topic is very actual. Target setting. The aim of the study is to investigate new kind of pipe mechanism based on differential frictions of bristles. Actual scientific researches and issues analysis. There are many mechanisms for inspection of narrow or hard-to-reach areas. Many of them are based on wheels or tank belt. This research investigates bristle-based pipe mechanism. Uninvestigated parts of general matters defining. Nowadays, the SMA materials or different kind of memory materials are always in the focus of researchers. The research objective is to develop and experimental test the new kind of mechanism based on SMA as well as steel spring mechanism. The statement of basic materials. The locomotion divided into two phases is introduced. Based on this locomotion the mathematical model was derived. Assuming mathematical model was developed control system for experimental pipe mechanism. Conclusions. The results of the experiments shows problems with cooling phase due to its long time consumption. For cooling was used external device. The cooling phase significantly decrease average velocity of pipe mechanism. The advantage of this kind of mechanism is simple control and utilization for the pipe with small diameters.

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Precipitation of NiHfsi phase in NiAl single crystals containing Hf

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100139032 ◽

1995 ◽

Vol 53 ◽

pp. 532-533

Author(s):

A. Garg ◽

R. D. Noebe ◽

R. Darolia

Keyword(s):

High Temperature ◽

Single Crystals ◽

High Temperature Strength ◽

Bridgman Technique ◽

Shell Mold ◽

Third Phase ◽

Unknown Phase ◽

Transmission Electron ◽

Two Phases ◽

Nial Matrix

Small additions of Hf to NiAl produce a significant increase in the high-temperature strength of single crystals. Hf has a very limited solubility in NiAl and in the presence of Si, results in a high density of G-phase (Ni16Hf6Si7) cuboidal precipitates and some G-platelets in a NiAl matrix. These precipitates have a F.C.C structure and nucleate on {100}NiAl planes with almost perfect coherency and a cube-on-cube orientation-relationship (O.R.). However, G-phase is metastable and after prolonged aging at high temperature dissolves at the expense of a more stable Heusler (β'-Ni2AlHf) phase. In addition to these two phases, a third phase was shown to be present in a NiAl-0.3at. % Hf alloy, but was not previously identified (Fig. 4 of ref. 2 ). In this work, we report the morphology, crystal-structure, O.R., and stability of this unknown phase, which were determined using conventional and analytical transmission electron microscopy (TEM).Single crystals of NiAl containing 0.5at. % Hf were grown by a Bridgman technique. Chemical analysis indicated that these crystals also contained Si, which was not an intentional alloying addition but was picked up from the shell mold during directional solidification.

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