scholarly journals Geometry optimization, factors screening, and introduce a predicting mathematical model of inhalation exposure chamber’s performance.

2020 ◽  
Author(s):  
Hassan Rajabi-Vardanjani ◽  
Hassan Asilian-Mahabadi ◽  
Morteza Bayareh ◽  
Morteza Sedehi
Keyword(s):  
Mathematical Model ◽  
Stable Distribution ◽  
Particle Concentration ◽  
Inhalation Exposure ◽  
Geometry Optimization ◽  
Inlet Concentration ◽  
Gas Density ◽  
Cylindrical Section ◽  
The Matrix ◽  
Test Atmosphere

Abstract Background Optimizing the geometry of an inhalation exposure chamber (IEC) results in a uniform and stable distribution of the test atmosphere and enables the modeling of its performance. This study was conducted for the first time to optimize and model the performance of an IEC.Methods The current study was performed on the initial design of the ASRA chamber and to optimize and model it. The matrix of experiments was determined by the design expert software (DE7). The mean of particle concentration (MPC) in the respiratory zone of animals as the response variable, and height of the cylindrical section of the chamber, carrier gas density, inlet concentration, and particle aerodynamic diameter ( da ) as independent variables were considered. Experiments were performed by numerical simulation using ANSYS Workbench package. Particle concentration sampling was measured in 40 points at the opening of each holder in CFD-Post software. To determine the optimal range of the chamber's height, the different of MPC among the holders’ opening was investigated by the ANOVA test. The final mathematical model was achieved by analyzing the response variables in DE7.Results Thirty designs in five geometries with different heights were introduced as the matrix of experiments by DE7. The optimal height was obtained 2-2.5 times the radial of the cylindrical section. Analysis of the results suggested a linear model (2FI) with coefficients of recognition higher than 99%. The final model was significant with the presence of the inlet concentration and da . Gas density and height had no significant effect and were removed ( P >0.05).Conclusion The optimization of the geometry of the ASRA chamber resulted in a uniform and stable distribution of the particles and provided an accurate mathematical model to predict the particle concentration in the target zone.

A NUMERICAL PROOF THAT CERTAIN CELLS FOLLOW THE TRAILS OF THE DIFFUSIONS OF SOME CHEMICALS IN THE EXTRACELLULAR MATRIX

2021 ◽  
pp. 2150027
Author(s):  
İREM ÇAY ◽  
SERDAL PAMUK
Keyword(s):  
Mathematical Model ◽  
Extracellular Matrix ◽  
Tumor Angiogenesis ◽  
Numerical Solutions ◽  
Extra Cellular Matrix ◽  
The Matrix ◽  
Good Agreement ◽  
Cellular Matrix

In this work, we obtain the numerical solutions of a 2D mathematical model of tumor angiogenesis originally presented in [Pamuk S, ÇAY İ, Sazci A, A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix, Math Biosci 306:32–48, 2018] to numerically prove that the certain cells, the endothelials (EC), pericytes (PC) and macrophages (MC) follow the trails of the diffusions of some chemicals in the extracellular matrix (ECM) which is, in fact, inhomogeneous. This leads to branching, the sprouting of a new neovessel from an existing vessel. Therefore, anastomosis occurs between these sprouts. In our figures we do see these branching and anastomosis, which show the fact that the cells diffuse according to the structure of the ECM. As a result, one sees that our results are in good agreement with the biological facts about the movements of certain cells in the Matrix.

FORC analysis of magnetically soft microparticles embedded in a polymeric elastic environment

2022 ◽  
Author(s):  
Dmitry Yu Borin ◽  
Mikhail V Vaganov
Keyword(s):  
Particle Concentration ◽  
Magnetic Hysteresis ◽  
Magnetic Response ◽  
Soft Matrix ◽  
First Order ◽  
Matrix Elasticity ◽  
Intrinsic Coercivity ◽  
The Matrix ◽  
Soft Particles ◽  
Elastomer Composites

Abstract First-order reversal curve (FORC) analysis allows one to investigate composite magnetic materials by decomposing the magnetic response of a whole sample into individual responses of the elementary objects comprising the sample. In this work, we apply this technique to analysing silicone elastomer composites reinforced with ferromagnetic microparticles possessing low intrinsic coercivity. Even though the material of such particles does not demonstrate significant magnetic hysteresis, the soft matrix of the elastomers allows for the translational mobility of the particles and enables their magnetomechanical hysteresis which renders into a wasp-waisted major magnetization loop of the whole sample. It is demonstrated that the FORC diagrams of the composites contain characteristic wing features arising from the collective hysteretic magnetization of the magnetically soft particles. The influence of the matrix elasticity and particle concentration on the shape of the wing feature is investigated, and an approach to interpreting experimental FORC diagrams of the magnetically soft magnetoactive elastomers is proposed. The experimental data are in qualitative agreement with the results of the simulation of the particle magnetization process obtained using a model comprised of two magnetically soft particles embedded in an elastic environment.

scholarly journals Mathematical model of methane driven by hydraulic fracturing in gassy coal seams

2020 ◽  
Vol 38 (3-4) ◽  
pp. 127-147
Author(s):  
Weiyong Lu ◽  
Bingxiang Huang
Keyword(s):  
Mathematical Model ◽  
Hydraulic Fracturing ◽  
Pore Pressure ◽  
Hydraulic Fracture ◽  
Water Saturation ◽  
Reduction Rate ◽  
Space Time ◽  
Matrix Block ◽  
The Matrix ◽  
Pore Pressure Gradient

During hydraulic fracturing in gassy coal, methane is driven by hydraulic fracturing. However, its mathematical model has not been established yet. Based on the theory of ‘dual-porosity and dual-permeability’ fluid seepage, a mathematical model is established, with the cleat structure, main hydraulic fracture and methane driven by hydraulic fracturing considered simultaneously. With the help of the COMSOL Multiphysics software, the numerical solution of the mathematical model is obtained. In addition, the space–time rules of water and methane saturation, pore pressure and its gradient are obtained. It is concluded that (1) along the direction of the methane driven by hydraulic fracturing, the pore pressure at the cleat demonstrates a trend of first decreasing and later increasing. The pore pressure gradient exhibits certain regional characteristics along the direction of the methane driven by hydraulic fracturing. (2) Along the direction of the methane driven by hydraulic fracturing, the water saturation exhibits a decreasing trend; however, near the cleat or hydraulic fracture, the water saturation first increases and later decreases. The water saturation in the central region of the coal matrix block is smaller than that of its surrounding region, while the saturation of water in the entire matrix block is greater than that in the cleat or hydraulic fracture surrounding the matrix block. The water saturation at the same space point increases gradually with the time progression. The space–time distribution rules of methane saturation are contrary to those of the water saturation. (3) The free methane driven by hydraulic fracturing includes the original free methane and the free methane desorbed from the adsorption methane. The reduction rate of the adsorption methane is larger than that of free methane.

scholarly journals Geometry optimization of uncoated silicon microcantilever-based gas density sensors

2015 ◽  
Vol 208 ◽  
pp. 600-607 ◽  
Author(s):  
M.T. Boudjiet ◽  
J. Bertrand ◽  
F. Mathieu ◽  
L. Nicu ◽  
L. Mazenq ◽  
...  
Keyword(s):  
Geometry Optimization ◽  
Gas Density

ALGORITHMIC SUPPORT FOR SELECTING OPTIMAL TRAFFIC ROUTE OF MOTOR CONVOY OF RAPID REACTION BORDER COMMAND POST

2019 ◽  
pp. 25-35
Author(s):  
O. Borovyk ◽  
V. Kupelskiy
Keyword(s):  
Mathematical Model ◽  
Traffic Safety ◽  
The State ◽  
Optimal Route ◽  
The Road ◽  
Starting Point ◽  
Branching Points ◽  
The Matrix ◽  
The Status ◽  
Speed Function

The rapid response border commandant's office is a structural unit of the border detachment, designed to protect and strengthen the protection of a certain section of the state border, and must quickly redeploy its forces and assets. The success of the tasks assigned to the unit depends largely on the timeliness of arrival at the destination. Operational transportation of a significant amount of weapons, personnel and dissimilar cargoes on land is carried out using equipment. At the preparatory stage of the organization of transportation, the problem of forming the optimal composition of the convoy of equipment is solved. The existing road network provides a sufficiently large number of traffic routes between the starting and ending points. Moreover, this takes place even for insignificant distances between points of departure and destination. The specified conditions for multivariance in the selection. In addition, the choice of the route of movement depends on many auxiliary conditions: driver training, technical characteristics and reliability of vehicles, traffic safety, road and environmental conditions, distance and timing of transportation, and the like. Poor accounting of these factors in the aggregate may lead to the choice of an irrational route of movement, will not ensure the timely arrival of the unit at the destination, and may lead to the failure to fulfill certain tasks. Therefore, the task of choosing the optimal route of movement of the column of equipment is relevant. At the substantive level, the task looks like the justification of the mathematical model for choosing the optimal route for the column of equipment, if the criterion of optimality is minimizing the time it takes to move from the starting point to the destination. The authors formed a mathematical model of the given problem, proposed an algorithm for its solution for three cases: discrete-stochastic, discretely-determined and continuously-indefinite, and the corresponding software was developed. The choice of routes is carried out for three options, taking into account the fact that the change in the weights of the ribs can be carried out: at times when the column is at a certain vertex of the graph, and the update of the matrix of weights is carried out precisely at these moments. This is the case when a decision on the further route of movement is formed at the road branching points, taking into account the situation, the status of individual sections changes dynamically and data for which appears periodically; at times when the column is at a certain vertex of the graph, and for these moments, the matrix of weights that will occur when the column hits the vertex are known in advance. This is the case when a decision on the route of movement can be formed at the beginning of the movement, taking into account the known situation on the state of the roads, dynamically change, but data on which can be taken into account in advance; randomly depending on the speed of the column at a fixed point in time for which the column speed function is known.

Isolation Ratio and Particle Performance Measurement of a SMIF System

1997 ◽  
Vol 40 (6) ◽  
pp. 23-28
Author(s):  
Benjamin Liu ◽  
Seong-Ho Yoo
Keyword(s):  
Performance Evaluation ◽  
Particle Concentration ◽  
Experimental System ◽  
The Other ◽  
High Isolation ◽  
System A ◽  
Interface System ◽  
Self Powered ◽  
Test Atmosphere ◽  
Measured Particle

This paper discusses the performance evaluation of a SMIF (Standard Mechanical Interface) system. A two-chamber experimental system is used with one chamber providing the test atmosphere of the cleanroom and the other providing the test atmosphere of the minienvironment. The cleanroom atmospher can be varied by adjusting the amount of particles injected into the chamber. Particle concentration ranges from 1,000/ft-3 to 10 million/ft3 can be created in the chamber to simulate different cleanroom conditions. The atmosphere of the second chamber is maintained at Class I or better equivalent by means of a self-powered ultra-low penetration air (ULPA) filter blower unit. By means of this system, the ability of the SMIF system to isolate the contaminants in the cleanroom atmosphere from the minienvironment atmosphere was measured. In addition, the particles added to the wafer during wafer cassette handling by the SMIF-Arm were also measured by a wafer scanner. The results indicate that the SMIF system tested is capable of providing extremely high isolation ratios in terms of its ability to isolate the cleanroom atmosphere from the atmosphere of the minienvironment. Isolation ratios in excess of 1 million to 1 or better have been measured. The measured particle per wafer per pass (PWP) numbers were generally around 0.02 or less for most wafers, with the average at 0.0118.

scholarly journals MENENTUKAN DETERMINAN SUATU MATRIKS DENGAN METODE CHIO

2016 ◽  
Vol 6 (1:) ◽  
pp. 33-40
Author(s):  
Asep Saepudin
Keyword(s):  
Mathematical Model ◽  
Matrix Element ◽  
Matrix Theory ◽  
Human Life ◽  
Equation System ◽  
Inverse Matrix ◽  
Matrix Methods ◽  
Linear Equation System ◽  
The Matrix ◽  
Mathematical Sciences

Matrix theory is a branch of linear algebra that discussed in the mathematical sciences. Mathematical sciences play an important role in human life, it is necessary to solve problems that can not be solved directly. Thus, the problem can be transformed into the form of a mathematical model. One is the SPL (Linear Equation System). Various methods can be used to solve it. But for the SPL with a large variable can be solved by matrix methods, namely the inverse matrix. In the inverse matrix of the determinants involved. If the search value that ordo major determinant of the matrix (𝑛×𝑛), it would require an effective method. One is the method of Chio. Chio method can be applied to all square matrixas long as the element is 𝑎11 not equal to zero (𝑎11≠0). Chio method of calculating the determinant of the matrix by decomposing determinant will look into sub-determinant of degree two (2×2) using the matrix element row 1 and column 1 as pointof departure. The decomposition is performed using the following sized matrix:   Keywords: Matrix, Matrix Determinant, Chio method.

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