scholarly journals Analytical calculation of time of reaching specific values based on visibility loss during a fire

2018 ◽  
Vol 193 ◽  
pp. 03007 ◽  
Author(s):  
Sergei Kolodyazhniy ◽  
Vladimir Kozlov
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Ventilation System ◽  
Analytical Calculation ◽  
Critical Time ◽  
Original Data ◽  
Critical Value ◽  
Time Intervals ◽  
Evacuation Time ◽  
Analytical Formulas

Using an integral mathematical model of a fire considering the assumptions typical of a starting stage of a fire, analytical dependencies were obtained for determining the time of reaching a critical value of the density of a smoke screen in a premises with a fire epicenter and adjoining premises. By means of analytical formulas for determining critical evacuation time intervals based on visibility loss, table values for different parameters that are included in the original equations were obtained. Simple engineering analytical solutions that describe the dynamics of smoke formation in premises in case of a fire when used in a certain combination are presented. The obtained dependencies allow one to identify the critical time of evacuation with no use of special PC software as well as to obtain original data without calculating an anti-smoke ventilation system.

Rotational Characteristics of the Green Solar Corona: 1947-1991

1994 ◽  
Vol 144 ◽  
pp. 139-141 ◽  
Author(s):  
J. Rybák ◽  
V. Rušin ◽  
M. Rybanský
Keyword(s):  
Solar Corona ◽  
World Wide ◽  
Rotation Period ◽  
Original Data ◽  
Coronal Emission ◽  
Time Intervals ◽  
Data Set ◽  
The World ◽  
Coronal Emission Line ◽  
Homogeneous Data

AbstractFe XIV 530.3 nm coronal emission line observations have been used for the estimation of the green solar corona rotation. A homogeneous data set, created from measurements of the world-wide coronagraphic network, has been examined with a help of correlation analysis to reveal the averaged synodic rotation period as a function of latitude and time over the epoch from 1947 to 1991.The values of the synodic rotation period obtained for this epoch for the whole range of latitudes and a latitude band ±30° are 27.52±0.12 days and 26.95±0.21 days, resp. A differential rotation of green solar corona, with local period maxima around ±60° and minimum of the rotation period at the equator, was confirmed. No clear cyclic variation of the rotation has been found for examinated epoch but some monotonic trends for some time intervals are presented.A detailed investigation of the original data and their correlation functions has shown that an existence of sufficiently reliable tracers is not evident for the whole set of examinated data. This should be taken into account in future more precise estimations of the green corona rotation period.

A reciprocating permanent magnetic actuator for driving magnetic micro robots in fluids

2021 ◽  
pp. 095440622110145
Author(s):  
Chuan Qu ◽  
Yong-Chen Pei ◽  
Qing-Yuan Xin ◽  
Zhen-Xing Li ◽  
Long Xu
Keyword(s):  
Permanent Magnet ◽  
Analytical Calculation ◽  
Magnetic Actuator ◽  
Cross Sectional ◽  
Permanent Magnetic Actuator ◽  
Element Simulation ◽  
Micro Robot ◽  
Analytical Formulas ◽  
Motion Performance ◽  
Motion Characteristics

Magnetic-based driving applications are receiving increasing attention. This study proposed a novel reciprocating permanent magnetic actuator (PMA) to manipulate magnetic micro robots to impact and clear blockages inside fluid pipes in a linear path. The PMA consisted of a cylindrical permanent magnet and a crank slider structure. A straight pipe with a circular cross-sectional area was located in front of the actuator to study the driving performance of PMA. A micro permanent magnet with a cylinder shape was employed as a working robot for manipulation inside the pipe. Firstly, analytical formulas were derived to obtain the magnetic driving force acting on the micro robot and determine the most suitable magnet configuration. The finite element simulation verified the analytical calculation. The developed reciprocating PMA prototype was then introduced, and the PMA and micro robot’s motion performance was analysed. Lastly, preliminary experiments were carried out for evaluating the micro robot’s motion characteristics. Performance tests for different excitation frequencies, flow rates, viscosities, and axial distances, indicating that PMA could manipulate the magnetic micro robot inside the pipe. The results confirmed that the developed PMA could effectively drive the micro robot with the advantage of consecutive magnetic driving. Especially, the micro robot featured good flexibility, rapid response, and a simple structure, suggesting that this micro robot may play an important role in industrial and medical applications, such as blockage elimination and thrombus clearance.

scholarly journals Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Caroline W. Kanyiri ◽  
Kimathi Mark ◽  
Livingstone Luboobi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Drug Resistance ◽  
Stability Analysis ◽  
Influenza A ◽  
Reproduction Number ◽  
Critical Value ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
High Morbidity

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

Modeling the Growth of Salmonella in Cut Red Round Tomatoes as a Function of Temperature

2010 ◽  
Vol 73 (8) ◽  
pp. 1502-1505 ◽  
Author(s):  
WENJING PAN ◽  
DONALD W. SCHAFFNER
Keyword(s):  
Mathematical Model ◽  
Growth Rates ◽  
Low Temperatures ◽  
Safety Concern ◽  
Time Intervals ◽  
Salmonella Serotypes ◽  
Increasing Temperature ◽  
Incubation Temperatures ◽  
Raw Poultry ◽  
The Relationship

Tomato-associated Salmonella outbreaks have recently become a significant food safety concern. Temperature abuse of cut tomatoes may have played a role in some of these outbreaks. The purpose of this study was to develop a mathematical model to describe the growth of Salmonella on cut tomatoes at various temperatures. Four Salmonella serotypes (Typhimurium, Newport, Javiana, and Braenderup) obtained from previous tomato-linked cases of salmonellosis were used in this study. These four serotypes were cultured separately, combined into a cocktail, and inoculated onto whole red round tomatoes and allowed to dry overnight. The tomatoes were then cut into pieces and incubated at a predetermined range of temperatures (10, 12.5, 15, 17.5, 20, 22.5, 25, 27.5, 30, and 35°C). Salmonella concentration was measured at specified time intervals to determine the growth curve for Salmonella on cut tomatoes at each temperature. The growth rates were calculated using DMFit and used to build a mathematical model to illustrate the relationship between the growth rates of Salmonella on tomatoes and incubation temperatures from 10 to 35°C. The resulting model compared favorably with a Salmonella growth model for raw poultry developed by our laboratory. The Pathogen Modeling Program underpredicted growth at low temperatures and overpredicted growth at high temperatures. ComBase predicted consistently slower growth rates than were observed in tomatoes but showed parallel increases in growth rate with increasing temperature.

scholarly journals Analysis of Pure Bending Vertical Deflection of Improved Composite Box Girders with Corrugated Steel Webs

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Chi Ma ◽  
Shi-zhong Liu ◽  
Jin Di ◽  
Rui-jie Zhang
Keyword(s):  
Shear Deformation ◽  
Analytical Solutions ◽  
Analytical Calculation ◽  
Load Condition ◽  
Width Ratio ◽  
Shear Lag ◽  
Vertical Deflection ◽  
Box Girders ◽  
Concentrated Load ◽  
Span Width

Steel bottom plates are applied as replacements for the concrete bottom plates in order to reduce the dead weight of the composite box girders with corrugated steel webs and steel bottom plates (CSWSB). Due to the change in the material, the previous analytical calculation methods of vertical deflection of composite box girders with corrugated steel webs (CSWs) cannot be directly applied to the improved composite box girders. The shear lag warpage displacement function was derived based on the shear deformation laws of the upper flange and the bottom plates of the improved composite box girders. The equations for the calculation of the shear deformation and the additional deflection due to the shear lag of continuous and simply supported composite box girders with CSWSB under concentrated and uniformly distribution loads were derived by considering the double effects of the shear lag and the shear deformations of the top and the bottom plates with different elastic moduli. The analytical solutions of the vertical deflection of the improved composite box girders include the theory of the bending deflection of elementary beams, shear deformation of CSWs, and the additional deflection caused by the shear lag. Based on the theoretical derivation, an analytical solution method was established and the obtained vertical deflection analytical solutions were compared with the finite element method (FEM) calculation results and the experimental values. The analytical equations of vertical deflection under the two supporting conditions and the two load cases have verified the analyses and the comparisons. Further, the additional deflections due to the shear lag and the shear deformation are found to be less than 2% and 34% of the total deflection values, respectively. Moreover, under uniform distributed load conditions, the deflection value was found to be higher than that of the under concentrated load condition. It was also found that the ratio of the deflection caused by the shear lag or the shear deformation to the total deflection decreased gradually with the increase in the span width ratio. When the value of the span width ratio of a single box and single chamber composite box girder with CSWSB was equal to or greater than 8, the deflections caused by the shear lag and the shear deformation could be ignored.

scholarly journals Optimizing air velocity for the underfloor forced ventilation to protect a refrigerated warehouse from frost heaving

2018 ◽  
Vol 38 (3) ◽  
pp. 321-327
Author(s):  
Jingfu Jia ◽  
Manjin Hao ◽  
Jianhua Zhao
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Natural Ventilation ◽  
Ventilation System ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Frost Heave ◽  
Forced Ventilation ◽  
Air Velocity ◽  
Set Up

Forced or natural ventilation is the most common measure of frost heave protection for refrigerated warehouse floor. To optimize air velocity for the underfloor forced ventilation system of refrigerated warehouse, a steady state three-dimensional mathematical model of heat transfer is set up in this paper. The temperature fields of this system are simulated and calculated by CFD software PHOENICS under different air velocity, 1.5m/s, 2.5m/s or 3.5m/s. The results show that the optimized air velocity is 1.5m/s when the tube spacing is 1.5m.

scholarly journals A Mathematical Model of Epidemics—A Tutorial for Students

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1174 ◽  
Author(s):  
Yutaka Okabe ◽  
Akira Shudo
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Sir Model ◽  
Exact Analytical Solutions ◽  
The Mathematical Model ◽  
Epidemic Diseases

This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

scholarly journals Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem

2014 ◽  
Author(s):  
Mohammad I. Younis
Keyword(s):  
Analytical Solutions ◽  
Galerkin Approximation ◽  
Single Mode ◽  
Beam Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Analytical Formulas ◽  
Euler Bernoulli Beam ◽  
Analytical Expressions ◽  
Multi Mode

We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data in the literature and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximations they are based on. In such cases, multi-mode reduced order models need to be utilized.

The effect of hydrodynamic dispersion on reactive flows in porous media

2001 ◽  
Vol 12 (5) ◽  
pp. 557-569 ◽  
Author(s):  
J. CHADAM ◽  
P. ORTOLEVA ◽  
Y. QIN ◽  
R. STAMICAR
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Critical Value ◽  
Reactive Flow ◽  
Hydrodynamic Dispersion ◽  
Reaction Interface ◽  
Shape Stability ◽  
Linearized Problem ◽  
New Feature ◽  
Moving Free Boundary

The shape stability of the reaction interface for reactive flow in a porous medium is investigated. Previous work showed that the Reaction-Infiltration Instability could cause the reaction zone to lose stability when the Peclet number exceeded a critical value. The new feature of this study is to include a velocity-dependent hydrodynamic dispersion. A mathematical model for this phenomenon is given in the form of a moving free-boundary problem. The spectrum of the linearized problem is obtained, and the related analysis and numerical calculations show that the onset of the instability is not eliminated by the new dispersive terms. The details of analysis show that the instability is reduced especially by the transverse dispersion.

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