Mathematical model of the short arc phenomena at the initial stage

2002 ◽  
Author(s):  
S.N. Kharin
Keyword(s):  
Mathematical Model ◽  
Initial Stage ◽  
Short Arc

scholarly journals A Modeling Study of the Initial Formation of Polar Lows in the Vicinity of the Arctic Front

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Igor Mingalev ◽  
Konstantin Orlov ◽  
Victor Mingalev
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Lower Atmosphere ◽  
The Arctic ◽  
Height Range ◽  
Limited Region ◽  
Polar Lows ◽  
Initial Stage ◽  
Polar Low ◽  
Arctic Front

A regional mathematical model of the wind system of the lower atmosphere, developed recently in the Polar Geophysical Institute, is applied to investigate the initial stage of the formation of polar lows at latitudes of the European Arctic. The mathematical model is based on numerical solving of nonsimplified gas dynamic equations and produces three-dimensional distributions of the atmospheric parameters in the height range from 0 to 15 km over a limited region of the Earth’s surface. Simulation results indicated that the origin of a convexity in the configuration of the arctic front can lead to the formation of a polar low during the period of about one day.

scholarly journals Discrete mathematical model of travelling wave of conveyor transport

2020 ◽  
Vol 168 ◽  
pp. 00030
Author(s):  
Viktor Kravets ◽  
Volodymyr Samusia ◽  
Dmytro Kolosov ◽  
Kostiantyn Bas ◽  
Serhii Onyshchenko
Keyword(s):  
Mathematical Model ◽  
Travelling Wave ◽  
Technical Parameters ◽  
Wave Transport ◽  
Initial Stage ◽  
Discrete Phase ◽  
New Type ◽  
Technical Possibility ◽  
Discrete Mathematical Model ◽  
Phase Angles

A mathematical model of a travelling wave in a matrix form is constructed. A degree of discreteness of the travelling wave and corresponding steps in phase and length are introduced. Asymmetric, unified matrices are compiled, which represent a generalized travelling wave, depending on a degree of discreteness. A generalized, dimensionless travelling wave is transformed into a required one with dimensions by specified technical parameters: amplitude and wavelength that is realized. A dependency of coordinates of points of a plane discrete travelling wave and discrete phase angles is established. A dependency of angular (phase) velocity and velocity of the travelling wave, which corresponds to the known results, is established. The presented matrix mathematical model is considered as an initial stage of technical possibility to realize a continuous travelling wave in a discrete form when developing a new type of transportation – wave transport.

Mathematical Model for Closed-Form Solution of Parameters of Cylinder Exhaust Port in Variable-Stroke Engine

2010 ◽  
Vol 97-101 ◽  
pp. 2724-2727
Author(s):  
Li Ming Di ◽  
Chun Jing Yang ◽  
Yong Sheng Zhao
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Alignment Method ◽  
Specific Time ◽  
Exhaust Port ◽  
Initial Stage ◽  
Relative Errors ◽  
Stroke Engine

A mathematical model for getting the closed-form solution of main parameters of cylinder exhaust port is present, based on a few known parameters of variable-stroke engine (VSE). Considering lack of parameters in the initial stage of design, empirical formula is applied to solve the initial specific time-area value of exhaust port, and the initial port timing angle is solved by using logarithmic alignment method, thereby height and width of the exhaust port can be solved, then the precise specific time-area value and port timing angle are solved by using the coefficient calculation method and logarithmic alignment method respectively, so that the relative errors between initial and precise values of specific time-area value and port timing angle are defined as the relative errors of the mathematical model. Application examples show that the relative errors of the model is less than 3%.

scholarly journals SIMULATION MODEL OF THE INFORMATION TECHNOLOGY FOR THE TECHNICAL DIAGNOSIS OF THE IMPULSE HEAT MACHINE

2020 ◽  
Vol 2 (61) ◽  
pp. 95-103
Author(s):  
Ye. Dobrynin ◽  
◽  
V. Davydov ◽  
Keyword(s):  
Mathematical Model ◽  
Information Technology ◽  
Simulation Model ◽  
Combustion Model ◽  
Combustion Gas ◽  
Technical Diagnosis ◽  
Initial Stage ◽  
Attenuation Rate ◽  
Propagation Law ◽  
Two Dimensional Flow

A simulation model of the information technology for the technical diagnosis of the impulse heat machine has been developed and studied. The model incorporates such mathematical models as barrel energy; ballistic wave parameters; pressure of powder gases blasting from the barrel face behind the shell and the shot blast and determination of its attenuation rate. The information model enables to obtain parameters of the ballistic wave that accompanies an shot. A simplified mathematical model allows of determining the oblique shock inclination angle to the stream speed depending on Mach number which is represented by the two-dimensional flow wedge. The model of powder gas pressure blasting from the barrel face behind the shell is based on the energy conservation law for the compresses powder gases and makes it possible to avoid solution of the complicated modified Lagrange problem. While the shot blast propagates, at the initial stage it is possible that this blast reaches the record point earlier than the ballistic wave. Such phenomenon can be avoided by selecting a proper angle. The adopted mathematical model determines the shot blast propagation law and allows of evaluating the shot blast speed attenuation. The barrel energy model was based on the solution of the inverse problem of pyrostatics by determining a composition of the combustion gas of the shot. The applied approach provided for use of the model that describes combustion of the fuel and oxidizer mixture. The peculiarity is a necessity to know composition of all components of the arbitrary mixture. The limitation is a necessity that all components are gaseous. The considered case needs to develop a combustion model of a single-component solid substance (nitrocellulose powder) that provides for a possibility to vary the composition of its active part because of its degradation with time.

A simple mathematical model to describe antibody-dependent enhancement in heterologous secondary infection in dengue

2018 ◽  
Vol 36 (4) ◽  
pp. 411-438 ◽  
Author(s):  
Miller Cerón Gómez ◽  
Hyun Mo Yang
Keyword(s):  
Mathematical Model ◽  
Secondary Infection ◽  
Denv Infection ◽  
Severe Dengue ◽  
Asymptotically Stable ◽  
Effective Response ◽  
Antibody Dependent Enhancement ◽  
Secondary Infections ◽  
Initial Stage

Abstract We develop a mathematical model to describe the role of antibody-dependent enhancement (ADE) in heterologous secondary infections, assuming that antibodies specific to primary dengue virus (DENV) infection are being produced by immunological memory. The model has a virus-free equilibrium (VFE) and a unique virus-presence equilibrium (VPE). VFE is asymptotically stable when VPE is unstable; and unstable, otherwise. Additionally, there is an asymptotic attractor (not a fixed point) due to the fact that the model assumes unbounded increase in memory cells. In the analysis of the model, ADE must be accounted in the initial stage of infection (a window of time of few days), period of time elapsed from the heterologous infection until the immune system mounting an effective response against the secondary infection. We apply the results yielded by model to evaluate ADE phenomonon in heterologous DENV infection. We also associate the possible occurrence of severe dengue with huge viremia mediated by ADE phenomenon.

scholarly journals Mathematical Modelling of Social Consciousness to Control the Outbreak of COVID-19

2020 ◽  
Author(s):  
Md. Shahriar Mahmud ◽  
Md Kamrujjaman ◽  
J. Jubyrea ◽  
Md. Shahidul Islam
Keyword(s):  
Mathematical Model ◽  
Economic Factor ◽  
Social Consciousness ◽  
Economic Stability ◽  
Great Loss ◽  
Satisfactory Outcome ◽  
Initial Stage ◽  
The World ◽  
Per Capita ◽  
Stable Economy

Background: The world, now in an emergency of preventing the drastic spread of COVID-19. After the infection was first reported in December 2019, almost every country did not pay attention to this highly contaminated disease and failed to react swiftly. Now the whole universe is in an vulnerable state, loosing a great loss of lives and facing difficulties in all socio-economic aspects. That is why we have the urge to develop an efficient mathematical model (quarantine) based on social consciousness to control the epidemic. Methods: This is a quarantine mathematical model. The outcome of the system is dependent on social consciousness. We have calculated the awareness level by considering various socio-economic factor of each country. In our model, the parameters are Education Index, GDP per capita, population density, high literacy and stable economy. To maximize the efficiency of the model, it has to be implemented in initial stage. However, strict application of the method in vigorous stage of epidemic will also bring a satisfactory outcome. Results: Higher social consciousness will decrease the number of infected population dramatically while minimal or lower awareness will do a outburst. Conclusion: Outbreak will be in control of health care system, lower the death rate and will ensure social and economic stability.

Numerical simulation of the spherically symmetric tumor growth in the lymph node

2010 ◽  
Vol 7 ◽  
pp. 143-152
Author(s):  
V.N. Kireev ◽  
O.A. Solnyshkina
Keyword(s):  
Mathematical Model ◽  
Lymph Node ◽  
Tumor Growth ◽  
Growth Parameters ◽  
Symmetric Case ◽  
Spherically Symmetric ◽  
Intercellular Interaction ◽  
Initial Stage ◽  
Multiphase Systems ◽  
The Mathematical Model

Within the framework of the multiphase systems mechanics we consider the mathematical model of the initial stage of the tumor growth in a lymph node consisting of two kinds of cells. Adhesive intercellular interaction and distribution of nutrients (oxygen) are taken into account. For a spherically symmetric case, the distribution of tumor growth parameters was numerically obtained and some features of its development at the initial stage were defined.

Modeling of Tea Infusion Kinetics Incorporating Swelling Kinetics

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Raosaheb A. Farakte ◽  
Geeta U. Yadav ◽  
Bhushan S. Joshi ◽  
Ashwin W. Patwardhan ◽  
Gurmeet Singh
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Interfacial Area ◽  
Swelling Kinetics ◽  
Empirical Parameter ◽  
Tea Infusion ◽  
Initial Stage ◽  
Kinetics Of ◽  
Solution Methodology ◽  
Fitting Parameters

Abstract Mathematical model to predict tea infusion kinetics which accounts for swelling kinetics of tea granules is presented. Swelling kinetics of tea granules has never been taken into account for models developed so far. Differential equations (DEs) for concentration of tea constituents inside tea granule with respect to radius and time were derived. Solution methodology for these DEs is developed based on Crank-Nicholson scheme. Tea infusion profile is obtained using this model by knowing the swelling kinetics, partition constant and initial contents in tea granules. Diffusivity and product of interfacial area (As) and backward rate constant (k−1) are the fitting parameters. Model prediction is fitted to the experimental data published previously (R2 = 0.90–0.98). The fitted diffusivity (3.33 × 10−10 m2/s) and Ask−1 (2 m3/(kg.s)) predicted the infusion profile of other sized tea granules very well. This model predicts the infusion during initial stage very accurately without any empirical parameter.

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