scholarly journals A UNIFIED ANALYTICAL SOLUTION FOR WAVE SCATTERING BY RECTANGULAR-SHAPED OBJECTS

2018 ◽  
pp. 7
Author(s):  
Jie Hu ◽  
Philip Li-Fan Liu
Keyword(s):  
Analytical Solution ◽  
General Solution ◽  
General Theory ◽  
Computer Program ◽  
Rectangular Plate ◽  
Analytical Solutions ◽  
Wave Scattering ◽  
Submerged Plate ◽  
Floating Breakwater ◽  
Stationary Objects

This paper presents a general solution for wave scattering by stationary objects, which consist of a submerged rectangular plate and a floating rectangular dock. The objects can be either permeable or solid. The general solution is capable to cover all the existing single rectangular objects, such as a surface-piercing breakwater, a bottom-mounted submerge breakwater and a submerged plate. Furthermore, this general solution can also yield new analytical solutions for different combinations of objects, i.e. a single floating breakwater, and a combination of a floating and a bottom-mounted breakwater. Based on the general theory, a MATLAB computer program has been developed. It can be used to further explore different breakwater configurations with different properties.

scholarly journals Analytical solution and adaptation to the parameter estimation of the SIR model

2020 ◽  
pp. 40-43
Author(s):  
S. M. Ivanov
Keyword(s):  
Parameter Estimation ◽  
Graduate Students ◽  
Analytical Solution ◽  
General Solution ◽  
Population Size ◽  
Analytical Solutions ◽  
Sir Model ◽  
Mathematical Epidemiology ◽  
Linear Regressions ◽  
Inverse Proportionality

The article deals with analytical solution and adaptation to the parameter estimation of the SIR model of the epidemic. By a special replacement of the exponential function by inverse proportionality, the approximate general solution of the SIR model is found. It is spoken in detail about the process of integration of ordinary differential equations of the SIR model. The equality of the sum of the obtained analytical solutions and population size is checked. The obtained solutions are simple and understandable. To parametrically estimate the SIR model, its general solution is adapted to paired linear regressions. The article is of interest for students, graduate students and scientists involved in mathematical epidemiology.

Zur Lösung der BETHE-GOLDSTONE-Gleichung bei nicht-verschwindendem Gesamtimpuls I

1963 ◽  
Vol 18 (4) ◽  
pp. 531-538
Author(s):  
Dallas T. Hayes
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Nuclear Matter ◽  
Analytical Solutions ◽  
Projection Operator ◽  
Center Of Mass ◽  
Separable Potential ◽  
Localized Solutions ◽  
Non Local ◽  
Square Well

Localized solutions of the BETHE—GOLDSTONE equation for two nucleons in nuclear matter are examined as a function of the center-of-mass momentum (c. m. m.) of the two nucleons. The equation depends upon the c. m. m. as parameter due to the dependence upon the c. m. m. of the projection operator appearing in the equation. An analytical solution of the equation is obtained for a non-local but separable potential, whereby a numerical solution is also obtained. An approximate solution for small c. m. m. is calculated for a square-well potential. In the range of the approximation the two analytical solutions agree exactly.

scholarly journals Dynamic Analytical Solution of a Piezoelectric Stack Utilized in an Actuator and a Generator

2018 ◽  
Vol 8 (10) ◽  
pp. 1779 ◽  
Author(s):  
Xinnan Liu ◽  
Jianjun Wang ◽  
Weijie Li
Keyword(s):  
Analytical Solution ◽  
Dynamic Characteristics ◽  
Analytical Solutions ◽  
External Load ◽  
Piezoelectric Actuators ◽  
Displacement Method ◽  
Proposed Model ◽  
Special Cases ◽  
Piezoelectric Stacks ◽  
Comprehensive Manner

This paper presents the dynamic analytical solution of a piezoelectric stack utilized in an actuator and a generator based on the linear piezo-elasticity theory. The solutions for two different kinds of piezoelectric stacks under external load were obtained using the displacement method. The effects of load frequency and load amplitude on the dynamic characteristics of the stacks were discussed. The analytical solutions were validated using the available experimental results in special cases. The proposed model is able not only to predict the output properties of the devices, but also to reflect the inner electrical and mechanical components, which is helpful for designing piezoelectric actuators and generators in a comprehensive manner.

The Effect of Biot Number on a One-Dimensional General Conduction Solution

2021 ◽  
Author(s):  
Robert L. McMasters ◽  
Filippo de Monte ◽  
James V. Beck
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Biot Number ◽  
Analytical Solutions ◽  
Heat Fluxes ◽  
Graphical Form ◽  
Large Temperature ◽  
Convection Coefficient ◽  
General Analytical Solution

Abstract Analytical solutions for thermal conduction problems are extremely important, particularly for verification of numerical codes. Temperatures and heat fluxes can be calculated very precisely, normally to eight or ten significant figures, even in situations involving large temperature gradients. It can be convenient to have a general analytical solution for a transient conduction problem in rectangular coordinates. The general solution is based on the principle that the three primary types of boundary conditions (prescribed temperature, prescribed heat flux, and convective) can all be handled using convective boundary conditions. A large convection coefficient closely approximates a prescribed temperature boundary condition and a very low convection coefficient closely approximates an insulated boundary condition. Since a dimensionless solution is used in this research, the effect of various values of dimensionless convection coefficients, or Biot number, are explored. An understandable concern with a general analytical solution is the effect of the choice of convection coefficients on the precision of the solution, since the primary motivation for using analytical solutions is the precision offered. An investigation is made in this study to determine the effects of the choices of large and small convection coefficients on the precision of the analytical solutions generated by the general convective formulation. Results are provided, in tablular and graphical form, to illustrate the effects of the choices of convection coefficients on the precision of the general analytical solution.

Hydrodynamic Pressure of Thrust Step Bearings

2009 ◽  
Author(s):  
Shuangbiao Liu ◽  
W. Wayne Chen ◽  
Diann Y. Hua
Keyword(s):  
Analytical Solution ◽  
Coordinate System ◽  
Laplace Equation ◽  
Analytical Solutions ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Hydrodynamic Pressure ◽  
Finite Width ◽  
Cylindrical Coordinate ◽  
Lubrication Models

Step bearings are frequently used in industry for better load capacity. Analytical solutions to the Rayleigh step bearing and a rectangular slider with a finite width are available in literature, but none for a fan-shaped thrust step bearing. This study starts with a known solution to the Laplace equation in a cylindrical coordinate system, which is in the form of infinite summation. An analytical solution to pressure is derived in this paper for hydrodynamic lubrication problems encountered in the fan-shaped step bearing. The presented solutions can be useful for designers to maximize bearing performance as well as for researchers to benchmark numerical lubrication models.

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.

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