Profile of a rotating string

1999 ◽  
Vol 77 (7) ◽  
pp. 505-513 ◽  
Author(s):  
P Mohazzabi ◽  
J R Schmidt
Keyword(s):  
Variational Principle ◽  
Elliptic Integrals ◽  
Newtonian Mechanics ◽  
Flexible Chain ◽  
Rotating String ◽  
Theoretical Results

The problem of a uniform flexible chain or string rotating about an axis with fixed ends is addressed in the context of both Newtonian mechanics and the variational principle. It is shown that, in the absence of gravity, the equations describing the profile of the string as well as the constraints of the system are all expressible in terms of Legendre's elliptic integrals of various kinds. The effectof gravity is discussed qualitatively, and it is shown that for high enough angularvelocities its effect is negligible. The profile of a rotating chain is obtained using stroboscopic photography and compared with the theoretical results. PACS No.: 46.00

scholarly journals Supplement to the Theory of Relativity

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Xiaoliang Miao
Keyword(s):  
Energy Equation ◽  
Newtonian Mechanics ◽  
Theory Of Relativity ◽  
Mass Energy ◽  
Theoretical Results

The problem about "who is right in relativity and Newtonian mechanics" is analyzed and discussed, and the theoretical results described in this study are only used as reference. This study reveals that there is no contradiction between relativity and Newtonian mechanics, and the essence of the relativity lies in the mass energy equation. 

scholarly journals Lyotropic colloidal and macromolecular liquid crystals

1993 ◽  
Vol 344 (1672) ◽  
pp. 419-440 ◽  
Keyword(s):  
Phase Transition ◽  
Nematic Phase ◽  
Concentrated Solutions ◽  
Flexible Chain ◽  
Chain Molecules ◽  
Charged Colloids ◽  
Hard Rods ◽  
Crystal Phases ◽  
Soft Interactions ◽  
Theoretical Results

We review the theory of the isotropic—nematic phase transition for solutions of thin hard rods and semi-flexible chain molecules along with the extensions to polydisperse systems and soft interactions. The occurrence of more highly ordered liquid crystal phases (smectic, columnar) in concentrated solutions of colloids and macromolecules is discussed briefly. Experimental results for a number of carefully studied uncharged and charged colloids and macromolecules are compared to theoretical results.

scholarly journals Instability of the printing jet during the three-dimensional-printing process

2021 ◽  
pp. 146134842110215
Author(s):  
Yuting Zuo ◽  
Hongjun Liu
Keyword(s):  
Variational Principle ◽  
Theoretical Prediction ◽  
Three Dimensional ◽  
Instability Criterion ◽  
Axial Motion ◽  
Printing Process ◽  
Three Dimensional Printing ◽  
Moving Jet ◽  
Dimensional Printing ◽  
Theoretical Results

Euler’s instability criterion is widely used in engineering to design a column. However, this criterion is not suitable for judging the instability of a three-dimensional printing process because the axial motion of the printing jet has to be considered. A variational principle is established, and an equivalent Eulerian load is obtained. The theoretical results show that a higher printing velocity makes the moving jet much more stable, and an experiment is designed to verify our theoretical prediction.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Investigating the Nonlinear Optical Response of Pepper Oil under Low Power Irradiation with Continuous Wave Visible Laser Beam

2020 ◽  
pp. 131-138
Keyword(s):  
Refractive Index ◽  
Nonlinear Refractive Index ◽  
Nonlinear Optical ◽  
Continuous Wave ◽  
Diffraction Integral ◽  
Visible Laser ◽  
Limiting Property ◽  
Kirchhoff Diffraction Integral ◽  
Theoretical Results ◽  
Good Agreement

The nonlinear optical properties of pepper oil are studied by diffraction ring patterns and Z-scan techniques with continuous wave beam from solid state laser at 473 nm wavelength. The nonlinear refractive index of the sample is calculated by both techniques. The sample show high nonlinear refractive index. Based on Fresnel-Kirchhoff diffraction integral, the far-field intensity distributions of ring patterns have been calculated. It is found that the experimental results are in good agreement with the theoretical results. Also the optical limiting property of pepper oil is reported. The results obtained in this study prove that the pepper oil has applications in nonlinear optical devices.

70 years of ITEP: some theoretical results

2016 ◽  
Vol 186 (8) ◽  
pp. 869-878
Author(s):  
Mikhail I. Vysotskii ◽  
Aleksandr D. Dolgov ◽  
Viktor A. Novikov
Keyword(s):  
Theoretical Results

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

2020 ◽  
Vol 7 (3) ◽  
pp. 52-56
Author(s):  
MMATMATISA JALILOV ◽  
◽  
RUSTAM RAKHIMOV ◽  
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Three Dimensional ◽  
Viscoelastic Plate ◽  
Constant Thickness ◽  
Regional Problem ◽  
Rigid Contact ◽  
Under Construction ◽  
Derivatives Of ◽  
Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

NUMERICAL AND STABILITY ANALYSIS OF THE TRANSMISSION DYNAMICS OF SVIR EPIDEMIC MODEL WITH STANDARD INCIDENCE RATE

2019 ◽  
Vol 4 (2) ◽  
pp. 349 ◽  
Author(s):  
Oluwatayo Michael Ogunmiloro ◽  
Fatima Ohunene Abedo ◽  
Hammed Kareem
Keyword(s):  
Reproduction Number ◽  
Disease Spread ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Transform Method ◽  
Globally Asymptotically Stable ◽  
Differential Transform ◽  
Mathematical Techniques ◽  
Fourth Order Method ◽  
Theoretical Results

In this article, a Susceptible – Vaccinated – Infected – Recovered (SVIR) model is formulated and analysed using comprehensive mathematical techniques. The vaccination class is primarily considered as means of controlling the disease spread. The basic reproduction number (Ro) of the model is obtained, where it was shown that if Ro<1, at the model equilibrium solutions when infection is present and absent, the infection- free equilibrium is both locally and globally asymptotically stable. Also, if Ro>1, the endemic equilibrium solution is locally asymptotically stable. Furthermore, the analytical solution of the model was carried out using the Differential Transform Method (DTM) and Runge - Kutta fourth-order method. Numerical simulations were carried out to validate the theoretical results. 

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