scholarly journals Lindstedt series solutions of the Fermi-Pasta-Ulam lattice

2007 ◽  
Vol 48 (5) ◽  
pp. 052702
Author(s):  
David C. Dooling ◽  
James E. Hammerberg
Keyword(s):  
Series Solutions ◽  
Lindstedt Series

How switching the substituent of a pyrene derivative from a methyl to a butyl affects the fluorescence response of polystyrene randomly labeled with pyrene

2010 ◽  
Vol 88 (3) ◽  
pp. 217-227 ◽  
Author(s):  
Mark Ingratta ◽  
Manoj Mathew ◽  
Jean Duhamel
Keyword(s):  
Organic Solvents ◽  
Excellent Agreement ◽  
Fluorescence Spectra ◽  
Series Solutions ◽  
Specific Nature ◽  
Polymer Backbone ◽  
Excimer Fluorescence ◽  
Fluorescence Response ◽  
Different Types ◽  
Blob Model

A series of polystyrenes randomly labeled with 1-pyrenebutanol were prepared by copolymerizing styrene and 1-pyrenebutylacrylate yielding the CoBuE–PS series. Solutions of CoBuE–PS were prepared in nine organic solvents having viscosities ranging from 0.36 to 5.5 mPa·s and the fluorescence spectra and pyrene monomer and excimer fluorescence decays were acquired. Analysis of the fluorescence spectra yielded the IE/IM ratio, whereas analysis of the fluorescence decays with the fluorescence blob model (FBM) yielded the parameters N blobo , <kblob × Nblob> , and k blobo . These parameters were compared to those obtained with two other series of pyrene-labeled polystyrenes, which had been studied earlier, namely CoA–PS and CoE–PS where pyrene was attached to the polymer backbone via a methylamide and benzyl methylether linker, respectively. Although the parameters IE/IM, N blobo , <kblob × Nblob>, and k blobo took different values according to the specific nature of the linker connecting pyrene to the polystyrene backbone, they exhibited trends that were quite similar for all the pyrene-labeled polystyrene constructs. The excellent agreement between the parameters retrieved for the three different types of pyrene-labeled polystyrenes suggests that the FBM accounts satisfyingly for differences in the nature of the label used, while still retrieving information pertinent to the polymer of interest.

A field theory approach to Lindstedt series for hyperbolic tori in three time scales problems

1999 ◽  
Vol 40 (12) ◽  
pp. 6430-6472 ◽  
Author(s):  
G. Gallavotti ◽  
G. Gentile ◽  
V. Mastropietro
Keyword(s):  
Field Theory ◽  
Time Scales ◽  
Theory Approach ◽  
Lindstedt Series

Sinusoidal Torsional Buckling of Bars of Angle Section Under Bending Loads, as a Problem in Plate Theory

1951 ◽  
Vol 18 (3) ◽  
pp. 285-292
Author(s):  
H. J. Plass
Keyword(s):  
Infinite Series ◽  
Plate Theory ◽  
Ritz Method ◽  
Compressive Load ◽  
Series Solutions ◽  
Torsional Buckling ◽  
Bending Load ◽  
Angle Section ◽  
Bending Loads

Abstract Timoshenko has applied plate theory to each leg of an angle-section bar to determine the critical compressive load needed to cause sinusoidal torsional buckling. In this paper his idea is used to calculate the critical bending load needed to cause sinusoidal torsional buckling of an angle bar. The bending is assumed to be applied so that the extreme fibers of the angle are in compression, the vertex in tension. Approximate results are first obtained by means of the Rayleigh-Ritz method. The approximate deflection functions from which the energy terms are computed are based upon certain infinite-series solutions. After having obtained approximate results, exact values are obtained, using the approximate values as a guide to limit the amount of calculation. The results of this calculation are shown in Fig. 5, where they are compared with those predicted by bar theory. Differences between the two theories become more noticeable as the bar becomes short compared to its flange width. It is found that the critical bending load becomes larger very rapidly as the ratio of length to width of the flanges decreases. Bar theory predicts no such increase. The reason for this difference is explained.

A symmetry-preserving difference scheme and analytical solutions of a generalized higher-order beam equation

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Shou-Fu Tian ◽  
Mei-Juan Xu ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Vector Fields ◽  
Higher Order ◽  
Beam Equation ◽  
Series Solutions ◽  
Local Conservation ◽  
Power Series Method ◽  
Potential System ◽  
Power Series Solutions ◽  
The Difference

Under investigation in this work is a generalized higher-order beam equation, which is an important physical model and describes the vibrations of a rod. By considering Lie symmetry analysis, and using the power series method, we derive the geometric vector fields, symmetry reductions, group invariant solutions and power series solutions of the equation, respectively. The convergence analysis of the power series solutions are also provided with detailed proof. Furthermore, by virtue of the multipliers, the local conservation laws of the equation are derived as well. Furthermore, an effective and direct approach is proposed to study the symmetry-preserving discretization for the equation via its potential system. Finally, the invariant difference models of the generalized beam equation are successfully constructed. Our results show that it is very useful to construct the difference models of the potential system instead of the original equation.

Sign in / Sign up

Export Citation Format

Share Document