scholarly journals Single-parameter scaling in one-dimensional Anderson localization: Exact analytical solution

2001 ◽  
Vol 64 (22) ◽  
Author(s):  
Lev I. Deych ◽  
A. A. Lisyansky ◽  
B. L. Altshuler
Keyword(s):  
Analytical Solution ◽  
Anderson Localization ◽  
Exact Analytical Solution ◽  
Single Parameter ◽  
One Dimensional

LOCALIZED BREATHER-LIKE EXCITATIONS IN THE HELICOIDAL PEYRARD–BISHOP MODEL OF DNA

2009 ◽  
Vol 02 (04) ◽  
pp. 405-417 ◽  
Author(s):  
CONRAD BERTRAND TABI ◽  
ALIDOU MOHAMADOU ◽  
TIMOLEON CREPIN KOFANE
Keyword(s):  
Analytical Solution ◽  
Continuous Wave ◽  
Exact Analytical Solution ◽  
Modulational Instability ◽  
Elliptic Functions ◽  
Instability Criterion ◽  
Dna Dynamics ◽  
Jacobian Elliptic Functions ◽  
One Dimensional ◽  
The One

We consider the one-dimensional helicoidal Peyrard–Bishop (PB) model of DNA dynamics. By means of a method based on the Jacobian elliptic functions, we obtain the exact analytical solution which describes the modulational instability and the propagation of a bright solitary wave on a continuous wave background. It is shown that these solutions depend on the modulational (or Benjamin-Feir) instability criterion. Numerical simulations of their propagation show these excitations to be long-lived and suggest that they are physically relevant for DNA.

Longitudinal Impact of Semi-Infinite Elastic Bars: Plane Any Time Solution

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
M. A. Malkov
Keyword(s):  
Analytical Solution ◽  
Exact Analytical Solution ◽  
The Other ◽  
Longitudinal Impact ◽  
Infinite Plane ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Contact Surfaces ◽  
The One ◽  
The Impact

Using the Sobolev–Smirnov method, we have found the exact analytical solution of a longitudinal impact of semi-infinite plane elastic bars for any time after the impact. After collision, there are loading waves from contact surfaces of bars and unloading waves from lateral surfaces. Then the unloading waves reach the opposite surface of the bars and create the reflected loading waves. These loading waves reach the other surface of the bars and generate new unloading waves. The number of waves grows exponentially. The sum of waves tends to the wave of the one-dimensional approximation.

A modified wave approach for calculation of natural frequencies and mode shapes in arbitrary non-uniform one-dimensional waveguides

2011 ◽  
Vol 225 (12) ◽  
pp. 2864-2880 ◽  
Author(s):  
M Khoshbayani-Arani ◽  
N Rasekh-Saleh ◽  
M Nikkhah-Bahrami
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Exact Analytical Solution ◽  
Mode Shapes ◽  
Transmission Matrix ◽  
Approximate Methods ◽  
One Dimensional ◽  
Wave Propagation Method ◽  
Number Of Segments

In this article, using the wave propagation method, the natural frequencies and mode shapes of an arbitrary non-uniform one-dimensional waveguide are calculated. The non-uniform rods and beams are partitioned into several continuous segments with constant cross-sections, for which there exists an exact analytical solution. At the end of each segment, waves in positive and negative directions are obtained in terms of waves at initial segment and subsequently, the calculations of the mode shapes become simple. By satisfying the boundary conditions, the characteristic equation is obtained and natural frequencies are calculated for both the arbitrary non-uniform rod and beam. Also, by adding waves in positive and negative directions at the end point of each segment, the mode shapes are obtained. To verify the modified wave method presented here, the frequencies and mode shapes of the rod and the beam with a polynomial cross-section having an exact analytical solution are compared and have been proven to be of high accuracy. Besides, comparisons of finite element method are also included. Therefore, this method can also be used to calculate the natural frequencies and mode shapes of rods and beams with any arbitrary variable cross-section for which no analytical solution is available. For the ‘Modified Wave Approach’ developed here, dimensions of transmission matrix remain constant if the number of segments is increased, while in general wave propagation method, dimensions of transmission matrix increase upon increasing the number of segments. Besides this novelty, this method has the advantage that it gives all the natural frequencies and mode shapes, unlike other approximate methods such as weighted residual, Rayleigh–Ritz, and finite difference methods which have their own shortcomings such as limited number of natural frequencies. Also, since each segment has an exact analytical solution, in contrast to other approximate methods, much higher accuracy is obtained even with only a few number of partitions.

scholarly journals Initial magnetic field distribution around high rectangular bus bars

2014 ◽  
Vol 11 (4) ◽  
pp. 523-534
Author(s):  
Grigore Cividjian
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Magnetic Fields ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
One Dimensional ◽  
Transient Electromagnetic ◽  
The One ◽  
Two Sides ◽  
Initial Magnetic Field

The one-dimensional transient electromagnetic field in and around a system of two nonmagnetic homogenous rectangular high thin bars can be analytically evaluated if the ratio of average initial magnetic field on the two sides of thin bar, or of the ratio of initial magnetic fields in middle of the bar height is known. In this paper, using appropriate conformal mappings, an exact analytical solution for these ratios are proposed in the case of very thin bars. Obtained values are compared with FEM results for relatively thick bars.

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