scholarly journals Mechanical unfolding of a simple model protein goes beyond the reach of one-dimensional descriptions

2014 ◽  
Vol 141 (13) ◽  
pp. 135102 ◽  
Author(s):  
R. Tapia-Rojo ◽  
S. Arregui ◽  
J. J. Mazo ◽  
F. Falo
2016 ◽  
Author(s):  
E. R. Méndez ◽  
G. D. Jiménez ◽  
A. A. Maradudin

1. Introduction .—Gamow's elegant deduction by general arguments of the law of radioactive decay by α-particle emission and his subsequent investigations on artificial disintegration suggested to us the desirability of investigating as closely as possible any simple model of a decaying nucleus as a verification of his general approximations. For the model chosen the exact investigation of the decay process is almost trivial. Since we obtained this, now some time ago, Dr. Gamow informed us that he had also obtained equivalent detailed results. Still more recently such results have been published by Kudar. We shall not therefore dwell upon them here. The application of the same ideals, however, to the reverse process of penetration presents points of very definite interest, which we think are well worth discussion. The main point that arises is that the chance of penetration α-particle is or is not equal to a characteristic energy of the nucleus itself. This is a point which is not dealt with by Gamow in his paper. We have discussed it with him, and now put forward the results we have obtained. Since the solution of the decay problem is required in the main discussion of the penetration of α-particles into the nucleus it is included here in 2 for reference. We must emphasise that we claim no novelty, except of detail, for the work of 2; the general lines by now are a matter of fairly common knowledge.


Author(s):  
A. J. Allnutt

SynopsisThe Langevin equation for the harmonic oscillator is solved by a different method from that normally used. The approximate solution for the case of the slightly anharmonic oscillator is then obtained by an iterative procedure and the results are illustrated by a numerical example based on a simple model of a crystalline solid.


1956 ◽  
Vol 52 (4) ◽  
pp. 712-718 ◽  
Author(s):  
H. N. V. Temperley

ABSTRACTA very simple model, consisting of N particles moving in a one-dimensional assembly divided by potential ‘humps’ into M cells, is studied. The process of passing from a quantum-mechanical description of such an assembly to the equation of diffusion type that governs it in practice is shown to consist of at least three separate steps: ‘averaging over phases’, and letting N and M become large. The effects of these steps are considered separately. Strict irreversibility in time appears after the first step, but the assembly remains ergodic until after the second step and fluctuations persist until after the third step.


2000 ◽  
Vol 5 (3) ◽  
pp. 179-187 ◽  
Author(s):  
I. Katzorke ◽  
A. Pikovsky

We consider complex dynamical behavior in a simple model of production dynamics, based on the Wiendahl’s funnel approach. In the case of continuous order flow a model of three parallel funnels reduces to the one-dimensional Bernoulli-type map, and demonstrates strong chaotic properties. The optimization of production costs is possible with the OGY method of chaos control. The dynamics changes drastically in the case of discrete order flow. We discuss different dynamical behaviors, the complexity and the stability of this discrete system.


2003 ◽  
Vol 59 (4) ◽  
pp. 456-462 ◽  
Author(s):  
H. Katzke ◽  
R. Schlögl

The rutile/corundum structural transformation which is based on crystallographic shear is discussed in terms of a one-dimensional disorder model. The transformation process is described by a simple model based on the structural relationship between the rutile-type and corundum-type phases. The model is able to handle randomly spaced crystallographic shear planes, the so-called Wadsley defects, as well as clustered CS planes. Calculations hsow that simply modifying the probability parameters of the model can lead to phase segregation. X-ray powder diffraction patterns are calculated for the proposed transformation mechanism as a function of the stoichiometry x in MO2−x in order to show the influence of such defects on the intensities and linewidths of the Bragg reflections.


Author(s):  
Jean Pierre Puel ◽  
Enrique Zuazua

SynopsisA simple model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional straight string is introduced. In both regions (n-dimensional body and a onedimensional string) the state is assumed to satisfy the wave equation. Simple boundary conditions are introduced at the junction. These conditions, in the absence of control, ensure conservation of the total energy of the system and imply some rigidity of the boundary of the n-d body on a neighbourhood of the junction. The exact boundary controllability of the system is proved by means of a Dirichlet control supported on a subset of the boundary of the n-d domain which excludes the junction region. Some extensions are discussed at the end of the paper.


2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Messaoud Guellal ◽  
Hamou Sadat ◽  
Christian Prax

A perturbation method is used to solve an unsteady one-dimensional heat conduction problem in a cylinder. A simple second order explicit solution is obtained. It is shown that this solution is accurate even for high values of the Biot number in a region surrounding the center of the cylinder.


2019 ◽  
Author(s):  
Soojeong Kim ◽  
Isabel K. Darcy

ABSTRACTAn experimental technique called difference topology combined with the mathematics of tangle analysis has been used to unveil the structure of DNA bound by the Mu transpososome. However, difference topology experiments can be difficult and time-consuming. We discuss a modification that greatly simplifies this experimental technique. This simple experiment involves using a topoisomerase to trap DNA crossings bound by a protein complex and then running a gel to determine the crossing number of the knotted product(s). We develop the mathematics needed to analyze the results and apply these results to model the topology of DNA bound by 13S condensin and by the condensin MukB.SUMMARY STATEMENTTangles are used to model protein-DNA complexes: A 3-dimensional ball represents protein while strings embedded in this ball represent protein-bound DNA. We use this simple model to analyze experimental results.


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