Continuous area-preserving models for self-interacting polymers
About: This article is published in Journal De Physique.The article was published on 1989-02-01. It has received 10 citations till now. The article focuses on the topics: Polymer.
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554 citations
TL;DR: In this article, a series of experiments aimed at the study of the interaction of slow very highly charged ions with conductor and insulator surfaces are reported, where charge state dependences of secondary electron, x-ray and secondary ion emission are measured.
Abstract: First results from a series of experiments aimed at the study of the interaction of slow very highly charged ions with conductor and insulator surfaces are reported. Charge state dependences of secondary electron, x-ray and secondary ion emission are measured. In addition, microscopic studies are performed using an ‘Atomic Force Microscope’ to investigate surface defects, produced through the stored electrostatic potential of the incident ion. The ions that have been used for these studies range from O7+ to Th80+, with low kinetic energies (generally 1–3 keV/amu). Overall, enhancement of the low energy secondary electron, sputter ion and photon emission are observed with increasing charge states. Saturation in the electron emission yield at very low velocities confirm present models for image charge acceleration effects. X-ray emission spectra are found to be consistent with the formation of so called ‘hollow’ atoms near the surface during the neutralization processes. The microscopic studies rev...
57 citations
TL;DR: In this paper, a self-contained introduction to polymer physics and to the application of field theoretical techniques to the statistical mechanics of polymer systems is given, focusing on the problem of describing the fluctuations of topologically linked polymers in a solution from a microscopical point of view.
Abstract: This is a self-contained introduction to polymer physics and to the application of field theoretical techniques to the statistical mechanics of polymer systems. Of course, since polymer physics is a highly interdisciplinary subject, involving different disciplines like knot theory, field theory, statistical mechanics and some notions of bio-chemistry and chemistry, it is not possible to cover all these topics in a single review. Particular emphasis is given here to the problem of describing the fluctuations of topologically linked polymers in a solution from a microscopical point of view. Some recent advances in this direction are presented. Another purpose of this work is to serve as a guide for whoever would like to apply the methods of field theory to polymers. To ease reading, technical terms have been quoted in boldface characters at the points in which their meaning is explained.
22 citations
TL;DR: In this paper, the probability of trivial knot formation on a lattice was estimated using the Kauffman algebraic invariants and the thermodynamic properties of 2D disordered Potts model.
Abstract: This paper reviews the state of affairs in a modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) we stimate the probability of trivial knot formation on a lattice using the Kauffman algebraic invariants and show the connection of this problem with the thermodynamic properties of 2D disordered Potts model; (ii) we investigate the limiting behavior of random walks in multiconnected spaces and on non-commutative groups related to knot theory. We discuss the application of the above-mentioned problems in the statistical physics of polymer chains. On the basis of non-commutative probability theory we derive some new results in the statistical physics of entangled polymer chains which unite rigorous mathematical facts with intuitive physical arguments.
9 citations
TL;DR: In this article, the size and shape of a closed, two-dimensional random walk with a pressure difference p between the inside and outside, which couples to an algebraic (signed) area is analyzed.
Abstract: This paper analyzes the size and shape of a closed, two-dimensional random walk with a pressure difference p between the inside and outside, which couples to an algebraic (signed) area This pressurized-random-walk (PRW) model is, in some respects, closely related to a computer model studied by Leibler, Singh, and Fisher [Phys Rev Lett 59, 1989 (1987)] Since all terms in the Hamiltonian are quadratic in the position-vector field r, the partition function and its derivatives can be evaluated exactly The most notable feature of the PRW model is an instability, which occurs at \ensuremath{\Vert}p\ensuremath{\Vert}=${\mathit{p}}_{\mathit{c}}$ For \ensuremath{\Vert}p\ensuremath{\Vert}${\mathit{p}}_{\mathit{c}}$, the system has a finite algebraic area and an anisotropic shape; for \ensuremath{\Vert}p\ensuremath{\Vert}\ensuremath{\ge}${\mathit{p}}_{\mathit{c}}$, the algebraic area diverges and the shape is circular The asphericity is also calculated A form of bending rigidity, also quadratic in r, is introduced into the model; however, the resulting macroscopic properties are quite different from those one might ordinarily expect This difference can be traced to the absence of a fixed link size in the model
6 citations
References
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554 citations
"Continuous area-preserving models f..." refers background in this paper
...The interested reader is also referred to work of Spitzer [8] who studied winding angle distributions, and to the monograph by Itô and McKean [9]....
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01 Jul 1967
TL;DR: In this paper, the entropy of very long flexible molecules in the presence of topological constraints is studied, and a formula deduced which needs the probability that a random walk will have a particular topological specification.
Abstract: The entropy of very long flexible molecules in the presence of topological constraints is studied, and a formula deduced which needs the probability that a random walk will have a particular topological specification. Examples are solved, including a plane random walk sweeping out a given angle around a point in the plane which is generalized to three dimensions including the passage of a random walk past many lines in space, and the probability that a random walk will penetrate through or become multiply entangled with a closed ring.
375 citations
TL;DR: In this paper, the authors derived a strong type theorem concerning the frequency of small values of R(t) in the Bachelier-Wiener process, which disproved a conjecture of Paul Levy.
Abstract: This paper consists of three separate parts(1) which are related mainly in that they treat different stochastic processes which arise in the study of plane brownian motion. §1 is concerned with the process R(t)=|Z(t)|, denoting the distance of the 2-dimensional separable Bachelier-Wiener process Z(t) =X(t)+iY(t) from the origin. We shall derive a law of the so-called strong type concerning the frequency of small values of R(t). This theorem disproves a conjecture of Paul Levy. In the next section we study the process θ(t) =arg Z(t). Results are obtained concerning the transition probabilities and absorption probabilities of θ(t). The limiting distribution of (2−1 log t) − 1 θ(t) is found to be the Cauchy distribution. This problem has also been considered by P. Levy, who showed that the distribution of θ(t) must have infinite variance. The two-sided absorption time is shown to be a random variable which has a finite nth moment if and only if the wedge which constitutes the absorbing barrier has an interior angle β<π/2n. In §3 we point out how plane brownian motion can be used to represent the Cauchy process. A theorem on brownian motion due to P. Levy is then used to gain information about the Cauchy process C(t). If −1 < C(0) = x <1 the probability that C(t)≧1 before C(t)≦−1 is found to be 1/2+π−1 sin−1 x.
324 citations
Book•
01 Jan 1986
TL;DR: In this article, the authors present an elementary account on the Wiener path integral as applied to Brownian motion, and the author progresses on to the statistics of polymers and polymer entanglements.
Abstract: This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman.After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter.
241 citations
"Continuous area-preserving models f..." refers background in this paper
...In many cases topological constraints can be interpreted to correspond to movements in magnetic fields [1], therefore most of these models can be used to study the quantum dynamics of charged particles in magnetic fields (provided time is allowed to take imaginary values)....
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...In spite of this there are very few exactly solvable models, which were reviewed in [1]....
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228 citations