Self-avoiding walk

In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. Very little is known rigorously about the self-avoiding walk from a mathematical perspective, although physicists have provided numerous conjectures that are believed to be true and are strongly supported by numerical simulations. In computational physics, a self-avoiding walk is a chain-like path in R2 or R3 with a certain number of nodes, typically a fixed step length and has the property that it doesn't cross itself or another walk. A system of SAWs satisfies the so-called excluded volume condition. In higher dimensions, the SAW is believed to behave much like the ordinary random walk. SAWs and SAPs play a central role in the modeling of the topological and knot-theoretic behavior of thread- and

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (3)

Related publications

Related people

Related units

Related concepts (3)

Related concepts

Related courses (4)

Related courses

Related lectures (10)

Related lectures

Entropy in the Coil-to-Globule Transition of Macromolecules

Carlo Maffi

The coil to globule transition is a fundamental phenomenon in the physics of macro-molecules by reason of the multiplicity of arrangements of their conformation. Such conformational freedom is the main source of entropy in the molecule and is the main opponent to the transition towards the compact state, since a system tends to the state of maximum entropy. This phenomenon is captured by very simple models, such as the ensemble of Interacting Self avoiding Walks on the lattice. This model shows that the coil to globule transition belongs to the universality class of continuous transition called Θ point. Starting from a critical inspection of the definition of the interacting walks model, we introduce a refinement aiming to represent more precisely the entropy sourced from the local fluctuations of the molecule around its equilibrium conformations; this contribution is absent in the standard model which includes only the entropy generated by the multiplicity of the global conformations. Through the study of the vibrational properties of the model and an exhaustive numerical simulation of the phase transition we show that the new model presents a transition which is different in character and belongs to a distinct universality class. In particular, in 3 dimensions the model shows a discontinuous transition; thanks to this, the model presents a common framework underlying the physics of both homo-polymers and proteins. Considering the results obtained in 2 and 3 dimensions we identify the convexity of the vibrational entropy as the responsible of the new class of transitions. These results and a revision of experimental measures of viscosity bring into question the standard description of the homo-polymer transition.

EPFL2012

Force-induced desorption of self-avoiding walks on Sierpinski gasket fractals

Stevan Arsenijevic

In this work we investigate force-induced desorption of linear polymers in good solvents in non-homogeneous environment, by applying the model of self-avoiding walk on two- and three-dimensional fractal lattices, obtained as generalization of the Sierpinski gasket fractal. For each of these lattices one of its boundaries represents an adsorbing wall, whereas along one of the fractal edges, not lying in the adsorbing wall, an external force acts on the self-avoiding walk. The hierarchical nature of the lattices under study enables an exact real-space renormalization group treatment, which yields the phase diagram of polymer critical behavior. We show that for this model there is no low-temperature reentrance in the cases of two-dimensional lattices, whereas in all studied three-dimensional cases the force-temperature dependance is reentrant. We also find that in all cases the force-induced desorption transition is of first order.

2011

Two-dimensional O(n) models and logarithmic CFTs

Bernardo Zan

We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG flow. When n is equal to two, which corresponds to the Kosterlitz-Thouless critical theory, the fixed points collide. We find that for n generic these CFTs are logarithmic and contain negative norm states; in particular, the O(n) currents belong to a staggered logarithmic multiplet. Using a conformal bootstrap approach we trace how the negative norm states decouple at n = 2, restoring unitarity. The IR fixed point possesses a local relevant operator, singlet under all known global symmetries of the CFT, and, nevertheless, it can be reached by an RG flow without tuning. Besides, we observe logarithmic correlators in the closely related Potts model.

SPRINGER2020

Polymer physics

Polymer physics is the field of physics that studies polymers, their fluctuations, mechanical properties, as well as the kinetics of reactions involving degradation and polymerisation of polymers and

Random walk

In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the rando

Polymer

A polymer (ˈpɒlᵻmər; Greek poly-, "many" + -mer, "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad

PHYS-441: Statistical physics of biomacromolecules

Introduction to the application of the notions and methods of theoretical physics to problems in biology.

PHYS-435: Statistical physics III

This course introduces statistical field theory, and uses concepts related to phase transitions to discuss a variety of complex systems (random walks and polymers, disordered systems, combinatorial optimisation, information theory and error correcting codes).

BIO-692: Symmetry and Conservation in the Cell

This course instructs students in the use of advanced computational models and simulations in cell biology. The importance of dimensionality, symmetry and conservation in models of self-assembly, membranes, and polymer/filament scaling laws reveals how cells exploit these principles in life.