اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدStochastic lattice models for the dynamics of linear polymers
224
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Linear polymers are represented as chains of hopping reptons and their motion is described as a stochastic process on a lattice. This admittedly crude approximation still catches essential physics of polymer motion, i.e. the universal properties as function of polymer length. More than the static properties, the dynamics depends on the rules of motion. Small changes in the hopping probabilities can result in different universal behavior. In particular the cross-over between Rouse dynamics and reptation is controlled by the types and strength of the hoppings that are allowed. The properties are analyzed using a calculational scheme based on an analogy with one-dimensional spin systems. It leads to accurate data for intermediately long polymers. These are extrapolated to arbitrarily long polymers, by means of finite-size-scaling analysis. Exponents and cross-over functions for the renewal time and the diffusion coefficient are discussed for various types of motion.
قيم البحث
اقرأ أيضاً
We study a model of self propelled particles exhibiting run and tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the motion of
bacteria such as E. coli. By defining a class of models with multiple species of particle and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run and tumble dynamics. We solve the externally driven non-interacting and zero-rang
Recently, it has been proposed that the adsorption transition for a single polymer in dilute solution, modeled by lattice walks in three dimensions, is not universal with respect to inter-monomer interactions. It has also been conjectured that key cr
itical exponents $phi$, measuring the growth of the contacts with the surface at the adsorption point, and $1/delta$, which measures the finite-size shift of the critical temperature, are not the same. However, applying standard scaling arguments the two key critical exponents should be identical, thus pointing to a potential breakdown of these standard scaling arguments. This is in contrast to the well studied situation in two dimensions, where there are exact results from conformal field theory: these exponents are both accepted to be $1/2$ and universal. We use the flatPERM algorithm to simulate self-avoiding walks and trails on the hexagonal, square and simple cubic lattices up to length $1024$ to investigate these claims. Walks can be seen as a repulsive limit of inter-monomer interaction for trails, allowing us to probe the universality of adsorption. For each model we analyze several thermodynamic properties to produce different methods of estimating the critical temperature and the key exponents. We test our methodology on the two-dimensional cases and the resulting spread in values for $phi$ and $1/delta$ indicates that there is a systematic error that exceeds the statistical error usually reported. We further suggest a methodology for consistent estimation of the key adsorption exponents which gives $phi=1/delta=0.484(4)$ in three dimensions. We conclude that in three dimensions these critical exponents indeed differ from the mean-field value of $1/2$, but cannot find evidence that they differ from each other. Importantly, we also find no substantive evidence of any non-universality in the polymer adsorption transition.
We develop a theoretical description of the topological disentanglement occurring when torus knots reach the ends of a semi-flexible polymer under tension. These include decays into simpler knots and total unknotting. The minimal number of crossings
and the minimal knot contour length are the topological invariants playing a key role in the model. The crossings behave as particles diffusing along the chain and the application of appropriate boundary conditions at the ends of the chain accounts for the knot disentanglement. Starting from the number of particles and their positions, suitable rules allow reconstructing the type and location of the knot moving on the chain. Our theory is extensively benchmarked with corresponding Molecular Dynamics simulations and the results show a remarkable agreement between the simulations and the theoretical predictions of the model.
Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived and inves
tigated theoretically and experimentally. Significantly, we demonstrate, in the context of Markovian stochastic dynamics, how these different fluctuation theorems arise from a simple fundamental time-reversal symmetry of a certain class of observables. Appealing to the notion of Gibbs entropy allows for a microscopic definition of entropy production in terms of these observables. We work with the master equation approach, which leads to a mathematically straightforward proof and provides direct insight into the probabilistic meaning of the quantities involved. Finally, we point to some experiments that elucidate the practical significance of fluctuation relations.
In the usual statistical model of a dense polymer (a single space-filling loop on a lattice) in two dimensions the loop does not cross itself. We modify this by including intersections in which {em three} lines can cross at the same point, with some
statistical weight w per crossing. We show that our model describes a line of critical theories with continuously-varying exponents depending on w, described by a conformally-invariant non-linear sigma model with varying coupling constant g_sigma^2 >0. For the boundary critical behavior, or the model defined in a strip, we propose an exact formula for the ell-leg exponents, h_ell=g_sigma^2 ell(ell-2)/8, which is shown numerically to hold very well.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
