Diffusion of active tracers in fluctuating fields

The problem of a particle diffusion in a fluctuating scalar field is studied. In contrast to most studies of advection diffusion in random fields we analyze the case where the particle position is also coupled to the dynamics of the field. Physical realizations of this problem are numerous and range from the diffusion of proteins in fluctuating membranes and the diffusion of localized magnetic fields in spin systems. We present exact results for the diffusion constant of particles diffusing in dynamical Gaussian fields in the adiabatic limit where the field evolution is much faster than the particle diffusion. In addition we compute the diffusion constant perturbatively, in the weak coupling limit where the interaction of the particle with the field is small, using a Kubo-type relation. Finally we construct a simple toy model which can be solved exactly.Comment: 13 pages, 1 figur

Monetary value of a supply chain relationship: What would it take to dump your partner?

Purpose – This paper introduces a framework for measuring B2B relationship value and tests whether relationship value changes across various relationship levels. It measures relationship value in monetary terms and tests whether higher level relationships have higher value both for buyers and sellers. Design/methodology/approach – The data was collected using structured interviews with marketing managers and purchasing officers within the food manufacturing sector in New Zealand. The data was subjected to ANOVA statistical analysis. Findings – The findings suggest that lower level relationships (transactional) could be dropped for minimal additional financial gain but firms were willing to forego extremely attractive scenarios to keep their cooperative partners. Originality/value – Implications suggest that managers value cooperative relationships and are willing to forego very attractive prices in order to keep the non-price value components. If managers can ascertain what these valued components are and how they can be utilized, they can make themselves a highly valued partner

The statistical mechanics of combinatorial optimization problems with site disorder

We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite temperature traveling salesman problem on several different domains and various problems in one dimension such as the so called descent problem. We first motivate our method by analyzing these problems using the annealed approximation, then the limit of a large number of points we develop a formalism to carry out the quenched calculation. This formalism does not require the replica method and its predictions are found to agree with Monte Carlo simulations. In addition our method reproduces an exact mathematical result for the Maximum traveling salesman problem in two dimensions and suggests its generalization to higher dimensions. The general approach may provide an alternative method to study certain systems with quenched disorder.Comment: 21 pages RevTex, 8 figure

On the distribution of estimators of diffusion constants for Brownian motion

We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.Comment: 14 pages, 5 figure

Fluctuations in the Site Disordered Traveling Salesman Problem

We extend a previous statistical mechanical treatment of the traveling salesman problem by defining a discrete "site disordered'' problem in which fluctuations about saddle points can be computed. The results clarify the basis of our original treatment, and illuminate but do not resolve the difficulties of taking the zero temperature limit to obtain minimal path lengths.Comment: 17 pages, 3 eps figures, revte

Performing pasts for present purposes: reenactment as embodied, performative history

History, Memory, Performance is an interdisciplinary collection of essays exploring performances of the past in a wide range of trans-national and historical contexts. At its core are contributions from theatre scholars and public historians discussing how historical meaning is shaped through performance (Palgrave Macmillan

Wrapping Transition and Wrapping-Mediated Interactions for Discrete Binding along an Elastic Filament: An Exact Solution

The wrapping equilibria of one and two adsorbing cylinders are studied along a semi-flexible filament (polymer) due to the interplay between elastic rigidity and short-range adhesive energy between the cylinder and the filament. We show that statistical mechanics of the system can be solved exactly using a path integral formalism which gives access to the full effect of thermal fluctuations, going thus beyond the usual Gaussian approximations which take into account only the contributions from the minimal energy configuration and small fluctuations about this minimal energy solution. We obtain the free energy of the wrapping-unwrapping transition of the filament around the cylinders as well as the effective interaction between two wrapped cylinders due to thermal fluctuations of the elastic filament. A change of entropy due to wrapping of the filament around the adsorbing cylinders as they move closer together is identified as an additional source of interactions between them. Such entropic wrapping effects should be distinguished from the usual entropic configuration effects in semi-flexible polymers. Our results may be applicable to the problem of adsorption of proteins as well as synthetic nano-particles on semi-flexible polymers such as DNA.Comment: 24 pages, 12 figure

The centred travelling salesman at high temperature

A recently formulated statistical mechanics method is used to study the phase transition occurring in a generalisation of the Traveling Salesman Problem (TSP) known as the centred TSP. The method shows that the problem has clear signs of a crossover, but is only able to access (unscaled) finite temperatures above the transition point. The solution of the problem using this method displays a curious duality

The statistics of critical points of Gaussian fields on large-dimensional spaces

We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of relevance to glassy and disordered systems, and to landscape scenarios coming from the anthropic approach to string theory.Comment: 5 page

Understanding Search Trees via Statistical Physics

We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain exact asymptotic results. In particular, we show that the probability distributions of extreme observables associated with a random search tree such as the height and the balanced height of a tree have a traveling front structure. In addition, the variance of the number of nodes needed to store a data string of a given size N is shown to undergo a striking phase transition at a critical value of the branching ratio m_c=26. We identify the mechanism of this phase transition, show that it is generic and occurs in various other problems as well. New results are obtained when each element of the data string is a D-dimensional vector. We show that this problem also has a phase transition at a critical dimension, D_c= \pi/\sin^{-1}(1/\sqrt{8})=8.69363...Comment: 11 pages, 8 .eps figures included. Invited contribution to STATPHYS-22 held at Bangalore (India) in July 2004. To appear in the proceedings of STATPHYS-2