Related papers: On 4-point correlation functions in simple polymer…
How accurate is pair additivity in describing interactions between soft polymer-based nanoparticles? Using numerical simulations we compute the free energy cost required to overlap multiple chains in the same region of space, and provide a…
We consider gapless models of statistical mechanics. At zero temperatures correlation functions decay asymptotically as powers of distance in these models. Temperature correlations decay exponentially. We used an example of solvable model…
Distance covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors. If the computation of distance covariance and distance correlation is implemented directly…
Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This…
In a variety of situations, isolated polymer molecules are found in a vacuum and here we examine their properties. Angular momentum conservation is shown to significantly alter the average size of a chain and its conservation is only broken…
We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at…
We study an independence test based on distance correlation for random fields $(X,Y)$. We consider the situations when $(X,Y)$ is observed on a lattice with equidistant grid sizes and when $(X,Y)$ is observed at random locations. We provide…
The conformational and electronic properties of conducting flexible random and self-avoiding walk polymer chains are under investigation. A Hamiltonian for conjugated flexible polymers is introduced and its physical consequences are…
Current models of phoretic transport rely on molecular forces creating a "diffuse" particle-fluid interface. We investigate theoretically an alternative mechanism, in which a diffuse interface emerges solely due to a non-vanishing…
We study the behavior of a flexible polymer chain in the presence of a low-molecular weight solvent in the vicinity of a liquid-gas critical point within the framework of a self-consistent field theory. The total free energy of the dilute…
We analyze correlation functions in a toy model of a random geometry interacting with matter. We show that in general the connected correlator will contain a long-range scaling part which is in some sense a remnant of the disconnected part.…
The dynamics of polymer-nanoparticle (NP) mixtures, which involves multiple scales and system-specific variables, has posed a long-standing challenge on its theoretical description. In this paper, we construct a microscopic theory for…
A coarse-graining strategy for dilute and semi-dilute solutions of interacting polymers, and of colloid polymer mixtures is briefly described. Monomer degrees of freedom are traced out to derive an effective, state dependent pair potential…
We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…
We give a descriptive review of the Fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way…
Polymer models play the special role of elucidating the elementary features describing the physics of long molecules and become essential to interpret the measurements of their magnitudes. In this work the end-to-end distance of an…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
Experiments on quasi-one-dimensional systems such as quantum wires and metallic chains on surfaces suggest the existence of electron-electron interactions of substantial range and hence physics beyond the Hubbard model. We therefore…
We use a recently proposed method [Berthier L.; Biroli G.; Bouchaud J.P.; Cipelletti L.; El Masri D.; L'Hote D.; Ladieu F.; Pierno M. Science 2005, 310, 1797.] to obtain an approximation to the 4-point dynamic correlation function from…