Related papers: Theory of Directed Polymers
Understanding the behavior of biomolecules such as proteins requires understanding the critical influence of the surrounding fluid (solvent) environment--water with mobile salt ions such as sodium. Unfortunately, for many studies, fully…
We introduce and analyze a broad class of continuous directed polymers in $\mathbb{R}^d$ driven by Gaussian environments that are white in time and spatially correlated, under Dalang's condition. Using an It\^o-renormalized…
Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in…
The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary…
We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely determined mesoscopic model for any continuum with…
The non-equilibrium structural and dynamical properties of a flexible polymer tethered to a reflecting wall and subject to oscillatory linear flow are studied by numerical simulations. Polymer is confined in two dimensions and is modeled as…
Non-local electrostatic interactions associated with the finite solvent size and ion polarizability are investigated within the mean-field linear response theory. To this end, we introduce a field theoretic model of a polar liquid composed…
Using the Poisson bracket method, we derive continuum equations for a fluid of deformable particles in two dimensions. Particle shape is quantified in terms of two continuum fields: an anisotropy density field that captures the deformations…
We investigate the global existence of weak solutions to a free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. We construct weak solutions of the two-phase model by performing the…
We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the…
Artificial microswimmers, or "microbots" have the potential to revolutionise non-invasive medicine and microfluidics. Microbots that are powered by self-phoretic mechanisms, such as Janus particles, often harness a solute fuel in their…
We discuss the appropriate techniques for modelling the geometry of open ended elastic polymer molecules. The molecule is assumed to have fixed endpoints on a boundary surface. In particular we discuss the concept of the winding number, a…
We derive the mean-field theory of disordered block-copolymers composed of two monomeric species, combining Edwards' functional method with the replica technique of disordered systems. In the absence of disorder we recover the canonical…
Nematic liquid crystals exhibit configurations in which the underlying ordering changes markedly on macroscopic length scales. Such structures include topological defects in the nematic phase and tactoids within nematic-isotropic…
Nematic polymeric networks are (heat and light) activable materials, which combine the features of rubber and nematic liquid crystals. When only the stretching energy of a thin sheet of nematic polymeric network is minimized, the intrinsic…
This paper is concerned with the dynamics of a binary mixture of rod--like, repulsive colloidal particles driven out of equilibrium by means of a steady shear flow (Couette geometry). To this end we first derive, starting from a microscopic…
We have developed a dynamic self-consistent field theory, without any adjustable parameters, for unentangled polymer blends under shear. Our model accounts for the interaction between polymers, and enables one to compute the evolution of…
We propose and compare different strategies to construct dynamic density functional theories (DDFTs) for inhomogeneous polymer systems close to equilibrium from microscopic simulation trajectories. We focus on the systematic construction of…
Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polymer and the effects it has on the free energy. These directed…
Nonlinear behavior of electro-osmosis in dilute non-adsorbing polymer solutions with low salinity is investigated with Brownian dynamics simulations and a kinetic theory. In the Brownian simulations, the hydrodynamic interaction between the…