Related papers: A generalized conservation law for main-chain poly…
The generalized Kawahara equation $u_t=a(t) u_{xxxxx} +b(t)u_{xxx} +c(t)f(u) u_x$ appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which…
We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N. This…
Living materials at different length scales manifest active nematic features such as orientational order, nematic topological defects, and active nematic turbulence. Using numerical simulations we investigate the impact of fluid inertia on…
We consider how beads can diffuse along a chain that wraps them, without becoming displaced from the chain; our proposed mechanism is analogous to the reptation of "stored length" in more familiar situations of polymer dynamics. The problem…
Using path integral technique, we show exactly that for a semiflexible biopolymer in constant extension ensemble, no matter how long the polymer and how large the external force, the effects of short range correlations in the…
Energy conservation imposes fundamental bounds on the polarizabilities of nanoparticles (NPs). While such bounds are well established for isotropic and bianisotropic NPs, they remain unexplored for magneto-optical NPs. Here, we derive the…
The research is important for a molecular theory of liquid and has a wide interest as an example solving the problem when dynamic parameters of systems can be indirectly connected with their equilibrium properties. In frameworks of the…
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the previous notions of self-adjoint and quasi self-adjoint…
Previous work shows that a net directed motion arises from a system of individual particles undergoing run-and-tumble dynamics in the presence of an array of asymmetric barriers. Here, we show that when the individual particle is replaced…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
Conserved quantities such as energy or the electric charge of a closed system, or the Runge-Lenz vector in Kepler dynamics are determined by its global, local, or accidental symmetries. They were instrumental to advances such as the…
We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments…
Topological entanglements in polymers are mimicked by sliding rings (slip-links) which enforce pair contacts between monomers. We study the force-extension curve for linear polymers in which slip-links create additional loops of variable…
We study the effects of intrinsic sequence-dependent curvature for a two dimensional semiflexible biopolymer with short-range correlation in intrinsic curvatures. We show exactly that when not subjected to any external force, such a system…
The presence of ordered structures such as helices in collapsed states of polymer chains is still an open question challenging physics and biology. In this work, we present a potential model for polymer chains with monomers that are not…
We argue that conservation laws based on the local matter-only stress-energy-momentum tensor (characterized by energy and momentum per unit volume) cannot adequately explain a wide variety of even very simple physical phenomena because they…
The aim of this work is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the "universality" of the Onsager exponent, $\alpha > 1/3$,…
The Abraham--Minkowski controversy refers to a long-standing inability to adequately address certain issues involving the conservation of the momentum of an electromagnetic field in a linear dielectric medium. We apply the usual assumption…
The structural properties of polymers adsorbed onto a surface have been widely investigated using self-consistent mean-field theories. Recently, analytical mean-field theories have been applied to study polymer adsorption on curved surfaces…
A Self Consistent Field Theory description of equilibrium, but non uniform, configurations adopted by semi flexible liquid crystal molecules is presented. Two cases are considered, isotropic-nematic phase boundaries, and topological defects…