Related papers: Looping of a long chain polymer in solution: Simpl…
We present a detailed study of the static and dynamic behavior of long semiflexible polymer chains in a melt. Starting from previously obtained fully equilibrated high molecular weight polymer melts [{\it Zhang et al.} ACS Macro Lett. 3,…
We introduce a two-phase approximation method designed to resolve singularities in three-dimensional harmonic Dirichlet problems. The approach utilizes the classical Green's function representation, decomposing the function into its…
For a regular transient diffusion, we provide a decomposition of its last passage time to a certain state $\alpha$. This is accomplished by transforming the original diffusion into two diffusions using the occupation time of the area above…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…
We employ 3D Langevin Dynamics simulations to study the dynamics of polymer chains translocating through a nanopore in presence of asymmetric solvent conditions. Initially a large fraction ($>$ 50%) of the chain is placed at the…
Taking into account the nonequivalence of fixed-force and fixed-length ensembles in the weak-force regime, equations of state are derived that describe the equilibrium extension or compression of an ideal Gaussian polymer chain in response…
The loop equation satisfied by Wilson's loops in QCD is reformulated as a functional Laplace equation. Discretizing the loop space by polygons, Green's function of the functional Laplacian is represented as a path integral of the Euclidean…
The kinetic theory of rarefied gases and numerical schemes based on the Boltzmann equation have evolved to the cornerstone of non-equilibrium gas dynamics. However, their counterparts in the dense regime remain rather exotic for practical…
We present a simple analytical theory of flexible polymer chain dissolved in a good solvent, carrying permanent freely oriented dipoles on the monomers. We take into account the dipole correlations within the random phase approximation…
Practical methods to compute dipole strengths for a three-body system by using a discretized continuum are analyzed. New techniques involving Green's function are developed, either by correcting the tail of the approximate wave function in…
We analyze the motion of individual beads of a polymer chain using a discrete version of De Gennes' reptation model that describes the motion of a polymer through an ordered lattice of obstacles. The motion within the tube can be evaluated…
The various equations at the surfaces and triple contact lines of a deformable body are obtained from a variational condition, by applying Green's formula in the whole space and on the Riemannian surfaces. The surface equations are similar…
In Green's function theory, the total energy of an interacting many-electron system can be expressed in a variational form using the Klein or Luttinger-Ward functionals. Green's function theory also naturally addresses the case where the…
The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers…
The analytic treatment of the non-inertial rotational diffusion equation, i.e., of the Smoluchowski's one (SE), in a symmetric genuinely double-well Maier-Saupe uniaxial potential of mean torque is considered. Such potential may find…
We consider the generalization of the Kramers escape over a barrier problem to the case of a long chain molecule. It involves the motion of chain molecule of N segments across a region where the free energy per segment is higher, so that it…
The dynamic structure factor of semiflexible polymers in solution is derived from the wormlike chain model. Special attention is paid to the rigid constraint of an inextensible contour and to the hydrodynamic interactions. For the cases of…
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…
The well-known expressions for the Green's functions for the Helmholtz equation in polar coordinates with Dirichlet and Neumann boundary conditions are transformed. The slowly converging double series describing these Green's functions are…
The competition between reptation and Rouse Dynamics is incorporated in the Rubinstein-Duke model for polymer motion by extending it with sideways motions, which cross barriers and create or annihilate hernias. Using the Density-Matrix…