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We investigate a system of dense polyelectrolytes in solution. The Langevin dynamics of the system with linearized hydrodynamics is formulated in the functional integral formalism and a transformation made to collective coordinates. Within…
The incompressible fluid dynamics is reformulated as dynamics of closed loops $C$ in coordinate space. This formulation allows to derive explicit functional equation for the generating functional $\Psi[C]$ in inertial range of spatial…
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is…
We study the dynamics of polymer chains in a bath of self-propelled particles (SPP) by extensive Langevin dynamics simulations in a two dimensional system. Specifically, we analyse the polymer looping properties versus the SPP activity and…
We consider a two-layer fluid with a depth-dependent upper-layer current (e.g. a river inflow, an exchange flow in a strait, or a wind-generated current). In the rigid-lid approximation, we find the necessary singular solution of the…
We study the equilibrium dynamics of a single polymer chain under good solvent condition. Special emphasis is laid on varying the drag force experienced by the chain while it moves. To this end we model the solvent in a mesoscopic manner by…
For the rigid, nonrotating motion of an extended charge in an arbitrary electromagnetic field, an equation of motion is derived by Lorentz-invariantly calculating the 4-Lorentz force = external 4-force + 4-self-force, acting upon the…
We study the long-time behavior of \textit{several} point particles in a 1D viscous compressible fluid. It is shown that the velocities of the point particles all obey the power law $t^{-3/2}$. This result extends author's previous works on…
Elastic waves that propagate in polycrystalline materials attenuate due to scattering of energy out of the primary propagation direction in addition to becoming dispersive in their group and phase velocities. Attenuation and dispersion are…
A non-Newtonian flow of a polymer melt is discussed. The description of the exponential decrease of the apparent viscosity by the well-known Eyring formula with an activation energy reduction proportional to the shear stress does not take…
We study the dynamics of a polymer when it is quenched from a $\theta$ solvent into a good or bad solvent by means of a Langevin equation. The variation of the radius of gyration is studied as a function of time. For the first stage of…
The non-linear response of entangled polymers to shear flow is complicated. Its current understanding is framed mainly as a rheological description in terms of the complex viscosity. However, the full picture requires an assessment of the…
Brownian motion and viscoelasticity of semiflexible polymers is a subject that has been studied for many years. Still, rigorous analysis has been hindered due to the difficulty in handling the constraint that polymer chains cannot be…
The Laplace transform method for solving of a wide class of initial value problems for fractional differential equations is introduced. The method is based on the Laplace transform of the Mittag-Leffler function in two parameters. To extend…
We solve the Fokker-Planck equation for Brownian motion in a logarithmic potential. When the diffusion constant is below a critical value the solution approaches a non-normalizable scaling state, reminiscent of an infinite invariant…
Velocity relaxation of a spherically symmetric polymer, immersed in a viscous incompressible fluid, and after a sudden small impulse or a sudden twist from a state of rest, is studied on the basis of the linearized Navier-Stokes equations…
The persistence length of macromolecules is one of their basic characteristics, describing their intrinsic local stiffness. However, it is difficult to extract this length from physical properties of the polymers, different recipes may give…
We develop Monte Carlo simulations for uniformly charged polymers and machine learning algorithm to interpret the intra-polymer structure factor of the charged polymer system, which can be obtained from small-angle scattering experiments.…
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 mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly…