Polymer deformation and particle tunneling from Schwarzschild black hole

In this paper, we investigate a tunneling mechanism of massless particles from the Schwarzschild black hole (S-BH) in the framework of polymer quantum mechanics. According to the corresponding invariant Liouville volume, we determine the tunneling rate from S-BH by the polymeric quantization procedure. In this regard, we show that the temperature and tunneling radiation of the black hole receive new corrections in such a way that the exact radiant spectrum is no longer precisely thermal.

The viscoelastic signature underpinning polymer deformation under shear flow

The structure of a large deformed polymer is divided into smaller layers, enabling an analytical fit to neutron scattering data.

Perturbative expansions of the conformation tensor in viscoelastic flows

We consider the problem of formulating perturbative expansions of the conformation tensor, which is a positive definite tensor representing polymer deformation in viscoelastic flows. The classical approach does not explicitly take into account that the perturbed tensor must remain positive definite – a fact that has important physical implications, e.g. extensions and compressions are represented similarly to within a negative sign, when physically the former are unbounded and the latter are bounded from below. Mathematically, the classical approach assumes that the underlying geometry is Euclidean, and this assumption is not satisfied by the manifold of positive definite tensors. We provide an alternative formulation that retains the conveniences of classical perturbation methods used for generating linear and weakly nonlinear expansions, but also provides a clear physical interpretation and a mathematical basis for analysis. The approach is based on treating a perturbation as a sequence of successively smaller deformations of the polymer. Each deformation is modelled explicitly using geodesics on the manifold of positive definite tensors. Using geodesics, and associated geodesic distances, is the natural way to model perturbations to positive definite tensors because it is consistent with the manifold geometry. Approximations of the geodesics can then be used to reduce the total deformation to a series expansion in the small perturbation limit. We illustrate our approach using direct numerical simulations of the nonlinear evolution of Tollmien–Schlichting waves.

Polymer translocation through nano-pores: influence of pore and polymer deformation

We have simulated polymer translocation across the a α-hemolysin nano-pore via a coarse grained computational model for both the polymer and the pore. We simulate the translocation process by allowing the protein cross a free-energy barrier from a metastable state, in the presence of thermal fluctuations. The deformation in the channel, which we model by making the radius of pore change from large to small size, can be originated by the random and non-random (systematic) cellular environment, drive out the polymer out of equilibrium during the transport dynamics. We expect that in more realistic conditions, effects originating on the translocation phenomena due to the deformability of the nano-pore can either decrease or increase the transport time of biomolecule passing through the channel. Deformation in channel can occurred because the structure of α-hemolysin channel is not completely immobile, hence a small pore deformation can be occurred during translocation process. We also discuss the effects of polymer deformation on the translocation process, which we achieve by varying the value of the empirical and dihedral potential constants. We investigate the dynamic and thermodynamical properties of the translocation process by revealing the statistics of translocation time as a function of the pulling inward force acting along the axis of the pore under the influence of small and large pore. We observed that a pore with small size can speed down the polymer translocation process, especially at the limit of small pulling force. A drastic increase in translocation time at the limit of low force for small pore clearly illustrate the strong interaction between the transport polymer and pore. Our results can be of fundamental importance for those experiments on DNA-RNA sorting and sequencing and drug delivery mechanism for anti-cancer therapy.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.