Density- and elongation speed-dependent error correction in RNA polymerization

Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process that enhances transcription fidelity. We model the backtracking mechanism of RNA polymerase, which usually happens when the polymerase tries to incorporate a noncognate or "mismatched" nucleotide triphosphate. Previous models have made simplifying assumptions such as neglecting the trailing polymerase behind the backtracking polymerase or assuming that the trailing polymerase is stationary. We derive exact analytic solutions of a stochastic model that includes locally interacting RNAPs by explicitly showing how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. We also provide two related methods for computing the mean times for error correction and incorporation given an initial local RNAP configuration. Using these results, we propose an effective interacting-RNAP lattice that can be readily simulated.

An Archimedes' Screw for Light

An Archimedes' Screw captures water, feeding energy into it by lifting it to a higher level. We introduce the first instance of an optical Archimedes' Screw, and demonstrate how this system is capable of capturing light, dragging it and amplifying it. We unveil new exact analytic solutions to Maxwell's Equations for a wide family of chiral space-time media, and show their potential to achieve chirally selective amplification within widely tunable parity-time-broken phases. Our work, which may be readily implemented via pump-probe experiments with circularly polarized beams, opens a new direction in the physics of time-varying media by merging the rising field of space-time metamaterials and that of chiral systems, and offers a new playground for topological and non-Hermitian photonics, with potential applications to chiral spectroscopy and sensing.

The cosmology of quadratic torsionful gravity

We study the cosmology of a quadratic metric-compatible torsionful gravity theory in the presence of a perfect hyperfluid. The gravitational action is an extension of the Einstein–Cartan theory given by the usual Einstein–Hilbert contribution plus all the admitted quadratic parity even torsion scalars and the matter action also exhibits a dependence on the connection. The equations of motion are obtained by regarding the metric and the metric-compatible torsionful connection as independent variables. We then consider a Friedmann–Lemaître–Robertson–Walker background, analyze the conservation laws, and derive the torsion modified Friedmann equations for our theory. Remarkably, we are able to provide exact analytic solutions for the torsionful cosmology.

Induced Currents and Aharonov–Bohm Effect in Effective Fermion Models and in Spaces with a Compact Dimension

We consider fermion models in 3D- and 5D-space-time with an Aharonov–Bohm potential and a domain wall. Induced current is calculated, which is due to vacuum effects in the topologically nontrivial space-time. Violation of chiral symmetry and appearance of induced current is demonstrated in a simple example of quantum mechanical violation of symmetry in a model of a massless Dirac fermion moving in a background vector field and domain walls as barriers for the electron propagation. The effective Dirac equation for massless electrons modeling monolayer graphene is used. One of the solutions to the problem of describing domain walls in planar systems is reduced to finding exact analytic solutions. In this paper, we consider appearance of induced current in two-fermion model with a compact dimension as a result of vacuum polarization in the field of the external gauge field in the 4 + 1 and the 2 + 1 dimensional models with one type of fermions and with two types of fermions living in the brane and in the bulk. Two different approaches (Kaluza–Klein and Aharonov–Bohm) to the problem of induced current are used. Production of an induced current in a planar model with a thin solenoid is also studied.

New Soliton Solutions for the Higher-Dimensional Non-Local Ito Equation

In this article, (2+1)-dimensional Ito equation that models waves motion on shallow water surfaces is analyzed for exact analytic solutions. Two reliable techniques involving the simplest equation and modified simplest equation algorithms are utilized to find exact solutions of the considered equation involving bright solitons, singular periodic solitons, and singular bright solitons. These solutions are also described graphically while taking suitable values of free parameters. The applied algorithms are effective and convenient in handling the solution process for Ito equation that appears in many phenomena.

Fully Developed Transport Constants of Annular Tubes, With Application to the Entrance Region

Description of the laminar thermal entry problem in annular tubes has historically been limited to a few geometric cases that require piecing together classical Graetz series and Lévêque series solutions to span all values of the Graetz number. The current work uses a recently developed generalized correlation to describe the full range of Graetz numbers for any annular tube geometry. However, the correlation requires fully developed Nusselt number values that have only been accurately reported in tabular and graphical forms. Exact analytic solutions for the constant wall heat flux condition are developed in this work, and simplified correlations are proposed for all wall conditions that reproduce exact Nusselt number solutions to within ± 0.4%. Using these results, a modified version of the generalized Graetz problem correlation is developed to reproduce the most published Nusselt numbers for the thermal entry problem in an annular tube to be within ± 5%.

Exact Steady Solutions for the Two Dimensional Broadwell Model

Existence and boundedness of the solutions of the boundary value problem for the four velocity two dimensional Broadwell model for bounded boundary conditions is proved and exact analytic solutions are built. An application to the determination of the accommodation coefficients on the boundaries of a flow in a box is performed.

Polarized Baryon Production in Heavy Ion Collisions: An Analytic Hydrodynamical Study

In this paper, we utilize known exact analytic solutions of perfect fluid hydrodynamics to analytically calculate the polarization of baryons produced in heavy-ion collisions. Assuming local thermodynamical equilibrium also for spin degrees of freedom, baryons get a net polarization at their formation (freeze-out). This polarization depends on the time evolution of the Quark-Gluon Plasma (QGP), which can be described as an almost perfect fluid. By using exact analytic solutions, we can thus analyze the necessity of rotation (and vorticity) for non-zero net polarization. In this paper, we give the first analytical calculations for the polarization four-vector. We use two hydrodynamical solutions; one is the spherically symmetric Hubble flow (a somewhat oversimplified model, to demonstrate the methodology); and the other solution is a somewhat more involved one that corresponds to a rotating and accelerating expansion, and is thus well-suited for the investigation of some of the main features of the time evolution of the QGP created in peripheral heavy-ion collisions (although there are still numerous features of real collision geometry that are beyond the scope of this simple model). Finally, we illustrate and discuss our results on the polarization.

Peculiarities of electromagnetic field oscillations of a charged particle rotating about a conductive ball

The paper investigates some characteristic features of the electromagnetic field of a relativistic charged particle that uniformly rotates about a conductive ball in its equatorial plane. It is assumed that the braking of the particle due to radiation is compensated by an external influence (e.g. the electric force) that compels the particle to turn uniformly in a circle. The magnetic permittivity of the ball is assumed to be one. The work is based on the corresponding exact analytic solutions of Maxwell’s equations. The generalized Drude-Lorentz-Sommerfeld formula for the dielectric function of the conductive ball is used in numerical calculations. It is shown that localized oscillations of a high-amplitude electromagnetic field can be generated at a given harmonic inside the ball at a certain (resonant) particle rotation frequency at a small distance from the surface of the ball. Herewith, at large distances from the trajectory of the particle, these localized oscillations are accompanied by intense radiation at the same harmonic, which is many times more intense than the analogous radiation in the case when the ball is absent. The possibilities of using this phenomenon to develop sources of quasi-monochromatic electromagnetic radiation in the range from giga- to terra hertz frequencies are discussed.