Scattering of plane-wave and twisted photons by helical media

By using quantumelectrodynamics in a dispersivemedium,we describe scattering of plane-wave and twisted photons by a slab made of a helical medium, the helix axis being normal to the slab plane and the medium being not translation invariant in this plane, in general. In the particular cases, the permittivity tensor of a helical medium corresponds to cholesteric liquid crystals, C∗-smectics, biaxial chiral nematics and smectics, Q-plates, chiral sculptured thin films, and helical dislocations. Both perturbative and nonperturbative approaches are considered. The explicit expressions for scattering amplitudes, probabilities, and Stokes parameters of photons are found taking into account the form of the photon wave packet. The selection rules are established showing that the helical medium transfers the momentum and the angular momentum to scattered photons. This property can be employed for production of twisted photons with large projection of the total angular momentum. We describe the device for shifting the projection of the total angular momentum of a photon and the principal scheme for signal coding in terms of twisted photons

Statistical Analysis of Precipitation Events

In the present paper we demonstrate the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential distributions based on the information-theoretical entropy reasoning. The proposed models can be also treated as the result of following the popular Bayesian approach.Comment: 5 pages, 4 figures; ICNAAM 201

Opening of DNA double strands by helicases. Active versus passive opening

Helicase opening of double-stranded nucleic acids may be "active" (the helicase directly destabilizes the dsNA to promote opening) or "passive" (the helicase binds ssNA available due to a thermal fluctuation which opens part of the dsNA). We describe helicase opening of dsNA, based on helicases which bind single NA strands and move towards the double-stranded region, using a discrete ``hopping'' model. The interaction between the helicase and the junction where the double strand opens is characterized by an interaction potential. The form of the potential determines whether the opening is active or passive. We calculate the rate of passive opening for the helicase PcrA, and show that the rate increases when the opening is active. Finally, we examine how to choose the interaction potential to optimize the rate of strand separation. One important result is our finding that active opening can increase the unwinding rate by 7 fold compared to passive opening.Comment: 13 pages, 3 figure

Growth, competition and cooperation in spatial population genetics

We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space is continuous and the total density of competing individuals fluctuates due to demographic stochasticity. By means of analytics and numerical simulations, we study the behavior of fixation probabilities, fixation times, and heterozygosity, in a neutral setting and in cases where the two species can compete or cooperate. By concluding with examples in which individuals are transported by fluid flows, we argue that this model is a natural choice to describe competition in marine environments.Comment: 29 pages, 14 figures; revised version including a section with results in the presence of fluid flow

Multiplexing signals with twisted photons by a circular arc phased array

The theory of multiplexing electromagnetic signals by means of twisted photons generated by a uniform circular array is developed in the case when the receiving antenna represents an array of elements located on a circular arc. The notion of discrete twisted photons of the order $N$ is introduced and orthogonality of these modes modulo $N$ is established. Both paraxial and planar discrete twisted photons are considered. It is shown that in the simplest scenario a $K$ times decrease of the circular arc where the receiving array antenna is placed results in a $K$ times decrease of the number of independent information channels. In the more sophisticated approach, one can restore all $N\gg1$ independent information channels in receiving the signal by an array antenna with $N$ elements located on a circular arc with the central angle $2\pi/K$. However, this problem becomes rapidly ill-conditioned as one increases $K$. The method mitigating this issue is described. The estimates for the corresponding condition numbers are found.Comment: 15 pp., 3 fig

Short wavelength band structure of photons in cholesteric liquid crystals

The band structure of photons in cholesteric liquid crystals (CLCs) is investigated in the shortwave approximation. The bound states or narrow resonances of photons in the CLC are formed by the extraordinary waves. The explicit expressions for the spectrum bands and the dispersion laws of photons in these bands are obtained. It is shown that these states describe photons propagating almost perpendicular to the CLC axis. The density of photon states acquires a sharp peak due to the presence of bound states. Near this peak, in the particular case of plasma permittivity, the photons posses a linear or quadratic dispersion relations in the directions perpendicular to the CLC axis depending on the sign of the anisotropy of the CLC permittivity tensor. The resonances in the CLC plate are also described.Comment: 23 pp., 4 figs, some elucidations adde

Radiation of twisted photons from charged particles moving in cholesterics

The radiation of twisted photons by charged particles traversing a cholesteric plate is studied in the framework of quantum electrodynamics in an anisotropic inhomogeneous dispersive medium. The complete set of solutions to the Maxwell equations in the cholesteric plate is constructed in the paraxial and small anisotropy approximations. The explicit expressions for the average numbers of plane-wave and twisted photons created by a charged point particle crossing the cholesteric plate are derived. The selection rules for the twisted photons radiated at the harmonic $n\in \mathbb{Z}$ are established. In the paraxial regime, the projection of the orbital angular momentum of a radiated twisted photon obeys the selection rule $l=\pm(2n+1)$. In the approximation of a small anisotropy of the permittivity tensor, the selection rule becomes $m=\pm 2n$, where $m$ is the projection of the total angular momentum of a radiated twisted photon. The sign "$\pm$" in these selection rules is related to the choice of the forward or reflected waves in the cholesteric and is realized at the different energies of radiated photons. As the examples, the radiation of optical twisted photons by electrons with the Lorentz factors $\gamma=235$ and $\gamma=500$ and by uranium nuclei with $\gamma=2$ are considered. It is shown that charged particles traversing normally a cholesteric plate can be used as a pure source of twisted photons.Comment: 23 pp., 4 figs; some misprints correcte

Guided random walk calculation of energies and <\sq {r^2} > values of the 1Σg^1\Sigma_g state of H_2 in a magnetic field

Energies and spatial observables for the $^1\Sigma_g$ state of the hydrogen molecule in magnetic fields parallel to the proton-proton axis are calculated with a guided random walk Feynman-Kac algorithm. We demonstrate that the accuracy of the results and the simplicity of the method may prove it a viable alternative to large basis set expansions for small molecules in applied fields.Comment: 10 pages, no figure

Determination of Ethanol Content in Fuels with Phononic Crystal Sensor

Introduction. In-line analysis of ethanol content in gasoline blends is currently one of the urgent needs of fuel industry. Developing safe and secure approaches is critical for real applications. A phononic crystal sensor have been introduced as an innovative approach to high performance gasoline sensing. Distinguishing feature of proposed sensor is the absence of any electrical contact with analysed gasoline blend, which allows the use of sensors directly in pipelines without the risk of explosion in an emergency.Aim. Investigation of the possibilities of using phononic sensor structures to determine the ethanol content in liquid hydrocarbons.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. For measurement, substances of ordinary gasoline and gasoline 63–80 with ethanol concentrations in the range of 1–10 % by volume in increments of 2 % were prepared. The phononic crystal sensor was designed as a stainless steel plate with cylindrical holes and a resonant cavity, formed as a running across the wave propagation path slit between two lattices.Results. In-line analysis of measuring the concentration of ethanol in alcohol-containing fuels on a phononic crystal structure with a resonant cavity was carried out. Using the Agilent4395A admittance meter, the transmission spectra of longitudinal acoustic waves through the gasoline-filled sensor structure with were obtained. The non-linear correlation between the composition and the speed of sound of the blend is presented in the article is due to the ability to reduce the speed of sound of the mixture with an increase in ethanol concentration in the range of 0–10 % by volume.Conclusion. A measurement structure on the basis of phononic crystal was created. The measurements of various gasoline-ethanol mixtures show that the sensor has significant sensitivity (0.91 kHz/ms−1 ) with quality factor of 200) to distinguish between regular fuels, gasoline based blends and the presence of additives in standard fuels. The sensor has prospects for in-line analyzes the composition of liquid hydrocarbons.Introduction. In-line analysis of ethanol content in gasoline blends is currently one of the urgent needs of fuel industry. Developing safe and secure approaches is critical for real applications. A phononic crystal sensor have been introduced as an innovative approach to high performance gasoline sensing. Distinguishing feature of proposed sensor is the absence of any electrical contact with analysed gasoline blend, which allows the use of sensors directly in pipelines without the risk of explosion in an emergency.Aim. Investigation of the possibilities of using phononic sensor structures to determine the ethanol content in liquid hydrocarbons.Materials and methods. A theoretical analysis of sensor structure was carried out on the basis of numerical simulation using COMSOL Multiphysics software. For measurement, substances of ordinary gasoline and gasoline 63–80 with ethanol concentrations in the range of 1–10 % by volume in increments of 2 % were prepared. The phononic crystal sensor was designed as a stainless steel plate with cylindrical holes and a resonant cavity, formed as a running across the wave propagation path slit between two lattices.Results. In-line analysis of measuring the concentration of ethanol in alcohol-containing fuels on a phononic crystal structure with a resonant cavity was carried out. Using the Agilent4395A admittance meter, the transmission spectra of longitudinal acoustic waves through the gasoline-filled sensor structure with were obtained. The non-linear correlation between the composition and the speed of sound of the blend is presented in the article is due to the ability to reduce the speed of sound of the mixture with an increase in ethanol concentration in the range of 0–10 % by volume.Conclusion. A measurement structure on the basis of phononic crystal was created. The measurements of various gasoline-ethanol mixtures show that the sensor has significant sensitivity (0.91 kHz/ms−1 ) with quality factor of 200) to distinguish between regular fuels, gasoline based blends and the presence of additives in standard fuels. The sensor has prospects for in-line analyzes the composition of liquid hydrocarbons