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1. Investigation of conditions necessary for inception of positive corona in air based on differential formulation of photoionization

   https://doi.org/10.1088/1361-6595/ace6d0  

   Pasko, Victor P. ; Janalizadeh, Reza ; Jansky, Jaroslav ( July 2023 , Plasma Sources Science and Technology)

   Sharp point electrodes generate significant electric field enhancements where electron impact ionization leads to the formation of electron avalanches that are seeded by photoionization. Photoionization of molecular oxygen due to extreme ultraviolet emissions from molecular nitrogen is a fundamental process in the inception of a positive corona in air. In a positive corona system, the avalanche of electrons in the bulk of the discharge volume is initiated by a specific distribution of photoionization far away from the region of maximum electron density near the electrode where these photons are emitted. Here, we present a new approach to finding the inception conditions for a positive corona, which is based on a differential formulation of the photoionization problem. The proposed iterative solution considers the same inception problem that has been solved in the existing literature by using either an integral approach to photoionization or a differential formulation of photoionization and considering the inception problem as a boundary-value eigenvalue problem. The results are validated by comparisons with previous integral formulations and time dynamic plasma fluid solutions in planar and spherical geometries. The results illustrate ideas advanced in Kaptzov (1950Elektricheskiye Yavleniya v Gazakh i Vacuumep 610) providing a physically transparent connection between an effective secondary electron emission coefficient due to volume photoionization in a positive corona system and the secondary electron emission in conventional Townsend discharge theory. The results also demonstrate the significance of boundary conditions for accurate corona solutions that are based on a differential formulation of photoionization.

    

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2. Asymptotics of noncolliding q-exchangeable random walks

   https://doi.org/10.1088/1751-8121/acedda  

   Petrov, Leonid ; Tikhonov, Mikhail ( August 2023 , Journal of Physics A: Mathematical and Theoretical)

   We consider a process of noncollidingq-exchangeable random walks on$\mathbb{Z}$making steps 0 (‘straight’) and −1 (‘down’). A single random walk is calledq-exchangeable if under an elementary transposition of the neighboring steps$(\text{down},\text{straight})\to (\text{straight},\text{down})$the probability of the trajectory is multiplied by a parameter$q\in (0,1)$. Our process ofmnoncollidingq-exchangeable random walks is obtained from the independentq-exchangeable walks via the Doob’sh-transform for a nonnegative eigenfunctionh(expressed via theq-Vandermonde product) with the eigenvalue less than 1. The system ofmwalks evolves in the presence of an absorbing wall at 0. The repulsion mechanism is theq-analogue of the Coulomb repulsion of random matrix eigenvalues undergoing Dyson Brownian motion. However, in our model, the particles are confined to the positive half-line and do not spread as Brownian motions or simple random walks. We show that the trajectory of the noncollidingq-exchangeable walks started from an arbitrary initial configuration forms a determinantal point process, and express its kernel in a double contour integral form. This kernel is obtained as a limit from the correlation kernel ofq-distributed random lozenge tilings of sawtooth polygons. In the limit as$m\to \mathrm{\infty }$,$q=e^{-\gamma /m}$withγ > 0 fixed, and under a suitable scaling of the initial data, we obtain a limit shape of our noncolliding walks and also show that their local statistics are governed by the incomplete beta kernel. The latter is a distinguished translation invariant ergodic extension of the two-dimensional discrete sine kernel.

    

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3. Polarized Maser Emission with In-source Faraday Rotation

   https://doi.org/10.3847/1538-4357/aca595  

   Tobin, T. L. ; Gray, M. D. ; Kemball, A. J. ( February 2023 , The Astrophysical Journal)

   We discuss studies of polarization in astrophysical masers with particular emphasis on the case where the Zeeman splitting is small compared to the Doppler profile, resulting in a blend of the transitions between magnetic substates. A semiclassical theory of the molecular response is derived, and coupled to radiative transfer solutions for 1 and 2-beam linear masers, resulting in a set of nonlinear, algebraic equations for elements of the molecular density matrix. The new code, PRISM, implements numerical methods to compute these solutions. Using PRISM, we demonstrate a smooth transfer between this case and that of wider splitting. For aJ= 1–0 system, with parameters based on thev= 1,J= 1–0 transition of SiO, we investigate the behavior of linear and circular polarization as a function of the angle between the propagation axis and the magnetic field, and with the optical depth, or saturation state, of the model. We demonstrate how solutions are modified by the presence of Faraday rotation, generated by various abundances of free electrons, and that strong Faraday rotation leads to additional angles where the StokesQchanges sign. We compare our results to a number of previous models, from the analytical limits derived by Goldreich, Keeley, and Kwan in 1973, through computational results by W. Watson and coauthors, to the recent work by Lankhaar and Vlemmings in 2019. We find that our results are generally consistent with those of other authors given the differences in the approach and the approximations made.

    

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4. Quantum‐classical path integral evaluation of reaction rates with a near‐equilibrium flux formulation

   https://doi.org/10.1002/qua.26618  

   Bose, Amartya ; Makri, Nancy ( February 2021 , International Journal of Quantum Chemistry)

   Quantum‐classical formulations of reactive flux correlation functions require the partial Weyl–Wigner transform of the thermalized flux operator, whose numerical evaluation is unstable because of phase cancelation. In a recent paper, we introduced a non‐equilibrium formulation which eliminates the need for construction of this distribution and which gives the reaction rate along with the time evolution of the reactant population. In this work, we describe a near‐equilibrium formulation of the reactive flux, which accounts for important thermal correlations between the quantum system and its environment while avoiding the numerical instabilities of the full Weyl–Wigner transform. By minimizing early‐time transients, the near‐equilibrium formulation leads to an earlier onset of the plateau regime, allowing determination of the reaction rate from short‐time dynamics. In combination with the quantum‐classical path integral methodology, the near‐equilibrium formulation offers an accurate and efficient approach for determining reaction rate constants in condensed phase environments. The near‐equilibrium formulation may also be combined with a variety of approximate quantum‐classical propagation methods.

    

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5. Constant spacing in filament bundles

   https://doi.org/10.1088/1367-2630/ab1c2d  

   Atkinson, Daria W. ; Santangelo, Christian D. ; Grason, Gregory M. ( June 2019 , New Journal of Physics)

   Assemblies of one-dimensional filaments appear in a wide range of physical systems: from biopolymer bundles, columnar liquid crystals, and superconductor vortex arrays; to familiar macroscopic materials, like ropes, cables, and textiles. Interactions between the constituent filaments in such systems are most sensitive to thedistance of closest approachbetween the central curves which approximate their configuration, subjecting these distinct assemblies to common geometric constraints. In this paper, we consider two distinct notions of constant spacing in multi-filament packings in${\mathbb{R}}^3$:equidistance, where the distance of closest approach is constant along the length of filament pairs; andisometry, where the distances of closest approach between all neighboring filaments are constant and equal. We show that, although any smooth curve in${\mathbb{R}}^3$permits one dimensional families of collinear equidistant curves belonging to a ruled surface, there are only two families of tangent fields with mutually equidistant integral curves in${\mathbb{R}}^3$. The relative shapes and configurations of curves in these families are highly constrained: they must be either (isometric) developable domains, which can bend, but not twist; or (non-isometric) constant-pitch helical bundles, which can twist, but not bend. Thus, filament textures that are simultaneously bent and twisted, such as twisted toroids of condensed DNA plasmids or wire ropes, are doubly frustrated: twist frustrates constant neighbor spacing in the cross-section, while non-equidistance requires additional longitudinal variations of spacing along the filaments. To illustrate the consequences of the failure of equidistance, we compare spacing in three ‘almost equidistant’ ansatzes for twisted toroidal bundles and use our formulation of equidistance to construct upper bounds on the growth of longitudinal variations of spacing with bundle thickness.

    

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