Installation for studying the parameters of localiInstallation for studying the parameters of localization of an electromagnetic wave in a waveguide of variable cross-section in the framework of the predictions of the 5-D extended space modelzation of an electromagnetic wave in a waveguide of variable cross-section in the framework of the predictions of the 5-D extended space model

The paper describes the creation and testing of an experimental setup for studying the parameters of localization of electromagnetic microwave radiation with a power of 0.001-0.004 W in the range of 36.0-79.0 GHz when propagating radiation in metal waveguides of variable cross-section. Measurements will also be carried out under conditions of filling the waveguide with dielectric materials with refractive indices from 1.46 to 4.0 for microwave radiation of the specified range. The installation is designed to measure the parameters of the localization of microwave radiation when it passes through a waveguide of variable cross-section, filled with materials with different refractive indices. Interpretation of the results will be carried out within the framework of the 5-D extended space model (ESM). The extended space model is formulated in (1+4)-dimensional space time-coordinate-interval. An additional spatial coordinate in the ESM is the interval. In the conjugate 5-D space, the energy-momentum-mass interval in the ESM corresponds to mass. In the ESM formalism, the question of the appearance of a nonzero variable mass in a photon and its localization under the influence of an external field is studied.

Mathematical modeling of the influence of non-catalytic dissociation / recombination of water molecules in the desalination channel on electric convection

The article formulates a two-dimensional mathematical model of non-stationary transport of 1: 1 electrolyte in a potentiodynamic mode, taking into account electroconvection and non-catalytic dissociation / recombination reaction of water molecules in electromembrane systems, which are considered as the desalting channel of an electrodialysis device. The model is described by a system of coupled Navier-Stokes and Nernst-Planck-Poisson equations taking into account the electric force and physically justified boundary conditions. The article establishes the basic laws of mass transport, taking into account the dissociation / recombination of water molecules. It was shown for the first time that a double electric layer of hydrogen and hydroxyl ions arises in the recombination region. It is shown that between the region of recombination and quasi-equilibrium regions of space charge there are regions of electroneutrality and equilibrium with an almost linear distribution of concentrations. It was found that even under prelimiting, but close enough to the limiting current, modes, non-catalytic dissociation of water molecules in the quasi-equilibrium region of space charge occurs so intensely that the concentration of hydrogen and hydroxyl ions becomes comparable to the concentration of potassium and chlorine ions. At overlimiting current densities, due to the appearance of an extended space charge region and intense dissociation of water molecules in this region, as well as an increase in the electric double layer in the recombination region, the space charge and the dissociation / recombination reaction of water molecules significantly affect each other. In turn, this has a decisive effect on electroconvection and, accordingly, on the transport of salt ions.

Charge algebra for non-abelian large gauge symmetries at O(r)

Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are O(1) in the large r expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with O(r) gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with O(r) gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which O(1) and O(r) charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra.

Discovery, TESS Characterization, and Modeling of Pulsations in the Extremely Low-mass White Dwarf GD 278

We report the discovery of pulsations in the extremely low-mass (ELM), likely helium-core white dwarf GD 278 via ground- and space-based photometry. GD 278 was observed by the Transiting Exoplanet Survey Satellite (TESS) in Sector 18 at a 2 minute cadence for roughly 24 days. The TESS data reveal at least 19 significant periodicities between 2447 and 6729 s, one of which is the longest pulsation period ever detected in a white dwarf. Previous spectroscopy found that this white dwarf is in a 4.61 hr orbit with an unseen >0.4 M ⊙ companion and has T eff = 9230 ± 100 K and log g = 6.627 ± 0.056 , which corresponds to a mass of 0.191 ± 0.013 M ⊙. Patterns in the TESS pulsation frequencies from rotational splittings appear to reveal a stellar rotation period of roughly 10 hr, making GD 278 the first ELM white dwarf with a measured rotation rate. The patterns inform our mode identification for asteroseismic fits, which, unfortunately, do not reveal a global best-fit solution. Asteroseismology reveals two main solutions roughly consistent with the spectroscopic parameters of this ELM white dwarf, but with vastly different hydrogen-layer masses; future seismic fits could be further improved by using the stellar parallax. GD 278 is now the tenth known pulsating ELM white dwarf; it is only the fifth known to be in a short-period binary, but is the first with extended, space-based photometry.

Mathematical Modeling of the Phenomenon of Space-Charge Breakdown in the Galvanostatic Mode in the Section of the Electromembrane Desalination Channel

One of the ways to increase the efficiency of the desalination process in membrane systems is to use intensive current modes. Recently, the phenomenon of space-charge breakdown was theoretically described for desalination under intensive current modes. The space-charge breakdown is a decrease in the magnitude and size of the extended space charge regions (SCRs) of opposite signs, formed at the cation- and anion-exchange membranes in the desalination channel, when they approach each other. Therefore, this phenomenon negatively affects the intensity of electroconvection and the efficiency of mass transfer in membrane systems. We report the results of the first theoretical analysis of the space-charge breakdown in the galvanostatic electric mode, which is generally used in the research and operation of membrane systems. For this purpose, a one-dimensional model of the ion transfer of the electrolyte solution in the section of the desalination channel at the direct current is developed. The regularities of changes in the extended SCRs in the galvanostatic mode are determined. A relation is obtained for the onset time of the space-charge breakdown, which makes it possible to determine the parameters of the effective operation of the membrane system.

Geometry and kinematics induced by biquaternionic and twistor structures

The algebra of biquaternions possess a manifestly Lorentz invariant form and induces an extended space-time geometry. We consider the links between this complex pre-geometry and real geometry of the Minkowski space-time. Twistor structures naturally arise in the framework of biquaternionic analysis. Both together, algebraic and twistor structures impose rigid restriction on the transport of singular points of biquaternion-valued fields identified with particle-like formations.

Anderson accelerated augmented Lagrangian for extended waveform inversion

The augmented Lagrangian (AL) method provides a flexible and efficient framework for solving extended-space full-waveform inversion (FWI), a constrained nonlinear optimization problem whereby we seek model parameters and wavefields that minimize the data residuals and satisfy the wave equation constraint. The AL-based wavefield reconstruction inversion, also known as iteratively refined wavefield reconstruction inversion, extends the search space of FWI in the source dimension and decreases sensitivity of the inversion to the initial model accuracy. Furthermore, it benefits from the advantages of the alternating direction method of multipliers (ADMM), such as generality and decomposability for dealing with non-differentiable regularizers, e.g., total variation regularization, and large scale problems, respectively. In practice any extension of the method aiming at improving its convergence and decreasing the number of wave-equation solves would have a great importance. To achieve this goal, we recast the method as a general fixed-point iteration problem, which enables us to apply sophisticated acceleration strategies like Anderson acceleration. The accelerated algorithm stores a predefined number of previous iterates and uses their linear combination together with the current iteration to predict the next iteration. We investigate the performance of the proposed accelerated algorithm on a simple checkerboard model and the benchmark Marmousi II and 2004 BP salt models through numerical examples. These numerical results confirm the effectiveness of the proposed algorithm in terms of convergence rate and the quality of the final estimated model.

Localized Kaluza-Klein 6-brane

We study the membrane wrapping mode corrections to the Kaluza-Klein (KK) 6-brane in eleven dimensions. We examine the localized KK6-brane in the extended space in E7(7) exceptional field theory. In order to discuss the physical origin of the localization in the extended space, we consider a probe M2-brane in eleven dimensions. We show that a three-dimensional $$ \mathcal{N} $$ N = 4 gauge theory is naturally interpreted as a membrane generalization of the two-dimensional $$ \mathcal{N} $$ N = (4, 4) gauged linear sigma model for the fundamental string. We point out that the vector field in the $$ \mathcal{N} $$ N = 4 model is identified as a dual coordinate of the KK6-brane geometry. We find that the BPS vortex in the gauge theory gives rise to the violation of the isometry along the dual direction. We then show that the vortex corrections are regarded as an instanton effect in M-theory induced by the probe M2-brane wrapping around the M-circle.