"Doubled" generalized Landau-Lifshiz hierarchies and special quasigraded Lie algebras

Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy which we call "doubled" generalized Landau-Lifshiz hierarchy. This hierarchy can be also interpreted as an anisotropic vector generalization of "modified" Sine-Gordon hierarchy or as a very special vector generalization of so(3) anisotropic chiral field hierarchy.Comment: 16 pages, no figures, submitted to Journal of Physics

Large-scale fluctuations and particle diffusion across external magnetic field in turbulent plasmas

Kinetic theory of electromagnetic fluctuations in turbulent plasmas in the external magnetic field has been worked out with regard for the effect of fluid-like random motions on fluctuation dynamics. The dielectric response functions and correlation functions of the Langevin sources for the system under consideration are calculated and general relations for fluctuation spectra are derived. Fluctuations associated with the diffusive particle motion across the external magnetic field are studied in detail.Розроблено кінетичну теорію електромагнітних флуктуацій у турбулентній плазмі за наявності зовнішнього магнітного поля з урахуванням впливу випадкових гідродинамічних рухів на динаміку флуктуацій. Обчислено функції діелектричного відгуку і кореляційні функції ланжевенових джерел та отримано загальні вирази для спектрів флуктуацій. Детально вивчено флуктуації пов’язані з дифузійним рухом частинок поперек зовнішнього магнітного поля

On Separation of Variables for Integrable Equations of Soliton Type

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg--de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg magnetic equations.Comment: 22 page

Modeling of Metallurgical Process of Copper Fire Refining

The refining of blister copper is based on the partial removal of impurities that have an increased affinity for oxygen. The most interesting is the process of centralized copper refining at one plant. This is because blister copper from the producer plants has a different chemical composition. Obviously, the batch of each loading also has a variable chemical composition. Therefore, for a constantly changing averageweighted composition of a liquid metal, a different amount of oxygen is required to oxidize and slag the impurities. The aim of the work is the method of creating a mathematical model for solving the single-criterion and multicriteria task of firerefining of copper. Algorithms of the model based on the passive experiment are presented, with the chosen assumptions and limitations. Mathematical models are developed using correlation regression analysis. The resultant variable in the models is the concentration of oxygen in the melt. The objective function is determined by the main variables of the refining process. The results of mathematical modeling allow us to quickly calculate the concentration of oxygen supplied in the air composition into the melt of a batch of different chemical composition for the oxidation of impurities. The models are consistent with the general theory of anode melting, and can be used to control and predict the process. Keywords: fire refining, blister copper, impurity oxidation, mathematical model, linear regressio

Verification of gyrokinetic particle simulation of current-driven instability in fusion plasmas. I. Internal kink mode

The gyrokinetic toroidal code (GTC) capability has been extended for simulating internal kink instability with kinetic effects in toroidal geometry. The global simulation domain covers the magnetic axis, which is necessary for simulating current-driven instabilities. GTC simulation in the fluid limit of the kink modes in cylindrical geometry is verified by benchmarking with a magnetohydrodynamic eigenvalue code. Gyrokinetic simulations of the kink modes in the toroidal geometry find that ion kinetic effects significantly reduce the growth rate even when the banana orbit width is much smaller than the radial width of the perturbed current layer at the mode rational surface

Enhanced Preconditioner for JOREK MHD Solver

The JOREK extended magneto-hydrodynamic (MHD) code is a widely used simulation code for studying the non-linear dynamics of large-scale instabilities in divertor tokamak plasmas. Due to the large scale-separation intrinsic to these phenomena both in space and time, the computational costs for simulations in realistic geometry and with realistic parameters can be very high, motivating the investment of considerable effort for optimization. In this article, a set of developments regarding the JOREK solver and preconditioner is described, which lead to overall significant benefits for large production simulations. This comprises in particular enhanced convergence in highly non-linear scenarios and a general reduction of memory consumption and computational costs. The developments include faster construction of preconditioner matrices, a domain decomposition of preconditioning matrices for solver libraries that can handle distributed matrices, interfaces for additional solver libraries, an option to use matrix compression methods, and the implementation of a complex solver interface for the preconditioner. The most significant development presented consists in a generalization of the physics based preconditioner to "mode groups", which allows to account for the dominant interactions between toroidal Fourier modes in highly non-linear simulations. At the cost of a moderate increase of memory consumption, the technique can strongly enhance convergence in suitable cases allowing to use significantly larger time steps. For all developments, benchmarks based on typical simulation cases demonstrate the resulting improvements

Non-Markovian effects in turbulent diffusion: kinetic theory and numerical simulation

The theory of time-nonlocal random processes formulated in terms of non-Markovian Fokker-Planck equation is used to describe the results of numerical simulations of particle diffusion in the random longitudinal field with prescribed statistical properties

Topological excitations in 2D spin system with high spin s>=1s>= 1

We construct a class of topological excitations of a mean field in a two-dimensional spin system represented by a quantum Heisenberg model with high powers of exchange interaction. The quantum model is associated with a classical one (the continuous classical analogue) that is based on a Landau-Lifshitz like equation, and describes large-scale fluctuations of the mean field. On the other hand, the classical model is a Hamiltonian system on a coadjoint orbit of the unitary group SU($2s {+} 1$) in the case of spin $s$. We have found a class of mean field configurations that can be interpreted as topological excitations, because they have fixed topological charges. Such excitations change their shapes and grow preserving an energy.Comment: 10 pages, 1 figur

Recreating Early Islamic Glass Lamp Lighting

Early Islamic light sources are not simple, static, uniform points, and the fixtures themselves are often combinations of glass, water, fuel and flame. Various physically based renderers such as Radiance are widely used for modeling ancient architectural scenes; however they rarely capture the true ambiance of the environment due to subtle lighting effects. Specifically, these renderers often fail to correctly model complex caustics produced by glass fixtures, water level, and fuel sources. While the original fixtures of the 8th through 10th century Mosque of Córdoba in Spain have not survived, we have applied information gathered from earlier and contemporary sites and artifacts, including those from Byzantium, to assume that it was illuminated by either single jar lamps or supported by polycandela that cast unique downward caustic lighting patterns which helped individuals to navigate and to read. To re-synthesize such lighting, we gathered experimental archaeological data and investigated and validated how various water levels and glass fixture shapes, likely used during early Islamic times, changed the overall light patterns and downward caustics. In this paper, we propose a technique called Caustic Cones, a novel data-driven method to ‘shape’ the light emanating from the lamps to better recreate the downward lighting without resorting to computationally expensive photon mapping renderers. Additionally, we demonstrate on a rendering of the Mosque of Cordoba how our approach greatly benefits archaeologists and architectural historians by providing a more authentic visual simulation of early Islamic glass lamp lighting