Mathematical modeling of bulk and directional crystallization with the moving phase transition layer

This paper is devoted to the mathematical modeling of a combined effect of directional and bulk crystallization in a phase transition layer with allowance for nucleation and evolution of newly born particles. We consider two models with and without fluctuations in crystal growth velocities, which are analytically solved using the saddle-point technique. The particle-size distribution function, solid-phase fraction in a supercooled two-phase layer, its thickness and permeability, solidification velocity, and desupercooling kinetics are defined. This solution enables us to characterize the mushy layer composition. We show that the region adjacent to the liquid phase is almost free of crystals and has a constant temperature gradient. Crystals undergo intense growth leading to fast mushy layer desupercooling in the middle of a two-phase region. The mushy region adjacent to the solid material is filled with the growing solid-phase structures and is almost desupercooled. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.Russian Science Foundation, RSF: 21-79-10012The authors gratefully acknowledge financial support from the Russian Science Foundation (project no. 21-79-10012). Open Access funding enabled and organized by Projekt DEAL

Mushy Layer Formation during Solidification of Binary Alloys from a Cooled Wall: the Role of Boundary Conditions

Motivated by metallurgical and geophysical applications we present a mathematical model describing the process of unidirectional solidification of binary melts or solutions, which is based on the classical Stefan thermodiffusion theory with a planar front up to a time of mushy layer initiation and on the quasi-equilibrium theory of solidification with a constitutionally supercooled region afterwards. The role of boundary conditions imposed at the cooled wall is studied in terms of heat flux coefficients describing ultimately nonlinear dynamics of the process

Phenomenology of Quantum Gravity and its Possible Role in Neutrino Anomalies

New phenomenological models of Quantum Gravity have suggested that a Lorentz-Invariant discrete spacetime structure may become manifest through a nonstandard coupling of matter fields and spacetime curvature. On the other hand, there is strong experimental evidence suggesting that neutrino oscillations cannot be described by simply considering neutrinos as massive particles. In this manuscript we motivate and construct one particular phenomenological model of Quantum Gravity that could account for the so-called neutrino anomalies.Comment: For the proceedings of "Relativity and Gravitation: 100 Years after Einstein in Prague" (June 2012, Prague

Environmental Mortality and Long-Run Growth

There is emerging evidence that environmental degradation increases human mortality. This paper provides a long-run consumer optimization model in which mortality is endogenous to emissions generated by production. Emissions are assumed to follow the EKC path, first rising and then falling along with ouput. In the optimum, some deaths are accepted as an exchange for consumption. The model is estimated for the European outdoor air pollution data, showing that Europe has reached the downward sloping sement of the EKC. Economic growth will thus decrease rather than increase air pollution and the associted deaths in most countries in Europe

Focal-plane detector system for the KATRIN experiment

The focal-plane detector system for the KArlsruhe TRItium Neutrino (KATRIN) experiment consists of a multi-pixel silicon p-i-n-diode array, custom readout electronics, two superconducting solenoid magnets, an ultra high-vacuum system, a high-vacuum system, calibration and monitoring devices, a scintillating veto, and a custom data-acquisition system. It is designed to detect the low-energy electrons selected by the KATRIN main spectrometer. We describe the system and summarize its performance after its final installation.Comment: 28 pages. Two figures revised for clarity. Final version published in Nucl. Inst. Meth.