Dendritic to globular morphology transition in ternary alloy solidification

The evolution of solidification microstructures in ternary metallic alloys is investigated by adaptive finite element simulations of a general multicomponent phase-field model. A morphological transition from dendritic to globular growth is found by varying the alloy composition at a fixed undercooling. The dependence of the growth velocity and of the impurity segregation in the solid phase on the composition is analyzed and indicates a smooth type of transition between the dendritic and globular growth structures.Comment: 4 pages, 2 figure

Parity-violating nucleon-nucleon interaction from different approaches

Two-pion exchange parity-violating nucleon-nucleon interactions from recent effective field theories and earlier fully covariant approaches are investigated. The potentials are compared with the idea to obtain better insight on the role of low-energy constants appearing in the effective field theory approach and the convergence of this one in terms of a perturbative series. The results are illustrated by considering the longitudinal asymmetry of polarized protons scattering off protons, $\vec{p}+p -> p+p$, and the asymmetry of the photon emission in radiative capture of polarized neutrons by protons, $\vec{n}+p -> d+\gamma$.Comment: 31 page

Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter

The goal in this paper is to demonstrate a new method for constructing global-in-time approximate (asymptotic) solutions of (pseudodifferential) parabolic equations with a small parameter. We show that, in the leading term, such a solution can be constructed by using characteristics, more precisely, by using solutions of the corresponding Hamiltonian system and without using any integral representation. For completeness, we also briefly describe the well-known scheme developed by V.P.Maslov for constructing global-in-time solutions.Comment: 27 page

Effectively Closed Infinite-Genus Surfaces and the String Coupling

The class of effectively closed infinite-genus surfaces, defining the completion of the domain of string perturbation theory, can be included in the category $O_G$, which is characterized by the vanishing capacity of the ideal boundary. The cardinality of the maximal set of endpoints is shown to be 2^{\mit N}. The product of the coefficient of the genus-g superstring amplitude in four dimensions by $2^g$ in the $g\to \infty$ limit is an exponential function of the genus with a base comparable in magnitude to the unified gauge coupling. The value of the string coupling is consistent with the characteristics of configurations which provide a dominant contribution to a finite vacuum amplitude.Comment: TeX, 33 page

Morphological stability diagram for slowly and rapidly solidifying binary systems

A linear morphological stability of the solid-liquid interface is analyzed for a binary alloy in the limit of low and high crystal growth velocities. Using the result of this analysis, a diagram of morphologies is derived for a whole range of solidification rates with indicating critical growth velocities for the transitions planar front ⇔ cellular/dendritic structure. It is specially noted that the speed of solute diffusion in the bulk liquid limits the absolute chemical stability velocity from the high-rate transition cells/dendrites ⇒ planar front. © 2020, The Author(s)

Graph hypersurfaces and a dichotomy in the Grothendieck ring

The subring of the Grothendieck ring of varieties generated by the graph hypersurfaces of quantum field theory maps to the monoid ring of stable birational equivalence classes of varieties. We show that the image of this map is the copy of Z generated by the class of a point. Thus, the span of the graph hypersurfaces in the Grothendieck ring is nearly killed by setting the Lefschetz motive L to zero, while it is known that graph hypersurfaces generate the Grothendieck ring over a localization of Z[L] in which L becomes invertible. In particular, this shows that the graph hypersurfaces do not generate the Grothendieck ring prior to localization. The same result yields some information on the mixed Hodge structures of graph hypersurfaces, in the form of a constraint on the terms in their Deligne-Hodge polynomials.Comment: 8 pages, LaTe

Four-body Efimov effect

We study three same spin state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384 < M/m < 13.607 where there exists a purely four-body Efimov effect, leading to the occurrence of weakly bound tetramers without Efimov trimers.Comment: 4 pages, 2 figure

Beam instabilities in Very Large Hadron Collider

The Very Large Hadron Collider (VLHC) is a supercon-ducting proton-proton collider with approximately 100 TeV cm and approximately 10{sup 34} s{sup -1}cm{sup -2} luminosity [1]. Currently, beam dynamics in this future accelerator is the subject of intensive studies within the framework of the US-wide VLHC R&D program. This presentation sum-marizes recent developments in the field. Besides general discussion on relevant VLHC parameters, we consider various beam instabilities and ways to avoid them. Finally, we outline possibilities for theoretical and experimental R&D