Passage through exceptional point: case study

The description of unitary evolution using non-Hermitian but ‘hermitizable’ Hamiltonians H is feasible via an ad hoc metric Θ = Θ ( H ) and a (non-unique) amendment 〈 ψ 1 | ψ 2 〉 → 〈 ψ 1 | Θ | ψ 2 〉 of the inner product in Hilbert space. Via a proper fine-tuning of Θ ( H ) this opens the possibility of reaching the boundaries of stability (i.e. exceptional points) in many quantum systems sampled here by the fairly realistic Bose–Hubbard (BH) and discrete anharmonic oscillator (AO) models. In such a setting, it is conjectured that the EP singularity can play the role of a quantum phase-transition interface between different dynamical regimes. Three alternative ‘AO ↔ BH’ implementations of such an EP-mediated dynamical transmutation scenario are proposed and shown, at an arbitrary finite Hilbert-space dimension N , exact and non-numerical.

Analytical solutions of mushy layer equations describing directional solidification in the presence of nucleation

The processes of particle nucleation and their evolution in a moving metastable layer of phase transition (supercooled liquid or supersaturated solution) are studied analytically. The transient integro-differential model for the density distribution function and metastability level is solved for the kinetic and diffusionally controlled regimes of crystal growth. The Weber–Volmer–Frenkel–Zel’dovich and Meirs mechanisms for nucleation kinetics are used. We demonstrate that the phase transition boundary lying between the mushy and pure liquid layers evolves with time according to the following power dynamic law: , where Z 1 ( t )= βt 7/2 and Z 1 ( t )= βt 2 in cases of kinetic and diffusionally controlled scenarios. The growth rate parameters α , β and ε are determined analytically. We show that the phase transition interface in the presence of crystal nucleation and evolution propagates slower than in the absence of their nucleation. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Effects of Surface Roughness on Bonding Behavior of Cold Spray Ti6Al4V Coatings

In this study, a penitential additive manufacturing method - cold spray was used to deposit Ti6Al4V powders onto Ti6Al4V substrates with different surface roughness by using a high pressure cold spray system. The coating quality was good with limited porosity and without phase transition. Interface bonding behavior between coating and substrate was studied, which indicated that smoother substrate surface would increase the bonding strength. Bending test showed that all the coated samples started to delaminate before substrate failure and smoother surface samples could resist higher stress than the rougher surface samples.

A Numerical Model of the Crystallization of Pure Aluminium

The model was originally designed to confirm and enhance the capabilities of experimental research in the crystallization of pure aluminium (99.99% Al), specifically to determine the zone of the occurrence of columnar and equiaxed crystals and the positions of the transition interface. The character of primary crystallization was investigated on a simple cylindrical sample, crystallizing in a cast-iron mould pre-heated to various temperatures. The experimental research comprised the measurement of temperatures using thermocouples, the evaluation of the experimentally acquired temperature gradients G, and the shift rate of the phase transition interface R. The numerical model had been developed to expand the limited experimental capabilities of the evaluation of G and R to every point of the longitudinal section, based on the investigation of the 3D transient temperature field within the system comprising the casting, the mould and ambient. This enabled the prediction of the character of the crystallization in greater detail.