P T $\mathcal {P}\mathcal {T}$ -symmetry in Compact Phase Space for a Linear Hamiltonian

International Journal of Theoretical Physics - We study the time evolution of a $\mathcal {P}\mathcal {T}$ -symmetric, non-Hermitian quantum system for which the associated phase space is compact....     

Melting and solidification characteristics of Zr-, Ni-, and Mn-containing 354-type Al-Si-Cu-Mg cast alloys

This study investigated the effects of adding Zr, as a base alloying element, besides Ni and Mn in different amounts and combinations on the melting and solidification characteristics of 354-type Al-Si-Cu-Mg alloys. Differential scanning calorimetry (DSC) was used to characterise the sequence of reactions occurring during the heating and/or cooling cycles; whereas scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) techniques were used to observe and identify existing intermetallic phases. Nickel proved to have a retarding effect on the kinetics of precipitation of the α-Al network and the eutectic Al-Si structure. Also, the presence of Ni consumed a considerable amount of Cu to form Al-Cu-Ni particles instead of Al₂Cu particles. Results revealed that solution treatment at 495°C for 5?h was sufficient to dissolve a large amount of Al₂Cu particles in the α-Al matrix, which is mandatory for a successful aging treatment of the alloys studied. Additions of these transition elements produced new intermetallic phases such as (Al,Si)₃(Ti,Zr), (Al,Si)₃Zr, Al₉FeNi, Al₃Ni, Al₃CuNi, and Al₉FeSi₃Ni₄Zr, in addition to the other phases, namely α-Al, eutectic silicon, Al₂Cu, Mg₂Si, Q-phase (Al₅Cu₂Mg₈Si₆), commonly observed in 354-type alloys, and Fe-based intermetallic phases including β-Al₅FeSi, α-Al₁₅(Fe, Mn)₃Si₂, and π-Al₈FeMg₃Si_6. Superheating the melt at 800°C instead of 750°C had an advantageous effect in that Al₃Zr particles originating from the Al-15%Zr master alloy were dissolved and hence coarse Zr-containing particles were barely spotted in the microstructures examined.     

Correspondence Rules for SU(1,1) Quasidistribution Functions and Quantum Dynamics in the Hyperbolic Phase Space

We derive the explicit differential form for the action of the generators of the SU(1,1) group on the corresponding s-parametrized symbols. This allows us to obtain evolution equations for the phase-space functions on the upper sheet of the two-sheet hyperboloid and analyze their semiclassical limits. Dynamics of quantum systems with SU(1,1) symmetry governed by compact and non-compact Hamiltonians are discussed in both quantum and semiclassical regimes.     

Relation between residual stresses and microstructure evolution in Al–Si alloys based on different casting parameters

Most designers take into consideration the stresses that act on a material but despite safety considerations, failure may occur due to other factors that were neglected in their design. These factors can be a pre-existing flaw, microstructure deficiency or the presence of residual stresses. Depending on the stress type, residual stresses combined with applied stresses can aid or hinder failures. Consequently, reducing the amount of residual stress can have a promising effect on the life of the component. Different casting parameters can change the microstructure and residual stresses of castings. In this research, the relation between residual stresses and microstructure evolution under the influence of different casting parameters was investigated, using both Al–Si–Mg (Al-356) and Al–Si–Mg–Cu (Al-319) alloys. Solidification rate, quenching rate, aging temperature and aging time were the main parameters considered for this study. The results indicate that the magnitude of the residual stresses increases with increasing solidification rate and quenching rate. Also, the residual stress relieving is proportional to the aging temperature