The effects of natural, forced and thermoelectric magnetohydrodynamic convection during the solidification of thin sample alloys

Using a fully coupled transient 3-dimensional numerical model, the effects of convection on the microstructural evolution of a thin sample of Ga-In25%wt. was predicted. The effects of natural convection, forced convection and thermoelectric magnetohydrodynamics were investigated numerically. A comparison of the numerical results is made to experimental results for natural convection and forced convection. In the case of natural convection, density variations within the liquid cause plumes of solute to be ejected into the bulk. When forced convection is applied observed effects include the suppression of solute plumes, preferential secondary arm growth and an increase in primary arm spacing. These effects were observed both numerically and experimentally. By applying an external magnetic field inter-dendritic flow is generated by thermoelectrically induced Lorentz forces, while bulk flow experiences an electromagnetic damping force. The former causes preferential secondary growth, while the latter slows the formation of solute plumes. This work highlights that the application of external forces can be a valuable tool for tailoring the microstructure and ultimately the macroscopic material properties

Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution

Directly in the thermodynamic limit, we show how to combine imaginary and real time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESS) of one-dimensional dissipative quantum lattices governed by the Lindblad master equation. The imaginary time evolution first bypasses any highly correlated portions of the real-time evolution trajectory by directly converging to the weakly correlated subspace of the NESS, after which real time evolution completes the convergence to the NESS with high accuracy. We demonstrate the power of the method with the dissipative transverse field quantum Ising chain. We show that a crossover of an order parameter shown to be smooth in previous finite-size studies remains smooth in the thermodynamic limit.Comment: 5+3 pages, 5 figures, 2 table

Mass Spectra of N=2 Supersymmetric SU(n) Chern-Simons-Higgs Theories

An algebraic method is used to work out the mass spectra and symmetry breaking patterns of general vacuum states in N=2 supersymmetric SU(n) Chern-Simons-Higgs systems with the matter fields being in the adjoint representation. The approach provides with us a natural basis for fields, which will be useful for further studies in the self-dual solutions and quantum corrections. As the vacuum states satisfy the SU(2) algebra, it is not surprising to find that their spectra are closely related to that of angular momentum addition in quantum mechanics. The analysis can be easily generalized to other classical Lie groups.Comment: 17 pages, use revte