The maximal excess charge in reduced Hartree–Fock molecule

We consider a molecule described by the Hartree–Fock model without the exchange term. We prove that the nuclei of total charge [Formula: see text] can bind at most [Formula: see text] electrons, where [Formula: see text] is a constant that is independent of [Formula: see text].

Glide symmetry breaking and Ising criticality in the quasi-1D magnet CoNb2O6

We construct a microscopic spin-exchange Hamiltonian for the quasi–one-dimensional (1D) Ising magnetCoNb2O6that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field–tuned quantum critical point inCoNb2O6corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and quasiparticle breakdown in the polarized phase at high transverse field.

Virtues and Weakness of Brown Micromagnetics

Micromagnetics and its particular case, the Stoner-Wohlfarth model, are reviewed. The possibility of occurrence of curling is discussed. The use of the Felix Bloch approximation for exchange energy description should be avoided. A tensor 3x3 has to be used for appropriate evaluation of the exchange energy in phases with less symmetry, as Nd2Fe14B, Sm2Co17 and SmCo5. The assumptions used in classic Brown micromagnetics make it less suitable for phases with high magnetocrystalline anisotropy. The role of the exchange term in the Stoner-Wohlfarth Callen-Liu-Cullen model is clarified.

Analysis of Powder Segregation in Powder Injection Molding

The powder injection molding (PIM) combines the thermoplastic and powder metallurgy technologies to manufacture intricate parts to nearly shape. The powder segregation is a special effect arising in PIM different from than the pure polymer injection. The two-fluid flow model is used to describe the flows of binder and powder so as to realize the prediction of powder segregation effect in PIM injection. To take into account binder–powder interaction, the mixture model of inter-phase exchange term is introduced in the two-fluid model. The two-fluid equations largely resemble those for single-fluid flow but are represented in terms of the mixture density and velocity. The volume fraction for each dispersed phase is solved from a phase continuity equation. As the key to calculate the phase exchange term, the drag coefficient is defined as a function of mixture viscosity. The effective viscosity of binder and powder are agreed with the additive principle. The volume fractions of binder and powder give directly the evolution of segregation during the injection course. Segregation during PIM injection was simulated by software CFX and results were compared with experimental data with good agreement. The basic reasons that caused segregation are identified as boundary effect, differences in density and viscosity of binder and powder. The segregation zones are well predicted. This showed that the two-fluid model is valid and efficient for the prediction of the segregation effects in PIM injection.