The two dimensional harmonic oscillator on a noncommutative space with minimal uncertainties

The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat noncommutative space and employ it to study the eigenvalue spectrum for the harmonic oscillator on this space. The perturbative expression for the eigenenergy indicates that the model might possess an exceptional point at which the spectrum becomes complex and its PT-symmetry is spontaneously broken.Comment: 4 pages, contribution to proceedings of "Analytic and algebraic methods in physics X", Pragu

Properties of soliton surfaces associated with integrable CPN−1\mathbb{C}P^{N-1} sigma models

We investigate certain properties of $\mathfrak{su}(N)$-valued two-dimensional soliton surfaces associated with the integrable $\mathbb{C}P^{N-1}$ sigma models constructed by the orthogonal rank-one Hermitian projectors, which are defined on the two-dimensional Riemann sphere with finite action functional. Several new properties of the projectors mapping onto one-dimensional subspaces as well as their relations with three mutually different immersion formulas, namely, the generalized Weierstrass, Sym-Tafel and Fokas-Gel'fand have been discussed in detail. Explicit connections among these three surfaces are also established by purely analytical descriptions and, it is demonstrated that the three immersion formulas actually correspond to the single surface parametrized by some specific conditions.Comment: 17 page

Effect of pseudoelasticity of nanocrystalline titanium-nickel on wear

The purpose of this research was to investigate the effect of nanocrystalline structure on shape memory (SM) property and pseudoelasticity (PE) of TiNi alloys with a special focus on the application in tribology. A binary TiNi alloy with 50.8at.% Ni was deformed using cold rolling and equal channel angular pressing (ECAP) method at 450 C to obtain the nanocrystalline structure. The martensitic transformation behaviour after deformation was studied by differential scanning calorimetry and the phase identification was done using X-ray diffraction. SM and pseudoelastic behaviour of the alloy was characterised by indentation and scratch testing. It was shown that after cold rolling and ECAP, the alloy showed higher pseudoelastic recovery. Even though the recovery was not complete, the depth recovery increased with the increasing amount of deformation strain. In addition, the alloy showed 6% SM strain recovery after ECAP processing. The effect of reduced grain size on the PE and SM was analysed and how these properties could be used to achieve a self-healing surface was discussed