Deligne categories and reduced Kronecker coefficients

The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups, namely, given three partitions λ,μ,τ of n, the multiplicity of λ in μ⊗τ is called the Kronecker coefficient g[superscript λ][subscript μ,τ]. When the first part of each of the partitions is taken to be very large (the remaining parts being fixed), the values of the appropriate Kronecker coefficients stabilize; the stable value is called the reduced (or stable) Kronecker coefficient. These coefficients also generalize the Littlewood–Richardson coefficients and have been studied quite extensively. In this paper, we show that reduced Kronecker coefficients appear naturally as structure constants of Deligne categories [bar under Rep](S[subscript t]). This allows us to interpret various properties of the reduced Kronecker coefficients as categorical properties of Deligne categories [bar under Rep](S[subscript t]) and derive new combinatorial identities

Nonlinear Waves in Rocks

We are interested in the nonlinear interaction of frequency components in large amplitude acoustic waves in rocks. As compared to other, more ordered solids, rocks are elastically highly nonlinear. The ratio of third order elastic constants to second order elastic constants in a typical rock is orders of magnitude greater than in solids such as iron [1]. This high degree of nonlinearity means that frequency components mix and elastic energy is transferred from the fundamentals to sum and difference frequencies. There are at least three reasons for our interest in these effects in rocks. 1) Accurate models of explosion and earthquake sources may depend on understanding nonlinear elastic effects. 2) Efficient frequency mixing in a highly nonlinear elastic material could lead to a low frequency seismic source generated from two high frequency input waves. 3) Accurate measurement of nonlinear coefficients in rock would provide a sensitive probe of physical characteristics such as consolidation and saturation

Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure

The spin-orbit interaction affects the electronic structure of solids in various ways. Topological insulators are one example where the spin-orbit interaction leads the bulk bands to have a non-trivial topology, observable as gapless surface or edge states. Another example is the Rashba effect, which lifts the electron-spin degeneracy as a consequence of spin-orbit interaction under broken inversion symmetry. It is of particular importance to know how these two effects, i.e. the non-trivial topology of electronic states and Rashba spin splitting, interplay with each other. Here we show, through sophisticated first-principles calculations, that BiTeI, a giant bulk Rashba semiconductor, turns into a topological insulator under a reasonable pressure. This material is shown to exhibit several unique features such as, a highly pressure-tunable giant Rashba spin splitting, an unusual pressure-induced quantum phase transition, and more importantly the formation of strikingly different Dirac surface states at opposite sides of the material.Comment: 5 figures are include

Pressure dependent electronic properties of MgO polymorphs: A first-principles study of Compton profiles and autocorrelation functions

The first-principles periodic linear combination of atomic orbitals method within the framework of density functional theory implemented in the CRYSTAL06 code has been applied to explore effect of pressure on the Compton profiles and autocorrelation functions of MgO. Calculations are performed for the B1, B2, B3, B4, B8_1 and h-MgO polymorphs of MgO to compute lattice constants and bulk moduli. The isothermal enthalpy calculations predict that B4 to B8_1, h-MgO to B8_1, B3 to B2, B4 to B2 and h-MgO to B2 transitions take place at 2, 9, 37, 42 and 64 GPa respectively. The high pressure transitions B8_1 to B2 and B1 to B2 are found to occur at 340 and 410 GPa respectively. The pressure dependent changes are observed largely in the valence electrons Compton profiles whereas core profiles are almost independent of the pressure in all MgO polymorphs. Increase in pressure results in broadening of the valence Compton profiles. The principal maxima in the second derivative of Compton profiles shifts towards high momentum side in all structures. Reorganization of momentum density in the B1 to B2 structural phase transition is seen in the first and second derivatives before and after the transition pressure. Features of the autocorrelation functions shift towards lower r side with increment in pressure.Comment: 19 pages, 8 figures, accepted for publication in Journal of Materials Scienc

Nano-mechanical properties of Fe-Mn-Al-C lightweight steels

High Al Low-density steels could have a transformative effect on the light-weighting of steel structures for transportation and achieving the desired properties with the minimum amount of Ni is of great interest from an economic perspective. In this study, the mechanical properties of two duplex low-density steels, Fe-15Mn-10Al-0.8C-5Ni and Fe-15Mn-10Al-0.8C (wt.%) were investigated through nano-indentation and simulation through utilization of ab initio formalisms in Density Functional Theory (DFT) in order to establish the hardness resulting from two critical structural features (ߢ-carbides and B2 intermetallic) as a function of annealing temperature (500 − 1050 ℃) and the addition of Ni. In the Ni-free sample, the calculated elastic properties of kappa-carbides were compared with those of the B2 intermetallic Fe3Al − L12, and the role of Mn in the kappa structure and its elastic properties were studied. The Ni-containing samples were found to have a higher hardness due to the B2 phase composition being NiAl rather than FeAl, with Ni-Al bonds reported to be stronger than the Fe-Al bonds. In both samples, at temperatures of 900 ℃ and above, the ferrite phase contained nano-sized discs of B2 phase, wherein the Ni-containing samples exhibited higher hardness, attributed again to the stronger Ni-Al bonds in the B2 phase. At 700 ℃ and below, the nano-sized B2 discs were replaced by micrometre sized needles of kappa in the Ni-free sample resulting in a lowering of the hardness. In the Ni-containing sample, the entire alpha phase was replaced by B2 stringers, which had a lower hardness than the Ni-Al nano-discs due to a lower Ni content in B2 stringer bands formed at 700 ℃ and below. In addition, the hardness of needle-like kappa-carbides formed in alpha phase was found to be a function of Mn content. Although it was impossible to measure the hardness of cuboid kappa particles in gamma phase because of their nano-size, the hardness value of composite phases, e.g. gamma + kappa was measured and reported. All the hardness values were compared and rationalized by bonding energy between different atoms