Large spin-orbit splitting and weakly-anisotropic superconductivity revealed with single-crystalline noncentrosymmetric CaIrSi3

We report normal and superconducting properties of the Rashba-type noncentrosymmetric com- pound CaIrSi3, using single crystalline samples with nearly 100% superconducting volume fraction. The electronic density of states revealed by the hard x-ray photoemission spectroscopy can be well explained by the relativistic first-principle band calculation. This indicates that strong spin-orbit interaction indeed affects the electronic states of this compound. The obtained H - T phase diagram exhibits only approximately 10% anisotropy, indicating that the superconducting properties are almost three dimensional. Nevertheless, strongly anisotropic vortex pinning is observed.Comment: 8 pages, 6 figures, 1 table, accepted for publication in Phys. Rev.

Crystallographic and superconducting properties of the fully-gapped noncentrosymmetric 5d-electron superconductors CaMSi3 (M=Ir, Pt)

We report crystallographic, specific heat, transport, and magnetic properties of the recently discovered noncentrosymmetric 5d-electron superconductors CaIrSi3 (Tc = 3.6 K) and CaPtSi3 (Tc = 2.3 K). The specific heat suggests that these superconductors are fully gapped. The upper critical fields are less than 1 T, consistent with limitation by conventional orbital depairing. High, non-Pauli-limited {\mu}0 Hc2 values, often taken as a key signature of novel noncentrosymmetric physics, are not observed in these materials because the high carrier masses required to suppress orbital depairing and reveal the violated Pauli limit are not present.Comment: 8 pages, 8 figure

Order statistics and heavy-tail distributions for planetary perturbations on Oort cloud comets

This paper tackles important aspects of comets dynamics from a statistical point of view. Existing methodology uses numerical integration for computing planetary perturbations for simulating such dynamics. This operation is highly computational. It is reasonable to wonder whenever statistical simulation of the perturbations can be much more easy to handle. The first step for answering such a question is to provide a statistical study of these perturbations in order to catch their main features. The statistical tools used are order statistics and heavy tail distributions. The study carried out indicated a general pattern exhibited by the perturbations around the orbits of the important planet. These characteristics were validated through statistical testing and a theoretical study based on Opik theory.Comment: 9 pages, 12 figures, submitted for publication in Astronomy and Astrophysic

KP solitons in shallow water

The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The classification is based on the far-field patterns of the solutions which consist of a finite number of line-solitons. Each soliton solution is then defined by a point of the totally non-negative Grassmann variety which can be parametrized by a unique derangement of the symmetric group of permutations. Our study also includes certain numerical stability problems of those soliton solutions. Numerical simulations of the initial value problems indicate that certain class of initial waves asymptotically approach to these exact solutions of the KP equation. We then discuss an application of our theory to the Mach reflection problem in shallow water. This problem describes the resonant interaction of solitary waves appearing in the reflection of an obliquely incident wave onto a vertical wall, and it predicts an extra-ordinary four-fold amplification of the wave at the wall. There are several numerical studies confirming the prediction, but all indicate disagreements with the KP theory. Contrary to those previous numerical studies, we find that the KP theory actually provides an excellent model to describe the Mach reflection phenomena when the higher order corrections are included to the quasi-two dimensional approximation. We also present laboratory experiments of the Mach reflection recently carried out by Yeh and his colleagues, and show how precisely the KP theory predicts this wave behavior.Comment: 50 pages, 25 figure

Theory of Ferromagnetic Superconductivity

It is argued that the pairing symmetry realized in a ferromagnetic superconductor UGe$_2$ must be a non-unitary triplet pairing. This particular state is free from the Pauli limitation and can survive under a huge internal molecular filed. To check our identification we examine its basic properties and several experiments are proposed. In particular, the external field is used to raise $T_c$ by controlling the internal spontaneous dipole field.Comment: 4 pages, no figure