Breakdown of adiabatic invariance in spherical tokamaks

Thermal ions in spherical tokamaks have two adiabatic invariants: the magnetic moment and the longitudinal invariant. For hot ions, variations in magnetic-field strength over a gyro period can become sufficiently large to cause breakdown of the adiabatic invariance. The magnetic moment is more sensitive to perturbations than the longitudinal invariant and there exists an intermediate regime, super-adiabaticity, where the longitudinal invariant remains adiabatic, but the magnetic moment does not. The motion of super-adiabatic ions remains integrable and confinement is thus preserved. However, above a threshold energy, the longitudinal invariant becomes non-adiabatic too, and confinement is lost as the motion becomes chaotic. We predict beam ions in present-day spherical tokamaks to be super-adiabatic but fusion alphas in proposed burning-plasma spherical tokamaks to be non-adiabatic.Comment: 6 pages, 8 figure

The spin alignment of galaxies with the large-scale tidal field in hydrodynamic simulations

The correlation between the spins of dark matter halos and the large-scale structure (LSS) has been studied in great detail over a large redshift range, while investigations of galaxies are still incomplete. Motivated by this point, we use the state-of-the-art hydrodynamic simulation, Illustris-1, to investigate mainly the spin--LSS correlation of galaxies at redshift of $z=0$. We mainly find that the spins of low-mass, blue, oblate galaxies are preferentially aligned with the slowest collapsing direction ($e_3$) of the large-scale tidal field, while massive, red, prolate galaxy spins tend to be perpendicular to $e_3$. The transition from a parallel to a perpendicular trend occurs at $\sim10^{9.4} M_{\odot}/h$ in the stellar mass, $\sim0.62$ in the g-r color, and $\sim0.4$ in triaxiality. The transition stellar mass decreases with increasing redshifts. The alignment was found to be primarily correlated with the galaxy stellar mass. Our results are consistent with previous studies both in N-body simulations and observations. Our study also fills the vacancy in the study of the galaxy spin--LSS correlation at $z=0$ using hydrodynamical simulations and also provides important insight to understand the formation and evolution of galaxy angular momentum.Comment: 9 pages, 6 figures, 1 table. Accepted for publication in ApJ, match the proof versio

Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

P-wave pi pi amplitude from dispersion relations

We solve the dispersion relation for the P-wave pi pi amplitude.We discuss the role of the left hand cut vs Castillejo-Dalitz-Dyson (CDD), pole contribution and compare the solution with a generic quark model description. We review the the generic properties of analytical partial wave scattering and production amplitudes and discuses their applicability and fits of experimental data.Comment: 10 pages, 7 figures, typos corrected, reference adde

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation