Riemann zeros, prime numbers and fractal potentials

Using two distinct inversion techniques, the local one-dimensional potentials for the Riemann zeros and prime number sequence are reconstructed. We establish that both inversion techniques, when applied to the same set of levels, lead to the same fractal potential. This provides numerical evidence that the potential obtained by inversion of a set of energy levels is unique in one-dimension. We also investigate the fractal properties of the reconstructed potentials and estimate the fractal dimensions to be $D=1.5$ for the Riemann zeros and $D = 1.8$ for the prime numbers. This result is somewhat surprising since the nearest-neighbour spacings of the Riemann zeros are known to be chaotically distributed whereas the primes obey almost poisson-like statistics. Our findings show that the fractal dimension is dependent on both the level-statistics and spectral rigidity, $\Delta_3$, of the energy levels.Comment: Five postscript figures included in the text. To appear in Phys. Rev.

Global well-posedness for the critical 2D dissipative quasi-geostrophic equation

We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate moduli of continuity.Comment: 7 page

Energy dissipation and ion heating at the heliospheric termination shock

The Los Alamos hybrid simulation code is used to examine heating and the partition of dissipation energy at the perpendicular heliospheric termination shock in the presence of pickup ions. The simulations are one-dimensional in space but three-dimensional in field and velocity components, and are carried out for a range of values of pickup ion relative density. Results from the simulations show that because the solar wind ions are relatively cold upstream, the temperature of these ions is raised by a relatively larger factor than the temperature of the pickup ions. An analytic model for energy partition is developed on the basis of the Rankine-Hugoniot relations and a polytropic energy equation. The polytropic index gamma used in the Rankine-Hugoniot relations is varied to improve agreement between the model and the simulations concerning the fraction of downstream heating in the pickup ions as well as the compression ratio at the shock. When the pickup ion density is less than 20%, the polytropic index is about 5/3, whereas for pickup ion densities greater than 20%, the polytropic index tends toward 2.2, suggesting a fundamental change in the character of the shock, as seen in the simulations, when the pickup ion density is large. The model and the simulations both indicate for the upstream parameters chosen for Voyager 2 conditions that the pickup ion density is about 25% and the pickup ions gain the larger share ( approximately 90%) of the downstream thermal pressure, consistent with Voyager 2 observations near the shock

Tree-level Split Helicity Amplitudes in Ambitwistor Space

We study all tree-level split helicity gluon amplitudes by using the recently proposed BCFW recursion relation and Hodges diagrams in ambitwistor space. We pick out the contributing diagrams and find that all of them can be divided into triangles in a suitable way. We give the explicit expressions for all of these amplitudes. As an example, we reproduce the six gluon split NMHV amplitudes in momentum space.Comment: 20 pages, 16 figures; minor changes; clarifications added, 22 pages, 16 figure

Accelerating charging dynamics in sub-nanometer pores

Having smaller energy density than batteries, supercapacitors have exceptional power density and cyclability. Their energy density can be increased using ionic liquids and electrodes with sub-nanometer pores, but this tends to reduce their power density and compromise the key advantage of supercapacitors. To help address this issue through material optimization, here we unravel the mechanisms of charging sub-nanometer pores with ionic liquids using molecular simulations, navigated by a phenomenological model. We show that charging of ionophilic pores is a diffusive process, often accompanied by overfilling followed by de-filling. In sharp contrast to conventional expectations, charging is fast because ion diffusion during charging can be an order of magnitude faster than in bulk, and charging itself is accelerated by the onset of collective modes. Further acceleration can be achieved using ionophobic pores by eliminating overfilling/de-filling and thus leading to charging behavior qualitatively different from that in conventional, ionophilic pores

Gluon chain formation in presence of static charges

We consider the origins of the gluon chain model. The model serves as a realization of the dynamics of the chromoelectric flux between static quark-antiquark sources. The derivation is based on the large-N_C limit of the Coulomb gauge Hamiltonian in the presence of a background field introduced to model magnetic confinement.Comment: 10 pages, 9 figure

An Upper Limit on Omega_matter Using Lensed Arcs

We use current observations on the number statistics of gravitationally lensed optical arcs towards galaxy clusters to derive an upper limit on the cosmological mass density of the Universe. The gravitational lensing statistics due to foreground clusters combine properties of both cluster evolution, which is sensitive to the matter density, and volume change, which is sensitive to the cosmological constant. The uncertainties associated with the predicted number of lensing events, however, currently do not allow one to distinguish between flat and open cosmological models with and without a cosmological constant. Still, after accounting for known errors, and assuming that clusters in general have dark matter core radii of the order ~ 35 h^-1 kpc, we find that the cosmological mass density, Omega_m, is less than 0.56 at the 95% confidence. Such a dark matter core radius is consistent with cluster potentials determined recently by detailed numerical inversions of strong and weak lensing imaging data. If no core radius is present, the upper limit on Omega_m increases to 0.62 (95% confidence level). The estimated upper limit on Omega_m is consistent with various cosmological probes that suggest a low matter density for the Universe.Comment: 6 pages, 3 figures. Accepted version (ApJ in press