Orbital approach to microstate free entropy

Motivated by Voiculescu's liberation theory, we introduce the orbital free entropy $\chi_orb$ for non-commutative self-adjoint random variables (also for "hyperfinite random multi-variables"). Besides its basic properties the relation of $\chi_orb$ with the usual free entropy $\chi$ is shown. Moreover, the dimension counterpart $\delta_{0,orb}$ of $\chi_orb$ is discussed, and we obtain the relation of $\delta_{0,orb}$ with the original free entropy dimension $\delta_0$ with applications to $\delta_0$ itself.Comment: 38 pages; Section 5 was largely improved and Section 6 was adde

Mechanically-Induced Transport Switching Effect in Graphene-based Nanojunctions

We report a theoretical study suggesting a novel type of electronic switching effect, driven by the geometrical reconstruction of nanoscale graphene-based junctions. We considered junction struc- tures which have alternative metastable configurations transformed by rotations of local carbon dimers. The use of external mechanical strain allows a control of the energy barrier heights of the potential profiles and also changes the reaction character from endothermic to exothermic or vice-versa. The reshaping of the atomic details of the junction encode binary electronic ON or OFF states, with ON/OFF transmission ratio that can reach up to 10^4-10^5. Our results suggest the possibility to design modern logical switching devices or mechanophore sensors, monitored by mechanical strain and structural rearrangements.Comment: 10 pages, 4 figure

A Simple Model for Estimating Water Balance and Salinity of Reservoirs and Outflow

Reservoir storage reduces fluctuation in streamflow salinity, yet increases outflow salinity because of water evaporation. These processes are highly relevant to developing water management strategy, yet the method to predict outflow salinity has not been adequately examined. The study reported here examined the water and salt balance in a reservoir using a two-layer model. This model assumes that inflow blends with the storage, but the water evaporation takes place from the surface layer, and the percolation losses from the subsurface. The thickness of the first layer where salinity increases with evaporation was estimated through calibration against the measured outflow salinity. The changes in salinity were computed using a moving average method on a monthly time step. This model was applied first to Red Bluff Reservoir of the Middle Pecos River, then to Elephant Butte, Amistad, and Falcon along the Rio Grande. The outflow salinity projected by the model was in good agreement with the measured, except under a few circumstances where mixing of inflow and reservoir storage was suspected to be incomplete. The accuracy of prediction can be improved by improving the estimate of initial salinity of reservoir storage, which is currently taken as being equal to outflow salinity at the onset of the simulation

Free initial wave packets and the long-time behavior of the survival and nonescape probabilities

The behavior of both the survival S(t) and nonescape P(t) probabilities at long times for the one-dimensional free particle system is shown to be closely connected to that of the initial wave packet at small momentum. We prove that both S(t) and P(t) asymptotically exhibit the same power-law decrease at long times, when the initial wave packet in momentum representation behaves as O(1) or O(k) at small momentum. On the other hand, if the integer m becomes greater than 1, S(t) and P(t) decrease in different power-laws at long times.Comment: 4 pages, 3 figures, Title and organization changed, however the results not changed, To appear in Phys. Rev.

Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras

We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also show that all these vertex operator algebras are C_2-cofinite.Comment: 21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is improved and one reference is adde

Darwin Tames an Andromeda Dwarf: Unraveling the Orbit of NGC 205 Using a Genetic Algorithm

NGC 205, a close satellite of the M31 galaxy, is our nearest example of a dwarf elliptical galaxy. Photometric and kinematic observations suggest that NGC 205 is undergoing tidal distortion from its interaction with M31. Despite earlier attempts, the orbit and progenitor properties of NGC 205 are not well known. We perform an optimized search for these unknowns by combining a genetic algorithm with restricted N-body simulations of the interaction. This approach, coupled with photometric and kinematic observations as constraints, allows for an effective exploration of the parameter space. We represent NGC 205 as a static Hernquist potential with embedded massless test particles that serve as tracers of surface brightness. We explore 3 distinct, initially stable configurations of test particles: cold rotating disk, warm rotating disk, and hot, pressure-supported spheroid. Each model reproduces some, but not all, of the observed features of NGC 205, leading us to speculate that a rotating progenitor with substantial pressure support could match all of the observables. Furthermore, plausible combinations of mass and scale length for the pressure-supported spheroid progenitor model reproduce the observed velocity dispersion profile. For all 3 models, orbits that best match the observables place the satellite 11+/-9 kpc behind M31 moving at very large velocities: 300-500 km/s on primarily radial orbits. Given that the observed radial component is only 54 km/s, this implies a large tangential motion for NGC 205, moving from the NW to the SE. These results suggest NGC 205 is not associated with the stellar arc observed to the NE of NGC 205. Furthermore, NGC 205's velocity appears to be near or greater than its escape velocity, signifying that the satellite is likely on its first M31 passage.Comment: 34 pages, 20 figures, accepted for publication in the Astrophysical Journal, A pdf version with high-resolution figures may be obtained from http://www.ucolick.org/~kirsten/ms.pd