Response of river-dominated delta channel networks to permanent changes in river discharge

Using numerical experiments, we investigate how river-dominated delta channel networks are likely to respond to changes in river discharge predicted to occur over the next century as a result of environmental change. Our results show for a change in discharge up to 60% of the initial value, a decrease results in distributary abandonment in the delta, whereas an increase does not significantly affect the network. However, an increase in discharge beyond a threshold of 60% results in channel creation and an increase in the density of the distributary network. This behavior is predicted by an analysis of an individual bifurcation subject to asymmetric water surface slopes in the bifurcate arms. Given that discharge in most river basins will change by less than 50% in the next century, our results suggest that deltas in areas of increased drought will be more likely to experience significant rearrangement of the delta channel network. Copyright 2010 by the American Geophysical Union

The Formation Rate of Blue Stragglers in 47 Tucanae

We investigate the effects of changes in the blue straggler formation rate in globular clusters on the blue straggler distribution in the color-magnitude diagram. We find that the blue straggler distribution is highly sensitive to the past formation rate. Comparing our models to new UBV observations of a region close to the core of 47 Tucanae suggests that this cluster may have stopped forming blue straggler formation several Gyr ago. This cessation of formation can be associated with an epoch of primordial binary burning which has been invoked in other clusters to infer the imminence of core collapse.Comment: 17 pages, 9 figures, submitted to the Astrophysical Journa

Fluvio-deltaic avulsions during relative sea-level fall.

Understanding river response to changes in relative sea level (RSL) is essential for predicting fluvial stratigraphy and source-to-sink dynamics. Recent theoretical work has suggested that rivers can remain aggradational during RSL fall, but field data are needed to verify this response and investigate sediment deposition processes. We show with field work and modeling that fluvio-deltaic systems can remain aggradational or at grade during RSL fall, leading to superelevation and continuation of delta lobe avulsions. The field site is the Goose River, Newfoundland-Labrador, Canada, which has experienced steady RSL fall of around 3–4 mm yr⁻¹ in the past 5 k.y. from post-glacial isostatic rebound. Elevation analysis and optically stimulated luminescence dating suggest that the Goose River avulsed and deposited three delta lobes during RSL fall. Simulation results from Delft3D software show that if the characteristic fluvial response time is longer than the duration of RSL fall, then fluvial systems remain aggradational or at grade, and continue to avulse during RSL fall due to superelevation. Intriguingly, we find that avulsions become more frequent at faster rates of RSL fall, provided the system response time remains longer than the duration of RSL fall. This work suggests that RSL fall rate may influence the architecture of falling-stage or forced regression deposits by controlling the number of deposited delta lobes

Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics

A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's equations reduce to a single equation.Comment: 8 page

Rotational States of Magnetic Molecules

We study a magnetic molecule that exhibits spin tunneling and is free to rotate about its anisotropy axis. Exact low-energy eigenstates of the molecule that are superpositions of spin and rotational states are obtained. We show that parameter $\alpha = 2(\hbar S)^2/(I\Delta)$ determines the ground state of the molecule. Here $\hbar S$ is the spin, $I$ is the moment of inertia, and $\Delta$ is the tunnel splitting. The magnetic moment of the molecule is zero at $\alpha \alpha_c$. At $\alpha \to \infty$ the spin of the molecule localizes in one of the directions along the anisotropy axis.Comment: 4 pages, 3 figure

Hierarchical mean-field approach to the J1J_1-J2J_2 Heisenberg model on a square lattice

We study the quantum phase diagram and excitation spectrum of the frustrated $J_1$-$J_2$ spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying {\it relevant} degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the {\it symmetric plaquette} covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) {\it plaquette crystal}, connected with the neighboring N\'eel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the N\'eel and columnar phases. Our results suggest that the quantum phase transition between N\'eel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.Comment: LaTeX 2e, 14 pages, 17 figure

Quantum computing with nearest neighbor interactions and error rates over 1%

Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure that requires only a 2-D square lattice of qubits that can interact with their nearest neighbors, yet can tolerate quantum gate error rates over 1%. The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 1.1--1.4% for various physically reasonable models. Even the lowest value represents the highest threshold error rate calculated to date in a geometrically constrained setting, and a 50% improvement over the previous record.Comment: 4 pages, 8 figure

Semiclassical Analysis of the Wigner 12j12j Symbol with One Small Angular Momentum

We derive an asymptotic formula for the Wigner $12j$ symbol, in the limit of one small and 11 large angular momenta. There are two kinds of asymptotic formulas for the $12j$ symbol with one small angular momentum. We present the first kind of formula in this paper. Our derivation relies on the techniques developed in the semiclassical analysis of the Wigner $9j$ symbol [L. Yu and R. G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant form of the multicomponent WKB wave-functions to derive asymptotic formulas for the $9j$ symbol with small and large angular momenta. When applying the same technique to the $12j$ symbol in this paper, we find that the spinor is diagonalized in the direction of an intermediate angular momentum. In addition, we find that the geometry of the derived asymptotic formula for the $12j$ symbol is expressed in terms of the vector diagram for a $9j$ symbol. This illustrates a general geometric connection between asymptotic limits of the various $3nj$ symbols. This work contributes the first known asymptotic formula for the $12j$ symbol to the quantum theory of angular momentum, and serves as a basis for finding asymptotic formulas for the Wigner $15j$ symbol with two small angular momenta.Comment: 15 pages, 14 figure