Growth Rates and Explosions in Sandpiles

We study the abelian sandpile growth model, where n particles are added at the origin on a stable background configuration in ? ^d . Any site with at least 2d particles then topples by sending one particle to each neighbor. We find that with constant background height h≤2d?2, the diameter of the set of sites that topple has order n ^1/d . This was previously known only for h<d. Our proof uses a strong form of the least action principle for sandpiles, and a novel method of background modification. We can extend this diameter bound to certain backgrounds in which an arbitrarily high fraction of sites have height 2d?1. On the other hand, we show that if the background height 2d?2 is augmented by 1 at an arbitrarily small fraction of sites chosen independently at random, then adding finitely many particles creates an explosion (a sandpile that never stabilizes).     

A Macrocyclic Furan with Accessible Oxidation States: Switching Between Aromatic and Antiaromatic Global Ring Currents

Macrocyclic furans are predicted to switch between global aromaticity and antiaromaticity, depending on their oxidation states. However, the macrocyclic furans reported to date are stabilized by electron withdrawing groups, which result in inaccessible oxidation states. To circumvent this problem, a post-macrocyclization approach was applied to introduce methylene-substituted macrocyclic furans, which display an extremely low oxidation potential of −0.23 vs. Fc/Fc⁺, and are partially oxidized in ambient conditions. Additional oxidation to the dication results in aromaticity switching to a global 30πe⁻ aromatic state, as indicated by the formation of a strong diatropic current observed in the ¹H NMR spectrum. NICS and ACID calculations support this trend and provide evidence for a different pathway for the global current in the neutral and dicationic states. According to these findings, macrocyclic furans can be rendered as promising p-type materials with stable oxidation states.     

The Radical Anion,Dianion and Electron Transport Properties of Tetraiodotetraazapentacene

Tetraiodotetraazapentacene I₄TAP , the last missing derivative in the series of halogenated silylated tetraazapentacenes, was synthesized via condensation chemistry from a TIPS-ethynylated diaminobenzothiadiazol in three steps. Single and double reduction furnished its air-stable monoanion and relatively air-stable dianion, both of which were characterized by crystallography. All three species are structurally and spectroscopically compared to non-halogenated TAP and Br₄TAP . I₄TAP is an n-channel material in thin-film transistors with average electron mobilities exceeding 1 cm² (Vs)⁻¹.     

A numerical method for acoustic normal modes for shear flows

The normal modes and their propagation numbers for acoustic propagation in wave guides with flow are the eigenvectors and eigenvalues of a boundary value problem for a non-standard Sturm-Liouville problem. It is non-standard because it depends non-linearly on the eigenvalue parameter. (In the classical problem for ducts with no flow, the problem depends linearly on the eigenvalue parameter.) In this paper a method is presented for the fast numerical solution of this problem. It is a generalization of a method that was developed for the classical problem. A finite difference method is employed that combines well known numerical techniques and a generalization of the Sturm sequence method to solve the resulting algebraic eigenvalue problem. Then a modified Richardson extrapolation method is used that dramatically increases the accuracy of the computed eigenvalues. The method is then applied to two problems. They correspond to acoustic propagation in the ocean in the presence of a current, and to acoustic propagation in shear layers over flat plates.     

Critique of the mechanism of superselectivity in ion exchange membranes

One possible origin of permselectivity in situations where the Donnan equilibrium cannot exert much influence is investigated. The suggested origin of enhanced current efficiency beyond the Donnan limit is the existence of a coarse grained inhomogeneity in the distribution of “fixed” ions in the ion exchange membrane. Approximate solutions of the Nernst—Planck and Poisson equation for such inhomogeneous membranes are obtained for relevant highly idealized schematic situations in which only this single effect is investigated. Only “trends” are indicated, and the results do imply that “superselectivity” might be due to such inhomogeneity (possibly resulting from dipole clustering of fixed ionic groups), and that further, more precise, work should be carried out.     

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.     

Geometric nature of the environment-induced Berry phase and geometric dephasing

We investigate the geometric phase or Berry phase acquired by a spin half which is both subject to a slowly varying magnetic field and weakly coupled to a dissipative environment (either quantum or classical). We study how this phase is modified by the environment and find that the modification is of a geometric nature. While the original Berry phase (for an isolated system) is the flux of a monopole field through the loop traversed by the magnetic field, the environment-induced modification of the phase is the flux of a quadrupolelike field. We find that the environment-induced phase is complex, and its imaginary part is a geometric contribution to dephasing. Its sign depends on the direction of the loop. Unlike the Berry phase, this geometric dephasing is gauge invariant for open paths of the magnetic field.     

The threshold for random -SAT is

Let be a random -CNF formula formed by selecting uniformly and independently out of all possible -clauses on variables. It is well known that if , then is unsatisfiable with probability that tends to 1 as . We prove that if , where , then is satisfiable with probability that tends to 1 as .

Our technique, in fact, yields an explicit lower bound for the random -SAT threshold for every . For our bounds improve all previously known such bounds.