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).     

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.     

Interplay of spin and charge channels in zero-dimensional systems

We study the interplay of charge and spin (zero-mode) channels in quantum dots. The latter affects the former in the form of a distinct signature on the differential conductance. We also obtain both longitudinal and transverse spin susceptibilities. All these observables, underlain by spin fluctuations, become accentuated as one approaches the Stoner instability. The nonperturbative effects of zero-mode interaction are described in terms of the propagation of gauge bosons associated with charge [U(1)] and spin [SU(2)] fluctuations in the dot, while transverse spin fluctuations are analyzed perturbatively.     

Q-switching an all-fiber laser using acousto-optic null coupler

A new method for Q-switching an all-fiber laser is presented. It is based on induced acoustic long period grating operating on a null coupler, which acts as acoustically controlled tunable output coupler. Q-switching is achieved by switching on and off the acoustic wave in a burst mode, thereby generating laser pulses that are ~400 times shorter than the acoustically controlled coupler’s rise time. Output pulse energy of 22 μJ and temporal width of ~100 ns were measured at a wavelength of 1.54 μm.     

Exploring the functional interaction between POSH and ALIX and the relevance to HIV-1 release

Background

The ALG2-interacting protein X (ALIX)/AIP1 is an adaptor protein with multiple functions in intracellular protein trafficking that plays a central role in the biogenesis of enveloped viruses. The ubiquitin E3-ligase POSH (plenty of SH3) augments HIV-1 egress by facilitating the transport of Gag to the cell membrane. Recently, it was reported, that POSH interacts with ALIX and thereby enhances ALIX mediated phenotypes in Drosophila.

Results

In this study we identified ALIX as a POSH ubiquitination substrate in human cells: POSH induces the ubiquitination of ALIX that is modified on several lysine residues in vivo and in vitro. This ubiquitination does not destabilize ALIX, suggesting a regulatory function. As it is well established that ALIX rescues virus release of L-domain mutant HIV-1, HIV-1Δ_PTAP, we demonstrated that wild type POSH, but not an ubiquitination inactive RING finger mutant (POSH^V14A), substantially enhances ALIX-mediated release of infectious virions derived from HIV-1Δ_PTAP L-domain mutant (YPX_nL-dependent HIV-1). In further agreement with the idea of a cooperative function of POSH and ALIX, mutating the YPX_nL-ALIX binding site in Gag completely abrogated augmentation of virus release by overexpression of POSH. However, the effect of the POSH-mediated ubiquitination appears to be auxiliary, but not necessary, as silencing of POSH by RNAi does not disturb ALIX-augmentation of virus release.

Conclusion

Thus, the cumulative results identified ALIX as an ubiquitination substrate of POSH and indicate that POSH and ALIX cooperate to facilitate efficient virus release. However, while ALIX is obligatory for the release of YPX_nL-dependent HIV-1, POSH, albeit rate-limiting, may be functionally interchangeable.     

Gate‐Induced Modification of Water Adsorption on Dielectrics Probed by EFM and Carbon Nanotube FETs

Humidity plays an important role in molecular electronics. It facilitates charge movement on top of dielectric layers and modifies the device transfer characteristics. Using two different methods to probe temporal charge redistribution on the surface of dielectrics, we were able to extract the surface humidity for the first time. The first method is based on the relaxation time constants of the current through carbon nanotube field‐effect transistors (CNTFETs), and the second is based on electric force microscopy (EFM) measurements. Moreover, we found that applying external gate biases modifies the surface humidity. A theoretical model based on dielectrophoretic attraction between the water molecules and the substrate is introduced to explain this observation, and the results support our hypothesis. Furthermore, it is found that upon the adsorption of two to three layers of water the surface conductivity saturates.     

The design of a Tort law to control accidents

In this paper we analyse a two-stage game involving the government and n agents who engage in a single activity (driving). The government establishes the legal policy setting and the agents proceed to play a non-cooperative game of incomplete information with a risk of accident in which their behavioral strategy is their level of care. We examine the Nash-equilibrium conditions for single-activity accidents between heterogeneous agents, ‘good’ drivers or ‘bad’ drivers allowing a variable damage function and a liability rule defined on the cube. The relative desirability for society of alternative equilibria and the conditions under which they can obtain are discussed. The constraints which circumscribe the ability of the government to induce an equilibrium involving careful driving are demonstrated. It transpires that when the proportion of good drivers increases, it becomes more difficult to sustain a careful equilibrium whereas an equilibrium of reckless behavior becomes easier to sustain. Various extensions of the models are also presented.     

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible Sandpile

The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our earlier work (Levine and Peres, Indiana Univ Math J 57(1):431–450, 2008). For the shape consisting of sites, where ω _d is the volume of the unit ball in , we show that the inradius of the set of occupied sites is at least r − O(logr), while the outradius is at most r + O(r ^α ) for any α > 1 − 1/d. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total mass. For the classical abelian sandpile model in two dimensions, with n = πr ² particles, we show that the inradius is at least , and the outradius is at most . This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions, improving on bounds of Fey and Redig. Yuval Peres is partially supported by NSF grant DMS-0605166.     

Motivic torsors

The torsorP _δ=Hom^⊗ (H _DR,H _σ) under the motivic Galois groupG _σ=Aut^⊗ H _δ of the Tannakian category generated by one-motives related by absolute Hodge cycles over a field κ with an embedding σ:k↪ℂ is shown to be determined by its projectionP _σ→P _σ/G _σ ⁰ to a Gal( )-torsor, and by its localizationsP _σ⊕_k k _ξ at a dense subset of orderings ϕ of the field κ, provided κ has virtual cohomological dimension (vcd) one. This result is an application of a recent local-global principle for connected linear algebraic groups over a field κ of vcd ≤1.