Helium Diffraction as a Probe of Structure and Proton Order on Model Ice Surfaces.

Helium diffraction has the potential to reveal the degree of proton order at an ice surface, and has been used in the past to benchmark theoretical work. We demonstrate that previous calculations do not represent the diffraction experiment to a sufficient degree of accuracy. By combining a realistic helium-water potential with quantum calculations using exact close-coupling methods we demonstrate that the scattering is strongly energy dependent. Proton order may be inferred best from selective adsorption resonances of the helium atom, which involve multiple scattering. We use the results to discuss the validity of the latest assumptions for the ice Ih surface with respect to proton ordering.For financial support, N.A. gratefully acknowledges the Blavatnik Foundation

A biased electrostatic probe in a continuum regime

Current collection of biased electrostatic probe in continuum plasm

Algorithmic and Hardness Results for the Colorful Components Problems

In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph $G$ such that in the resulting graph $G'$ all the connected components are colorful (i.e., any two vertices of the same color belong to different connected components). We want $G'$ to optimize an objective function, the selection of this function being specific to each problem in the framework. We analyze three objective functions, and thus, three different problems, which are believed to be relevant for the biological applications: minimizing the number of singleton vertices, maximizing the number of edges in the transitive closure, and minimizing the number of connected components. Our main result is a polynomial time algorithm for the first problem. This result disproves the conjecture of Zheng et al. that the problem is $NP$-hard (assuming $P \neq NP$). Then, we show that the second problem is $APX$-hard, thus proving and strengthening the conjecture of Zheng et al. that the problem is $NP$-hard. Finally, we show that the third problem does not admit polynomial time approximation within a factor of $|V|^{1/14 - \epsilon}$ for any $\epsilon > 0$, assuming $P \neq NP$ (or within a factor of $|V|^{1/2 - \epsilon}$, assuming $ZPP \neq NP$).Comment: 18 pages, 3 figure

PIGLE — Particles Interacting in Generalized Langevin Equation simulator

We present a package using Simulink and MATLAB to perform molecular dynamics simulations of interacting particles obeying a Generalized Langevin Equation. The package, which accounts for three spatial dimensions and rigid-body like rotation, is tuned to explore surface diffusion of co-adsorbed species. The physical parameters are species specific, and include userdefined colored noise spectra and memory friction kernels acting independently on translational and rotational degrees of freedom. We benchmark the simulations using established analytical results for dynamical correlation functions, and we use the package to numerically verify novel analytical results concerning dissipative rotational motion and mutli-exponential friction kernels. The package provides a straight-forward way to expand the modeling of ultra-fast surface diffusion problems at the atomic scale.Herchel Smith Fund, Blavatnik Foundatio

Ultrafast Diffusion at the Onset of Growth: O/Ru(0001).

Nanoscopic clustering in a 2D disordered phase is observed for oxygen on Ru(0001) at low coverages and high temperatures. We study the coexistence of quasistatic clusters (with a characteristic length of ∼9  Å) and highly mobile atomic oxygen which diffuses between the energy-inequivalent, threefold hollow sites of the substrate. We determine a surprisingly low activation energy for diffusion of 385±20  meV. The minimum of the O-O interadsorbate potential appears to be at lower separations than previously reported.Isaac Newton Trust, grant 17.37(j) Herchel Smith Fun

Length-dependent disassembly maintains four different flagellar lengths in Giardia.

With eight flagella of four different lengths, the parasitic protist Giardia is an ideal model to evaluate flagellar assembly and length regulation. To determine how four different flagellar lengths are maintained, we used live-cell quantitative imaging and mathematical modeling of conserved components of intraflagellar transport (IFT)-mediated assembly and kinesin-13-mediated disassembly in different flagellar pairs. Each axoneme has a long cytoplasmic region extending from the basal body, and transitions to a canonical membrane-bound flagellum at the 'flagellar pore'. We determined that each flagellar pore is the site of IFT accumulation and injection, defining a diffusion barrier functionally analogous to the transition zone. IFT-mediated assembly is length-independent, as train size, speed, and injection frequencies are similar for all flagella. We demonstrate that kinesin-13 localization to the flagellar tips is inversely correlated to flagellar length. Therefore, we propose a model where a length-dependent disassembly mechanism controls multiple flagellar lengths within the same cell