Evidence for contact delocalization in atomic scale friction

We analyze an advanced two-spring model with an ultra-low effective tip mass to predict nontrivial and physically rich 'fine structure' in the atomic stick-slip motion in Friction Force Microscopy (FFM) experiments. We demonstrate that this fine structure is present in recent, puzzling experiments. This shows that the tip apex can be completely or partially delocalized, thus shedding new light on what is measured in FFM and, possibly, what can happen with the asperities that establish the contact between macroscopic sliding bodies.Comment: 4 pages text and 3 figure

On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.Comment: 44 pages, introduction revised, references expanded. To appear in Arch. Rational Mech. Ana

Uniqueness of Lagrangian Self-Expanders

We show that zero-Maslov class Lagrangian self-expanders in C^n which are asymptotic to a pair of planes intersecting transversely are locally unique if n>2 and unique if n=2.Comment: 32 page

The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic

Non-affine geometrization can lead to nonphysical instabilities

Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out within geometrical frameworks, by measuring the broadening rate of a bundle of geodesics. Two known formalisms are via Jacobi and Eisenhart metrics. We find that this geometrical analysis measures the actual stability when the length of any geodesic is proportional to the corresponding time interval. We prove that the Jacobi metric is not always an appropriate parametrization by showing that it predicts chaotic behavior for a system of harmonic oscillators. Furthermore, we show, by explicit calculation, that the correspondence between dynamical- and geometrical-spread is ill-defined for the Jacobi metric. We find that the Eisenhart dynamics corresponds to the actual tangent dynamics and is therefore an appropriate geometrization scheme.Comment: Featured on the Cover of the Journal. 9 pages, 6 figures: http://iopscience.iop.org/1751-8121/48/7/07510

Coarse-graining protein energetics in sequence variables

We show that cluster expansions (CE), previously used to model solid-state materials with binary or ternary configurational disorder, can be extended to the protein design problem. We present a generalized CE framework, in which properties such as energy can be unambiguously expanded in the amino-acid sequence space. The CE coarse grains over nonsequence degrees of freedom (e.g., side-chain conformations) and thereby simplifies the problem of designing proteins, or predicting the compatibility of a sequence with a given structure, by many orders of magnitude. The CE is physically transparent, and can be evaluated through linear regression on the energies of training sequences. We show, as example, that good prediction accuracy is obtained with up to pairwise interactions for a coiled-coil backbone, and that triplet interactions are important in the energetics of a more globular zinc-finger backbone.Comment: 10 pages, 3 figure

Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion

In this paper, we consider a product of a symmetric stable process in $\mathbb{R}^d$ and a one-dimensional Brownian motion in $\mathbb{R}^+$. Then we define a class of harmonic functions with respect to this product process. We show that bounded non-negative harmonic functions in the upper-half space satisfy Harnack inequality and prove that they are locally H\"older continuous. We also argue a result on Littlewood-Paley functions which are obtained by the $\alpha$-harmonic extension of an $L^p(\mathbb{R}^d)$ function.Comment: 23 page

Amphiphilic Elastin-Like Block Co-Recombinamers Containing 2 Leucine Zippers: Cooperative Interplay between Both Domains 3 Results in Injectable and Stable Hydrogels

Many biological processes are regulated by reversible binding events, with these interactions between macromolecules representing the core of dynamic chemistry. As such, any attempt to gain a better understanding of such interactions, which would pave the way to the extrapolation of natural designs to create new advanced systems, is clearly of interest. This work focuses on the development of a leucine zipper-elastin-like recombinamer (ZELR) in order to elucidate the behavior of such domains when coexisting along the same molecule and to engineer reversible, injectable and stable hydrogels. The unique propensity of the Z-moiety selected to dimerize, together with the thermosensitive behavior of the ELR, which has been constructed as a thermosensitive amphiphilic tetrablock, has been engineered into a single recombinant molecule. In this molecular design, the Z-moieties are unable to form a network, while the ELR is below its Tt, thus, guaranteeing the liquid-like state of the system. However, this situation changes rapidly as the temperature increases above Tt, where a stable hydrogel is formed, as demostrated by rheological tests. The inability of the ELR molecule (without Z-domains) to form such a stable hydrogel above Tt clearly points to a positive cooperative effect between these two domains (Z and EL), and no conformational changes in the former are involved, as demonstrated by circular dichroism analysis. AFM shows that Z-motifs seem to induce the aggregation of micelles, which supports the enhanced stability displayed by ZELRs when compared to ELR at the macroscale level. To the best of our knowledge, this is the first time that such an interplay between these two domains has been reported. Furthermore, the cytocompatibility of the resulting hydrogels opens the door to their use in biomedical applications.Este trabajo forma parte de Proyectos de Investigación financiados por la Comisión Europea a través del Fondo Social Europeo (FSE) y el Fondo Europeo de Desarrollo Regional (ERDF), por el del MINECO (MAT2013-41723R, MAT2013-42473-R, MAT2012-38043 y PRI-PIBAR-2011-1403), la Junta de Castilla y León (VA049A11, VA152A12 y VA155A12) y el Instituto de Salud Carlos III bajo el Centro en Red de Medicina Regenerativa y Terapia Celular de Castilla y León