Invariant Manifolds and Collective Coordinates

We introduce suitable coordinate systems for interacting many-body systems with invariant manifolds. These are Cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold. In this sense these coordinates are collective. We make a connection to Zickendraht's collective coordinates and present certain configurations of few-body systems where rotations and vibrations decouple from single-particle motion. These configurations do not depend on details of the interaction.Comment: 15 pages, 2 EPS-figures, uses psfig.st

Estimating Discharge in Low-Order Rivers With High-Resolution Aerial Imagery

Remote sensing of river discharge promises to augment in situ gauging stations, but the majority of research in this field focuses on large rivers (\u3e50 m wide). We present a method for estimating volumetric river discharge in low-order (wide) rivers from remotely sensed data by coupling high-resolution imagery with one-dimensional hydraulic modeling at so-called virtual gauging stations. These locations were identified as locations where the river contracted under low flows, exposing a substantial portion of the river bed. Topography of the exposed river bed was photogrammetrically extracted from high-resolution aerial imagery while the geometry of the remaining inundated portion of the channel was approximated based on adjacent bank topography and maximum depth assumptions. Full channel bathymetry was used to create hydraulic models that encompassed virtual gauging stations. Discharge for each aerial survey was estimated with the hydraulic model by matching modeled and remotely sensed wetted widths. Based on these results, synthetic width-discharge rating curves were produced for each virtual gauging station. In situ observations were used to determine the accuracy of wetted widths extracted from imagery (mean error 0.36 m), extracted bathymetry (mean vertical RMSE 0.23 m), and discharge (mean percent error 7% with a standard deviation of 6%). Sensitivity analyses were conducted to determine the influence of inundated channel bathymetry and roughness parameters on estimated discharge. Comparison of synthetic rating curves produced through sensitivity analyses show that reasonable ranges of parameter values result in mean percent errors in predicted discharges of 12%–27%

Spontaneous Embedding of DNA Mismatches Within the RNA:DNA Hybrid of CRISPR-Cas9.

CRISPR-Cas9 is the forefront technology for editing the genome. In this system, the Cas9 protein is programmed with guide RNAs to process DNA sequences that match the guide RNA forming an RNA:DNA hybrid structure. However, the binding of DNA sequences that do not fully match the guide RNA can limit the applicability of CRISPR-Cas9 for genome editing, resulting in the so-called off-target effects. Here, molecular dynamics is used to probe the effect of DNA base pair mismatches within the RNA:DNA hybrid in CRISPR-Cas9. Molecular simulations revealed that the presence of mismatched pairs in the DNA at distal sites with respect to the Protospacer Adjacent Motif (PAM) recognition sequence induces an extended opening of the RNA:DNA hybrid, leading to novel interactions established by the unwound nucleic acids and the protein counterpart. On the contrary, mismatched pairs upstream of the RNA:DNA hybrid are rapidly incorporated within the heteroduplex, with minor effect on the protein-nucleic acid interactions. As a result, mismatched pairs at PAM distal ends interfere with the activation of the catalytic HNH domain, while mismatches fully embedded in the RNA:DNA do not affect the HNH dynamics and enable its activation to cleave the DNA. These findings provide a mechanistic understanding to the intriguing experimental evidence that PAM distal mismatches hamper a proper function of HNH, explaining also why mismatches within the heteroduplex are much more tolerated. This constitutes a step forward in understanding off-target effects in CRISPR-Cas9, which encourages novel structure-based engineering efforts aimed at preventing the onset of off-target effects

Ultra-short solitons and kinetic effects in nonlinear metamaterials

We present a stability analysis of a modified nonlinear Schroedinger equation describing the propagation of ultra-short pulses in negative refractive index media. Moreover, using methods of quantum statistics, we derive a kinetic equation for the pulses, making it possible to analyze and describe partial coherence in metamaterials. It is shown that a novel short pulse soliton, which is found analytically, can propagate in the medium.Comment: 6 pages, 2 figures, to appear in Phys. Rev.

Temporally resolved second-order photon correlations of exciton-polariton Bose-Einstein condensate formation

Second-order time correlation measurements with a temporal resolution better than 3 ps were performed on a CdTe microcavity where spontaneous Bose-Einstein condensation is observed. After the laser pulse, the nonresonantly excited thermal polariton population relaxes into a coherent polariton condensate. Photon statistics of the light emitted by the microcavity evidences a clear phase transition from the thermal state to a coherent state, which occurs within 3.2 ps after the onset of stimulated scattering. Following this very fast transition, we show that the emission possesses a very high coherence that persists for more than 100 ps after the build-up of the condensate.Comment: 4 pages, 3 figure

Local information transfer as a spatiotemporal filter for complex systems

We present a measure of local information transfer, derived from an existing averaged information-theoretical measure, namely transfer entropy. Local transfer entropy is used to produce profiles of the information transfer into each spatiotemporal point in a complex system. These spatiotemporal profiles are useful not only as an analytical tool, but also allow explicit investigation of different parameter settings and forms of the transfer entropy metric itself. As an example, local transfer entropy is applied to cellular automata, where it is demonstrated to be a novel method of filtering for coherent structure. More importantly, local transfer entropy provides the first quantitative evidence for the long-held conjecture that the emergent traveling coherent structures known as particles (both gliders and domain walls, which have analogues in many physical processes) are the dominant information transfer agents in cellular automata.Comment: 12 page

Wafer scale texturing of LiNbO3

We report a novel technique for micro texturing of LiNbO<sub>3</sub>. Well-defined raised ridges and etched trenches are demonstrated. This technique is suitable for the realization of surface relief gratings and photonic crystals