Activation barrier scaling and crossover for noise-induced switching in a micromechanical parametric oscillator

We explore fluctuation-induced switching in a parametrically-driven micromechanical torsional oscillator. The oscillator possesses one, two or three stable attractors depending on the modulation frequency. Noise induces transitions between the coexisting attractors. Near the bifurcation points, the activation barriers are found to have a power law dependence on frequency detuning with critical exponents that are in agreement with predicted universal scaling relationships. At large detuning, we observe a crossover to a different power law dependence with an exponent that is device specific.Comment: 5 pages, 5 figure

Piezoelectric copolymer hydrophones for ultrasonic field characterization

Hydrophones to be used in the characterization of medical ultrasonic transducers have been fabricated using a new polyvinylidene fluoride/trifluoroethylene (VF2/VF3) copolymer. The copolymer has an advantage over VF2 in that it does not require prestretching before poling. Thin copolymer films can be cast from solution and then poled using the corona discharge method. As there is a need for small‐diameter hydrophones to provide good spatial resolution in measuring highly focused ultrasonic beams, hydrophones with diameter as small as 0.1 mm have been made. Both needle‐type and line hydrophones have been tested and their performance reported. In the case of line hydrophones, the output signal is proportional to the line integral of the acoustic pressure and a computer tomographic technique has been used to reconstruct the beam profiles

Roles of the Bloom's syndrome helicase in the maintenance of genome stability

The RecQ family of DNA helicases is highly conserved in evolution from bacteria to humans. Of the five known human RecQ family members, three (BLM, WRN and RECQ4, which cause Bloom's syndrome, Werner's syndrome and Rothmund-Thomson syndrome respectively) are mutated in distinct clinical disorders associated with cancer predisposition and/or premature aging. BLM forms part of a multienzyme complex including topoisomerase IIIalpha, replication protein A and a newly identified factor called BLAP75. Together, these proteins play a role in the resolution of DNA structures that arise during the process of homologous recombination repair. In the absence of BLM, cells show genomic instability and a high incidence of sister-chromatid exchanges. In addition to a DNA structure-specific helicase activity, BLM also catalyses Holliday-junction branch migration and the annealing of complementary single-stranded DNA molecules

Measurables of CPCP Violation in Bd→DCP0KSB_d\to D^0_{CP}K_S at a BB-meson Factory

In the context of the standard electroweak model, we emphasize that $B_d\rightarrow D^0_{CP}K_S$ ($D^0_{CP}$ denotes a $CP$ eigenstate of $D^0$ or $\bar{D}^0$) can compete with $B_d\rightarrow \pi^+\pi^-$ in studying $CP$ violation and probing the Cabibbo-Kobayashi-Maskawa unitarity triangle. We discuss the measurables of direct and indirect $CP$ asymmetries in $B^0_d$ vs $\bar{B}^0_d\rightarrow D^0_{CP}K_S$ under the circumstance of an asymmetric $B$-meson factory running on the $\Upsilon(4S)$ resonance, and show that both the weak and strong phases are experimentally determinable even in the presence of unknown final-state interactions.Comment: 6 Postscript pages, accepted for publication in IL Nuovo Cimento A as a "Note Brevi

Studies related to primitive chemistry. A proton and nitrogen-14 nuclear magnetic resonance amino acid and nucleic acid constituents and a and their possible relation to prebiotic

Preliminary proton nuclear magnetic resonance (NMR) studies were made to determine the applicability of this technique for the study of interactions between monomeric and polymeric amino acids with monomeric nucleic acid bases and nucleotides. Proton NMR results for aqueous solutions (D2O) demonstrated interactions between the bases cytosine and adenine and acidic and aromatic amino acids. Solutions of 5'-AMP admixed with amino acids exhibited more complex behavior but stacking between aromatic rings and destacking at high amino acids concentration was evident. The multisite nature of 5'-AMP was pointed out. Chemical shift changes for adenine and 5'-AMP with three water soluble polypeptides demonstrated that significant interactions exist. It was found that the linewidth-pH profile of each amino acid is unique. It is concluded that NMR techniques can give significant and quantitative data on the association of amino acid and nucleic acid constituents

Fluctuation-enhanced frequency mixing in a nonlinear micromechanical oscillator

We study noise-enhanced frequency mixing in an underdamped micromechanical torsional oscillator. The oscillator is electrostatically driven into bistability by a strong, periodic voltage at frequency $\omega_d$. A second, weak ac voltage is applied at a frequency $\omega$ close to $\omega_d$. Due to nonlinearity in the system, vibrations occur at both $\omega$ and $2\omega_d-\omega$. White noise is injected into the excitation, allowing the system to occasionally overcome the activation barrier and switch between the two states. At the primary drive frequency where the occupations of the two states are approximately equal, we observe noise-induced enhancement of the oscillation amplitudes at both $\omega$ and the down-converted frequency $2\omega_d-\omega$, in agreement with theoretical predictions. Such enhancement occurs as a result of the noise-induced interstate transitions becoming synchronous with the beating between the two driving frequencies.Comment: 4 pages 5 figure

A practical guide to density matrix embedding theory in quantum chemistry

Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample S$_{\text{N}}$2 reaction. The source code for the calculations in this work can be obtained from \url{https://github.com/sebwouters/qc-dmet}.Comment: 41 pages, 10 figure

Light Spanners

A $t$-spanner of a weighted undirected graph $G=(V,E)$, is a subgraph $H$ such that $d_H(u,v)\le t\cdot d_G(u,v)$ for all $u,v\in V$. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all edge weights), both being important measures of the spanner's quality -- in this work we focus on the latter. Specifically, it is shown that for any parameters $k\ge 1$ and $\epsilon>0$, any weighted graph $G$ on $n$ vertices admits a $(2k-1)\cdot(1+\epsilon)$-stretch spanner of weight at most $w(MST(G))\cdot O_\epsilon(kn^{1/k}/\log k)$, where $w(MST(G))$ is the weight of a minimum spanning tree of $G$. Our result is obtained via a novel analysis of the classic greedy algorithm, and improves previous work by a factor of $O(\log k)$.Comment: 10 pages, 1 figure, to appear in ICALP 201