Evidence for quantized displacement in macroscopic nanomechanical oscillators

We report the observation of discrete displacement of nanomechanical oscillators with gigahertz-range resonance frequencies at millikelvin temperatures. The oscillators are nanomachined single-crystal structures of silicon, designed to provide two distinct sets of coupled elements with very low and very high frequencies. With this novel design, femtometer-level displacement of the frequency-determining element is amplified into collective motion of the entire micron-sized structure. The observed discrete response possibly results from energy quantization at the onset of the quantum regime in these macroscopic nanomechanical oscillators.     

Synthetic spectra from rough-surface scattering

We present a method for designing a one-dimensional, deterministic, perfectly conducting rough surface that scatters light at a fixed scattering angle with an intensity whose dependence on the frequency of a plane wave incident normally upon it reproduces the infrared spectrum of a known substance within a specified region of frequencies. Such a surface can therefore be used in a correlation spectrometer for the identification of unknown substances.     

Exact results for the Barabási model of human dynamics

Human activity patterns display a bursty dynamics with interevent times following a heavy tailed distribution. This behavior has been recently shown to be rooted in the fact that humans assign their active tasks different priorities, a process that can be modeled as a priority queueing system [A.-L. Barabási, Nature (London) 435, 207 (2005)]. In this Letter we obtain exact results for the Barabási model with two tasks, calculating the priority and waiting time distribution of active tasks. We demonstrate that the model has a singular behavior in the extremal dynamics limit, when the highest priority task is selected first. We find that independently of the selection protocol, the average waiting time is smaller or equal to the number of active tasks, and discuss the asymptotic behavior of the waiting time distribution. These results have important implications for understanding complex systems with extremal dynamics.     

Thermodynamic properties of internal water molecules in the hydrophobic cavity around the catalytic center of cytochrome c oxidase

Cytochrome c oxidase is a redox-driven proton pump that creates a membrane proton gradient responsible for driving ATP synthesis in aerobic cells. The crystal structure of the enzyme has been recently solved; however, the details of the mechanism of its proton pumping remain unknown. The enzyme internal water molecules play a key role in proton translocation through the enzyme. Here, we examine the thermodynamic properties of internal water in a hydrophobic cavity around the catalytic center of the enzyme. The crystal structure does not show any water molecules in this region; it is believed, however, that, since protons are delivered to the catalytic center, where the reduction of molecular oxygen occurs, at least some water molecules must be present there. The goal of the present study was to examine how many water molecules are present in the catalytic center cavity and why these water molecules are not observed in the crystal structure of the enzyme. The behavior of water molecules is discussed in the context of redox-coupled proton translocation in the enzyme.     

Generalized little -difference operators

We consider the polynomials obtained from the little -Jacobi polynomials by inserting a discrete mass at in the orthogonality measure. We show that for , the polynomials are eigensolutions of a linear -difference operator of order with polynomial coefficients. This provides a -analog of results recently obtained for the Krall polynomials.

     

Inflationary Cosmology with Two-component Fluid and Thermodynamics

We present a simple and self-consistent cosmology with a phenomenological model of quantum creation of radiation and matter due to the decay of the cosmological constant . The decay drives a non-isentropic inflationary epoch, which exits smoothly to the radiation-dominated era, without reheating, and then evolves to the dust era. The initial vacuum for radiation and matter is a regular Minkowski vacuum. The created radiation and matter obeys standard thermodynamic laws, and the total entropy produced is consistent with the accepted value. This paper is an extension of the model with the decaying cosmological constant considered in [1]. We compare our model with the quantum field theory approach to creation of particles in curved space.     

Electronic transport through carbon nanotubes: effects of structural deformation and tube chirality

Atomistic simulations using a combination of classical force field and density-functional theory (DFT) show that carbon atoms remain essentially sp(2) coordinated in either bent tubes or tubes pushed by an atomically sharp atomic-force microscope (AFM) tip. Subsequent Green's-function-based transport calculations reveal that for armchair tubes there is no significant drop in conductance, while for zigzag tubes the conductance can drop by several orders of magnitude in AFM-pushed tubes. The effect can be attributed to simple stretching of the tube under tip deformation, which opens up an energy gap at the Fermi surface.     

Proton inventory study of the base-catalyzed hydrolysis of formamide. Consideration of the nucleophilic and general base mechanisms

An NMR study of the rates of hydroxide-promoted hydrolysis of formamide in aqueous media of varying mole fraction D(2)O (n) was performed at [LO(-)] = 1.42 M, T = 25 degrees C, to shed light on whether the mechanism involves a nucleophilic attack of HO(-) on the C=O or HO(-) acting as a general base to remove a proton from an attacking water. The solvent deuterium kinetic isotope effect under these conditions is inverse, k(OH)/k(OD) = 0.77 +/- 0.02 or k(OD)/k(OH) = 1.30 +/- 0.03. Proton inventory analysis of the k(n)() versus n data was undertaken through NLLSQ fits to equations representing four possible mechanisms encompassing nucleophilic and general base ones with waters of solvation on the attacking hydroxide, and with or without waters of solvation on the developing amide hydrate oxyanion. Both nucleophilic and general base mechanisms can be accommodated, but there are restraints on each that are discussed. The preferred mechanism is a nucleophilic one proceeding through a transition state having two solvating waters remaining on the attacking hydroxide and three additional waters attached to the developing amide hydrate oxyanion.     

A Non-Finitely Based Variety of Centre-by-Abelian-by-Nilpotent Groups of Exponent 8

The first example of a non-finitely based variety of centre-by-abelian-by-nilpotentgroups was found in 1995. This example has an infinite exponentbut it can be seen that the method used to construct it alsogives a variety that has an exponent of 128. Later it was provedthat there exists a variety with similar properties but withan exponent of 32. The paper constructs a non-finitely basedvariety of centre-by-abelian-by-nilpotent groups which has anexponent of 8.