Meyniel's conjecture holds for random d‐regular graphs

In the game of cops and robber, the cops try to capture a robber moving on the vertices of the graph. The minimum number of cops required to win on a given graph G is called the cop number of G. The biggest open conjecture in this area is the one of Meyniel, which asserts that for some absolute constant C, the cop number of every connected graph G is at most . In a separate paper, we showed that Meyniel's conjecture holds asymptotically almost surely for the binomial random graph. The result was obtained by showing that the conjecture holds for a general class of graphs with some specific expansion‐type properties. In this paper, this deterministic result is used to show that the conjecture holds asymptotically almost surely for random d‐regular graphs when d = d(n) ≥ 3.     

A 1D Roe decomposition of a system of equations governing wave height transformation

A Roe‐type decomposition for a system of equations governing onshore/offshore wave transformation in coastal waters is derived. The equation set approximated pertains to coastal waters prior to wave breaking, and is based on depth‐averaging and time‐averaging of the Euler equations. The equations are those used in many commercial codes for simulation of wave height and wave‐averaged currents. This novel approach uses a combination of some standard Roe averages, together with physical reasoning and power series expansions to derive a Roe‐averaged Jacobian (with real, linearly independent eigenvectors) and ensures conservation, and thereby effects the decomposition. It is shown that the resulting derived Roe‐averaged quantities are accurate to a high degree, by comparing them with their analytical equivalents for a wide range of nondimensional water depths and slopes likely to be encountered in coastal problems. Numerical tests of time‐invariant wave height transformation and wave group propagation are undertaken; these indicate good performance of the scheme in practice. Copyright © 2011 John Wiley & Sons, Ltd.     

Mode I fatigue of the carbon fiber-reinforced plastic—concrete interface bond

Experimental Techniques - As the reinforced concrete infrastructure continues to decline, the engineering community is turning to rehabilitative methods as cost effective alternatives to...     

Spectrally selective coatings of gold nanorods on architectural glass

Infrared-blocking coatings on window glass can be produced by dispersing gold nanorods into a polymer coating. The spectral selectivity of the coating is controlled by the shape and aspect ratio of the nanoparticles, which are in turn determined by the conditions applied during their synthesis. Coatings of nanorods in polyvinyl alcohol were deposited onto glass and characterized in both laboratory and sun-lit conditions. Selective attenuation of the near-infrared was demonstrated with the test panels transmitting approximately one-third of the incident solar radiation and absorbing nearly two-thirds. The high absorptive cross sections of the gold nanorods suggest that they can be applied in efficacious coatings at relatively low volume fractions.     

Peptide structural analysis using continuous Ar cluster and C60 ion beams

A novel application of time-of-flight secondary ion mass spectrometry (ToF-SIMS) with continuous Ar cluster beams to peptide analysis was investigated. In order to evaluate peptide structures, it is necessary to detect fragment ions related to multiple neighbouring amino acid residues. It is, however, difficult to detect these using conventional ToF-SIMS primary ion beams such as Bi cluster beams. Recently, C₆₀ and Ar cluster ion beams have been introduced to ToF-SIMS as primary ion beams and are expected to generate larger secondary ions than conventional ones. In this study, two sets of model peptides have been studied: (des-Tyr)-Leu-enkephalin and (des-Tyr)-Met-enkephalin (molecular weights are approximately 400 Da), and [Asn¹ Val⁵]-angiotensin II and [Val⁵]-angiotensin I (molecular weights are approximately 1,000 Da) in order to evaluate the usefulness of the large cluster ion beams for peptide structural analysis. As a result, by using the Ar cluster beams, peptide molecular ions and large fragment ions, which are not easily detected using conventional ToF-SIMS primary ion beams such as Bi₃ ⁺, are clearly detected. Since the large fragment ions indicating amino acid sequences of the peptides are detected by the large cluster beams, it is suggested that the Ar cluster and C₆₀ ion beams are useful for peptide structural analysis.