Robinson-Trautman equations and Chandrasekhar's special perturbation of the Schwarzschild metric

A perturbation wave solution of the Robinson-Trautman equations is proved to be a perturbation of the Schwarzschild black hole which describes an outgoing axial gravitational wave and corresponds to a special case of Chandrasekhar's algebraically special perturbation of the Schwarzschild metric.     

Generation and detection of acoustic solitons in crystalline slabs by laser ultrasonics

Acoustic solitons have been recently observed in different systems (Si, Sapphire, MgO, alpha-quartz). Such acoustic waves could lead to sub-picosecond acoustic pulses. In this paper, we report on the formation of acoustic solitons in a GaAs crystalline slab. A short picosecond acoustic pulse is generated by absorption of a femtosecond laser pulse in an aluminum thin film deposited on one side of the slab. This strain pulse travels through the sample up to the opposite side where it is detected by a time delayed laser pulse reflected by an aluminum transducer. We use interferometric detection to measure independently the real and imaginary parts of the relative change in optical reflectivity induced by the acoustic pulse. We find that, at low temperature and with a laser pump pulse energy of 10 nJ, an acoustic soliton clearly separates from the acoustic pulse in GaAs slab. The soliton shape is compared with numerical simulations for different excitation conditions. From the very unique properties of solitons, we infer a soliton pulse duration of about 2.3 ps which corresponds to a spatial extent of only 12 nm.     

SIMS as a subnanometer probe: A new tool for chemical profile analysis of grafted molecules

The complexity of modern engineered surfaces requires the development of very powerful methods to analyze and characterize them. We demonstrate that it is possible to obtain chemical information about the skeleton of organic molecules constituting SAMs grafted on a silicon surface by using a new type of SIMS method. A profile can be achieved by the investigation of the temporal variation of secondary ion intensities that correspond to the fractional parts of the molecule constituting the SAMs. The equivalent ablation rate is less than 0.5 nm/min.     

Charmed-meson decay constants in three-flavor lattice QCD

We present the first lattice QCD calculation with realistic sea quark content of the D+-meson decay constant f(D+). We use the MILC Collaboration's publicly available ensembles of lattice gauge fields, which have a quark sea with two flavors (up and down) much lighter than a third (strange). We obtain f(D+)=201+/-3+/-17 MeV, where the errors are statistical and a combination of systematic errors. We also obtain f(Ds)=249+/-3+/-16 MeV for the Ds meson.     

Characterization of Kovar-to-Kovar laser welded joints and its mechanical strength

For the packaging of a pump laser in butterfly package, the most crucial assembly step is the fiber-to-laser diode coupling and attachment. The use of laser welding as the joining method offers several advantages if compared with the adhesive joints: strong joining strength, short process time and less contamination. This paper reports on laser welding process characteristics; weld strength and its fracture mode. The penetration depth and melt area of laser spot welds were found to be complicated functions of laser pulse energy, intensity, and beam diameter. Effects of pulse width, input power and size of the focal spot on the rate of energy input to the workpieces and consequently, the weld strength were reported. The weld strength was found to be dependent on the overlapping area between the two joining materials. Surface roughness, R_a, has influence on the fraction of energy absorbed, A, and therefore, affecting the penetration depth. Thermal analysis was carried out on the laser-welded joints and its heat-affected zone (HAZ) induced by various power densities was examined. These data are important in order to optimize and utilize the laser welding process as an effective manufacturing tool for fabrication of reliable pump laser.     

Local structural order in carbonic acid polymorphs: Raman and FT‐IR spectroscopy

Two different polymorphs of carbonic acid, α‐ and β‐H₂CO₃, were identified and characterized using infrared spectroscopy (FT‐IR) previously. Our attempts to determine the crystal structures of these two polymorphs using powder and thin‐film X‐ray diffraction techniques have failed so far. Here, we report the Raman spectrum of the α‐polymorph, compare it with its FT‐IR spectrum and present band assignments in line with our work on the β‐polymorph [Angew. Chem. Int. Ed. 48 (2009) 2690–2694]. The Raman spectra also contain information in the wavenumber range ∼90–400 cm⁻¹, which was not accessible by FT‐IR spectroscopy in the previous work. While the α‐polymorph shows Raman and IR bands at similar positions over the whole accessible range, the rule of mutual exclusion is obeyed for the β‐polymorph. This suggests that there is a center of inversion in the basic building block of β‐H₂CO₃ whereas there is none in α‐H₂CO₃. Thus, as the basic motif in the crystal structure we suggest the cyclic carbonic acid dimer containing a center of inversion in case of β‐H₂CO₃ and a catemer chain or a sheet‐like structure based on carbonic acid dimers not containing a center of inversion in case of α‐H₂CO₃. This hypothesis is strengthened when comparing Raman active lattice modes at < 400 cm⁻¹ with the calculated Raman spectra for different dimers. In particular, the intense band at 192 cm⁻¹ in β‐H₂CO₃ can be explained by the inter‐dimer stretching mode of the centrosymmetric RC(OHO)₂ CR entity with ROH. The same entity can be found in gas‐phase formic acid (RH) and in β‐oxalic acid (RCOOH) and produces an intense Raman active band at a very similar wavenumber. The absence of this band in α‐H₂CO₃ confirms that the difference to β‐H₂CO₃ is found in the local coordination environment and/or monomer conformation rather than on the long range. Copyright © 2011 John Wiley & Sons, Ltd.     

Computing the Abel map

We present the next step in an ongoing research program to allow for the black-box computation of the so-called finite-genus solutions of integrable differential equations. This next step consists of the black-box computation of the Abel map from a Riemann surface to its Jacobian. Using a plane algebraic curve representation of the Riemann surface, we provide an algorithm for the numerical computation of this Abel map. Since our plane algebraic curves are of arbitrary degree and may have arbitrary singularities, the Abel map of any connected compact Riemann surface may be obtained in this way. This generality is necessary in order for these algorithms to be relevant for the computation of the finite-genus solutions of any integrable equation.