An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

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Absence of Quantum States Corresponding to Unstable Classical Channels

We develop a general theory of absence of quantum states corresponding to unstable classical scattering channels. We treat in detail Hamiltonians arising from symbols of degree zero in x and outline a generalization in an Appendix. E. Skibsted is (partially) supported by MaPhySto – A Network in Mathematical Physics and Stochastics, funded by The Danish National Research Foundation. Submitted: September 18, 2007. Accepted: January 14, 2008.     

An Approach to NMR Assignment of Intrinsically Disordered Proteins

An efficient approach to NMR assignments in intrinsically disordered proteins is presented, making use of the good dispersion of cross peaks observed in [¹⁵N,¹³C′]‐ and [¹³C′,¹H^N]‐correlation spectra. The method involves the simultaneous collection of {3D (H)NCO(CAN)H and 3D (HACA)CON(CA)HA} spectra for backbone assignments via sequential H^N and H^α correlations and {3D (H)NCO(CACS)HS and 3D (HS)CS(CA)CO(N)H} spectra for side‐chain ¹H and ¹³C assignments, employing sequential ¹H data acquisitions with direct detection of both the amide and aliphatic protons. The efficacy of the approach for obtaining resonance assignments with complete backbone and side‐chain chemical shifts is demonstrated experimentally for the 61‐residue [¹³C,¹⁵N]‐labelled peptide of a voltage‐gated potassium channel protein of the Kv1.4 channel subunit. The general applicability of the approach for the characterisation of moderately sized globular proteins is also demonstrated.     

Microdrilling and micromachining with diode-pumped solid-state lasers

The trend of the ever-continuing miniaturization requires fast and flexible processing tools. Lasers are flexible tools which have proven their reliability in manufacturing of macrofeatures for many years already. However, to process small features the requirements of the laser source, e.g. in regard to the beam profile, are very high. Innovative laser sources which meet these requirements, such as diode-pumped solid-state lasers, and the progress in processing technology, have made microfeature processing commercially viable during recent years. Examples of industrial applications are laser-drilled micro-injection nozzles for highly efficient automobile engines or manufacturing of complex spinnerets for production of synthetic fibers. The unique advantages of laser-based techniques stem from their ability to produce high-aspect-ratio holes, while yielding small heat-affected zones with exceptional surface quality, roundness and taper tolerances. Additionally, the ability to drill blind holes and slots in very hard materials such as diamond, silicon, sapphire, ceramics and steel is of great interest for many applications in the microelectronics, semiconductor and automotive industries. This kind of high-quality, high-aspect-ratio micromachining requires high peak powers and short pulse durations. PACS 42.55.Xi; 42.62.Cf; 81.40.-z     

Rotational spectrum of trans-trans diethyl ether in the ground and three excited vibrational states

We report the results of a comprehensive reinvestigation of the rotational spectrum of diethyl ether based on broadband millimetre-wave spectra recently recorded at The Ohio State University and in Warsaw, covering the frequency region 108-366 GHz. The data set for the ground vibrational state of trans-trans diethyl ether has been extended to over 2000 lines and improved spectroscopic constants have been determined. Rotational spectra in the first excited vibrational states of the three lowest vibrational modes of trans-trans-diethyl ether, ν₂₀, ν₃₉, and ν₁₂ have been assigned. The v₂₀ = 1 and v₃₉ = 1 states are near 100 cm⁻¹ in vibrational term value and are coupled by a strong c-axis Coriolis interaction, which gives rise to many spectacular manifestations in the rotational spectrum. All of these effects have been successfully fitted for a dataset comprising over 3000 transitions, leading to precise determination of the energy difference between these states, (ΔE/hc)=10.400222(5) cm⁻¹. A newly developed software package for assignment and analysis of broadband spectra is described and made available.     

A 200 mJ unstable resonator Nd:YAG oscillator

We have designed and operated a positive branch 6.3 mm diameter rod Nd:YAG unstable resonator oscillator with a 12 nsec, 200 mJ Q-switched output at 10 Hz repetition rate. When followed by a single 9 mm diameter Nd:YAG amplifier output energies up to 750 mJ were obtained with a divergence less than 0.5 mrad.     

Temporal exponential decay for the Stark effect in atoms

Let $\text{H}{}_1\text{= ?∑}{}_{\mathrm{i\; =\; 1}}{}^{\mathrm{N}}\text{(Δ}{}_{\mathrm{i}}\text{+ V(}\text{x}{}_{\mathrm{i}}\text{)) + ∑}{}_{\mathrm{1\; ?\; i\; <j\; ?\; N}}\text{¦}\text{x}{}_{\mathrm{i}}\text{?}\text{x}{}_{\mathrm{j}}\text{¦}{}^{\mathrm{?1}}\text{, V(}\text{x}{}_{\mathrm{i}}\text{) = N ∝ ¦}\text{x}\text{?}\text{y}\text{¦}{}^{\mathrm{?1}}\text{?(}\text{y}\text{)d}\text{y}$, with ? a normalized Gaussian. Suppose $\text{E}$ ≠ 0 and that $\text{H = H}{}_1\text{+}\text{E}\text{· (∑}{}_{\mathrm{i\; =\; 1}}{}^{\mathrm{N}}\text{x}{}_{\mathrm{i}}\text{)}$ has no eigenfunctions in L²($\text{R}$^3N. If H₁ψ = μψ with μ < infσ_ess(H₁), then (ψ, e^?itHψ) decays exponentially at a rate governed by the positions of the resonances of H.