Free-induction decay in a fluctuating two-level system

We study theoretically free-induction decay (FID) in an inhomogeneously broadened system of two-level atoms whose transition frequencies fluctuate according to the Ornstein-Uhlenbeck process. A numerical solution of the model shows that at low intensities the saturation behaviour of FID may depend strongly on the statistics of the fluctuations, but at high intensities the fluctuations play a minor role. The results mimic qualitatively the recent experimental data of DeVoe and Brewer, but a full quantitative agrrement with experiments is not reached.     

A statistical study of the additivities of substituent effects in the 13C NMR chemical shifts of hydroxy- and chloro-substituted benzenes

The ¹³C NMR spectra of six hydroxybenzenes, all chlorobenzenes, all chlorophenols and eight chlorocatechols are measured and assigned. The additivity of the substituent effects and the usefulness of some corrective parameters are studied with regression analysis. The order of the chemical shifts is most efficiently predicted by the simplest substituent effect model, containing only the direct effects of the substituents, although the 95% confidence limits of the calculated shifts are as high as 5.6 ppm. If the chemical shifts need to be predicted within the measuring errors (approximately 0.05–0.10 ppm, in the present data), the number of necessary corrections is very impractical. The correction parameters are found to be independent of the solvent if no conformational effects are operative. These corrections, or the non-additivity parameters, are thus theoretically interesting. Approximate ¹J(CH) couplings are also reported and the additivity of substitution effects on these parameters are discussed.     

The discrete maximal operator in metric spaces

We study the action of the so-called discrete maximal operator on Newtonian, Hölder and BMO spaces on metric measure spaces equipped with a doubling measure and a Poincaré inequality. The discrete maximal operator has better regularity properties than the standard Hardy-Littlewood maximal operator and hence is a more flexible tool in this context.     

On unitary analogs of GCD reciprocal LCM matrices

A divisor d ∈ ?₊ of n ∈ ?₊ is said to be a unitary divisor of n if (d, n/d) = 1. In this article we examine the greatest common unitary divisor (GCUD) reciprocal least common unitary multiple (LCUM) matrices. At first we concentrate on the difficulty of the non-existence of the LCUM and we present three different ways to overcome this difficulty. After that we calculate the determinant of the three GCUD reciprocal LCUM matrices with respect to certain types of functions arising from the LCUM problematics. We also analyse these classes of functions, which may be referred to as unitary analogs of the class of semimultiplicative functions, and find their connections to rational arithmetical functions. Our study shows that it does make a difference how to extend the concept of LCUM.     

Atomistic simulation of the transition from atomistic to macroscopic cratering

Using large-scale atomistic simulations, we show that the macroscopic cratering behavior emerges for projectile impacts on Au at projectile sizes between 1000 and 10000 Au atoms at impact velocities comparable to typical meteoroid velocities. In this size regime, we detect a compression of material in Au nanoparticle impacts similar to that observed for hypervelocity macroscopic impacts. The simulated crater volumes agree with the values calculated using the macroscopic crater size scaling law, in spite of a downwards extrapolation over more than 15 orders of magnitude in terms of the impactor volume. The result demonstrates that atomistic simulations can be used as a tool to understand the strength properties of materials in cases where only continuum models have been possible before.     

Nonlinear phenomenology from quantum mechanics: soliton in a lattice

We study a soliton in an optical lattice holding bosonic atoms quantum mechanically using both an exact numerical solution and quantum Monte Carlo simulations. The computation of the state is combined with an explicit account of the measurements of the numbers of the atoms at the lattice sites. In particular, importance sampling in the quantum Monte Carlo method arguably produces faithful simulations of individual experiments. Even though the quantum state is invariant under lattice translations, an experiment may show a noisy version of the localized classical soliton.     

Vibrations of a continuous web on elastic supports

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports.     

On all-optical laser cleaning and inspection of contaminated concave metal surfaces

A technique for all-optical laser cleaning and surface quality monitoring of concave metal surfaces is suggested. Contaminated pharmaceutical punches from a tablet compression machine were cleaned using high-energy laser pulses. Image information obtained from a diffractive-optical-element-based sensor was used in inspection of the surface quality change of the concave punches due to laser cleaning. Alternative method for mechanical cleaning of punches is introduced, which is based on simultaneous laser cleaning and surface quality inspection of the punches.     

A mass spectrometric study of metal binding to osteocalcin

Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry was used to investigate Ca(2+), Mg(2+), and La(3+) binding to bovine bone osteocalcin (OCN). OCN was shown to bind 3 mol Ca(2+) per mol protein. There was also evidence for the presence of four additional metal binding sites. Ca(2+) increased the formation of the OCN dimer. Mg(2+) bound to OCN to the same extent as Ca(2+) but did not induce the dimerization of OCN. La(3+) bound to a lesser extent than either Ca(2+) or Mg(2+) to OCN and, like Mg(2+), did not influence dimerization. Each Gla residue of OCN participates in Ca(2+) binding, whereas Mg(2+) binding may occur preferentially at sites other than Gla residues. This implies that the different natures of Ca(2+)- and Mg(2+)-containing OCN complexes influence the tendency of OCN to form a dimer.