Classical stochastic theory for the sticking probability of atoms scattered on surfaces

A stochastic theory is formulated for the sticking probability of a projectile scattered from a surface. The theory is then explored by applying it to a generalized Langevin equation model of the scattering dynamics. The theory succeeds in describing the known features of trapping on surfaces. At low energies sticking will occur only if there is an attractive interaction between the projectile and the surface. The probability of sticking at low energies is greater the lower the temperature and the deeper the attractive well of the particle as it approaches the surface. The sticking probability in the absence of horizontal friction tends to be lower as the stiffness of the surface increases. However, in the presence of horizontal friction, increased stiffness may lead to an increase in the sticking coefficient. A cos(2)(θ(i)) scaling is found only in the absence of corrugation and horizontal friction. The theory is then applied successfully to describe experimentally measured sticking probabilities for the scattering of Xe on a Pt(111) surface.     

Relative weak mixing is generic

A classical result of Halmos asserts that among measure preserving transformations the weak mixing property is generic. We extend Halmos' result to the collection of ergolic extensions of a fixed, but arbitrary,aperiodic transformation T_0. We then use a result of Ornstein and Weiss to extend this relative theorem to the general(countable) amenable group.     

Intersection of Isomorphic Linear Codes

Given an (n, k) linear code over GF(q), the intersection of with a codeπ( ), whereπS_n, is an (n, k₁) code, where max{0, 2k−n}k₁k. The intersection problem is to determine which integers in this range are attainable for a given code . We show that, depending on the structure of the generator matrix of the code, some of the values in this range are attainable. As a consequence we give a complete solution to the intersection problem for most of the interesting linear codes, e.g. cyclic codes, Reed–Muller codes, and most MDS codes.     

N.m.r. spectra of cyclic amines. II—Factors influencing the chemical shifts of α-protons in aziridines

Proton magnetic resonance spectra of trans and cis-2,3-diphenylaziridine (1 and 2) and their N-ethyl derivatives 3 and 4 were measured in carbon tetrachloride, chloroform, and benzene-d₆ at low temperatures (1 and 3) and in dry conditions (1 and 2). On the basis of these results it was concluded that an N-ethyl group exerts a shielding influence on a cis ring proton and a deshielding influence on a trans ring proton. From results obtained by measuring the ¹H n.m.r. spectra of 1–4 in deuterochlorofom-trifluoroacetic acid it was derived that the lone pair of the aziridine nitrogen exerts a shielding influence on cis related ring hydrogens. In most N-alkylaziridines the effect of the N-alkyl group predominates.     

A simple classical prediction of quantal resonances in collinear reactive scattering

Quantal collinear reactive scattering computations have shown that in the vicinity of thresholds of reactant or product vibrational states, one finds resonances in the state to state reaction probability. We find that these resonances can be explained classically in terms of energy transfer between adiabatic reactant and product channels. This transfer is attributable to resonant periodic orbits, resonating between reactants and products. The classical condition for a quantal resonance is that the action of the orbit over one period be an integer (in units of h) and that the energy at which this occurs be lower than the adiabatic barrier heights of the resonating states. These conditions suffice for a prediction of the location of the quantal resonance within a 1% accuracy!     

Strong imploding shock,the representative curve

The representative curve of the ideal gas behind the front of a spherically, or cylindrically, symmetric strong imploding shock is shown to pass through the point where the reduced pressure is maximum, P(ζ_m) = P_max.