Resonance-induced cluster-mobility: Dynamics of a finite Frenkel-Kontorova model

Statics and dynamics of a finite incommensurate Frenkel-Kontorova chain are studied in the framework of both continuum and discrete models. Since the ground state of the finite chain is not degenerate it cannot freely slide along the substrate, i.e., the finite chain does not possess the “supermobility” of the infinitely long incommensurate chain. Instead, the finite chain shows a “resonance mobility”. Simulating the behaviour of the finite chain in an external field we observe resonances around the lowest frequency in the acoustic branch of the chain spectrum. This frequency depends on the chain size and the degree of incommensurability and corresponds to vibration “in-phase” of all solitons in the chain. The resonance leads to a significantly increased diffusive mobility of clusters of a specific size. This selectively enhanced cluster-mobility persists also in the presence of stochastic forces and friction.     

Semi-microscopic calculation of the level density in spherical nuclei

The level density at the neutron binding energy for 90 spherical nuclei in the interval 50 < A < 205 is calculated by a method of direct counting of the number of states taking into account collective vibrational excitations. The results of calculations are in satisfactory agreement with the experimental data. The difference in the level density of doubly even and odd-A nuclei is correctly described. The effect of nuclear vibrations on the level density is studied, and it is shown that the account of them leads to an increase in the density by a factor of 1.5–10 and to a decrease in the density fluctuations. It is also studied how the level density depends on excitation energy. With increasing excitation energy, our results come nearer the corresponding values obtained by the statistical model. It is found that the density fluctuations decrease with increasing excitation energy but remain still strong at the neutron binding energy for nuclei with A = 50–70 and for nuclei around closed shells. The density ρ(I^π) is studied as a function of spin and parity. It is shown that at the neutron binding energy the ratio $\text{ρ(I}{}^{\mathrm{+}}\text{)}\text{ρ(I}{}^{\mathrm{?}}\text{)}$ is different from unity for the majority of nuclei. This difference is especially striking for ⁵⁷Fe and ⁵⁸Fe nuclei.     

Reactive surface micropatterning by wet stamping

Hydrogel stamps are used to reactively micropattern various types of substrates. The method, called reactive wet stamping (r-WETS), is general in nature and overcomes several limitations of conventional soft-lithographic techniques. Illustrative applications of r-WETS in surface wettability modification, deposition of metallic microstructures, preparation of supports for electrostatic self-assembly, and multistep reactive patterning are discussed.     

Statistical characterization of the pore space of random systems of hard spheres

An improved statistical characterization of disordered structures such as metallic glasses, random porous media, or granular matter is presented. Suitable structure models follow the idea of dense random packed spheres, where the spheres represent atoms and particles in the case of metallic glasses and porous or granular matter, respectively. The geometry of the empty space between the atoms or particles is described by means of the already otherwise successful concept of so-called contact distributions. Their exact mathematical forms are unknown for hard sphere systems. Knowledge on these is obtained by means of Monte Carlo simulations of the structure models. The numerical results are approximated by simple and general mathematical expressions, with parameters that can be easily determined. These may serve as additional tools for the structural characterization of disordered matter, including systems of partly penetrable spheres.     

Blocking sets of Rédei type in projective Hjelmslev planes

In this paper, we introduce Rédei type blocking sets in projective Hjelmslev planes over finite chain rings. We construct, in Hjelmslev planes over chain rings of nilpotency index 2 that contain the residue field as a proper subring, the Baer subplanes associated with this subring as Rédei type blocking sets. Two further examples of Rédei type blocking sets are given for planes over Galois rings generalizing familiar constructions in projective planes over finite fields.