Regular packings on periodic lattices

We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction φ(d)(X). It is proved to be continuous with an infinite number of singular points X(ν)(min), X(ν)(max), ν = 0, ±1, ±2,…. In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of φ(d)(X) is discussed in the context of geometrical frustration effects, transitions in the contact numbers, and number-theoretical properties. Implications and generalizations for more general packing problems are outlined.     

Combinatorial Markov chains on linear extensions

We consider generalizations of Schützenberger’s promotion operator on the set $\mathcal{L}$ of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on $\mathcal{L}$ . By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other have a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence $\mathcal{L}=S_{n}$ is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is $\mathcal {R}$ -trivial and then using Steinberg’s extension of Brown’s theory for Markov chains on left regular bands to $\mathcal {R}$ -trivial monoids.     

Intrinsic stability of quasicrystals under the generation of Frenkel pairs

Under irradiation metastable quasicrystals undergo a phase transition to an amorphous state. This transition can be reversed by annealing. As in normal crystalline materials the phase transition is considered to be triggered by generation and recombination of vacancies and interstitial atoms (Frenkel pairs). We have classified the possible Frenkel defects in a metastable monatomic quasicrystal with respect to geometric and energetic properties. With numerical simulation we have studied the behaviour of the quasicrystal under a load of Frenkel defects for various defect concentrations. We find three ranges of behaviour: up to 5% defects per atom the structure remains icosahedral, in a middle range it stays disordered icosahedral or it becomes either disordered or perfect crystalline, depending on the implementation of the defects. If there are more than 10% defects the structure becomes irreversibly amorphous. We finally compare our results with experimental data.     

Shell effects in the evolution of the mass asymmetry in heavy-ion collisions leading to composite systems withZ=108

Fragment mass distributions are presented obtained in the heavy-ion reactions²²Ne+²⁴⁹Cf,³²S+²³⁸U,⁴⁰Ar+²³²Th and⁵⁶Fe+²⁰⁸Pb leading to composite systems with equal nuclear charge numberZ=108. The experiments were performed at the heavy-ion cyclotron U 300 of the Laboratory of Nuclear Reactions in Dubna. The spectrometer DEMAS was used to measure the time-of-flight values and the laboratory angles of the correlated fragments. The shape of the mass distributions strongly depends on the initial mass asymmetry. When decreasing the bombarding energy down to values near the Coulomb barrier, the mass distributions obtained in the reactions³²S+²³⁸U and⁴⁰Ar+²³²Th exhibit relative maxima ofM≈205 interpreted to be due to stabilizing effects of nuclear shells during the fragmentation process.     

Depletion-induced percolation in networks of nanorods

Above a certain density threshold, suspensions of rodlike colloidal particles form system-spanning networks. Using Monte Carlo simulations, we investigate how the depletion forces caused by spherical particles affect these networks in isotropic suspensions of rods. Although the depletion forces are strongly anisotropic and favor alignment of the rods, the percolation threshold of the rods decreases significantly. The relative size of the effect increases with the aspect ratio of the rods. The structural changes induced in the suspension by the depletant are characterized in detail and the system is compared to an ideal fluid of freely interpenetrable rods.     

Electronic coupling and scaling effects during dielectric barrier electrospray ionization

The mechanism of the previously published technique of dielectric barrier electrospray ionization (DB-ESI) was investigated in more detail. Two independent current signals occurring during the DB-ESI could be explained and allocated to sub-processes. The modulated shape of the HV signal, the applied frequency as well as the inner diameter of the emitter capillary have a big impact on the spray. Furthermore, there exists a cut-off frequency which depends on the electronic properties of the DB-ESI interface. Comparable mass spectra for lysine employing both conventional ESI and DB-ESI show a good analytical potential of the new technique.