Using network-flow techniques to solve an optimization problem from surface-physics

The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.Comment: 8 Pages LaTeX, using Elsevier preprint style (macros included

Ground-State Roughness of the Disordered Substrate and Flux Line in d=2

We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux lines arrays in presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise study of the interface widths than from Monte Carlo simulations at finite temperature. Using $d=2$ systems up to size $420^2$, with a minimum of $2 \times 10^3$ realizations at each size, we find very strong evidence for a $\ln^2(L)$ super-rough state at low temperatures.Comment: 10 pages, 3 PS figures, to appear in PR

Dissociation of vertical semiconductor diatomic artificial molecules

We investigate the dissociation of few-electron circular vertical semiconductor double quantum dot artificial molecules at 0 T as a function of interdot distance. Slight mismatch introduced in the fabrication of the artificial molecules from nominally identical constituent quantum wells induces localization by offsetting the energy levels in the quantum dots by up to 2 meV, and this plays a crucial role in the appearance of the addition energy spectra as a function of coupling strength particularly in the weak coupling limit.Comment: Accepted for publication in Phys. Rev. Let

Rearrangement of cluster structure during fission processes

Results of molecular dynamics simulations of fission reactions $Na_{10}^{2+} \to Na_7^+ + Na_3^+$ and $Na_{18}^{2+} \to 2 Na_9^+$ are presented. Dependence of the fission barriers on isomer structure of the parent cluster is analyzed. It is demonstrated that the energy necessary for removing homothetic groups of atoms from the parent cluster is largely independent of the isomer form of the parent cluster. Importance of rearrangement of the cluster structure during the fission process is elucidated. This rearrangement may include transition to another isomer state of the parent cluster before actual separation of the daughter fragments begins and/or forming a "neck" between the separating fragments

Structure and properties of small sodium clusters

We have investigated structure and properties of small metal clusters using all-electron ab initio theoretical methods based on the Hartree-Fock approximation and density functional theory, perturbation theory and compared results of our calculations with the available experimental data and the results of other theoretical works. We have systematically calculated the optimized geometries of neutral and singly charged sodium clusters having up to 20 atoms, their multipole moments (dipole and quadrupole), static polarizabilities, binding energies per atom, ionization potentials and frequencies of normal vibration modes. Our calculations demonstrate the great role of many-electron correlations in the formation of electronic and ionic structure of small metal clusters and form a good basis for further detailed study of their dynamic properties, as well as structure and properties of other atomic cluster systems.Comment: 47 pages, 16 figure

Rough droplet model for spherical metal clusters

We study the thermally activated oscillations, or capillary waves, of a neutral metal cluster within the liquid drop model. These deformations correspond to a surface roughness which we characterize by a single parameter $\Delta$. We derive a simple analytic approximate expression determining $\Delta$ as a function of temperature and cluster size. We then estimate the induced effects on shell structure by means of a periodic orbit analysis and compare with recent data for shell energy of sodium clusters in the size range $50 < N < 250$. A small surface roughness $\Delta\simeq 0.6$ \AA~ is seen to give a reasonable account of the decrease of amplitude of the shell structure observed in experiment. Moreover -- contrary to usual Jahn-Teller type of deformations -- roughness correctly reproduces the shape of the shell energy in the domain of sizes considered in experiment.Comment: 20 pages, 4 figures, important modifications of the presentation, to appear in Phys. Rev.

PTEN/MMAC1 expression in melanoma resection specimens

PTEN/MMAC1, a tumour suppressor gene located on chromosome 10q23.3, has been found to be deleted in several types of human malignancies. As the chromosomal region 10q22-qter commonly is affected by losses in melanomas, we addressed this gene as tumour suppressor candidate in melanomas. Investigating PTEN/MMAC1 expression at mRNA level by semi-quantitative reverse transcription-polymerase chain reaction, we did not find a statistically significant down-regulation in melanoma resection specimens in comparison to acquired melanocytic nevi from which melanomas quite often are known to arise. Upon immunohistochemistry, PTEN/MMAC1 protein expression in melanomas was not lost. Sequencing the PTEN/MMAC1 cDNAs in 26 melanoma resection specimens (21 primary melanomas, five metastases), we detected three point mutations and two nucleotide deletions which did not represent genetic polymorphisms. With respect to the predicted protein sequences, all three point mutations were silent whereas the two frame shifts at the extreme C-terminus resulted in a loss of the putative PDZ-targeting consensus sequence. As loss of this motif possibly impairs localization and function of PTEN/MMAC1 in the two corresponding primary tumours, alterations of this tumour suppressor protein may participate in some melanomas