Futtermittel

Ohne Zusammenfassung     

On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators

This paper shows, by means of an operator called asplitting operator, that the Douglas—Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm. Therefore, applications of Douglas—Rachford splitting, such as the alternating direction method of multipliers for convex programming decomposition, are also special cases of the proximal point algorithm. This observation allows the unification and generalization of a variety of convex programming algorithms. By introducing a modified version of the proximal point algorithm, we derive a new,generalized alternating direction method of multipliers for convex programming. Advances of this sort illustrate the power and generality gained by adopting monotone operator theory as a conceptual framework.This paper is drawn largely from the dissertation research of the first author. The dissertation was performed at M.I.T. under the supervision of the second author, and was supported in part by the Army Research Office under grant number DAAL03-86-K-0171, and by the National Science Foundation under grant number ECS-8519058.     

Sputtering studies with the Monte Carlo Program TRIM.SP

The Monte Carlo Program TRIM.SP (sputtering version of TRIM) was used to determine sputtering yields and energy and angular distributions of sputtered particles in physical (collisional) sputtering processes. The output is set up to distinguish between the contributions of primary and secondary knock-on atoms as caused by in- and outgoing incident ions, in order to get a better understanding of the sputtering mechanisms and to check on previous theoretical models. The influence of the interatomic potential and the inelastic energy loss model as well as the surface binding energy on the sputtering yield is investigated. Further results are sputtering yields versus incident energy and angle as well as total angular distributions of sputtered particles and energy distributions in specific solid angles for non-normal incidence. The calculated data are compared with experimental results as far as possible. From this comparison it turns out that the TRIM.SP is able to reproduce experimental results even in very special details of angular and energy distributions.     

Approximate iterations in Bregman-function-based proximal algorithms

This paper establishes convergence of generalized Bregman-function-based proximal point algorithms when the iterates are computed only approximately. The problem being solved is modeled as a general maximal monotone operator, and need not reduce to minimization of a function. The accuracy conditions on the iterates resemble those required for the classical “linear” proximal point algorithm, but are slightly stronger; they should be easier to verify or enforce in practice than conditions given in earlier analyses of approximate generalized proximal methods. Subjects to these practically enforceable accuracy restrictions, convergence is obtained under the same conditions currently established for exact Bregman-function-based proximal methods.     

The use of multidimensional chromatography for the isolation of synthetic oligodeoxyribonucleotides on a preparative scale

Summary A critical step in the chemical preparation of oligonucleotides is the chromatographic purification of the deprotected oligomers. In case of large quantities of reaction products, the oligonucleotides are first enriched on a QAE-Sephadex column at low pressure. The obtained fractions are then purified by multidimensional chromatography making use of three independent physical properties of the solutes: molecular size, ionic net charge and hydrophobicity. In the first dimension size exclusion chromatography (Sephadex G-15) is used. In the second dimension the high molecular weight fraction from the size exclusion chromatography is applied to a HPLC ion-exchange column (Partisil-10 SAX). Usually the last peak is collected and transferred to a HPLC reversed phase column (Nucleosil C18) where the components are separated according to their hydrophobicity in the third dimension. The efficiency of this multi-dimensional chromatographic procedure is demonstrated by the unequivocal fingerprints after radioactive labelling of the isolated oligonucleotides. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Ultra‐Fast Control of Magnetic Relaxation in a Periodically Driven Hubbard Model

Motivated by cold atom and ultra‐fast pump‐probe experiments we study the melting of long‐range antiferromagnetic order of a perfect Néel state in a periodically driven repulsive Hubbard model. The dynamics is calculated for a Bethe lattice in infinite dimensions with non‐equilibrium dynamical mean‐field theory. In the absence of driving melting proceeds differently depending on the quench of the interactions to hopping ratio from the atomic limit. For decay occurs due to mobile charge‐excitations transferring energy to the spin sector, while for it is governed by the dynamics of residual quasi‐particles. Here we explore the rich effects that strong periodic driving has on this relaxation process spanning three frequency ω regimes: (i) high‐frequency , (ii) resonant with integer l, and (iii) in‐gap away from resonance. In case (i) we can quickly switch the decay from quasi‐particle to charge‐excitation mechanism through the suppression of ν₀. For (ii) the interaction can be engineered, even allowing an effective regime to be reached, giving the reverse switch from a charge‐excitation to quasi‐particle decay mechanism. For (iii) the exchange interaction can be controlled with little effect on the decay. By combining these regimes we show how periodic driving could be a potential pathway for controlling magnetism in antiferromagnetic materials. Finally, our numerical results demonstrate the accuracy and applicability of matrix product state techniques to the Hamiltonian DMFT impurity problem subjected to strong periodic driving.     

Metal-insulator transition and its relation to magnetic structure in (LaMnO3)2n/(SrMnO3)n superlattices

Superlattices of (LaMnO3){2n}/(SrMnO3){n} (1or=3. Measurements of transport, magnetization, and polarized neutron reflectivity reveal that the ferromagnetism is relatively uniform in the metallic state, and is strongly modulated in the insulating state, being high in LaMnO3 and suppressed in SrMnO3. The modulation is consistent with a Mott transition driven by the proximity between the (LaMnO3)/(SrMnO3) interfaces. The insulating state for n>or=3 obeys variable range hopping at low temperatures. We suggest that this is due to states at the Fermi level that emerge at the (LaMnO3)/(SrMnO3) interfaces and are localized by disorder.