Interband excitations in the 1D limit of two-band fractional Chern insulators

We investigate the stability of the one-dimensional limit of $\nu =1/3$ Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and show that the energy gap remains finite in the thermodynamic limit. Next, by means of exact diagonalization and Density Matrix Renormalization Group approaches, we consider deviations from ideal dimerization and show that they reduce the stability of the FCI-like states. Finally, to show that our approach is not restricted to one model, we identify the dimer structure behind the thin-torus limit of other system – the checkerboard lattice.     

Supramolecular Materials Comprising Nucleic Acid Biopolymers

We have generated a supramolecular self-assembling film by exchanging the counter-ions of the phosphate moieties in nucleic acid with those of cationic amphiphiles as didodecyldimethylammonium bromide (or DDAB). SAXS and WAXS data for all film samples showed similar harmonic peaks suggesting a lamellar multilayer structure with layers of nucleic acids being separated by lipid bilayers of DDAB. AFM height images also showed that double stranded nucleic acid film can form the step or plateau type of structure and shorter nucleic acid film showed shorter step feature. Moreover, the length and the molecular structure of DNA and RNA can be used to manipulate the mechanical properties of these self-assembled films.     

Mu-Synthesis for Magnetic Bearings of Flywheel

In this paper, the μ-Synthesis Control method is applied to control Active Magnetic Bearings (AMBs) Flywheel. The dynamics of the open-loop system is influenced by external disturbances, nonlinearities, uncertainties and signal limits. Thus, a design methodology, which covers the practical issues of optimal robust control like the modelling of uncertainties, selection of optimal weighting functions is presented. The goal of this paper is the experimental evaluation robust performance of the AMBs system. The laboratory stand with the high speed rotor supported magnetically was built and presented. The stable operation, good stiffness of the rotor suspension and robust performances of the closed-loop AMBs is reached. Finally, the success of the robust control is demonstrated through results of computer simulations and experimental results. The experimental results show the effectiveness of the control system as well as good vibrations reduction of the designed controllers. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Minimum Query Set for Decision Tree Construction

A new two-stage method for the construction of a decision tree is developed. The first stage is based on the definition of a minimum query set, which is the smallest set of attribute-value pairs for which any two objects can be distinguished. To obtain this set, an appropriate linear programming model is proposed. The queries from this set are building blocks of the second stage in which we try to find an optimal decision tree using a genetic algorithm. In a series of experiments, we show that for some databases, our approach should be considered as an alternative method to classical ones (CART, C4.5) and other heuristic approaches in terms of classification quality.     

Efficient second‐order time integration for single‐species aerosol formation and evolution

The dynamics of a single‐species aerosol composed of droplets in air is described in terms of nucleation, evaporation, condensation, and coagulation processes. We present a comprehensive overview of the Euler–Euler formulation, which gives rise to a model in which fast nucleation that initiates aerosol droplets co‐exists with comparably slow condensation. The latter process is responsible for the subsequent growth of the droplets. To accurately represent the dynamical consequences of the fast nucleation process, while retaining numerical efficiency, a new second‐order time‐integration method for the nucleation, evaporation, and condensation processes is proposed and analyzed. The new time‐integration method takes the form of a ‘corrected Euler forward’ method. It includes rapid nucleation bursts and their possible cessation within a time step Δt. If the current nucleation burst persists for longer than the next time step, it is included fully, whereas cessation of the nucleation burst within the next Δt implies corrections to the effective rates in the algorithm. The identification of these two situations corresponds to the physical mechanism by which nucleation of a supersaturated vapor is halted because of the progressing condensation onto the already formed droplets. The resulting time‐integration method is shown to be second‐order accurate in time, whereas the computational costs per time step were found to be increased by less than 25% compared with the Euler forward method. The new method is also applied in combination with advective transport of the aerosol forming vapor to investigate a front of rapid nucleation. Adopting robust first‐order upwinding for the spatial discretization, we arrive at a flexible method that shows an overall first‐order convergence in Δt. For the full, spatially dependent system motivated by an aerosol of water droplets in air, the computational benefits of the new time‐integration method over the Euler forward scheme, are a factor of about 10 improvements in accuracy at a given Δt and a similar factor in computing time when keeping the same level of accuracy. Copyright © 2013 John Wiley & Sons, Ltd.     

Macrocyclic receptors containing sucrose skeleton

Crown ether analogues with incorporated sucrose unit were prepared by reaction of 1′,2,3,3′,4,4′-hexa-O-benzylsucrose with polyethylene ditosylates in up to 52% yield. Stability constants of their complexes with Li⁺, Na⁺, K⁺, NH₄⁺ were determined by the NMR titration method. The macrocycles were also tested as catalysts in the enantioselective Michael reaction, but with little success (ee up to only 22%). The macrocycle containing nitrogen in the ring was also prepared in good yield. All prepared macrocycles were easily converted into the free sucrose crowns (H₂/Pd/C) without destroying the (very labile) glycosidic bond. The crystal structure of the selected receptor was determined.     

Calculations of the exciton coupling elements between the DNA bases using the transition density cube method

Excited states of the double-stranded DNA model (A)12.(T)12 were calculated in the framework of the Frenkel exciton theory. The off-diagonal elements of the exciton matrix were calculated using the transition densities and ideal dipole approximation associated with the lowest energy pipi* excitations of the individual nucleobases as obtained from time-dependent density functional theory calculations. The values of the coupling calculated with the transition density cubes (TDC) and ideal dipole approximation (IDA) methods were found to be significantly different for the small interchromophore distances. It was shown that the IDA overestimates the coupling significantly. The effects of structural fluctuations of the DNA chain on the magnitude of dipolar coupling were also found to be very significant. The difference between the maximum and minimum values was as large as 1000 and 300 cm(-1) for the IDA and TDC methods, respectively. To account for these effects, the properties of the excited states were averaged over a large number of conformations obtained from the molecular dynamics simulations. Our calculations using the TDC method indicate that the absorption of the UV light creates exciton states carrying the majority of the oscillator strength that are delocalized over at least six DNA bases. Upon relaxation, the excitation states localize over at least four contiguous bases.     

Controlling Emissive Properties by Intramolecular Hydrogen Bonds: Alkyl and Aryl meso-Substituted Porphycenes

Porphycene, a porphyrin isomer, is an efficient fluorophore. However, four-fold meso substitution with alkyl groups decreases the fluorescence quantum yield by orders of magnitude. For aryl substituents, this effect is small. To explain this difference, we have synthesized and studied a mixed aryl-alkyl-substituted compound, 9,20-diphenyl-10,19-dimethylporphycene, as well as the 9,20-diphenyl and 9,20-dimethyl derivatives. Analysis of the structural, spectroscopic, and photophysical data of the six porphycenes, combined with quantum chemical calculations, shows a clear correlation between the strength of the intramolecular NH⋅⋅⋅N hydrogen bonds and the efficiency of the radiationless depopulation of the lowest-excited singlet state. This result led us to propose a model in which the delocalization of the inner protons in the cavity of the macrocycle is responsible for the nonradiative deactivation channel. The applicability of the model is confirmed by the literature data for other alkyl- or aryl-substituted porphycenes. The finding of a correlation between structural and emissive characteristics enables a rational design of porphycenes with desired photophysical properties.