Oscillation criteria for nonlinear second-order differential equations with damping

Some new oscillation criteria are given for general nonlinear second order ordinary differential equations with damping of the form x′′ + p(t)x′ + q(t) f (x) = 0, where f is with or without monotonicity. Our results generalize and extend some earlier results of Deng.Наведено деякі нові осцнляційні критерії для загальних нелінійних звичайних диференціальних рівнянь другого порядку із затуханням вигляду x" + p(t)x' + q(t)f(x) = 0, де функція f або монотонна, або немонотонна. Наведені результати узагальнюють та розширюють деякі результати, отримані раніше Денгом

Effects of long-range disorder and electronic interactions on the optical properties of graphene quantum dots

We theoretically investigate the effects of long-range disorder and electron-electron interactions on the optical properties of hexagonal armchair graphene quantum dots consisting of up to 10806 atoms. The numerical calculations are performed using a combination of tight-binding, mean-field Hubbard and configuration interaction methods. Imperfections in the graphene quantum dots are modelled as a long-range random potential landscape, giving rise to electron-hole puddles. We show that, when the electron-hole puddles are present, tight-binding method gives a poor description of the low-energy absorption spectra compared to meanfield and configuration interaction calculation results. As the size of the graphene quantum dot is increased, the universal optical conductivity limit can be observed in the absorption spectrum. When disorder is present, calculated absorption spectrum approaches the experimental results for isolated monolayer of graphene sheet

Protecting the SWAP\sqrt{SWAP} operation from general and residual errors by continuous dynamical decoupling

We study the occurrence of errors in a continuously decoupled two-qubit state during a $\sqrt{SWAP}$ quantum operation under decoherence. We consider a realization of this quantum gate based on the Heisenberg exchange interaction, which alone suffices for achieving universal quantum computation. Furthermore, we introduce a continuous-dynamical-decoupling scheme that commutes with the Heisenberg Hamiltonian to protect it from the amplitude damping and dephasing errors caused by the system-environment interaction. We consider two error-protection settings. One protects the qubits from both amplitude damping and dephasing errors. The other features the amplitude damping as a residual error and protects the qubits from dephasing errors only. In both settings, we investigate the interaction of qubits with common and independent environments separately. We study how errors affect the entanglement and fidelity for different environmental spectral densities.Comment: Extended version of arXiv:1005.1666. To appear in PR

Effects of random atomic disorder on the magnetic stability of graphene nanoribbons with zigzag edges

We investigate the effects of randomly distributed atomic defects on the magnetic properties of graphene nanoribbons with zigzag edges using an extended mean-field Hubbard model. For a balanced defect distribution among the sublattices of the honeycomb lattice in the bulk region of the ribbon, the ground state antiferromagnetism of the edge states remains unaffected. By analyzing the excitation spectrum, we show that while the antiferromagnetic ground state is susceptible to single spin flip excitations from edge states to magnetic defect states at low defect concentrations, it's overall stability is enhanced with respect to the ferromagnetic phase.Comment: 5 pages, 4 figure

Embedded NiTi wires for improved dynamic thermomechanical performance of silicone elastomers

The extraordinary properties of shape memory NiTi alloy are combined with the inherent viscoelastic behavior of a silicon elastomer. NiTi wires are incorporated in a silicon elastomer matrix. Benefits include features as electrical/thermal conductivity, reinforcement along with enhanced damping performance and flexibility. To gain more insight of this composite, a comprehensive dynamic thermomechanical analysis is performed and the temperature- as well as frequency-dependent storage modulus and the mechanical loss factor are obtained. The analyses are realized for the composite and single components. Moreover, the models to express the examined properties and their temperature along with the frequency dependencies are also presented

COMPARISON OF VIRTUAL FIELDS METHOD, PARALLEL NETWORK MATERIAL MODEL AND FINITE ELEMENT UPDATING FOR MATERIAL PARAMETER DETERMINATION

Extracting material parameters from test specimens is very intensive in terms of cost and time, especially for viscoelastic material models, where the parameters are dependent of time (frequency), temperature and environmental conditions. Therefore, three different methods for extracting these parameters were tested. Firstly, digital image correlation combined with virtual fields method, secondly, a parallel network material model and thirdly, finite element updating. These three methods are shown and the results are compared in terms of accuracy and experimental effort

Computational speed-up with a single qudit

Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical algorithm. For $2d$ permutation functions defined on a set of $d$ elements, deciding whether a given permutation is even or odd, requires evaluation of the function for at least two elements. We demonstrate that a quantum circuit with a single qudit can determine the parity of the permutation with only one evaluation of the function. Our algorithm provides an example for quantum computation without entanglement since it makes use of the pure state of a qudit. We also present an experimental realization of the proposed quantum algorithm with a quadrupolar nuclear magnetic resonance using a single four-level quantum system, i.e., a ququart.Comment: Combined version of arXiv:1403.5861 [quant-ph] and arXiv:1406.3579 [quant-ph

Effect of molecular and electronic structure on the light harvesting properties of dye sensitizers

The systematic trends in structural and electronic properties of perylene diimide (PDI) derived dye molecules have been investigated by DFT calculations based on projector augmented wave (PAW) method including gradient corrected exchange-correlation effects. TDDFT calculations have been performed to study the visible absorbance activity of these complexes. The effect of different ligands and halogen atoms attached to PDI were studied to characterize the light harvesting properties. The atomic size and electronegativity of the halogen were observed to alter the relaxed molecular geometries which in turn influenced the electronic behavior of the dye molecules. Ground state molecular structure of isolated dye molecules studied in this work depends on both the halogen atom and the carboxylic acid groups. DFT calculations revealed that the carboxylic acid ligands did not play an important role in changing the HOMO-LUMO gap of the sensitizer. However, they serve as anchor between the PDI and substrate titania surface of the solar cell or photocatalyst. A commercially available dye-sensitizer, ruthenium bipyridine (RuBpy), was also studied for electronic and structural properties in order to make a comparison with PDI derivatives for light harvesting properties. Results of this work suggest that fluorinated, chlorinated, brominated, and iyodinated PDI compounds can be useful as sensitizers in solar cells and in artificial photosynthesis.Comment: Single pdf file, 14 pages with 7 figures and 4 table