Self-Dual Conformal Supergravity and the Hamiltonian Formulation

In terms of Dirac matrices the self-dual and anti-self-dual decomposition of a conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variabes include the self-dual spin connection i.e. the Ashtekar connection rather than the triad. The Hamiltonian formulation and the constraints are obtained by using the Dirac-Bergmann algorithm. PACS numbers: 04.20.Cv, 04.20.Fy,04.65.+

Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators

Correlation functions $C(t) \sim$ in ohmically damped systems such as coupled harmonic oscillators or optical resonators can be expressed as a single sum over modes $j$ (which are not power-orthogonal), with each term multiplied by the Petermann factor (PF) $C_j$, leading to "excess noise" when $|C_j| > 1$. It is shown that $|C_j| > 1$ is common rather than exceptional, that $|C_j|$ can be large even for weak damping, and that the PF appears in other processes as well: for example, a time-independent perturbation \sim\ep leads to a frequency shift \sim \ep C_j. The coalescence of $J$ ($>1$) eigenvectors gives rise to a critical point, which exhibits "giant excess noise" ($C_j \to \infty$). At critical points, the divergent parts of $J$ contributions to $C(t)$ cancel, while time-independent perturbations lead to non-analytic shifts \sim \ep^{1/J}.Comment: REVTeX4, 14 pages, 4 figures. v2: final, 20 single-col. pages, 2 figures. Streamlined with emphasis on physics over formalism; rewrote Section V E so that it refers to time-dependent (instead of non-equilibrium) effect

Hamiltonian and Linear-Space Structure for Damped Oscillators: I. General Theory

The phase space of $N$ damped linear oscillators is endowed with a bilinear map under which the evolution operator is symmetric. This analog of self-adjointness allows properties familiar from conservative systems to be recovered, e.g., eigenvectors are "orthogonal" under the bilinear map and obey sum rules, initial-value problems are readily solved and perturbation theory applies to the_complex_ eigenvalues. These concepts are conveniently represented in a biorthogonal basis.Comment: REVTeX4, 10pp., 1 PS figure. N.B.: `Alec' is my first name, `Maassen van den Brink' my family name. v2: extensive streamlinin

Excitonic energy transfer in light-harvesting complexes in purple bacteria

Two distinct approaches, the Frenkel-Dirac time-dependent variation and the Haken-Strobl model, are adopted to study energy transfer dynamics in single-ring and double-ring light-harvesting systems in purple bacteria. It is found that inclusion of long-range dipolar interactions in the two methods results in significant increases in intra- or inter-ring exciton transfer efficiency. The dependence of exciton transfer efficiency on trapping positions on single rings of LH2 (B850) and LH1 is similar to that in toy models with nearest-neighbor coupling only. However, owing to the symmetry breaking caused by the dimerization of BChls and dipolar couplings, such dependence has been largely suppressed. In the studies of coupled-ring systems, both methods reveal interesting role of dipolar interaction in increasing energy transfer efficiency by introducing multiple intra/inter-ring transfer paths. Importantly, the time scale (~4ps) of inter-ring exciton transfer obtained from polaron dynamics is in good agreement with previous studies. In a double-ring LH2 system, dipole-induced symmetry breaking leads to global minima and local minima of the average trapping time when there is a finite value of non-zero dephasing rate, suggesting that environment plays a role in preserving quantum coherent energy transfer. In contrast, dephasing comes into play only when the perfect cylindrical symmetry in the hypothetic system is broken. This study has revealed that dipolar interaction between chromophores may play an important part in the high energy transfer efficiency in the LH2 system and many other natural photosynthetic systems.Comment: 14 pages 9 figure

A construction of bent functions from plateaued functions

In this presentation, a technique for constructing bent functions from plateaued functions is introduced and analysed. This generalizes earlier techniques for constructing bent from near-bent functions. Using this construction, we obtain a big variety of inequivalent bent functions, some weakly regular and some non-weakly regular. Classes of bent function with some additional properties that enable the construction of strongly regular graphs are constructed, and explicit expressions for bent functions with maximal degree are presented

Growth Dynamics and Processes Governing the Stability of Electrodeposited Size-Controlled Cubic Cu Catalysts

The renewable energy-powered conversion of industrially generated CO2 into useful chemicals and fuels is considered a promising technology for the sustainable development of our modern society. The electrochemical reduction of CO2 (CO2RR) is one of the possible conversion processes that can be employed to close the artificial carbon cycle, mimicking nature’s photosynthesis. Nevertheless, to enable green catalytic processes, selectivity for the desired products must be achieved. In the case of CO2RR, the selectivity is strongly dependent on the electrocatalyst structure. Here, we explore the phase space of synthesis parameters required for the electrodeposition of Cu cubes with {100} facets on glassy carbon substrates and elucidate their influence on the size, shape, coverage, and uniformity of the cubes. We found that the concentration of Cl– ions in solution controls the cube size, shape, and coverage, whereas the ratio of the reduction versus oxidation time and number of cycles in the alternating potential electrodeposition protocol can be used to further tune the cube size. Cyclic voltammetry experiments were complemented with in situ electrochemical scanning electron microscopy to follow the growth dynamics and ex situ transmission electron microscopy and electron diffraction. Our results indicate that the cube growth starts from nuclei formed during the first cycle, followed by a layered deposition and partial dissolution of new material in subsequent cycles

Structural and thermal characterizations of silica nanoparticles grafted with pendant maleimide and epoxide groups

Grafting of free maleimide and epoxide pendant groups onto the surface of approximately 7-nm silica nanoparticles was investigated. Glycidyloxypropyl groups (3-glycidyloxypropyltrimethoxysilane and 3-aminopropyltrimethoxysilane) that carried epoxide groups and aminopropyl groups were grafted to the silica surface with the help of condensation reactions. Maleimide groups [1,1(')-(methylenedi-4,1-phenelene) bismaleimide] were introduced to the silica surface via nucleophilic addition reaction with the aminopropyl groups pre-grafted onto the surface. The grafted silica samples were characterized using CHN, FTIR, DSC, TGA-FTIR, and 13C and 29Si CP/MAS NMR spectroscopy. NMR analyses revealed that all the functional groups were covalently bonded to the silica surface and most of the maleimide and epoxide rings remained intact on surface. DSC analysis showed that the epoxide groups were more reactive than the maleimide groups