On multiple visits in lattice random walks

In the present work we treat in detail the problem of multiple visits in lattice random walks. We show that this problem is closely related to the well-studied property of the number of distinct sites visited at least one in ann-step walk. With simple algebraic manipulations we provide new analytical solutions for the mean number of sites visited exactly a certain number of times, and the mean number of sites visited at least a certain number of times. We find that the moments of these quantities vary asymptotically with time. The resulting exponents exhibit constant gap scaling. Computer simulations are given that are within excellent agreement with the derived expressions.     

Spectroscopic studies of ArF laser photoablation of PMMA

A Spectroscopic study has been made of the emission spectra arising from ArF laser initiated photoablation of PMMA samples. This process leads to direct etching of the polymer. The thermal temperature of the CH fragment species in the plume immediately above the ablated site was found to be 3200 ±200 K. The translational velocity of this species was found to be 4.2×10⁵ cm/s corresponding to a translational temperature of 11,000 K. These results are consistent with a rapid direct bond scission model for ablation.     

Fractal Dimension of Microbead Assemblies Used for Protein Detection

We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1 μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest–Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70–1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles.     

Density of states,level-statistics and localization of fractons in 2- and 3-dimensional disordered systems

We calculate by the Lanczos method the density of spin wave states, and its fluctuation properties on the infinite percolating cluster of a randomly site-dilute Heisenberg ferromagnet. Our results demonstrate that the averaged density follows the fracton laws with spectral dimension valuesd _s =1.32 andd _s =1.30 in two and three dimensions, respectively, and is smooth at the magnon-fracton crossover. Similar laws are also shown in the case of continuous disorder on the bonds of the clusters. The density fluctuations are studied via the nearest energylevel-spacing distribution functionP(S), which is shown to obey the Wigner surmise with level-repulsion far from the percolation thresholdp _c and an almost Poisson law with uncorrelated spectrum atp _c . The localization properties of excitations are investigated by considering the density of states fluctuations and also via the participation ratio of the eigenvector amplitudes. It is seen that the fracton states are sharply localized. Our results are further discussed in connection to previous theories and numerical data.     

A combined quantum mechanical and experimental approach towards chiral diketopiperazine hydroperoxides

In order to improve hydroperoxide formation from heterocyclic compounds relating to the formation rate and to allow a suitable choice of starting materials for autoxidation, theoretical studies on a set of different amino acid‐derived diketopiperazines and pyrazinoquinazolines were carried out. To estimate their reactivity towards hydroperoxide formation, bond dissociation enthalpies (BDEs) of tertiary α‐C? H bonds as well as reaction enthalpies to the corresponding hydroperoxides were calculated at the B3LYP/TZVP and RMP2/aug‐cc‐pVTZ level of theory. The Evans–Polanyi relation was then used to correlate substrate reactivity with calculated BDEs. Thermal and zero point vibrational energy (ZPE) corrections were determined in the classical harmonic oscillator‐rigid rotor‐particle in a box model. While for the investigated set of diketopiperazines BDEs of 318.8–327.0 kJ mol^?1 were found, BDEs for pyrazinoquinazolines spread between 248.4 and 368.4 kJ mol^?1 at the B3LYP/TZVP level of theory. A selected subset of heterocycles was converted to the corresponding hydroperoxides and the diketopiperazines were obtained in up to 39% yield after 5–7 days, whereas the pyrazinoquinazoline hydroperoxides were isolated in up to 67% yield after 24 h. Thus, replacing an amido moiety in an N‐aryl‐imino moiety when using pyrazinoquinazolines instead of diketopiperazines leads indeed to an improved captodative stabilization of the radical intermediate. Furthermore the theoretical calculations allowed a distinctive forecast of the preferred regioisomeric hydroperoxide. Copyright © 2010 John Wiley & Sons, Ltd.     

Purcell effect in triangular plasmonic nanopatch antennas with three-layer colloidal quantum dots

A model describing a plasmonic nanopatch antenna based on triangular silver nanoprisms and multilayer cadmium chalcogenide quantum dots is introduced. Electromagnetic-field distributions in nanopatch antennas with different orientations of the quantum-dot dipoles are calculated for the first time with the finite element method for numerical electrodynamics simulations. The energy flux through the surface of an emitting quantum dot is calculated for the configurations with the dot in free space, on an aluminum substrate, and in a nanopatch antenna. It is shown that the radiative part of the Purcell factor is as large as 1.7 × 10₂ The calculated photoluminescence lifetimes of a CdSe/CdS/ZnS colloidal quantum dot in a nanopatch antenna based on a silver nanoprism agree well with the experimental results.     

The structural role of weak and strong links in a financial market network

We investigate the properties of correlation based networks originating from economic complex systems, such as the network of stocks traded at the New York Stock Exchange (NYSE). The weaker links (low correlation) of the system are found to contribute to the overall connectivity of the network significantly more than the strong links (high correlation). We find that nodes connected through strong links form well defined communities. These communities are clustered together in more complex ways compared to the widely used classification according to the economic activity. We find that some companies, such as General Electric (GE), Coca Cola (KO), and others, can be involved in different communities. The communities are found to be quite stable over time. Similar results were obtained by investigating markets completely different in size and properties, such as the Athens Stock Exchange (ASE). The present method may be also useful for other networks generated through correlations.     

Hybrid neural nets with poisson and gaussian connectivities

The dynamic behavior of neural nets with different patterns of interneuronal synaptic connectivity is investigated. Our method is based on probabilistic neural nets for the net structure and dynamics. Each net is divided into several different subsystems, which are characterized by different distribution laws for the number of connections that the neurons make. We start from the binomial distribution, which, under appropriate conditions, reduces to the Poisson and Gaussian distributions. The overall net now acquires a hybrid character. The expression for the neural activity is generalized to include this effect, and new expressions are derived, based on the isolated single-net equations. The dynamics of nets with sustained external inputs is also studied. The results obtained by this approach also show multiple stability and multiple hysteresis effects, as in the case of single nets. The differences between pure Poisson, Gaussian, and hybrid nets are explained in terms of the structural properties of the model. As expected, the hybrid case falls in between the two other distributions. Finally, we performed Monte Carlo computer calculations for the hybrid nets. For the range of parameters examined we find very good agreement with the developed formalism     

Absence of kinetic effects in reaction-diffusion processes in scale-free networks

We show that the chemical reactions of the model systems of A+A-->0 and A+B-->0 when performed on scale-free networks exhibit drastically different behavior as compared to the same reactions in normal spaces. The exponents characterizing the density evolution as a function of time are considerably higher than 1, implying that both reactions occur at a much faster rate. This is due to the fact that the discerning effects of the generation of a depletion zone (A+A) and the segregation of the reactants (A+B) do not occur at all as in normal spaces. Instead we observe the formation of clusters of A (A+A reaction) and of mixed A and B (A+B reaction) around the hubs of the network. Only at the limit of very sparse networks is the usual behavior recovered.