Traveling Salesman Problem with Clustering

In the original traveling salesman problem, the traveling salesman has the task to find the shortest closed tour through a proposed set of nodes, touching each node exactly once and returning to the initial node at the end. For the sake of the tour length to be minimized, nodes close to each other might not be visited one after the other but separated in the tour. However, for some practical applications, it is useful to group nodes to clusters, such that all nodes of a cluster are visited contiguously. Here we present an approach which leads to an automatic clustering with a clustering parameter governing the sizes of the clusters.     

Characterization of Coupled Ground State and Excited State Equilibria by Fluorescence Spectral Deconvolution

Fluorescence probes with multiparametric response based on the relative variation in the intensities of several emission bands are of great general utility. An accurate interpretation of the system requires the determination of the number, positions and intensities of the spectral components. We have developed a new algorithm for spectral deconvolution that is applicable to fluorescence probes exhibiting a two-state ground-state equilibrium and a two-state excited-state reaction. Three distinct fluorescence emission bands are resolved, with a distribution of intensities that is excitation-wavelength-dependent. The deconvolution of the spectrum into individual components is based on their representation as asymmetric Siano-Metzler log-normal functions. The application of the algorithm to the solvation response of a 3-hydroxychromone (3HC) derivative that exhibits an H-bonding-dependent excited-state intramolecular proton transfer (ESIPT) reaction allowed the separation of the spectral signatures characteristic of polarity and hydrogen bonding. This example demonstrates the ability of the method to characterize two potentially uncorrelated parameters characterizing dye environment and interactions.     

Leakage current study of Si1−xCx embedded source/drain junctions

This work investigates the impact of various processing parameters on the leakage current of in situ P-doped Si_1−xC_x embedded source/drain (S/D) junctions, i.e., the carbon content x (%) and the thermal budget used either before or after the selective epitaxial deposition. It is shown that while the area leakage current density, generated by defects in the depletion region is not affected by the epitaxial process or the strain in the substrate, the perimeter leakage current density (J_P) increases with x. From the stronger reverse bias dependence of J_P, it is derived that a higher electric field exists along the junction periphery. This is confirmed by capacitance-voltage (C-V) measurements, demonstrating a higher p-well B doping density for increasing x. It is believed that this originates from the strain dependence of the B diffusivity in the p-well region. No evidence of electrically active extended defect formation was found, so it is expected that the off-state current of embedded Si_1−xC_x S/D nMOSFETs will not be adversely affected by the selective epitaxial deposition.     

Coherent Raman and Infrared Studies of Sulfur Trioxide

High-resolution (0.001 cm⁻¹) coherent anti-Stokes Raman scattering (CARS) was used to observe the Q-branch structure of the IR-inactive ν₁ symmetric stretching mode of ³²S¹⁶O₃ and its various ¹⁸O isotopomers. The ν₁ spectrum of ³²S¹⁶O₃ reveals two intense Q-branches in the region 1065–1067 cm⁻¹, with surprisingly complex vibrational–rotational structure not resolved in earlier studies. Efforts to simulate this with a simple Fermi-resonance model involving ν₁ and 2ν₄ states do not reproduce the spectral detail, nor do they yield reasonable spectroscopic parameters. A more subtle combination of Fermi resonance and indirect Coriolis interactions with nearby states, 2ν₄(1=0, ±2), ν₂+ν₄(1=±1), 2ν₂(1=0), is suspected and a determination of the location of these coupled states by high-resolution infrared measurements is under way. At medium resolution (0.125 cm⁻¹), the infrared spectra reveal Q-branch features from which approximate band origins are estimated for the ν₂, ν₃, and ν₄ fundamental modes of ³²S¹⁸O₃, ³²S¹⁸O₂¹⁶O, and ³²S¹⁸O¹⁶O₂. These and literature data for ³²S¹⁶O₃ are used to calculate force constants for SO₃ and a comparison is made with similar values for SO₂ and SO. The frequencies and force constants are in excellent agreement with those obtained by Martin in a recent ab initio calculation.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

Positive Lyapunov exponents for a class of deterministic potentials

LetV() be a smooth, non-constant function on the torus and letT be a hyperbolic toral automorphism. Consider a discrete one dimensional Schrödinger operatorH, whose potential at sitej is given bygV _j =gV(T ^j ). We prove that wheng0 is small andg ^1/2 |E|2–g ^1/2 , the Lyapunov exponent for the cocycle generated byH-E is proportional tog ². The proof relies on a formula of Pastur and Figotin and on symbolic dynamics.     

Growth,structure and optical properties of an efficient NLO crystal-aqua maleatocopper(II)

A promising non-linear optical (NLO) crystal, aqua maleatocopper(II) (CuC₄H₂O₄·H₂O), was grown at room temperature by the controlled ionic diffusion technique. Fourier transform infrared spectrum could identify the various functional groups in the crystal. Structural analysis using single crystal XRD revealed that the compound crystallizes in the monoclinic system with space group P2₁ and unit cell parameters a = 7.7277(5) Å, b = 5.2967(3) Å, c = 7.7179(4) Å, α = γ = 109.170(5)°, β = 111.995(2)°. The thermal stability and decomposition pattern of the material were explored using thermogravimetry (TG) and differential thermal analysis (DTA). The optical band gap energy of the material was estimated as 2.2 eV from the diffuse reflectance spectroscopy. The Kurtz and Perry powder technique established the crystal to be an efficient non-linear optical (NLO) material.