Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions

Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled energy whose minimizers are free from uncontrollable errors on the atomistic/continuum interface. In this paper a consistent coupling in three dimensions is proposed. The main achievement of this work is to identify and efficiently treat a modified Cauchy-Born continuum model which can be coupled to the exact atomistic model. The convergence and stability of the method is confirmed with numerical tests.Comment: 29 pages, 1 Matlab code. Typos corrected, exposition improve

How mobile are dye adsorbates and acetonitrile molecules on the surface of TiO2 nanoparticles? A quasi-elastic neutron scattering study

Motions of molecules adsorbed to surfaces may control the rate of charge transport within monolayers in systems such as dye sensitized solar cells. We used quasi-elastic neutron scattering (QENS) to evaluate the possible dynamics of two small dye moieties, isonicotinic acid (INA) and bis-isonicotinic acid (BINA), attached to TiO2 nanoparticles via carboxylate groups. The scattering data indicate that moieties are immobile and do not rotate around the anchoring groups on timescales between around 10 ps and a few ns (corresponding to the instrumental range). This gives an upper limit for the rate at which conformational fluctuations can assist charge transport between anchored molecules. Our observations suggest that if the conformation of larger dye molecules varies with time, it does so on longer timescales and/or in parts of the molecule which are not directly connected to the anchoring group. The QENS measurements also indicate that several layers of acetonitrile solvent molecules are immobilized at the interface with the TiO2 on the measurement time scale, in reasonable agreement with recent classical molecular dynamics results

Assessing the influence of the Merzbacher Lake outburst floods on discharge using the hydrological model SWIM in the Aksu headwaters, Kyrgyzstan/NW China

Glacial lake outburst floods (GLOF) often have a significant impact on downstream users. Including their effects in hydrological models, identifying past occurrences and assessing their potential impacts are challenges for hydrologists working in mountainous catchments. The regularly outbursting Merzbacher Lake is located in the headwaters of the Aksu River, the most important source of water discharge to the Tarim River, northwest China. Modelling its water resources and the evaluation of potential climate change impacts on river discharge are indispensable for projecting future water availability for the intensively cultivated river oases downstream of the Merzbacher Lake and along the Tarim River. The semi-distributed hydrological model SWIM was calibrated to the outlet station Xiehela on the Kumarik River, by discharge the largest tributary to the Aksu River. The glacial lake outburst floods add to the difficulties of modelling this high-mountain, heavily glaciated catchment with poor data coverage and quality. The aims of the study are to investigate the glacier lake outburst floods using a modelling tool. Results include a two-step model calibration of the Kumarik catchment, an approach for the identification of the outburst floods using the measured gauge data and the modelling results and estimations of the outburst flood volumes. Results show that a catchment model can inform GLOF investigations by providing ‘normal’ (i.e. without the outburst floods) catchment discharge. The comparison of the simulated and observed discharge proves the occurrence of GLOFs and highlights the influences of the GLOFs on the downstream water balance. © 2013 The Authors. Hydrological Processes Published by John Wiley & Sons Ltd

SLOCC determinant invariants of order 2^{n/2} for even n qubits

In this paper, we study SLOCC determinant invariants of order 2^{n/2} for any even n qubits which satisfy the SLOCC determinant equations. The determinant invariants can be constructed by a simple method and the set of all these determinant invariants is complete with respect to permutations of qubits. SLOCC entanglement classification can be achieved via the vanishing or not of the determinant invariants. We exemplify the method for several even number of qubits, with an emphasis on six qubits.Comment: J. Phys. A: Math. Theor. 45 (2012) 07530

Conflict-free connection numbers of line graphs

A path in an edge-colored graph is called \emph{conflict-free} if it contains at least one color used on exactly one of its edges. An edge-colored graph $G$ is \emph{conflict-free connected} if for any two distinct vertices of $G$, there is a conflict-free path connecting them. For a connected graph $G$, the \emph{conflict-free connection number} of $G$, denoted by $cfc(G)$, is defined as the minimum number of colors that are required to make $G$ conflict-free connected. In this paper, we investigate the conflict-free connection numbers of connected claw-free graphs, especially line graphs. We first show that for an arbitrary connected graph $G$, there exists a positive integer $k$ such that $cfc(L^k(G))\leq 2$. Secondly, we get the exact value of the conflict-free connection number of a connected claw-free graph, especially a connected line graph. Thirdly, we prove that for an arbitrary connected graph $G$ and an arbitrary positive integer $k$, we always have $cfc(L^{k+1}(G))\leq cfc(L^k(G))$, with only the exception that $G$ is isomorphic to a star of order at least~$5$ and $k=1$. Finally, we obtain the exact values of $cfc(L^k(G))$, and use them as an efficient tool to get the smallest nonnegative integer $k_0$ such that $cfc(L^{k_0}(G))=2$.Comment: 11 page

Experiments with explicit for-loops in genetic programming

Evolving programs with explicit loops presents major difficulties, primarily due to the massive increase in the size of the search space. Fitness evaluation becomes computationally expensive and a method for dealing with infinite loops must be implemented. We have investigated ways of dealing with these problems by the evolution of for-loops of increasing semantic complexity. We have chosen two problems - a modified Santa Fe ant problem and a sorting problem - which have natural looping constructs in their solution and a solution without loops is not possible unless the tree depth is very large. We have shown that by controlling the complexity of the loop structures it is possible to evolve smaller and more understandable programs for these problems

Ultraviolet photonic crystal laser

We fabricated two dimensional photonic crystal structures in zinc oxide films with focused ion beam etching. Lasing is realized in the near ultraviolet frequency at room temperature under optical pumping. From the measurement of lasing frequency and spatial profile of the lasing modes, as well as the photonic band structure calculation, we conclude that lasing occurs in the strongly localized defect modes near the edges of photonic band gap. These defect modes originate from the structure disorder unintentionally introduced during the fabrication process.Comment: 4 pages, 4 figure

Critical Current Density and Resistivity of MgB2 Films

The high resistivity of many bulk and film samples of MgB2 is most readily explained by the suggestion that only a fraction of the cross-sectional area of the samples is effectively carrying current. Hence the supercurrent (Jc) in such samples will be limited by the same area factor, arising for example from porosity or from insulating oxides present at the grain boundaries. We suggest that a correlation should exist, Jc ~ 1/{Rho(300K) - Rho(50K)}, where Rho(300K) - Rho(50K) is the change in the apparent resistivity from 300 K to 50 K. We report measurements of Rho(T) and Jc for a number of films made by hybrid physical-chemical vapor deposition which demonstrate this correlation, although the "reduced effective area" argument alone is not sufficient. We suggest that this argument can also apply to many polycrystalline bulk and wire samples of MgB2.Comment: 11 pages, 3 figure

ALMA Observations of Ethyl Formate toward Orion KL

Orion KL is one of the prime templates of astrochemical and prebiotic chemical studies. We wish to explore more organic molecules with increasing complexity in this region. In particular, we have searched for one of the most complex organic molecules detected in space so far, ethyl formate (C$_{2}$H$_{5}$OCHO). This species is the next step in chemical complexity after the simplest member of esters (methyl formate, CH$_{3}$OCHO). The mechanisms leading to its formation are still poorly known. We have used high angular resolution ($\sim$ 1.$^{\prime\prime}$5) ALMA observations covering a large bandwidth from 214 to 247 GHz. We have detected 82 unblended lines of C$_{2}$H$_{5}$OCHO (49 and 33 of the trans and gauche conformers, respectively). The line images showed that C$_{2}$H$_{5}$OCHO arises mainly from the compact ridge and the hot core-southwest regions. The derived rotational temperatures and column densities are 122 $\pm$ 34 K, (0.9 $\pm$ 0.3) $\times$ 10$^{16}$ cm$^{-2}$ for the hot core-SW, and 103 $\pm$ 13 K, (0.6 $\pm$ 0.3) $\times$ 10$^{16}$ cm$^{-2}$ for the compact ridge. The comparison of spatial distribution and abundance ratios with chemically related molecules (methyl formate, ethanol and formic acid) indicates that C$_{2}$H$_{5}$OCHO is likely formed on the surface of dust grains by addition of CH$_{3}$ to functional-group radicals (CH$_{2}$OCHO) derived from methyl formate (CH$_{3}$OCHO)