Rational Krylov methods for fractional diffusion problems on graphs

BIT Numerical Mathematics - In this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph...     

Reactivite des carbanions benzyliques : VIII. Etude de la structure d'alkyl-9 lithio-10 dihydro-9,10 anthracenes par rmn du proton et spectrometrie d'absorption electronique; influence du substituant,du solvant et de la temperature

The structure of the 9,10-dihydroanthracenyl anion and of a series of 9-alkyl-10-lithio-9-10-dihydroanthracenes (9-R-10-LiDHA, I–V where R = H, Me, Et, i-Pr, t-Bu) was studied in solution by electronic absortion spectrometry and proton magnetic resonance. Our electronic absorption results, in addition to those of other authors, show that the contact ion pairs (c.i.p.) have an absorption at λ_max}- 400 nm (I–III) and 415 nm (V) whereas the loose ion pairs (l.i.p.) absorb at λmax}- 450 nm (I–V). In the NMR the chemical shift of the proton para with respect to the carbanionic center was examined as a function of solvent (THF, THF/HMPA, and in some cases ether or pure HMPA) and temperature (+20 to ?40°C). The para proton is shielded significantly with regard to the aromatic protons of the hydrocarbon (Δδ(H_para) ca. 1–1.7 ppm). The weakest shielding was observed in ether, in agreement with the existence of c.i.p. The largest shielding (THF/HMPA or pure HMPA) is in connection with the presence of l.i.p. where the negative charge is less localised at position 10. Moreover, in the same solvent, and at the same temperature, Δδ(H_para) was observed to increase with the substituent bulk, up to the point that there are only l.i.p. present. As found previously (namely for the fluorenyl anion) the l.i.p./c.i.p. ratio increases when temperature decreases. The results of this structural study allow to rationalize the protonation stereochemistry of 9-alkyl-10-lithio-9,10-dihydroanthracenes in the above-mentioned solvents.     

Examination of the electrophoretic behavior of liposomes

The electromigration of liposomes is a complex process resulting in many unexpected behaviors that are difficult to address with existing theories. In this study, the electrophoretic behaviors of liposome populations under various conditions were examined through the use of capillary electrophoresis and the results compared to classical electrokinetic, colloid, and spheroid theories. To elucidate the possible effects of applied field strength, bilayer rigidity, and surface charge on these behaviors, the electrophoretic mobilities of liposome populations were monitored while varying the applied potential, ionic strength of the medium, and the surface charge and cholesterol content of the liposomes. On the basis of comparisons made to the theoretical predictions, our results suggest that liposomal deformation and field-induced polarization may occur during electrophoresis and these mechanisms help to describe many of the observed behaviors.     

Properties of balanced and perfect matrices

In this paper we define wheel matrices and characterize some properties of matrices that are perfect but not balanced. A consequence of our results is that if a matrixA is perfect then we can construct a polynomial number of submatricesA _I,,A _n ofA such thatA is balanced if and only if all the submatricesA ₁,,A _n ofA are perfect. This implies that if the problem of testing perfection is polynomially solvable, then so is the problem of testing balancedness.Partial support under NSF Grants DMS-8606188, ECS-8800281 and DDM-8800281.     

Characterization of bronze Roman coins of the fifth century called <Emphasis Type=Italic>nummi</Emphasis> through different analytical techniques

Mixing of different organic charge-transfer-complexes (CT-complexes) might allow the adjustment of the optical and morphological properties of the resulting material system. In this work, a study of two CT-complexes, mixed by thermal coevaporation at different concentrations by substituting only the acceptor molecules, is presented. Electron diffraction patterns, which were collected on samples of the ternary system of the prototypical CT-complexes DBTTF-TCNQ and DBTTF-F₄TCNQ do not show any indication of a mixed crystalline phase or novel crystalline order. X-ray diffraction measurements additionally confirm the phase separation in the ternary system. However, upon mixing of the complexes, the degree of crystallinity of the individual phases is reduced. This effect correlates with the mixing ratio of the CT-complexes in the ternary compound. Furthermore, we do not observe a shift or the appearance of new peaks in the infrared spectra of (DBTTF-TCNQ) _x :(DBTTF-F₄TCNQ)_1?x . Hence, there is no indication for a pronounced or novel chemical interaction between the individual CT-complexes in the mixed compound.     

Tight-binding models for ultracold atoms in optical lattices: general formulation and applications

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.     

Solvent effects on charge spatial extent in DNA and implications for transfer

To clarify the role played by water in facilitating long-range DNA charge transport, carefully designed, state-of-the-art, self-interaction corrected density-functional quantum mechanical and molecular mechanical (SIC-QM/MM) simulations are performed for the first time on two ionized adenine:thymine bridge models in explicit water solvent at finite temperature. For random solvent configurations, the charge is partially delocalized. However, a charge localization on different, well-separated adenines can be induced and is correlated with a restructuring of their first solvation shells. Thus, the importance of water in the mechanism of long-range charge transport is explicitly demonstrated, and the microscopic conditions for a charge localization are revealed.     

Conservative numerical methods for the Full von Kármán plate equations

This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large‐amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Kármán system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semidiscrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretizations. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1948–1970, 2015     

Packing T-joins

A consequence of Seymour's characterization of binary clutters with the Max Flow Min Cut property is that the minimum cardinality of a T-cut is equal to the largest number of edge-disjoint T-joins in every graph that cannot be T-contracted to an odd K_2,3. We give a simple “graphic” proof of this fact. © 1996 John Wiley & Sons, Inc.