Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes.

Topological massive Dirac edge modes and long-range superconducting Hamiltonians

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower-band eigenvector and the winding number of the Hamiltonians. For exponentially decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive nonlocal Dirac fermion localized at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.

Development of synthetic light-chain antibodies as novel and potent HIV fusion inhibitors

This is a non-final version of an article published in final form in AIDS. 2016 Jul 17;30(11):1691-701.

Liquid Mixtures Involving Hydrogenated and Fluorinated Alcohols: Thermodynamics, Spectroscopy, and Simulation

This article reports a combined thermodynamic, spectroscopic, and computational study on the interactions and structure of binary mixtures of hydrogenated and fluorinated substances that simultaneously interact through strong hydrogen bonding. Four binary mixtures of hydrogenated and fluorinated alcohols have been studied, namely, (ethanol + 2,2,2-trifluoroethanol (TFE)), (ethanol + 2,2,3,3,4,4,4-heptafluoro-1-butanol), (1-butanol (BuOH) + TFE), and (BuOH + 2,2,3,3,4,4,4-heptafluoro-1-butanol). Excess molar volumes and vibrational spectra of all four binary mixtures have been measured as a function of composition at 298 K, and molecular dynamics simulations have been performed. The systems display a complex behavior when compared with mixtures of hydrogenated alcohols and mixtures of alkanes and perfluoroalkanes. The combined analysis of the results from different approaches indicates that this results from a balance between preferential hydrogen bonding between the hydrogenated and fluorinated alcohols and the unfavorable dispersion forces between the hydrogenated and fluorinated chains. As the chain length increases, the contribution of dispersion increases and overcomes the contribution of H-bonds. In terms of the liquid structure, the simulations suggest the possibility of segregation between the hydrogenated and fluorinated segments, a hypothesis corroborated by the spectroscopic results. Furthermore, a quantitative analysis of the infrared spectra reveals that the presence of fluorinated groups induces conformational changes in the hydrogenated chains from the usually preferred all-trans to more globular arrangements involving gauche conformations. Conformational rearrangements at the CCOH dihedral angle upon mixing are also disclosed by the spectra.