Cooling nonlinear lattices toward localisation

We describe the energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators. Spontaneous emergence of localised vibrations dramatically slows down dissipation and gives rise to quasi-stationary states where energy is trapped in the form of a gas of weakly interacting discrete breathers. In one dimension (1D), strong enough on--site coupling may yield stretched--exponential relaxation which is reminiscent of glassy dynamics. We illustrate the mechanism generating localised structures and discuss the crucial role of the boundary conditions. For two--dimensional (2D) lattices, the existence of a gap in the breather spectrum causes the localisation process to become activated. A statistical analysis of the resulting quasi-stationary state through the distribution of breathers' energies yield information on their effective interactions.Comment: 10 pages, 11 figure

Slow energy relaxation and localization in 1D lattices

We investigate the energy relaxation process produced by thermal baths at zero temperature acting on the boundary atoms of chains of classical anharmonic oscillators. Time-dependent perturbation theory allows us to obtain an explicit solution of the harmonic problem: even in such a simple system nontrivial features emerge from the interplay of the different decay rates of Fourier modes. In particular, a crossover from an exponential to an inverse-square-root law occurs on a time scale proportional to the system size $N$. A further crossover back to an exponential law is observed only at much longer times (of the order $N^3$). In the nonlinear chain, the relaxation process is initially equivalent to the harmonic case over a wide time span, as illustrated by simulations of the $\beta$ Fermi-Pasta-Ulam model. The distinctive feature is that the second crossover is not observed due to the spontaneous appearance of breathers, i.e. space-localized time-periodic solutions, that keep a finite residual energy in the lattice. We discuss the mechanism yielding such solutions and also explain why it crucially depends on the boundary conditions.Comment: 16 pages, 6 figure

Discrete Breathers in a Realistic Coarse-Grained Model of Proteins

We report the results of molecular dynamics simulations of an off-lattice protein model featuring a physical force-field and amino-acid sequence. We show that localized modes of nonlinear origin (discrete breathers) emerge naturally as continuations of a subset of high-frequency normal modes residing at specific sites dictated by the native fold. In the case of the small $\beta$-barrel structure that we consider, localization occurs on the turns connecting the strands. At high energies, discrete breathers stabilize the structure by concentrating energy on few sites, while their collapse marks the onset of large-amplitude fluctuations of the protein. Furthermore, we show how breathers develop as energy-accumulating centres following perturbations even at distant locations, thus mediating efficient and irreversible energy transfers. Remarkably, due to the presence of angular potentials, the breather induces a local static distortion of the native fold. Altogether, the combination of this two nonlinear effects may provide a ready means for remotely controlling local conformational changes in proteins.Comment: Submitted to Physical Biolog

Multifunctions determined by integrable functions

Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee i

Apparatus for time‐resolved measurements of acoustic birefringence in particle dispersions

An apparatus for time‐resolved measurements of the birefringence induced in a particle suspension by an acoustic wave pulse is described. Efficient acoustic coupling is obtained by operating near the transducer resonant frequency and by matching the acoustic impedances of the cell constituents. An almost‐overdamped acoustic configuration can alternatively be employed whenever a faster response is needed. Careful design of the optical setup and of the detection unit minimize diffraction and stress‐birefringence parasitic effects and yields a good responsivity at fairly low acoustic intensities. A test of the apparatus on a colloidal suspension of PTFE rodlike particles is presented and discussed

Energy transfer in nonlinear network models of proteins

We investigate how nonlinearity and topological disorder affect the energy relaxation of local kicks in coarse-grained network models of proteins. We find that nonlinearity promotes long-range, coherent transfer of substantial energy to specific, functional sites, while depressing transfer to generic locations. Remarkably, transfer can be mediated by the self-localization of discrete breathers at distant locations from the kick, acting as efficient energy-accumulating centers.Comment: 4 pages, 3 figure

Calibration of a photomultiplier array spectrometer

A systematic approach to the calibration of a photomultiplier array spectrometer is presented. Through this approach, incident light radiance derivation is made by recognizing and tracing gain characteristics for each photomultiplier tube

Jeremy Corbyn according to the BBC: ideological representation and identity construction of the Labour Party leader

There have been many complaints that the BBC coverage of the rise of Jeremy Corbyn has been partial and biased. This paper is part of an interdisciplinary project on the television representation of Jeremy Corbyn that brings together scholars in the disciplines of linguistics (critical discourse analysis), journalism and politics. The paper is a small scale case study examining the coverage of Jeremy Corbyn’s speech on the 28th September 2016 after he won the leadership by election for the second time in a year. In the first stage we compared the scripting of the reports for the main national UK TV news programmes and the representation of the Labour leader’s identity offered to viewers. In the second, we also evaluate Newsnight, a BBC programme coverage of a slightly different genre, which constructed Corbyn as a particular kind of leader. In addition to the verbal text of the reports, we considered the interplay between the presenter and political correspondent and their tone. This enabled us to broaden our critical discourse analysis to a multimodal investigation and tease out non-textual, nuanced ways of creating partiality. We concluded that some BBC coverage does demonstrate bias and partiality against Corbyn in subtle modes where tone alters the meaning of the script and visuals and the BBC fared badly compared to other mainstream TV news