Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field h. Using ideas from dynamical systems and functional analysis, we show that the free energy f in the vicinity of the second-order phase transition is given, exactly, by $$f\sim\frac{t}{\log t}-\frac{1}{2}\frac{h^2}{t}\quad\mbox{for }h^2\ll t\ll1.$$ Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_{c}})$ is a reduced temperature, so that the deviation from the critical point is scaled by the Lyapunov exponent of the Gauss map, λ _G . It follows that λ _G determines the amplitude of both the specific heat and susceptibility singularities. To our knowledge, there is only one other microscopically defined interacting model for which the free energy near a phase transition is known as a function of two variables. Our results confirm what was found previously with a cluster approximation, and show that a clustering mechanism is in fact responsible for the transition. However, the results disagree in part with a renormalisation group treatment.     

Mechanism for room-temperature single-atom lateral manipulations on semiconductors using dynamic force microscopy

Vacancy-mediated lateral manipulations of intrinsic adatoms of the Si(111)-(7x7) surface at room temperature are reported. The topographic signal during the manipulation combined with force spectroscopy measurements reveals that these manipulations can be ascribed to the so-called pulling mode, and that the Si adatoms were manipulated in the attractive tip-surface interaction regime at the relatively low short-range force value associated to the manipulation set point. First-principles calculations reveal that the presence of the tip induces structural relaxations that weaken the adatom surface bonds and manifests in a considerable local reduction of the natural diffusion barriers to adjacent adsorption positions. Close to the short-range forces measured in the experiments, these barriers are lowered near the limit that enables a thermally activated hopping at room temperature.     

Biolabeling with nanoparticles based on Y2O3: Nd and luminescence detection in the near-infrared

Neodymium based fluorescence presents several advantages in comparison to conventional rare earth or enzyme-substrate based fluorescence emitting sources (e.g.Tb, HRP) . Based on this fact we have herein explored a Nd-based fluoroimmunoassay. We efficiently detected the presence of an oxidized low-density lipoprotein (oxLDL) in human plasma a well-known marker for cardiovascular diseases, which causes around 30% of deaths worldwide. Conventional fluoroimmunoassay uses time-resolved luminescence techniques, with detection in the visible range, to eliminate the fluorescence background from the biological specimens. By using an immunoassay based on functionalized Y₂O₃:Nd³⁺ nanoparticles, where the excitation and emission processes in the Nd³⁺ ion occur in the near-infrared (NIR) region, we have succeeded in eliminating the interferences from the biological fluorescence background, avoiding the use of time-resolved techniques. This yields higher emission intensity from the Nd³⁺-nanolabels and efficient detection of anti-oxidized low-density lipoproteins (anti-oxLDL) by Y₂O₃:Nd³⁺-antibody-antigen conjugation, leading to a novel biolabeling method.     

Complex Convexity and Vector-Valued Littlewood-Paley Inequalities

Let 2 p > , and let X be a complex Banach space. It is shownthat X is p-uniformly PL-convex if and only if there exists > 0 such that , for all f H^p(X). Applications to embeddings between vector-valued BMOAspaces defined via Poisson integral or Carleson measures areprovided. 2000 Mathematics Subject Classification 46B20, 46L52.     

Engineered pixels using active plasmonic holograms with liquid crystals

Digital holography requires arrays of small reconfigurable elements to achieve complex reconstruction of the hologram with common systems based on pixels utilizing liquid crystal on silicon (LCoS) technology. The backplane of a typical pixel element is potentially underutilized and thus relatively large physical areas exist in which information can be stored and exploited to give additional functionality to pixel elements. Polarisation and wavelength dependent optical properties can be achieved in small areas using the plasmonic effects of optical antennae. The integration of LCs with optical antennae‐based plasmonic holograms allows active modulation of the far field pattern. The work here demonstrates the concept that conventional LCoS pixel elements can be greatly enhanced with the integration of plasmonic holograms, composed of optical antennae patterned on the surface, giving rise to new levels of modulation capability for holographic pixel elements. Using LCs, polarisation dependent effects in plasmonic holograms can be switched. ‘Engineered pixels', with sub‐wavelength multiplexing over both polarisation and wavelength, can increase the channel capacity of a typical LC display device. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Precision measurements in nuclear beta decay

Precision measurements in nuclear beta decay provide sensitive means to determine the fundamental coupling of charged fermions to weak bosons and to test discrete symmetries in the weak interaction. The main motivation of such measurements is to find deviations from Standard Model predictions as possible indications of new physics. I focus here on two topics related to precision measurements in beta decay, namely: (i) the determination of the V _ud element of the Cabibbo-Kobayashi-Maskawa quark mixing matrix from nuclear mirror transitions and (ii) selected measurements of time reversal violating correlations in nuclear and neutron decays. These topics complement those presented in other contributions to this conference.     

Solute-diffusion-controlled dislocation creep in pure aluminium containing 0.026 at.% Fe

Pure aluminium containing about 200?at.ppm Fe in solution is shown to creep about 10⁶ times slower at 200°C than the same aluminium containing a negligible amount of iron in solution. The high creep resistance of the Al–200?at.ppm?Fe alloy is attributed to the presence of subgrain boundaries containing iron solute atoms. It is proposed that the opposing stress fields from subgrain boundaries and from the piled-up dislocations during creep are cyclically relaxed, by iron solute diffusion, to allow climb of the lead dislocation in the pile-up. The mechanism is a form of mechanical ratcheting. The model is applied to Al–Fe alloys and correctly predicts that the creep rate is controlled by the rate of iron solute diffusion and by a temperature dependence equal to the activation energy for iron diffusion, namely Q _c?=?221?kJ?mol^?1. Basic creep studies on solid-solution alloying with solute atoms that diffuse slowly in the lattice of aluminium (e.g. manganese, chromium, titanium and vanadium) appear worthy of study as a way of enhancing creep strength and of understanding creep mechanisms involving solute-atom-containing subgrain boundaries.     

Leptoquark effects on ν τ propagation in the Earth

The proposal of pilgrim dark energy is based on the idea that phantom dark energy possesses enough resistive force to preclude black hole formation. We work on this proposal by choosing an interacting framework with cold dark matter and three cutoffs such as Hubble as well as event horizon and conformal age of the universe. We present a graphical analysis and focus our study on the pilgrim dark energy as well as interacting parameters. It is found that these parameters play an effective role on the equation of state parameter for exploring the phantom region of the universe. We also make the analysis of ω–ω′ and point out freezing region in the ω–ω′ plane. Finally, it turns out that the ΛCDM is achieved in the statefinders plane for all models.     

Prescriptions for gravitational initial data as judged by a simple radiating model

Several methods of prescribing initial data for gravitational and matter fields, which are intended to eliminate extraneous radiation that is not produced by the matter source, are analysed in a simple exactly soluble radiating model. The model consists of an harmonic oscillator coupled to a scalar field along future light cones of Minkowski space time. In particular we analyze the asymptotic regime of the oscillator and find it is characterized essentially by two distinct decay modes. They differ in the way they behave both in the limit of small coupling constant and in a certain Newtonian limit. As a criterion to select initial data for the field with no extra radiation, we require that these initial data sets should put the oscillator from the start into the asymptotic regime. The underlying hypothesis here is that initial transients result from excitation of the oscillator by incoming radiation. We then see that the requirement of a uniform Newtonian limit leads to unique data for the scalar field for each arbitrary data set for the oscillator. We further find that this unique data set indeed satisfies our criterion.