Interacting Field Theories in Robertson-Walker Spacetimes: Analytic Approximations

The renormalization of a scalar field theory with a quartic self-coupling via adiabatic regularization in a Robertson-Walker spacetime is discussed. The adiabatic counterterms are presented in a way that is most conducive to numerical computations. A variation of the adiabatic regularization method is presented which leads to analytic approximations for the energy–momentum tensor of the quantum field and the quantum contribution to the effective mass of the mean field. Conservation of the energy–momentum tensor for the field is discussed and it is shown that the part of the energy–momentum tensor which depends only on the mean field is not conserved but the full renormalized energy–momentum tensor is conserved, as expected and required by the semiclassical Einstein's equation. It is also shown that if the analytic approximations are used the resulting approximate energy–momentum tensor is conserved. This allows a self-consistent backreaction calculation to be performed using the analytic approximations. The usefulness of the approximations is discussed.     

Symmetric and asymmetric fission of charged sodium clusters

A deformed-jellium model is used to calculate the fission barrier height of Na ₂₄ ²⁺ → Na ₂₁ ⁺ +Na ₃ ⁺ and Na ₄₂ ²⁺ → 2Na ₂₁ ⁺ within the Kohn—Sham Density Functional Theory (i.e., including shell effects). Although the shape of the barrier obviously depends on the parametrization of the fission path, we have found that the barrier maximum corresponds to a configuration in which the emerging fragments are already formed and rather well apart. The two examples chosen serve to illustrate the influence of the electronic shell effects.     

Single-shot extreme ultraviolet laser imaging of nanostructures with wavelength resolution

We have demonstrated near-wavelength resolution microscopy in the extreme ultraviolet. Images of 50 nm diameter nanotubes were obtained with a single ~1 ns duration pulse from a desktop-size 46.9 nm laser. We measured the modulation transfer function of the microscope for three different numerical aperture zone plate objectives, demonstrating that 54 nm half-period structures can be resolved. The combination of near-wavelength spatial resolution and high temporal resolution opens myriad opportunities in imaging, such as the ability to directly investigate dynamics of nanoscale structures.     

Association Phenomena of Poly(arylene ether sulfone)s in Dimethylformamide

Three poly(arylene ether sulfone)s (two polymers and one copolymer) containing diphenylfluorene, phenolphthalein and 2,4-bis[(4-chlorophenyl)sulfonyl]-1-(phenyltio) benzene)] units were synthesized by the classical Williamson polyetherification reaction. The association phenomenon in N,N-dimethylformamide (DMF) was investigated by different methods: gel permeation chromatography (GPC), viscosity, atomic force microscopy (AFM), fluorescence spectroscopy and dynamic light scattering (DLS). Both AFM and DLS measurements evidenced the formation of aggregates with spherical or ellipsoidal shape at a concentration around 0.05 wt.%. This behavior could be explained by dipole-dipole interactions between macromolecular chains, probably with the participation of solvent molecules, and by H-bonds involving hydroxyl end groups.     

Observation of a centrality-dependent dijet asymmetry in lead-lead collisions at sqrt[S(NN)] =2.76 TeV with the ATLAS detector at the LHC

By using the ATLAS detector, observations have been made of a centrality-dependent dijet asymmetry in the collisions of lead ions at the Large Hadron Collider. In a sample of lead-lead events with a per-nucleon center of mass energy of 2.76 TeV, selected with a minimum bias trigger, jets are reconstructed in fine-grained, longitudinally segmented electromagnetic and hadronic calorimeters. The transverse energies of dijets in opposite hemispheres are observed to become systematically more unbalanced with increasing event centrality leading to a large number of events which contain highly asymmetric dijets. This is the first observation of an enhancement of events with such large dijet asymmetries, not observed in proton-proton collisions, which may point to an interpretation in terms of strong jet energy loss in a hot, dense medium.     

Neutral Community Theory: How Stochasticity and Dispersal-Limitation Can Explain Species Coexistence

Neutral community theory explains biodiversity, i.e. the coexistence of several species, as the result of a stochastic balance between immigration and extinction on a local level, and between speciation and extinction on a regional level. The most popular model, presented by Hubbell in 2001, has seen many analytical developments in recent years, which can be used in model analysis, model testing and model comparison. We review these developments here, and present alternative derivations and shine previously unnoticed lights on them.     

Complete maximal surfaces in static Robertson–Walker 3-spaces

We construct a large family of complete maximal surfaces in the static Robertson–Walker 3-spaces with negative base curvature. These examples provide a wide variety of non-standard foliations of such spaces by entire maximal graphs.     

A mathematical and computational review of Hartree–Fock SCF methods in quantum chemistry

We present a review of the fundamental topics of Hartree–Fock theory in quantum chemistry. From the molecular Hamiltonian, using and discussing the Born–Oppenheimer approximation, we arrive at the Hartree and Hartree–Fock equations for the electronic problem. Special emphasis is placed on the most relevant mathematical aspects of the theoretical derivation of the final equations, and on the results regarding the existence and uniqueness of their solutions. All Hartree–Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. The discretization of the one-electron orbital space is then reviewed and the Roothaan–Hall formalism introduced. This leads to an exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing on algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (especially those related to the design of linear-scaling methods) are commented on and linked to the issues discussed. The paper is intentionally introductory and rather self-contained, and may be useful for non-experts intending to use quantum chemical methods in interdisciplinary applications. Moreover, much material that can be found scattered in the literature has been put together to facilitate comprehension and to serve as a handy reference.     

Multiplexing and transmission of RF signals using an optical fiber

Ultrasonic non-destructive testing systems designed to control huge structures normally use several transducers in the reception stage. To avoid increasing the cost of electronics, a multiplexer is used to send all received signals to the same processing module. Traditionally, transmission of such signals is carried out using copper cables. For special applications (i.e. continuous monitoring of nuclear plants) metallic cables are not suitable because of their high sensitivity to electromagnetic perturbations. Moreover, the multiplexing is made electronically. When the distance between the transducers and the reception unit is large and/or electromagnetic noise is important, signal degradation takes place. The proposed system implements the transmission and multiplexing of ultrasonic electrical signals obtained by means of broadband transducers (up to 1 MHz), using an optical fiber. Optical fibers are made of dielectric materials (silica or plastic) so they are inherently passive to electromagnetic noise. Wavelength division multiplexing is utilized for adding channels to the system by means of fiber optic couplers and different light sources. The wavelengths of the optical signals utilized are located far apart in the optical spectrum in order to avoid serious crosstalk in transmission. The limit to the number of multiplexed channels depends on the optical fiber selected, the spectrum of the light sources and the wavelength division multiplexers or couplers utilized.     

Nanoparticle electrostatic loss within corona needle charger during particle-charging process

A numerical investigation has been carried out to examine the electrostatic loss of nanoparticles in a corona needle charger. Two-dimensional flow field, electric field, particle charge, and particle trajectory were simulated to obtain the electrostatic deposition loss at different conditions. Simulation of particle trajectories shows that the number of charges per particle during the charging process depends on the particle diameter, radial position from the symmetry axis, applied voltage, Reynolds number, and axial distance along the charger. The numerical results of nanoparticle electrostatic loss agreed fairly well with available experimental data. The results reveal that the electrostatic loss of nanoparticles increases with increasing applied voltage and electrical mobility of particles; and with decreasing particle diameter and Reynolds number. A regression equation closely fitted the obtained numerical results for different conditions. The equation is useful for directly calculating the electrostatic loss of nanoparticles in the corona needle charger during particle-charging process.