Cosmic γ-ray bursts: Observations and modeling

It is now commonly accepted that cosmic γ-ray bursts (GRBs) are of cosmological origin. This conclusion is based on the statistical analysis of GRBs and the measurements of line redshifts in GRB optical afterglows, i.e., in the so-called long GRBs. In this review, the models of radiation and models of GRB sources are considered. In most of these models, if not in all of them, the isotropic radiation cannot provide the energy release necessary for the appearance of a cosmological GRB. No correlation is noted between the redshift, the GRB-spectrum shape, and the total detected energy. The comparison between data obtained in the Soviet experiment KONUS and the American experiment BATSE shows that they substantially differ in statistical properties and the detection of hard x-ray lines. The investigation of hard gamma (0.1–10 GeV) afterglows, the measurement of prompt optical spectra during the GRB detection, and the further investigation of hard x-ray lines is of obvious importance for gaining insight into the GRB origin. Observations of two bright optical GRB afterglows point to the fact that an initially bright optical flare is directly related to the GRB itself, and the subsequent weak and much more continuous optical radiation is of a different nature. The results of observations of optical GRB afterglows are discussed. They point to the fact that the GRBs originate in distant galaxies with a high matter density, where intense star formation takes place. The interaction of the cosmological GRB radiation with a dense surrounding molecular cloud results in the appearance of long-duration (up to 10 years) weak optical afterglows associated with the heating and reradiation of gas. Results of 2D numerical simulation of the heating and reradiation of gas in various variants of the relative disposition of GRB and molecular clouds are presented. In conclusion, the possible relation between the so-called short GRBs and recurrent sources of soft γ rays in our Galaxy, the so-called “soft gamma repeaters,” is discussed.     

Influence of the counterion size on swelling and collapse of polyelectrolyte gel

A theory that predicts the effect of the counterion size on the swelling and collapse of a weakly charged polyelectrolyte gel was developed. In addition to excluded-volume interactions between monomer units of the gel, the theory involves the counterion-monomer unit and counterion-counterion interactions in terms of the virial approximation. The character of interactions between different units in the system varies from repulsion to attraction depending on the type of solvent, counterion, and dielectric permittivity of the solvent. For solvents with a low permittivity, the effect of condensation of counterions resulting in the formation of ion pairs is taken into account.     

Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Strain-induced modification of magnetic structure and new magnetic phases in rare-earth epitaxial films

Rare earths exhibit complex magnetic phase diagrams resulting from the competition between various contributions to the magnetic energy: exchange, anisotropy and magnetostriction. The epitaxy of a rare-earth film on a substrate induces (i) a clamping to the substrate and (ii) pseudomorphic strains. Both these effects are shown to lead to modifications of the magnetic properties in (0 0 1)Dy, (0 0 1)Tb and (1 1 0)Eu films. In Dy and Tb films, spectacular variations of the Curie temperature have been evidenced. Additionally, Tb films exhibit a new large wavelength magnetic modulation. In Eu films, one of the helical magnetic domains disappears at low temperature whereas the propagation vectors of the other helices are tilted. The link between structural and magnetic properties is underlined via magnetoelastic models. Moreover, molecular beam epitaxy permits the growth of Sm in a metastable dhcp phase. The magnetic structure of dhcp Sm has been elucidated for the first time. In this review, neutron scattering is shown to be a powerful technique to reveal the magnetic structures of rare-earth films.     

Electro-optic pulse response of ferroelectric liquid crystals

The electro-optic response of ferroelectric smectic C* liquid crystals has been studied. Anomalous switching behaviour of such materials which possess a negative dielectric anisotropy has been reported. These materials show a minimum in response time at a sufficiently high field. We present results showing the dependency of this minimum upon spontaneous polarisation and the effect of AC bias. Calculations based upon the equation of motion of the director around the cone are presented which describe this effect and its dependence on the relative magnitudes of the spontaneous polarization and dielectric anisotropy of the material. Good agreement with the experimental results is found.     

Recent changes in A-level Mathematics: is the availability and uptake of mechanics declining yet more?

In the past 6 years changes have occurred in GCE A-levels. Inparticular, there have been several major changes in A-levelMathematics courses. As engineering students are usually requiredto have studied A-level Mathematics, or its equivalent, thesechanges have had an effect on their prior mathematical knowledge.Moreover, engineering students traditionally obtained a goodgrounding in mechanics as part of their A-level Mathematicsqualification. However, mechanics, which was once included inthe core syllabus, is now optional. This article investigatesthe current availability and uptake of mechanics modules withinA-level Mathematics courses in schools. Comparisons are drawnbetween these results and results of a survey of schools in2004 and surveys of first year engineering students conductedin 2004 and 2005. It is found that there is a decline in theavailability of mechanics modules and the uptake of more thanone mechanics module has also decreased. The implications ofthese findings for engineering educators are discussed.     

Studies on calcium‐containing poly(urethane ether)s

The calcium salt of mono(hydroxyethoxyethyl)phthalate [Ca(HEEP)₂] was synthesized by the reaction of diethylene glycol, phthalic anhydride, and calcium acetate. Calcium‐containing poly(urethane ether)s (PUEs) were synthesized by the reaction of hexamethylene diisocyanate (HMDI) or tolylene 2,4‐diisocyanate (TDI) with a mixture of Ca(HEEP)₂ and poly(ethylene glycol) (PEG₃₀₀ or PEG₄₀₀) with di‐n‐butyltin dilaurate as a catalyst. A series of calcium‐containing PUEs of different compositions were synthesized with Ca(HEEP)₂/PEG₃₀₀ (or PEG₄₀₀)/diisocyanate (HMDI or TDI) molar ratios of 2:2:4, 3:1:4, and 1:3:4 so that the coating properties of the PUEs could be studied. Blank PUEs without calcium‐containing ionic diols were also prepared by the reaction of PEG₃₀₀ or PEG₄₀₀ with HMDI or TDI. The PUEs were well characterized by Fourier transform infrared, ¹H and ¹³C NMR, solid‐state cross‐polarity/magic‐angle‐spinning ¹³C NMR, viscosity, solubility, and X‐ray diffraction studies. The thermal properties of the polymers were also studied with thermogravimetric analysis and differential scanning calorimetry. The PUEs were applied as top coats on acrylic‐coated leather, and their physicomechanical properties were also studied. The coating properties of PUEs, such as the tensile strength, elongation at break, tear strength, water vapor permeability, flexing endurance, cold crack resistance, abrasion resistance, color fastness, and adhesive strength, were better than the standard values. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2865–2878, 2003     

Chaos-controlling technique for suppressing self-modulation in backward-wave tubes

A method for suppressing self-modulation in backward-wave tubes is proposed. Additional delay is introduced into the feedback circuit, owing to which the output signal amplitude affects the electron beam current that enters into the interaction space. Numerical simulations demonstrate that the operating current in the single-frequency oscillation mode may be increased roughly twofold.     

1,1,3-Trimethyl-3-phenylindan as a Luminescent Additive to a Plastic Scintillator Based on Poly(methyl Methacrylate)

The luminescence and scintillation properties of poly(methyl methacrylate) containing 1,1,3-trimethyl-3-phenylindan were studied.