Theory of the thermal magnetocapacitance of multicomponent silicate glasses at low temperature

An explanation is put forward for the early findings of Zeller and Pohl (, Phys. Rev. B, 4, 2029) and, in particular, Stephens (, Phys. Rev. B, 13, 852), and then for the more comprehensive recent findings of Meißner and Strehlow () for the anomalous magnetic-field-dependent behaviour of the heat capacity of some multicomponent glasses at low temperature (0.1?<?T?<?4?K) and in weak-to-moderate fields (0?<?B?<?8T). An essential new ingredient of this theory, together with the standard two-level system approach for cold glasses, is a multi-minima local potential for the quantum motion of metallic ions between near-degenerate wells, separated by relatively shallow barriers. Taking the tunneling entities as independent and assuming a novel probability distribution for the parameters of the multi-welled potential, an expression for the heat capacity C(T,B) is obtained with features that match rather well the reported unusual experimental data for the glasses. The indication coming from this theory for the data available is that the entities involved in tunnelling are nanoclusters of coherent ions.     

Analysis of interdiffusion via vacancy-pairs in strongly ionic solids

In this paper, we analyse chemical interdiffusion via Schottky vacancy-pairs in strongly ionic crystals for diffusion couples (AY–BY), where A and B take the same valence. We derive a sum-rule relating the phenomenological coefficients that is based on an earlier sum-rule derived by Moleko and Allnatt (Phil. Mag. A, 58 () 677) for diffusion in the multicomponent random alloy via the agency of isolated vacancies. With this sum-rule and other relationships derived by us, we show that the ratio of the intrinsic diffusivities can be expressed in exactly the same simple form as the case for diffusion via isolated vacancies. The functional form for the interdiffusion coefficient when expressed in terms of atom-vacancy exchange frequencies for diffusion is found to be essentially the same as that for isolated vacancies. The difference centres only on the relative differences of the local jump coordination of the vacancies in each case.     

Computer simulation of the phenomenological transport coefficient in the lattice gas and Fick's First Law

A direct steady state computer simulation method for calculating the Onsager phenomenological transport coefficient from the gradient of the chemical potential in the one component lattice gas is presented. It is shown that the results are in good agreement with the Einsteinian method. A recent alternative formulation for Fick's First Law that had been proposed to replace the standard Fick's First Law formulation is also analysed using the same model. It is shown that the alternative formulation gives poor agreement with the simulation data whereas the standard Fick's First Law gives excellent agreement. Accordingly, the alternative formulation does not appear to have merit as a new definition of the diffusion coefficient. It is shown that the alternative formulation is a rough approximation for the dependence of the interstitial solute diffusion coefficient on solute concentration in an interstitial solid solution if information about the activity coefficient and solute diffusion coefficient at very dilute concentrations is available. However, in this role, this is not an entirely new idea.     

Nanoscale global mixed ordering of B-site cations in Pb2M′M′′O6 complex perovskite relaxors

We have observed compositionally heterogeneous, uniformly distributed and closely interconnected nanoscale and sub-nanoscale domains in complex perovskite-structured relaxors. These domains are interpreted as originating from global mixed ordering, formed by numerous non-stoichiometric combinations of B-site cations across the entire bulk of the relaxor crystals and ceramics. The association between global mixed ordering and the origin of the forbidden reflections has been explained theoretically and experimentally. Various models of global mixed order–disorder are proposed, simulated and subsequently compared with dark-field and high-resolution TEM images, showing unambiguous agreement between the models and the observed TEM images and the diffraction patterns. Careful and extensive case studies of Pb₂(ScTa)O₆ crystals and (0.4)Pb₂(InNb)O₆:(0.6)Pb(Mg_1/3Nb_2/3)O₃ ceramics show that mixed order–disorder originates from a global B-site chemical heterogeneity. The findings are analyzed using a normal statistical distribution approach, which is supported by the length-scale of the experimentally observed domains.     

Controlling continuum harmonic generation with attosecond pulses

Photo-ionization and high-order harmonic generation (HOHG) in molecular systems under the combined action of infrared femtosecond (fs) and UV attosecond (as) intense laser pulses are investigated numerically for a one-dimensional non-Born–Oppenheimer H⁺ ₂ ion. It is shown that such a coherent control scheme of fs–as ionization leads to significant enhancement of HOHG, with efficiencies exceeding the one obtained from a single fs pulse by several orders of magnitude. The basic mechanism for this enhancement is established as enhanced ionization and control of the recollision of a high-energy non-zero-velocity ionized electron, as compared to tunneling ionization models where the ionized electron has initial zero velocity. The combined superposition of fs–as pulses results in broad HOHG spectra with a large continuum near the cutoff, thus providing a new source for synthesizing new X-ray (vacuum ultraviolet) as pulses. PACS 33.60.-q; 33.80.-b     

Remarks on the Transfer Factors for Unipotent Orbital Integrals in p-adic Classical Split Groups

This article studies unipotent orbital integrals on symplectic and orthogonal groups from the point of view of endoscopy. It begins by partitioning stable unipotent classes into packets and goes on to propose a transfer of these packets. It then discusses (in rough form) the associated transfer factors. Some supporting calculations in split odd orthogonal groups are given.     

Monitoring of Zn(II) and Cd(II) adsorption on activated carbon from aqueous multicomponent solutions by differential pulse polarography (DPP)

The adsorption process of Zn(II) and Cd(II) from aqueous solution has been investigated from both kinetic and equilibrium standpoints, using differential pulse polarography (DPP) on a mercury dropping electrode as the analytical technique. With such an aim, adsorption experiments were performed using not only a single metal ion–Zn(II) or Cd(II) solution but also a multi-component ion metal–Zn(II), Cd(II) and Hg(II) solution. The influence of the pH change in the multi-component ion metal solution on the adsorption of Zn(II) and Cd(II) was also studied. The adsorption processes is relatively fast for Zn(II) and Cd(II). The presence of two foreign ions in the solution slightly speeds up the adsorption process for Zn(II) and significantly slows it down for Cd(II). The adsorption isotherms are similarly shaped for Zn(II) and Cd(II). The addition of the foreign ions has a more unfavourable effect on the adsorption for Cd(II) than for Zn(II). At pH 2, neither Zn(II) nor Cd(II) is adsorbed practically on the carbon. The voltammetric approach has proved to be a fast and efficient method that, at the same time, enables one to monitor the adsorption of Zn(II) and Cd(II) with potential on-line application, which could be useful in waste-water treatment.     

Some mathematical aspects of wave motion

A survey is made of some mathematical techniques and theorems which can have relevance at a moderately advanced level to certain classes of wave propagation problems.     

Case Studies in cancer and its treatment by radiotherapy

Mathematical modelling has played a major role in certain aspects of the wide area of study of cancer and its treatment. Relevant background material is followed by mathematical modelling case studies in tumour growth and the response of tumour cells to irradiation. These components are synthesized in Case Study 4 where the problem of the derivation of optimal radiotherapy treatment schedules is discussed. The case studies are presented in a form suitable for classroom development.     

Identifying a spherically symmetric conductivity in a nonlinear parabolic equation

In this article we determine, i.e. we prove existence and uniqueness of a radially symmetric operator conductivity in a nonlinear heat equation of the form (1.1) related to a spherical corona Ω ? R ³ under a suitable additional information.