Detection of Mixing Dynamics During Pumping of a Flooded Coal Mine

In complex hydrogeological environments the effective management of groundwater quality problems by pump-and-treat operations can be most confidently achieved if the mixing dynamics induced within the aquifer by pumping are well understood. The utility of isotopic environmental tracers (C-, H-, O-, S-stable isotopic analyses and age indicators—14C, 3H) for this purpose is illustrated by the analysis of a pumping test in an abstraction borehole drilled into flooded, abandoned coal mineworkings at Deerplay (Lancashire, UK). Interpretation of the isotope data was undertaken conjunctively with that of major ion hydrochemistry, and interpreted in the context of the particular hydraulic setting of flooded mineworkings to identify the sources and mixing of water qualities in the groundwater system. Initial pumping showed breakdown of initial water quality stratification in the borehole, and gave evidence for distinctive isotopic signatures (d34S(SO4) ~= -1.6‰, d18O(SO4) ~= +15‰) associated with primary oxidation of pyrite in the zone of water table fluctuation—the first time this phenomenon has been successfully characterized by these isotopes in a flooded mine system. The overall aim of the test pumping—to replace an uncontrolled outflow from a mine entrance in an inconvenient location with a pumped discharge on a site where treatment could be provided—was swiftly achieved. Environmental tracing data illustrated the benefits of pumping as little as possible to attain this aim, as higher rates of pumping induced in-mixing of poorer quality waters from more distant old workings, and/or renewed pyrite oxidation in the shallow subsurface.

Polynomial Functions and the Riesz Interpolation Property

Building on a proof by D. Handelman of a generalisation of an example due to L. Fuchs, we show that the space of real-valued polynomials on a non-empty set X of reals has the Riesz Interpolation Property if and only if X is bounded.

Disjoint mixing operators

Chan and Shapiro showed that each (non-trivial) translation operator acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing.

Mixing operators on spaces with weak topology

We prove that a continuous linear operator T on a topological vector space X with weak topology is mixing if and only if the dual operator T' has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic operators on the space $\omega$ due to Herzog and Lemmert and implies the result of Bayart and Matheron, who proved that for any hypercyclic operator T on $\omega$, $T\oplus T$ is also hypercyclic.

Hypercyclic and mixing operator semigroups

We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group $\{T_t\}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also
describe a class of topological vector spaces admitting no supercyclic strongly continuous operator semigroups $\{T_t\}_{t\geq 0}$.

ARTICLE: Property and the Definition of Slavery

Currently there is no clear understanding of the meaning of ‘slavery’ in modern international law. While generally it is accepted that the
authoritative definition of slavery is provided by Article 1 of the Slavery Convention 1926, in recent times slavery has been understood in such a wide variety of ways that effectively it is a meaningless term. This paper reflects on this interpretation problem and aims to redress this balance by reclaiming the core meaning of the legal definition. It applies property law perspectives to explain the conception of ownership invoked by Article 1, to argue that it remains relevant and to explore how it might be applied in identifying modern cases of slavery.

The City as Laboratory and the Urban-Rural Divide: the Revival of Private Property and its Limits in Post-Mao China

This paper focuses on the revival of private property and its limits in urban China. It explores the emergence of urban property markets; urban property-holding in relation to the complexity of urban governance; “minor property rights apartments” that form a de facto real estate market and cross over the urban-rural divide; the “grey areas” of blurring legal and administrative boundaries in modern China; and recent changes to the rural land system and the rural-urban divide. The conclusion flags the theme of the city as laboratory with regard to the blurring legal and governmental urban-rural distinction.

Harmonic generation and wave mixing in nonlinear metamaterials and photonic crystals (Invited paper)

The basic concepts and phenomenology of wave mixing and harmonic generation are reviewed in context of the recent advances in the enhanced nonlinear activity in metamaterials and photonic crystals. The effects of dispersion, field confinement and phase synchronism are illustrated by the examples of the on-purpose designed artificial nonlinear structures. (c) 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22:469482, 2012.

Gaussian pulse mixing and scattering by finite nonlinear layered structures

Multiple Gaussian pulse interactions and scattering in the nonlinear layered dielectric structures have been examined. The Gaussian pulses with different centre frequencies and lengths are incident at oblique angles on the finite stack of nonlinear dielectric layers. The properties of the reflected and refracted waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed. It is shown that the efficiency of forward emission at the combinatorial frequency can be considerably increased when the wavelengths of interacting pulses are close to the edges of electromagnetic bandgap. © 2012 IEEE.