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Strong encryption can prevent anybody from accessing user data, including the technology companies responsible for its implementation. As strong encryption technology has become increasingly prevalent, law enforcement agencies have sought legislation to secure continued lawful access to the data affected. Following analysis of the encryption debates in the United States and the United Kingdom, this article will propose three rules that governments should follow to facilitate open debate and prevent the implementation of unsafe lawful access solutions. Firstly, we will provide context on current encryption policy. Secondly, it will be shown that continuous open debate must be facilitated in order to prevent the implementation of unsafe lawful access solutions. Finally, it will be argued that governments should be held to three rules when engaging in debate about lawful access: legislation governing lawful access must state clearly on its face whether decryption can be mandated; the encryption debate must not be oversimplified or reduced to emotive examples in order to secure public support for unsafe solutions; and safeguards on warrants must not be conflated with safeguards on lawful access mechanisms in order to suggest that solutions are safer than is actually the case.

Turbulent fluctuations of the scalar dissipation rate have a major impact on extinction in non-premixed combustion. Recently, an unsteady extinction criterion has been developed (Hewson, 2013) that predicts extinction dependent on the duration and the magnitude of dissipation rate fluctuations exceeding a critical quenching value; this quantity is referred to as the dissipation impulse. The magnitude of the dissipation impulse corresponding to unsteady extinction is related to the difficulty with which a flamelet is exintguished, based on the steady-state S-curve. In this paper we evaluate this new extinction criterion for more realistic dissipation rates by evolving a stochas- tic Ornstein–Uhlenbeck process for the dissipation rate. A comparison between unsteady flamelet evolution using this dissipation rate and the extinction criterion exhibit good agreement. The rate of predicted ex- tinction is examined over a range of Damkohler and Reynolds numbers and over a range of the extinction difficulty. The results suggest that the rate of extinction is proportional to the average dissipation rate and the area under the dissipation rate probability density function exceeding the steady-state quenching value. It is also inversely related to the actual probability that this steady-state quenching dissipation rate is observed and the difficulty of extinction associated with the distance between the upper and middle branches of the S-curve.

The suitability of crude and purified struvite (MgNH4PO4), a major precipitate in wastewater streams, was investigated for renewable replacement of conventional nitrogen and phosphate resources for cultivation of microalgae. Bovine effluent wastewater stone, the source of crude struvite, was characterized for soluble N/P, trace metals, and biochemical components and compared to the purified mineral. Cultivation trials using struvite as a major nutrient source were conducted using two microalgae production strains, Nannochloropsis salina and Phaeodactylum tricornutum, in both lab and outdoor pilot-scale raceways in a variety of seasonal conditions. Both crude and purified struvite-based media were found to result in biomass productivities at least as high as established media formulations (maximum outdoor co-culture yield ∼20±4gAFDW/m(2)/day). Analysis of nutrient uptake by the alga suggest that struvite provides increased nutrient utilization efficiency, and that crude struvite satisfies the trace metals requirement and results in increased pigment productivity for both microalgae strains.

In this study, Chlorella zofingiensis harvesting by dissolved air flotation (DAF) was critically evaluated with regard to algal concentration, culture conditions, type and dosage of coagulants, and recycle ratio. Harvesting efficiency increased with coagulant dosage and leveled off at 81%, 86%, 91%, and 87% when chitosan, Al3+, Fe3+, and cetyl trimethylammonium bromide (CTAB) were used at dosages of 70, 180, 250, and 500 mg g(-1), respectively. The DAF efficiency-coagulant dosage relationship changed with algal culture conditions. Evaluation of the influence of the initial algal concentration and recycle ratio revealed that, under conditions typical for algal harvesting, it is possible that the number of bubbles is insufficient. A DAF algal harvesting model was developed to explain this observation by introducing mass-based floc size distributions and a bubble limitation into the white water blanket model. The model revealed the importance of coagulation to increase floc-bubble collision and attachment, and the preferential interaction of bubbles with larger flocs, which limited the availability of bubbles to the smaller sized flocs. The harvesting efficiencies predicted by the model agree reasonably with experimental data obtained at different Al3+ dosages, algal concentrations, and recycle ratios. Based on this modeling, critical parameters for efficient algal harvesting were identified. (C) 2014 Wiley Periodicals, Inc.

Autoflocculation is triggered by the coordination of cationic surface sites on mineral precipitates, or Ca + 2 and Mg + 2 , to anionic algal carboxylate groups. The solution composition controls on autoflocculation can be quantitatively described using surface complexation models of algal, Mg(OH) 2 , hydroxylapatite, and calcite interfaces. Cation bridging of adjacent algae triggers autoflocculation at lower pH than does Mg(OH) 2 formation. Autoflocculation in response to lime addition reaches a maximum at pH ~ 11 because of Mg(OH) 2 formation, but then plateaus with further lime addition because of the decrease in Mg(OH) 2 surface charge with increasing pH. Hydroxylapatite surfaces are positively charged, hence able to autoflocculate algae, under most conditions. Calcite surfaces are positively charged, and autoflocculation potential is high, when dissolved Ca + 2 and Mg + 2 levels are high; calcite has low autoflocculation potential when Ca + 2 and Mg + 2 levels are low and sulfate levels are high, and the calcite surface is negatively charged.

The existence of a critical dissipation rate, above which a steady nonpremixed flame is extinguished, is well known. Recent advances in modeling have allowed the simulation of turbulent nonpremixed flames that include local extinction as a consequence of the stochastic variation in dissipation rates. In this paper we present an extinction criterion for flames subject to unsteady dissipation rates. This criterion is expressed in terms of the critical dissipation-impulse magnitude, which depends on the time-integrated excess dissipation rate and stoichiometric factors. Limiting behaviors for large and small fluctuations of the dissipation rate above the critical value are identified. For large dissipation-rate fluctuations, the critical dissipation-impulse magnitude is independent of the details of the temporal dissipation-rate evolution. This critical dissipation-impulse magnitude is found to depend only on the steady-state characteristics of the particular fuel-oxidizer mixture present, namely the shape of the steady-state S-curve. In this way, a useful extinction criterion is developed that defines conditions for which unsteady mixing dynamics lead to extinction based on information available from steady-state flames. This criterion is found applicable for a diverse set of flames including n-heptane, diluted n-heptane, methane, partially premixed methane and CO/H 2 /N 2 mixtures when dissipation-rate fluctuations are large. As the magnitude of the dissipation rate fluctuations approaches zero, the critical impulse approaches zero, which corresponds to the well-known steady extinction limit. Thus, this work extends the prediction of extinction from the steady limit to the unsteady.

The effects of changes in cellular characteristics and dissolved organic matter (DOM) on dissolved air flotation (DAF) harvesting of Chlorella zofingiensis at the different growth phases were studied. Harvesting efficiency increased with Al(3+) dosage and reached more than 90%, regardless of growth phases. In the absence of DOM, the ratio of Al(3+) dosage to surface functional group concentration determined the harvesting efficiency. DOM in the culture medium competed with algal cell surface functional groups for Al(3+), and more Al(3+) was required for cultures with DOM than for DOM-free cultures to achieve the same harvesting efficiency. As the culture aged, the increase of Al(3+) dosage due to increased DOM was less than the decrease of Al(3+) dosage associated with reduced cell surface functional groups, resulting in overall reduced demand for Al(3+). The interdependency of Al(3+) dosage and harvesting efficiency on concentrations of cell surface functional groups and DOM was successfully modeled.

Within the UK, local and regional government drives to reduce the quantity of waste being sent to landfill have led to an increase in small-scale composting schemes, instigated by local councils and not-for-profit organisations. The composting process relies upon the proliferation of microorganisms, leading to their emission into the ambient environment. In this investigative study, total bacteria and Aspergillus fumigatus emitted from a small-scale composting facility in central London were measured in different spatial and temporal dimensions. Bioaerosols did not disperse in concentrations significantly higher than those measured at 'background' locations, where maximum geometric mean was 55 x 10(2) Colony Forming Units (CFU) per m(-3). Concentrations on-site and at the nearest potential receptor were comparable to those found at commercial facilities, reaching 25 x 10(4) and 29 x 10(3) CFU m(-3) for total bacteria and A. fumigatus respectively. The room housing the facility was contaminated by moulds; likely to result from high relative humidity of the air (consistently above 80% during this study), building material, and the generation of organic dust. The complex diurnal meteorological variations of urban environments are likely to influence bioaerosol dispersal, and consequent exposure risk for sensitive receptors. Site planning tools including Geographical Information Systems (GIS) mapping with buffer zones around schools and hospitals, and use of computerised models for the design of rooms housing urban composting facilities are proposed as methods for reducing the risk of occupational and off-site receptor exposure. (C) 2010 Elsevier Ltd. All rights reserved.

We present broadband, dual-pump coherent anti-Stokes Raman scattering (CARS) measurements of N2 and O2 in 2 m diameter methanol pool fires. The design of the fiber-optically coupled CARS instrument for fire measurements is described. Single-shot temperatures and O2/N2 ratios were obtained simultaneously from a single measurement point at the center of the fire plume, and the measured temperature–oxygen statistics are compared to results of a time-domain-filtered Reynolds-averaged Navier-Stokes simulation. The measured and simulated mean fire temperatures agree to within 2–4%, with larger turbulent fluctuations observed in the measured temperatures. The behavior of the mean temperature conditioned on the O2/N2 ratio is similar for both simulation and experiment, but with simulated temperatures that are up to 10% lower than measured values for O2/N2 below 0.18. The uncertainty in the CARS measurements is described. A single-shot detection limit of O2/N2 = 0.06 was determined from the observed signal to nois...

The interaction between soot and enthalpy evolution in a buoyant turbulent flame, exhibiting key attributes of a fire, is studied using a novel approach. This approach is based on a spatially evolving form of the one-dimensional turbulence (ODT) model that resolves the full range of scales, in a single spatial dimension, from the scale of the plume evolution to that of the soot layers. The model is compared with limited experimental data available. The evolved flow field of a meter-scale flame is then analyzed both in terms of conventional spatial averages and conditional averages. The conditional moments of the terms in the soot and enthalpy evolution equations are analyzed to elucidate the balance between the large-scale evolution (advective terms), the source terms, and the turbulent mixing (dissipative terms). The results show the significant influence of the mixture evolution on the transport of soot relative to the flame (in mixture-fraction space).

Modeling soot formation in turbulent nonpremixed combustion is a difficult problem. Unlike most gaseous combustion species, soot lacks a strong state relationship with the mixture fraction due to unsteady formation rates which overlap transport timescales, and strong differential diffusion between gaseous species and soot. The conditional moment closure model (CMC) has recently been applied to the problem of turbulent soot formation. A challenge in CMC modeling is the treatment of differential diffusion. Three-dimensional direct numerical simulation (DNS) of a nonpremixed ethylene jet flame with soot formation has been performed using a 19 species reduced ethylene mechanism and a four-step, three-moment, semi-empirical soot model. The DNS provides full resolution of the turbulent flow field and is used to perform a-priori analysis of a recent CMC model derived from the joint scalar PDF transport equation. Unlike other approaches, this CMC model does not require additional transport equations to treat differentially diffusing species. A budget of the terms of the CMC equation for both gaseous species and soot is presented. In particular, exact expressions for unclosed terms are compared to typical closure models for scalar dissipation, cross-dissipation, differential diffusion, and reactive source terms. The differential diffusion model for gaseous species is found to be quite accurate, while that for soot requires an additional model for the residual term.

The characteristics of auto-ignition in HCCI engines in the presence of charge stratification is studied theoretically using activation energy asymptotics. The analysis accounts for the effects of pressure rise due to piston motion and heat release, and the consequent compression-heating of the charge. The chemical kinetics are approximated using a single reaction step with a large activation energy and the compression-heating effects are accounted for through an entropy variable. The resultant model is simple and suitable for extensive parametric studies of HCCI engine combustion. Some preliminary results on the effects of mixture and composition stratification on the duration of burning are presented using a presumed Gaussian PDF for the initial temperature distribution. The effects of mixture stratification on the feasible operating conditions is demonstrated using simple criteria to delineate the knocking and incomplete end-gas combustion regimes.

Parametric studies were conducted for a coalescing and evaporating turbulent water spray using a stochastic separated flow technique that includes submodels for droplet dynamics, heat and mass transfer, and droplet–droplet binary collisions. While the initial droplet size distribution, in general, is not known due to the difficulty in the optical access to the nozzle exit region, the size distribution is modeled using the analytical PDFs (probability density functions) such as log-normal, Rosin–Rammler, Gaussian, and Nukiyama–Tanasawa distribution model. Standard deviation of the PDFs is varied and their effects on droplet size and speed distribution in the downstream are reported. The arithmetic mean droplet size at the nozzle exit, which is used as input for simulations, was extrapolated using the existing experimental data obtained at downstream locations.

We analyze the properties of the quasiparticle excitations of metallic antiferromagnetic states in a strongly correlated electron system. The study is based on dynamical mean field theory (DMFT) for the infinite dimensional Hubbard model with antiferromagnetic symmetry breaking. Self-consistent solutions of the DMFT equations are calculated using the numerical renormalization group (NRG). The low energy behavior in these results is then analyzed in terms of renormalized quasiparticles. The parameters for these quasiparticles are calculated directly from the NRG derived self-energy, and also from the low energy fixed point of the effective impurity. They are found to be in good agreement. We show that the main low energy features of the $\bf k$-resolved spectral density can be understood in terms of the quasiparticle picture. We also find that Luttinger's theorem is satisfied for the total electron number in the doped antiferromagnetic state., 15 pages, 17 figures; some minor changes and additional figure

The effect of unsteady strain on n-heptane autoignition at elevated pressure is studied numerically with detailed chemistry and transport in the counterflow configuration. Specifically, fuel and air temperatures are chosen so that two-stage ignition occurs, as is typical, in the negative temperature-coefficient regime, and the strain perturbations are selected to rapidly rise and fall to mimic rapid turbulent strain-rate fluctuations. For these rapid fluctuations, the response of the mixing layer is unsteady. Small to moderate strain-rate fluctuations result in a small increase in the ignition delay. For sufficiently large strain rates such that the critical scalar dissipation rate is exceeded, the ignition delay is substantially greater. The latter delay results from both the time required for the dissipation rate to decay to below its critical value and the longer ignition delay time for systems with dissipation rates near the critical dissipation rate. For all magnitudes of strain-rate fluctuation, there is evidence that the second stage of the two-stage ignition is more sensitive to inhibition by higher dissipation rates. For sufficiently large dissipation rates, the heat losses force the second stage to the border between the low- and intermediate-temperature chemistries.

This study compares experimental measurements and numerical simulations of liquid droplets over heated (to a near surface temperature of 423 K) and unheated cylinders. The numerical model is based on an unsteady Reynolds-averaged Navier–Stokes (RANS) formulation using a stochastic separated flow (SSF) approach for the droplets that includes submodels for droplet dispersion, heat and mass transfer, and impact on a solid surface. The details of the droplet impact model are presented and the model is used to simulate water spray impingement on a cylinder. Computational results are compared with experimental measurements using phase Doppler interferometry (PDI). Overall, good agreement is observed between predictions and experimental measurements of droplet mean size and velocity downstream of the cylinder.

The Collaboratory for Multi-scale Chemical Science (CMCS) is developing a powerful informatics-based approach to synthesizing multi-scale information in support of systems-based research and is applying it within combustion science. An open source multi-scale informatics toolkit is being developed that addresses a number of issues core to the emerging concept of knowledge grids including provenance tracking and lightweight federation of data and application resources into cross-scale information flows. The CMCS portal is currently in use by a number of high-profile pilot groups and is playing a significant role in enabling their efforts to improve and extend community maintained chemical reference information.

Experimental measurements and numerical simulations of a high-speed water spray are presented. The numerical model is based on a stochastic separated flow technique that includes submodels for droplet dynamics, heat and mass transfer, and droplet–droplet collisions. Because the spray characteristics near the nozzle are difficult to ascertain, a new method for initialization of particle diameter size is developed that assumes a Rosin–Rammler distribution for droplet size, which correctly reproduces experimentally measured Sauter and arithmetic mean diameters. By relating the particle initialization to lower moments of the droplet statistics, it is possible to take advantage of measurements without substantial penalties associated with the greater experimental uncertainty of individual droplet measurements. Overall, very good agreement is observed in the comparisons of experimental measurements to computational predictions for the streamwise development of mean drop size and velocity. In addition, the importance of modeling droplet–droplet collisions is highlighted with comparison of selected droplet–droplet collision models.

We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective level $\tilde\epsilon_d$, an effective hybridization $\tilde V$, and a quasiparticle interaction $\tilde U$. The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a Falikov-Kimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a Falikov-Kimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level., Comment: 14 pages, 12 figures; Revised Sec. 2 and 4

In practical combustors, high-intensity mixing is often desirable in order to minimize combustor volume and also minimize the production of certain pollutants. However, high-intensity mixing may al...

The one-dimensional turbulence (ODT) model is applied to the study of turbulent jet CO/H2/N2 flames. The ODT model retains the full range of length scales and no assumption of scale separation is required. In the present case, the ODT model describes the evolution of the entire flowfield; the ability of ODT to model the flowfield evolution is discussed. Predictions of the conditional means and fluctuations of temperature and the species mass fractions are compared with measurements and the level of closure required to address certain phenomena is discussed. The ODT model is shown to be useful for studying extinction/re-ignition phenomena and differential diffusion. The streamwise evolution in multidimensional flows is affected by dilatation in a manner not captured by the ODT model, and this results in discrepancies between the ODT mixing rates and the mixing rates evident in the measurements.

We have studied the critical behaviour of a doped Mott insulator near the metal-insulator transition for the infinite-dimensional Hubbard model using a linearized form of dynamical mean-field theory. The discontinuity in the chemical potential in the change from hole to electron doping, for $U$ larger than a critical value $U_c$, has been calculated analytically and is found to be in good agreement with the results of numerical methods. We have also derived analytic expressions for the compressibility, the quasiparticle weight, the double occupancy and the local spin susceptibility near half-filling as functions of the on-site Coulomb interaction and the doping., Comment: 13 pages, 3 figures

We explore the quantum phase transitions between two ordered states in the infinite dimensional Hubbard-Holstein model at half filling. Our study is based on the dynamical mean field theory (DMFT) combined with the numerical renormalization group (NRG), which allows us to handle both strong electron-electron and strong electron-phonon interactions. The transition line is characterized by an effective electron-electron interaction. Depending on this effective interaction and the phonon frequency ω 0 one finds either a continuous transition or discontinuous transition. Here, the analysis focuses on the behavior of the system when the electron-electron repulsion U and the phonon-mediated attraction λ are equal. We first discuss the adiabatic and antiadiabatic limiting cases. For finite ω 0 we study the differences between the antiferromagnetic (AFM) and charge order, and find that when present the AFM state has a lower energy on the line.

We present renormalised perturbation theory calculations for the description of the dynamics of quasiparticles in the Anderson impurity model in magnetic field. Our calculations are compared with NRG spectra and good agreement is found for magnetic fields of the order of the Kondo temperature, when an appropriate perturbation series is chosen. We point out how this approach can be generalised to the non-equilibrium situation, where it is relevant for the description of quantum dots.

The author gives explicit quasi-particle Hamiltonians, including interactions, for several magnetic impurity models and shows that the application of mean field theory to these gives asymptotically exact results as T to 0 and H to 0 corresponding to Fermi liquid theory. This approach provides a conceptual link between the intuitive phenomenological theory of Landau and Nozieres, and the microscopic theory of Luttinger and Yamada.

The transport coefficients of the Anderson model require knowledge of both the temperature and frequency dependence of the single--particle spectral densities and consequently have proven difficult quantities to calculate. Here we show how these quantities can be calculated via an extension of Wilson's numerical renormalization group method. Accurate results are obtained in all parameter regimes and for the full range of temperatures of interest ranging from the high temperature perturbative regime $T>>T_{K}$, through the cross--over region $T\approx T_{K}$, and into the low temperature strong coupling regime $T<, Comment: 11 pages, 5 figures. Old paper, submitted here for archival purposes only. Short version of http://de.arxiv.org/abs/cond-mat/9310032

We present a detailed study of the spectral properties of a locally correlated site embedded in a Bardeen–Cooper–Schrieffer (BCS) superconducting medium. To this end the Anderson impurity model with a superconducting bath is analysed by means of numerical renormalization group calculations. We calculate one-and two-particle dynamic response functions to elucidate the spectral excitations and the nature of the ground state for different parameter regimes with and without particle–hole symmetry. The position and weight of the Andreev bound states is given for all relevant parameters. We present phase diagrams for the different ground state parameter regimes. This work is also relevant for dynamical mean field theory extensions with superconducting symmetry breaking.

The ionic model proposed by Jefferson and Stevens (see ibid., vol.9, p.2151 (1976)) for the magnetic properties of rare earth compounds that display intermediate valence-behaviour is studied. The f-electrons of the rare earth ions are described by localised atomic-like configurations which are hybridised with a conduction band. The free energy and susceptibility are calculated perturbationally in powers of the hybridisation matrix element mod V mod to order mod V mod 4. When only virtual valence transitions are possible the leading correction to the Curie law susceptibility is due to the Kondo moment flip scattering. An effective interaction between the f- and conduction electrons is derived in this regime which is a generalisation of that given by Coqblin and Schrieffer (1969). The one-electron Green function is also calculated perturbationally and the results indicate that the spectral density has a virtual bound state resonance due to the incoherent scattering of the f-moments similar to that caused by impurity scattering.

It is shown that the spin-dependent shift of the subbands considered by Roth for the treatment of ferromagnetic solutions of the Hubbard model plays a decisive role in making antiferromagnetism possible on this model. A relation is given which allows to calculate the Neel temperature TN for a simple cubic lattice and a half-filled band in dependence on the parameters of the Hubbard model and which includes in the limit a criterion formerly obtained by the simple Hubbard decoupling. Es wird gezeigt, das die von Roth bei der Behandlung ferromagnetischer Losungen des Hubbardmodells berucksichtigte spinabhangige Energieverschiebung der Unterbander nuch fur antiferroniagnetische Losungen eine entscheidende Rolle spielt. Es wird eine Beziehung angegeben, die die Neeltemperatur TN fur ein einfach kubisches Gitter bei halbgefulltem Band in Abhangigkeit von den Paranietern des Hubbardmodells zu berechnen gestattet und die ein friiher niit der einfachen Hubbardentkopplung abgeleitetes Briterium als Grenzfall enthalt.

The antiferromagnetic phase of a narrow energy band material with one electron per atom is studied using the Hubbard model in the 'alloy analogy'. An electron of a particular spin sees the potential due to a 'frozen' configuration of the electrons of opposite spin, these being distributed on two sublattices with probabilities 1/2(1+or-m), where m is the antiferromagnetic order parameter. This problem of a partially ordered alloy is treated within the coherent potential approximation. The order parameter m is determined self-consistently and the detailed calculations are given for an alternant lattice with a semicircular density of states. It is found that, contrary to Hartree-Fock calculations, antiferromagnetism appears only when the intra-atomic Coulomb interaction U exceeds a critical value. The metal-insulator transition occurs at a lower value of U so that antiferromagnetism does not appear in the metallic state. The general features of the electronic density of states in the antiferromagnetic phase are discussed.

The spin-orbit degenerate Anderson model is investigated in the limit of large spin-orbit degeneracy (N). Low-temperature properties are discussed, yielding the full range of intermediate to local moment behaviour. The relation between ground state susceptibility and valence is examined to leading and next-leading orders in 1/N.

The author derives a general solution of the linear dispersion s-d exchange model which is not based on the Bethe ansatz. The spectrum of energy levels is the same as that obtained by Wiegmann but the solutions are shown to be very general. This derivation clarifies certain assumptions made by Wiegmann (1980) and the recent controversies on the completeness of the Wiegmann states.

Recent experimental measurements such as susceptibility, specific heat, thermopower, and UPS on a wide range of intermetallic intermediate valence systems, e.g. YbCuAl, CeSn3, support a high degree of universality in the properties of such materials which apparently form a unique class of metallic compounds. The ratio χ(0)/γ≂g2μ2B (J+1) (J+1/2)/π2k2B is a good constant for compounds of a given rare earth (though g and J are rare earth dependent). A class of compounds of a given IV rare earth ion shows scaling of properties in terms of an effective temperature, or energy, scale TF, which is strong function of valence. We review the success of theoretical approaches such as perturbation theory, local Fermi liquid theory, the Bethe Ansatz technique, and large‐N perturbation theory in understanding these experimental facts. A challenge continues to be the understanding of the ground state, in which lattice periodicity plays a fundamental role, giving rise to ραT2 in some metallic, and a several meV gap in ins...

The authors give a brief outline of a 'poor man's' scaling approach as applied to locally coupled electron-phonon systems. For these systems they show that the retardation of the effective interactions have to be taken into account. The approach is extended to the calculation of one-electron Green functions and applied to the spinless Anderson model coupled to phonons. A general expression is obtained for the renormalisation of the resonance width due to phonons. This gives the results of Hewson and Newns (1979, 1980) in the appropriate limits but is more general in being applicable to a continuum spectrum of local phonons and for all values of the coupling strength.

A fluid of infinite electrical conductivity without an internal magnetic field and at uniform pressure is in equilibrium outside an infinitely long irregular cylindrical cavity. The cavity is prevented from collapsing by the magnetic field of a finite number of line currents parallel to the axis of the cylinder. The systematic method of solution of this problem is given in the case when the trace of the cavity is a single, simply connected region. The character of the solution is governed by the number of magnetic neutral points inside the cavity, as well as the nature of the magnetic singularities. The method is illustrated by considering the case of two unequal line currents, and the case of a dipole with equal and oppositely-directed line currents at equal distances on either side. It is shown that the solution can be extended to cases when the external hydrostatic pressure is nonuniform. In illustration, the cases of a line current and a line dipole immersed in an exponential atmosphere are considered. (Author)

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of n line currents are considered. The general problem is formulated and solved in the case of an initially flat-faced cloud of flux approaching and passing the magnetic field of n line currents. The special case of a line dipole is analysed in some detail.

This paper concerns the time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of a line current. The two-dimensional problem is formulated and solved with two particular classes of solutions being given; namely, the steady-state solutions and the time-history of the interaction with a cloud of flux.