Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Experimental and theoretical evidence for homogeneous catalysis in the gas-phase reaction of SiH2 with H2O (and D2O): a combined kinetic and quantum chemical study

Time-resolved kinetic studies of the reaction of silylene, SiH2, with H2O and with D2O have been carried out in the gas phase at 297 K and at 345 K, using laser flash photolysis to generate and monitor SiH2. The reaction was studied independently as a function of H2O (or D2O) and SF6 (bath gas) pressures. At a fixed pressure of SF6 (5 Torr), [SiH2] decay constants, k(obs), showed a quadratic dependence on [H2O] or [D2O]. At a fixed pressure of H2O or D2O, k(obs) Values were strongly dependent on [SF6]. The combined rate expression is consistent with a mechanism involving the reversible formation of a vibrationally excited zwitterionic donor-acceptor complex, H2Si...OH2 (or H2Si...OD2). This complex can then either be stabilized by SF6 or it reacts with a further molecule of H2O (or D2O) in the rate-determining step. Isotope effects are in the range 1.0-1.5 and are broadly consistent with this mechanism. The mechanism is further supported by RRKM theory, which shows the association reaction to be close to its third-order region of pressure (SF6) dependence. Ab initio quantum calculations, carried out at the G3 level, support the existence of a hydrated zwitterion H2Si...(OH2)(2), which can rearrange to hydrated silanol, with an energy barrier below the reaction energy threshold. This is the first example of a gas-phase-catalyzed silylene reaction.

A pilot randomised, open, uncontrolled, clinical study of two dosages of St John's wort (Hypericum perforatum) herb extract (LI-160) as an aid to motivational/behavioural support in smoking cessation

There is an association between smoking and depression, yet the herbal antidepressant St John's wort (Hypericum perforatum L.: SJW) herb extract has not previously been investigated as an aid in smoking cessation. In this open, uncontrolled, pilot study, 28 smokers of 10 or more cigarettes per day for at least one year were randomised to receive SJW herb extract (LI-160) 300mg once or twice daily taken for one week before and continued for 3 months after a target quit date. In addition, all participants received motivational/behavioural support from a trained pharmacist. At 3 months, the point prevalence and continuous abstinence rates were both 18%, and at 12 months were 0%. Fifteen participants (54%) reported 23 adverse events up to the end of the 3-month follow-up period. There was no statistically significant difference in the frequency of adverse events for participants taking SJW once or twice daily (p > 0.05). Most adverse events were mild, transient and non-serious. This preliminary study has not provided convincing evidence that a SJW herb extract plus individual motivational/behavioural support is likely to be effective as an aid in smoking cessation. However, it may be premature to rule out a possible effect on the basis of a single, uncontrolled pilot study, and other approaches involving SJW extract may warrant investigation.

Reduced-order modelling of a high-voltage oscillatory impulse generator

The design of high-voltage equipment encompasses the study of oscillatory surges caused by transients such as those produced by switching. By obtaining a model, the response of which reconstructs that observed in the actual system, simulation studies and critical tests can be carried out on the model rather than on the equipment itself. In this paper, methods for the construction of simplified models are described and it is shown how the use of a complex model does not necessarily result in superior response pattern reconstruction.

Reduced-order dynamics of the Martian atmospheric dynamics

In this paper we explore the possibility of deriving low-dimensional models of the dynamics of the Martian atmosphere. The analysis consists of a Proper Orthogonal Decomposition (POD) of the atmospheric streamfunction after first decomposing the vertical structure with a set of eigenmodes. The vertical modes were obtained from the quasi-geostrophic vertical structure equation. The empirical orthogonal functions (EOFs) were optimized to represent the atmospheric total energy. The total energy was used as the criterion to retain those modes with large energy content and discard the rest. The principal components (PCs) were analysed by means of Fourier analysis, so that the dominant frequencies could be identified. It was possible to observe the strong influence of the diurnal cycle and to identify the motion and vacillation of baroclinic waves.

Reduced-order modeling of light transport in tissue for real-time monitoring of brain hemodynamics using diffuse optical tomography

This paper proposes a new reconstruction method for diffuse optical tomography using reduced-order models of light transport in tissue. The models, which directly map optical tissue parameters to optical flux measurements at the detector locations, are derived based on data generated by numerical simulation of a reference model. The reconstruction algorithm based on the reduced-order models is a few orders of magnitude faster than the one based on a finite element approximation on a fine mesh incorporating a priori anatomical information acquired by magnetic resonance imaging. We demonstrate the accuracy and speed of the approach using a phantom experiment and through numerical simulation of brain activation in a rat's head. The applicability of the approach for real-time monitoring of brain hemodynamics is demonstrated through a hypercapnic experiment. We show that our results agree with the expected physiological changes and with results of a similar experimental study. However, by using our approach, a three-dimensional tomographic reconstruction can be performed in ∼3  s per time point instead of the 1 to 2 h it takes when using the conventional finite element modeling approach

Diversity in a honey bee pathogen: first report of a third master variant of the Deformed Wing Virus quasispecies

Treatment of emerging RNA viruses is hampered by the high mutation and replication rates that enable these viruses to operate as a quasispecies. Declining honey bee populations have been attributed to the ectoparasitic mite Varroa destructor and its affiliation with Deformed Wing Virus (DWV). In the current study we use next-generation sequencing to investigate the DWV quasispecies in an apiary known to suffer from overwintering colony losses. We show that the DWV species complex is made up of three master variants. Our results indicate that a new DWV Type C variant is distinct from the previously described types A and B, but together they form a distinct clade compared with other members of the Iflaviridae. The molecular clock estimation predicts that Type C diverged from the other variants ~319 years ago. The discovery of a new master variant of DWV has important implications for the positive identification of the true pathogen within global honey bee populations.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Blind equalization of nonminimum phase channels: higher order cumulant based algorithm

Higher order cumulant analysis is applied to the blind equalization of linear time-invariant (LTI) nonminimum-phase channels. The channel model is moving-average based. To identify the moving average parameters of channels, a higher-order cumulant fitting approach is adopted in which a novel relay algorithm is proposed to obtain the global solution. In addition, the technique incorporates model order determination. The transmitted data are considered as independently identically distributed random variables over some discrete finite set (e.g., set {±1, ±3}). A transformation scheme is suggested so that third-order cumulant analysis can be applied to this type of data. Simulation examples verify the feasibility and potential of the algorithm. Performance is compared with that of the noncumulant-based Sato scheme in terms of the steady state MSE and convergence rate.

Response of the lower St. Lawrence Estuary to external forcing in winter

Mostly because of a lack of observations, fundamental aspects of the St. Lawrence Estuary's wintertime response to forcing remain poorly understood. The results of a field campaign over the winter of 2002/03 in the estuary are presented. The response of the system to tidal forcing is assessed through the use of harmonic analyses of temperature, salinity, sea level, and current observations. The analyses confirm previous evidence for the presence of semidiurnal internal tides, albeit at greater depths than previously observed for ice-free months. The low-frequency tidal streams were found to be mostly baroclinic in character and to produce an important neap tide intensification of the estuarine circulation. Despite stronger atmospheric momentum forcing in winter, the response is found to be less coherent with the winds than seen in previous studies of ice-free months. The tidal residuals show the cold intermediate layer in the estuary is renewed rapidly ( 14 days) in late March by the advection of a wedge of near-freezing waters from the Gulf of St. Lawrence. In situ processes appeared to play a lesser role in the renewal of this layer. In particular, significant wintertime deepening of the estuarine surface mixed layer was prevented by surface stability, which remained high throughout the winter. The observations also suggest that the bottom circulation was intensified during winter, with the intrusion in the deep layer of relatively warm Atlantic waters, such that the 3 C isotherm rose from below 150 m to near 60 m.