Differential equations for the cuspoid canonical integrals

Differential equations satisfied by the cuspoid canonical integrals I_n(a) are obtained for arbitrary values of n≥2, where n−1 is the codimension of the singularity and a=(ɑ_1,ɑ_2,...,ɑ_(n−1)). A set of linear coupled ordinary differential equations is derived for each step in the sequence I_n(0,0,...,0,0) →I_n(0,0,...,0,ɑ_(n−1)) →I_n(0,0,...,ɑ_(n−2),ɑ_(n−1)) →...→I_n(0,ɑ_2,...,ɑ_(n−2),ɑ_(n−1)) →I_n(ɑ_1,ɑ_2,...,ɑ_n−2,ɑ_(n−1)). The initial conditions for a given step are obtained from the solutions of the previous step. As examples of the formalism, the differential equations for n=2 (fold), n=3 (cusp), n=4 (swallowtail), and n=5 (butterfly) are given explicitly. In addition, iterative and algebraic methods are described for determining the parameters a that are required in the uniform asymptotic cuspoid approximation for oscillating integrals with many coalescing saddle points. The results in this paper unify and generalize previous researches on the properties of the cuspoid canonical integrals and their partial derivatives

Dynamical Phase Transitions In Driven Integrate-And-Fire Neurons

We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron's natural firing period and that of the oscillatory rhythm, leads to a rich structure of asymptotic phase locking patterns and ordering dynamics. The phase transitions between these states can be classified as either tangent or discontinuous bifurcations, each with its own characteristic scaling laws. The discontinuous bifurcations exhibit a new kind of phase transition that may be viewed as intermediate between continuous and first order, while tangent bifurcations behave like continuous transitions with a diverging coherence scale.Comment: 4 pages, 5 figure

Dual equilibrium in a finite aspect ratio tokamak

A new approach to high pressure magnetically-confined plasmas is necessary to design efficient fusion devices. This paper presents an equilibrium combining two solutions of the Grad-Shafranov equation, which describes the magnetohydrodynamic equilibrium in toroidal geometry. The outer equilibrium is paramagnetic and confines the inner equilibrium, whose strong diamagnetism permits to balance large pressure gradients. The existence of both equilibria in the same volume yields a dual equilibrium structure. Their combination also improves free-boundary mode stability

Derivation of tropospheric methane from TCCON CH₄ and HF total column observations

The Total Carbon Column Observing Network (TCCON) is a global ground-based network of Fourier transform spectrometers that produce precise measurements of column-averaged dry-air mole fractions of atmospheric methane (CH₄). Temporal variability in the total column of CH₄ due to stratospheric dynamics obscures fluctuations and trends driven by tropospheric transport and local surface fluxes that are critical for understanding CH₄ sources and sinks. We reduce the contribution of stratospheric variability from the total column average by subtracting an estimate of the stratospheric CH₄ derived from simultaneous measurements of hydrogen fluoride (HF). HF provides a proxy for stratospheric CH₄ because it is strongly correlated to CH₄ in the stratosphere, has an accurately known tropospheric abundance (of zero), and is measured at most TCCON stations. The stratospheric partial column of CH₄ is calculated as a function of the zonal and annual trends in the relationship between CH₄ and HF in the stratosphere, which we determine from ACE-FTS satellite data. We also explicitly take into account the CH₄ column averaging kernel to estimate the contribution of stratospheric CH₄ to the total column. The resulting tropospheric CH₄ columns are consistent with in situ aircraft measurements and augment existing observations in the troposphere

Cooling in the X-ray halo of the rotating, massive early-type galaxy NGC 7049

The relative importance of the physical processes shaping the thermodynamics of the hot gas permeating rotating, massive early-type galaxies is expected to be different from that in non-rotating systems. Here, we report the results of the analysis of XMM-Newton data for the massive, lenticular galaxy NGC 7049. The galaxy harbours a dusty disc of cool gas and is surrounded by an extended hot X-ray emitting gaseous atmosphere with unusually high central entropy. The hot gas in the plane of rotation of the cool dusty disc has a multi-temperature structure, consistent with ongoing cooling. We conclude that the rotational support of the hot gas is likely capable of altering the multiphase condensation regardless of the $t_{\rm cool}/t_{\rm ff}$ ratio, which is here relatively high, $\sim 40$. However, the measured ratio of cooling time and eddy turnover time around unity ($C$-ratio $\approx 1$) implies significant condensation, and at the same time, the constrained ratio of rotational velocity and the velocity dispersion (turbulent Taylor number) ${\rm Ta_t} > 1$ indicates that the condensing gas should follow non-radial orbits forming a disc instead of filaments. This is in agreement with hydrodynamical simulations of massive rotating galaxies predicting a similarly extended multiphase disc.Comment: 11 pages, 12 figures, accepted for publication in MNRA

Primary Care Atrial Fibrillation Service: outcomes from consultant-led anticoagulation assessment clinics in the primary care setting in the UK

OBJECTIVE: Stroke-risk in atrial fibrillation (AF) can be significantly reduced by appropriate thromboembolic prophylaxis. However, National Institute for Health and Care Excellence estimates suggest that up to half of eligible patients with AF are not anticoagulated, with severe consequences for stroke prevention. We aimed to determine the outcome of an innovative Primary Care AF (PCAF) service on anticoagulation uptake in a cohort of high-risk patients with AF in the UK. METHODS: The PCAF service is a novel cooperative pathway providing specialist resources within general practitioner (GP) practices. It utilises a four-phase protocol to identify high-risk patients with AF (CHA(2)DS(2)-VASc ≥1) who are suboptimally anticoagulated, and delivers Consultant-led anticoagulation assessment within the local GP practice. We assessed rates of anticoagulation in high-risk patients before and after PCAF service intervention, and determined compliance with newly-initiated anticoagulation at follow-up. RESULTS: The PCAF service was delivered in 56 GP practices (population 386 624; AF prevalence 2.1%) between June 2012 and June 2014. 1579 high-risk patients with AF with suboptimal anticoagulation (either not taking any anticoagulation or taking warfarin but with a low time-in-therapeutic-range) were invited for review, with 86% attending. Of 1063 eligible patients on no anticoagulation, 1020 (96%) agreed to start warfarin (459 (43%)) or a non-vitamin K antagonist oral anticoagulant (NOAC, 561 (53%)). The overall proportion of eligible patients receiving anticoagulation improved from 77% to 95% (p<0.0001). Additionally, 111/121 (92%) patients suboptimally treated with warfarin agreed to switch to a NOAC. Audit of eight practices after 195 (185–606) days showed that 90% of patients started on a new anticoagulant therapy had continued treatment. Based on data extrapolated from previous studies, around 30–35 strokes per year may have been prevented in these previously under-treated high-risk patients. CONCLUSIONS: Systematic identification of patients with AF with high stroke-risk and consultation in PCAF consultant-led clinics effectively delivers oral anticoagulation to high-risk patients with AF in the community

Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers

Free energies and other thermodynamical quantities are investigated in canonical and grand canonical ensembles of statistical mechanics involving unstable states which are described by the generalized eigenstates with complex energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is applied to the systems containing parabolic potential barriers (PPB's). The entropy and energy productions from PPB systems are studied. An equilibrium for a chemical process described by reactions $A+CB\rightleftarrows AC+B$ is also discussed.Comment: 14 pages, AmS-LaTeX, no figur

Semiclassical ionization dynamics of the hydrogen molecular ion in an electric field of arbitrary orientation

Quasi-static models of barrier suppression have played a major role in our understanding of the ionization of atoms and molecules in strong laser fields. Despite their success, in the case of diatomic molecules these studies have so far been restricted to fields aligned with the molecular axis. In this paper we investigate the locations and heights of the potential barriers in the hydrogen molecular ion in an electric field of arbitrary orientation. We find that the barriers undergo bifurcations as the external field strength and direction are varied. This phenomenon represents an unexpected level of intricacy even on this most elementary level of the dynamics. We describe the dynamics of tunnelling ionization through the barriers semiclassically and use our results to shed new light on the success of a recent theory of molecular tunnelling ionization as well as earlier theories that restrict the electric field to be aligned with the molecular axis