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We consider the evolution of a shock wave generated by an impulsively accelerated, two-dimensional, almost planar piston with a sinusoidally corrugated surface of amplitude $\epsilon$. We develop a complex-variable formulation for a nonlinear theory of generalized geometrical shock dynamics (GGSD) (Best, Shock Waves, vol. 1, issue 4, 1991, pp. 251–273; Best, Proc. R. Soc. Lond. A, vol. 442, 1993, pp. 585–598) as a hierarchical expansion of the Euler equations that can be closed at any order. The zeroth-order truncation of GGSD is related to the equations of Whitham's geometrical shock dynamics (GSD), while higher-order corrections incorporate non-uniformity of the flow immediately behind the piston-driven shock. Numerical solutions to GGSD systems up to second order are coupled to an edge-detection algorithm in order to investigate the hypothesized development of a shock-shape curvature singularity as the rippled shock evolves. This singular behaviour, together with the simultaneous development of a Mach-number discontinuity, is found at all orders of the GGSD hierarchy for both weak and strong shocks. The critical time at which a curvature singularity occurs converges as the order of the GGSD system increases at fixed $\epsilon$, and follows a scaling inversely proportional to $\epsilon$ at sufficiently small values. This result agrees with the weakly nonlinear GSD analysis of Mostert et al. (J. Fluid Mech., vol. 846, 2018, pp. 536–562) for a general Mach-number perturbation on a planar shock, and suggests that this represents the universal behaviour of a slightly perturbed, planar shock.
We investigate the effects of magnetisation on the two-fluid plasma Richtmyer–Meshkov instability of a single-mode thermal interface using a computational approach. The initial magnetic field is normal to the mean interface location. Results are presented for a magnetic interaction parameter of 0.1 and plasma skin depths ranging from 0.1 to 10 perturbation wavelengths. These are compared to initially unmagnetised and neutral fluid cases. The electron flow is found to be constrained to lie along the magnetic field lines resulting in significant longitudinal flow features that interact strongly with the ion fluid. The presence of an initial magnetic field is shown to suppress the growth of the initial interface perturbation with effectiveness determined by plasma length scale. Suppression of the instability is attributed to the magnetic field's contribution to the Lorentz force. This acts to rotate the vorticity vector in each fluid about the local magnetic-field vector leading to cyclic inversion and transport of the out-of-plane vorticity that drives perturbation growth. The transport of vorticity along field lines increases with decreasing plasma length scales and the wave packets responsible for vorticity transport begin to coalesce. In general, the two-fluid plasma Richtmyer–Meshkov instability is found to be suppressed through the action of the imposed magnetic field with increasing effectiveness as plasma length scale is decreased. For the conditions investigated, a critical skin depth for instability suppression is estimated.
The Coronavirus (Covid-19) pandemic is exerting unprecedented pressure on NHS Health and Social Care provisions, with frontline staff, such as those of critical care units, encountering vast practical and emotional challenges on a daily basis. Although staff are being supported through organisational provisions, facilitated by those in leadership roles, the emergence of mental health difficulties or the exacerbation of existing ones amongst these members of staff is a cause for concern. Acknowledging this, academics and healthcare professionals alike are calling for psychological support for frontline staff, which not only addresses distress during the initial phases of the outbreak but also over the months, if not years, that follow. Fortunately, mental health services and psychology professional bodies across the United Kingdom have issued guidance to meet these needs. An attempt has been made to translate these sets of guidance into clinical provisions via the recently established Homerton Covid Psychological Support (HCPS) pathway delivered by Talk Changes (Hackney & City IAPT). This article describes the phased, stepped-care and evidence-based approach that has been adopted by the service to support local frontline NHS staff. We wish to share our service design and pathway of care with other Improving Access to Psychological Therapies (IAPT) services who may also seek to support hospital frontline staff within their associated NHS Trusts and in doing so, lay the foundations of a coordinated response.
Key learning aims
(1) To understand the ways staff can be psychologically and emotionally impacted by working on the frontline of disease outbreaks.
(2) To understand the ways in which IAPT services have previously supported populations exposed to crises.
(3) To learn ways of delivering psychological support and interventions during a pandemic context based on existing guidance and research.
The hot Jupiter HD189733b is expected to be a source of strong radio emission, due to its close proximity to its magnetically active host star. Here, we model the stellar wind of its host star, based on reconstructed surface stellar magnetic field maps. We use the local stellar wind properties at the planetary orbit obtained from our models to compute the expected radio emission from the planet. Our findings show that the planet emits with a peak flux density within the detection capabilities of LOFAR. However, due to absorption by the stellar wind itself, this emission may be attenuated significantly. We show that the best time to observe the system is when the planet is near primary transit of the host star, as the attenuation from the stellar wind is lowest in this region.
Background: Surgical treatment of trigeminal neuralgia (TN) can be highly effective, but durability of pain relief varies and factors influencing surgical failure are poorly understood. We hypothesized that structural brain differences—assessed using magnetic resonance imaging (MRI)—might distinguish surgical responders from early non-responders. Methods: We retrospectively identified 35 TN patients treated surgically from 2005-2017 with high-resolution, -pre-operative MRI scans adequate for quantitative structural analysis. Patients were classified as non-responders if, within 12-months after surgery, they: 1) underwent or were offered another surgical procedure; or 2) reported persistent, inadequately-controlled pain. Volumes of pain-relevant subcortical structures (amygdala, thalamus, and hippocampus) were measured on T1-weighted MRI scans using an automated approach (FSL-FIRST). Results: Surgical responders had significantly larger hippocampi bilaterally compared to early non-responders. Thalamus and amygdala volumes did not differ between groups. Conclusions: Pre-operative differences in brain structure, notably in the hippocampus, may predict durability of response to surgery in patients with TN.
We present an analysis that predicts the time to development of a singularity in the shape profile of a spatially periodic perturbed, planar shock wave for ideal gas dynamics. Beginning with a formulation in complex coordinates of Whitham’s approximate model geometrical shock dynamics (GSD), we apply a spectral treatment to derive the asymptotic form for the leading-order behaviour of the shock Fourier coefficients for large mode numbers and time. This is shown to determine a critical time at which the coefficients begin to decay, with respect to mode number, at an algebraic rate with an exponent of
, indicating loss of analyticity and the formation of a singularity in the shock geometry. The critical time is found to be inversely proportional to a representative measure of perturbation amplitude
with an explicit analytic form for the constant of proportionality in terms of gas and shock parameters. To leading order, the time to singularity formation is dependent only on the first Fourier mode. Comparison with results of numerical solutions to the full GSD equations shows that the predicted critical time somewhat underestimates the time for shock–shock (triple-point) formation, where the latter is obtained by post-processing the numerical GSD results using an edge-detection algorithm. Aspects of the analysis suggest that the appearance of loss of analyticity in the shock surface may be a precursor to the first appearance of shock–shocks, which may account for part of the discrepancy. The frequency of oscillation of the shock perturbation is accurately predicted. In addition, the analysis is extended to the evolution of a perturbed planar, fast magnetohydrodynamic shock for the case when the external magnetic field is aligned parallel to the unperturbed shock. It is found that, for a strong shock, the presence of the magnetic field produces only a higher-order correction to the GSD equations with the result that the time to loss of analyticity is the same as for the gas-dynamic flow. Limitations and improvements for the analysis are discussed, as are comparisons with the analogous appearance of singularity formation in vortex-sheet evolution in an incompressible inviscid fluid.
We computationally investigate the Richtmyer–Meshkov instability of a density interface with a single-mode perturbation in a two-fluid, ion–electron plasma with no initial magnetic field. Self-generated magnetic fields arise subsequently. We study the case where the density jump across the initial interface is due to a thermal discontinuity, and select plasma parameters for which two-fluid plasma effects are expected to be significant in order to elucidate how they alter the instability. The instability is driven via a Riemann problem generated precursor electron shock that impacts the density interface ahead of the ion shock. The resultant charge separation and motion generates electromagnetic fields that cause the electron shock to degenerate and periodically accelerate the electron and ion interfaces, driving Rayleigh–Taylor instability. This generates small-scale structures and substantially increases interfacial growth over the hydrodynamic case.
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as
is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock.
The yields of spring barley during a medium-term (7 years) compost and slurry addition experiment and the soil carbon (C) and nitrogen (N) contents, bacterial community structure, soil microbial biomass and soil respiration rates have been determined to assess the effects of repeated, and in some cases very large, organic amendments on soil and crop parameters. For compost, total additions were equivalent to up to 119 t C/ha and 1·7 t N/ha and for slurry they were 25 t C/ha and 0·35 t N/ha over 7 years, which represented very large additions compared to control soil C and N contents (69 t C/ha and 0·3 t N/ha in the 0–30 cm soil depth). There was an initial positive response to compost and slurry addition on barley yield, but over the experiment the yield differential between the amounts of compost addition declined, indicating that repeated addition of compost at a lower rate over several years had the same cumulative effect as a large single compost application. By the end of the experiment it was clear that the addition of compost and slurry increased soil C and N contents, especially towards the top of the soil profile, as well as soil respiration rates. However, the increases in soil C and N contents were not proportional to the amount of C and N added, suggesting either that: (i) a portion of the added C and N was more vulnerable to loss; (ii) that its addition rendered another C or N pool in the soil more susceptible to loss; or (iii) that the C inputs from additional crop productivity did not increase in line with the organic amendments. Soil microbial biomass was depressed at the highest rate of organic amendment, and whilst this may have been due to genuine toxic or inhibitory effects of large amounts of compost, it could also be due to the inaccuracy of the substrate-induced respiration approach used for determining soil biomass when there is a large supply of organic matter. At the highest compost addition, the bacterial community structure was significantly altered, suggesting that the amendments significantly altered soil community dynamics.
We investigate the convergence behaviour of a cylindrical, fast magnetohydrodynamic (MHD) shock wave in a neutrally ionized gas collapsing onto an axial line current that generates a power law in time, azimuthal magnetic field. The analysis is done within the framework of a modified version of ideal MHD for an inviscid, non-dissipative, neutrally ionized compressible gas. The time variation of the magnetic field is tuned such that it approaches zero at the instant that the shock reaches the axis. This configuration is motivated by the desire to produce a finite magnetic field at finite shock radius but a singular gas pressure and temperature at the instant of shock impact. Our main focus is on the variation with shock radius
, of the shock Mach number
and pressure behind the shock
as a function of the magnetic field power-law exponent
gives a constant-in-time line current. The flow problem is first formulated using an extension of geometrical shock dynamics (GSD) into the time domain to take account of the time-varying conditions ahead of the converging shock, coupled with appropriate shock-jump conditions for a fast, symmetric MHD shock. This provides a pair of ordinary differential equations describing both
and the time evolution on the shock, as a function of
, constrained by a collapse condition required to achieve tuned shock convergence. Asymptotic, analytical results for
are obtained over a range of
, and for both small and large
. In addition, numerical solutions of the GSD equations are performed over a large range of
, for selected parameters using
. The accuracy of the GSD model is verified for some cases using direct numerical solution of the full, radially symmetric MHD equations using a shock-capturing method. For the GSD solutions, it is found that the physical character of the shock convergence to the axis is a strong function of
both approach unity at shock impact
owing to the dominance of the strong magnetic field over the amplifying effects of geometrical convergence. When
), geometrical convergence is dominant and the shock behaves similarly to a converging gas dynamic shock with singular
three distinct regions of
variation are identified. For each of these
is singular at the axis.
Offload delay is a prolonged interval between ambulance arrival in the emergency department (ED) and transfer of patient care, typically occurring when EDs are crowded. The offload zone (OZ), which manages ambulance patients waiting for an ED bed, has been implemented to mitigate the impact of ED crowding on ambulance availability. Little is known about the safety or efficiency. The study objectives were to process map the OZ and conduct a hazard analysis to identify steps that could compromise patient safety or process efficiency.
A Health Care Failure Mode and Effect Analysis was conducted. Failure modes (FM) were identified. For each FM, a probability to occur and severity of impact on patient safety and process efficiency was determined, and a hazard score (probability X severity) was calculated. For any hazard score considered high risk, root causes were identified, and mitigations were sought.
The OZ consists of six major processes: 1) patient transported by ambulance, 2) arrival to the ED, 3) transfer of patient care, 4) patient assessment in OZ, 5) patient care in OZ, and 6) patient transfer out of OZ; 78 FM were identified, of which 28 (35.9%) were deemed high risk and classified as impact on patient safety (n=7/28, 25.0%), process efficiency (n=10/28, 35.7%), or both (n=11/28, 39.3%). Seventeen mitigations were suggested.
This process map and hazard analysis is a first step in understanding the safety and efficiency of the OZ. The results from this study will inform current policy and practice, and future work to reduce offload delay.
This study aimed to assess the speed of referral, diagnosis and treatment of patients with lymphoma presenting with a neck lump, and to identify where delays are occurring that prevent UK national targets from being met.
The study entailed a retrospective survey of patients presenting with a neck lump secondary to lymphoma between 2006 and 2008 in Gloucestershire, UK.
Forty-seven of 54 patients (87 per cent) were seen within 2 weeks of referral. However, the 62-day rule, which covers the time from referral to the initiation of treatment, was met in only 32 of the 54 cases (59 per cent). There were no breaches of the 31-day target, which concerned the time from decision to treat to the initiation of treatment. Subsequent target breaches were due to longer waiting times for radiological and pathological investigations.
Radiological examinations should be ordered at the first consultation and biopsies performed as soon as possible. Establishing one-stop, rapid access clinics should improve the achievement of a maximum 62-day wait for patients with lymphoma presenting with neck lumps.