A Unification of Models of Tethered Satellites

In this paper, different conservative models of tethered satellites are related mathematically, and it is established in what limit they may provide useful insight into the underlying dynamics. An infinite dimensional model is linked to a finite dimensional model, the slack-spring model, through a conjecture on the singular perturbation of tether thickness. The slack-spring model is then naturally related to a billiard model in the limit of an inextensible spring. Next, the motion of a dumbbell model, which is lowest in the hierarchy of models, is identified within the motion of the billiard model through a theorem on the existence of invariant curves by exploiting Moser's twist map theorem. Finally, numerical computations provide insight into the dynamics of the billiard model

On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in R3\mathbb{R}^3

In this paper we use the blow up method of Dumortier and Roussarie \cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \cite{filippov1988differential} in $\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided a certain non-resonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance.Comment: To appear in SIAM Journal of Applied Dynamical System

Postoperative complications and waiting time for surgical intervention after radiologically guided drainage of intra-abdominal abscess in patients with Crohn’s disease

Postoperative complications; DrainageComplicacions postoperatòries; DrenatgeComplicaciones postoperatorias; DrenajeBackground In patients with active Crohn’s disease (CD), treatment of intra-abdominal abscess usually comprises antibiotics and radiologically guided percutaneous drainage (PD) preceding surgery. The aim of this study was to investigate the risk of postoperative complications and identify the optimal time interval for surgical intervention after PD. Methods A multicentre, international, retrospective cohort study was carried out. Details of patients with diagnosis of CD who underwent ultrasonography- or CT-guided PD were retrieved from hospital records using international classification of disease (ICD-10) diagnosis code for CD combined with procedure code for PD. Clinical variables were retrieved and the following outcomes were measured: 30-day postoperative overall complications, intra-abdominal septic complications, unplanned intraoperative adverse events, surgical-site infections, sepsis and pathological postoperative ileus, in addition to abscess recurrence. Patients were categorized into three groups according to the length of the interval from PD to surgery (1–14 days, 15–30 days and more than 30 days) for comparison of outcomes. Results The cohort comprised 335 CD patients with PD followed by surgery. Median age was 33 (i.q.r. 24–44) years, 152 (45.4 per cent) were females, and median disease duration was 9 (i.q.r. 3.6–15) years. Overall, the 30-day postoperative complications rate was 32.2 per cent and the mortality rate was 1.5 per cent. After adjustment for co-variables, older age (odds ratio 1.03 (95 per cent c.i. 1.01 to 1.06), P < 0.012), residual abscess after PD (odds ratio 0.374 (95 per cent c.i. 0.19 to 0.74), P < 0.014), smoking (odds ratio 1.89 (95 per cent c.i. 1.01 to 3.53), P = 0.049) and low serum albumin concentration (odds ratio 0.921 (95 per cent c.i. 0.89 to 0.96), P < 0.001) were associated with higher rates of postoperative complications. A short waiting interval, less than 2 weeks after PD, was associated with a high incidence of abscess recurrence (odds ratio 0.59 (95 per cent c.i. 0.36 to 0.96), P = 0.042). Conclusion Smoking, low serum albumin concentration and older age were significantly associated with postoperative complications. An interval of at least 2 weeks after successful PD correlated with reduced risk of abscess recurrence

On the approximation of the canard explosion point in singularly perturbed systems without an explicit small parameter

A canard explosion is the dramatic change of period and amplitude of a limit cycle of a system of nonlinear ODEs in a very narrow interval of the bifurcation parameter. It occurs in slow–fast systems and is well understood in singular perturbation problems where a small parameter epsilon defines the time-scale separation. We present an iterative algorithm for the determination of the canard explosion point which can be applied for a general slow–fast system without an explicit small parameter. We also present assumptions under which the algorithm gives accurate estimates of the canard explosion point. Finally, we apply the algorithm to the van der Pol equations, a Templator model for a self-replicating system and a model for intracellular calcium oscillations with no explicit small parameters and obtain very good agreement with results from numerical simulations.<br/

The regularized visible fold revisited

The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow 0$. Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper is to demonstrate the use of consecutive blowup transformations in this setting, allowing us to obtain detailed information about a transition map near the fold under very general assumptions. We apply this information to prove, for the first time, the existence of a locally unique saddle-node bifurcation in the case where a limit cycle, in the singular limit $\epsilon\rightarrow 0$, grazes the discontinuity set. We apply this result to a mass-spring system on a moving belt described by a Stribeck-type friction law

The Lyman-alpha glow of gas falling into the dark matter halo of a z=3 galaxy

Quasars are the visible signatures of super-massive black holes in the centres of distant galaxies. It has been suggested that quasars are formed during ``major merger events'' when two massive galaxies collide and merge, leading to the prediction that quasars should be found in the centres of the regions of largest overdensity in the early Universe. In dark matter (DM)-dominated models of the early Universe, massive DM halos are predicted to attract the surrounding gas, which falls towards its centre. The neutral gas is not detectable in emission by itself, but gas falling into the ionizing cone of such a quasar will glow in the Lyman-alpha line of hydrogen, effectively imaging the DM halo. Here we present a Lyman-alpha image of a DM halo at redshift 3, along with a two-dimensional spectrum of the gaseous halo. Our observations are best understood in the context of the standard model for DM halos; we infer a mass of (2-7) x 10^12 solar masses (Msun) for the halo.Comment: 4 pages, 4 figures. Published as a Letter to Nature in the August 26, 2004 issue; see accompanying News and Views article by Z. Haiman in the same issu

Postoperative complications and waiting time for surgical intervention after radiologically guided drainage of intra-abdominal abscess in patients with Crohn's disease

In patients with active Crohn's disease (CD), treatment of intra-abdominal abscess usually comprises antibiotics and radiologically guided percutaneous drainage (PD) preceding surgery. The aim of this study was to investigate the risk of postoperative complications and identify the optimal time interval for surgical intervention after PD

Development and Validation of The SMAP Enhanced Passive Soil Moisture Product

Since the beginning of its routine science operation in March 2015, the NASA SMAP observatory has been returning interference-mitigated brightness temperature observations at L-band (1.41 GHz) frequency from space. The resulting data enable frequent global mapping of soil moisture with a retrieval uncertainty below 0.040 cu m/cu m at a 36 km spatial scale. This paper describes the development and validation of an enhanced version of the current standard soil moisture product. Compared with the standard product that is posted on a 36 km grid, the new enhanced product is posted on a 9 km grid. Derived from the same time-ordered brightness temperature observations that feed the current standard passive soil moisture product, the enhanced passive soil moisture product leverages on the Backus-Gilbert optimal interpolation technique that more fully utilizes the additional information from the original radiometer observations to achieve global mapping of soil moisture with enhanced clarity. The resulting enhanced soil moisture product was assessed using long-term in situ soil moisture observations from core validation sites located in diverse biomes and was found to exhibit an average retrieval uncertainty below 0.040 cu m/cu m. As of December 2016, the enhanced soil moisture product has been made available to the public from the NASA Distributed Active Archive Center at the National Snow and Ice Data Center

International practice patterns and factors associated with non-conventional hemodialysis utilization

<p>Abstract</p> <p>Background</p> <p>The purpose of our study was to determine characteristics that influence the utilization of non-conventional hemodialysis (NCHD) therapies and its subtypes (nocturnal (NHD), short daily (SDHD), long conventional (LCHD) and conventional hemodialysis (CHD) as well as provider attitudes regarding the evidence for NCHD use.</p> <p>Methods</p> <p>An international cohort of subscribers of a nephrology education website <url>http://www.nephrologynow.com</url> was invited to participate in an online survey. Non-conventional hemodialysis was defined as any forms of hemodialysis delivered > 3 treatments per week and/or > 4 hours per session. NHD and SDHD included both home and in-centre. Respondents were categorized as CHD if their centre only offered conventional thrice weekly hemodialysis. Variables associated with NCHD and its subtypes were determined using multivariate logistic regression analysis. The survey assessed multiple domains regarding NCHD including reasons for initiating and discontinuing, for not offering and attitudes regarding evidence.</p> <p>Results</p> <p>544 surveys were completed leading to a 15.6% response rate. The final cohort was limited to 311 physicians. Dialysis modalities utilized among the respondents were as follows: NCHD194 (62.4%), NHD 83 (26.7%), SDHD 107 (34.4%), LCHD 81 (26%) and CHD 117 (37.6%). The geographic regions of participants were as follows: 11.9% Canada, 26.7% USA, 21.5% Europe, 6.1% Australia/New Zealand, 10% Africa/Middle East, 10.9% Asia and 12.9% South America. Variables associated with NCHD utilization included NCHD training (OR 2.47 CI 1.25-4.16), government physician reimbursement (OR 2.66, CI 1.11-6.40), practicing at an academic centre (OR 2.28 CI 1.25-4.16), higher national health care expenditure and number of ESRD patients per centre. Hemodialysis providers with patients on NCHD were significantly more likely to agree with the statements that NCHD improves quality of life, improves nutritional status, reduces EPO requirements and is cost effective. The most common reasons to initiate NCHD were driven by patient preference and the desire to improve volume control and global health outcomes.</p> <p>Conclusion</p> <p>Physician attitudes toward the evidence for NCHD differ significantly between NCHD providers and conventional HD providers. Interventions and health policy targeting these areas along with increased physician education and training in NCHD modalities may be effective in increasing its utilization.</p

A glucagon-like peptide-1 receptor agonist reduces intracranial pressure in a rat model of hydrocephalus

GLP-1R agonists show promise as a therapeutic agent to lower intracranial pressure in rodents.</jats:p