A posteriori error control for discontinuous Galerkin methods for parabolic problems

We derive energy-norm a posteriori error bounds for an Euler time-stepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For accessibility, we address first the spatially semidiscrete case, and then move to the fully discrete scheme by introducing the implicit Euler time-stepping. All results are presented in an abstract setting and then illustrated with particular applications. This enables the error bounds to hold for a variety of discontinuous Galerkin methods, provided that energy-norm a posteriori error bounds for the corresponding elliptic problem are available. To illustrate the method, we apply it to the interior penalty discontinuous Galerkin method, which requires the derivation of novel a posteriori error bounds. For the analysis of the time-dependent problems we use the elliptic reconstruction technique and we deal with the nonconforming part of the error by deriving appropriate computable a posteriori bounds for it.Comment: 6 figure

Sequential Injection-flow Reversal Mixing (Si-frm) Untuk Penentuan Kreatinin Dalam Urin

Jumlah kreatinin yang diekskresikan melalui urin menunjukkan keadaan ginjal seseorang. Dalam penelitian ini, dikembangkan metode untuk penentuan kreatinin secara otomatis yaitu sequential injection-flow reversal mixing (SI-FRM). Pendeteksian kreatinin didasarkan pada pembentukan senyawa berwarna (merah-orange) yang dihasilkan dari reaksi antara kreatinin dan asam pikrat dalam suasana basa dan diukur pada panjang gelombang 530 nm. Reaksi pembentukan senyawa kreatinin-pikrat dilakukan melalui pembentukan segmen antara sampel dan reagen di-holding coil dan selanjutnya dilakukan proses flow reversal di-mixing coil. Parameter-parameter yang mempengaruhi metode ini diuji secara detail. Hasil penelitian menunjukkan bahwa kondisi optimum pengukuran kreatinin yaitu menggunakan konsentrasi asam pikrat 0,035 M dan NaOH 3,5%, laju alir flow reversal 5 µL/detik, laju alir produk reaksi 20 µL/detik, jumlah flow reversal empat kali dan menggunakan tiga segmen (pikrat-kreatinin-pikrat) dengan masing-masing volume segmen 100 µL. Metode SI-FRM ini telah diaplikasikan langsung untuk penentuan kadar kreatinin dalam urin dengan limit deteksi 1,7 µg/g. The amount of creatinine excreted in urine indicates kidney condition. In this experiment, the automatic determination method of determining creatinine was developed by using sequential injection-flow reversal mixing (SI-FRM). The detection of creatinine is based on the formation of a colored product (red-orange) yielded from the reaction of creatinine with picrate at alkaline medium. The absorbance is measured at wavelength of 530 nm.  The formation of creatinine-picrate complex is performed through the segment formation between sample and reagent in the holding coil and then flow reversal process in the mixing coil of SI-FRM. Several parameters affecting to this method are investigated in detail. The results show that the optimum concentrations of picric acid and NaOH are 0.035 M and 3.5%, respectively. Other optimized conditions, such as the flow reversal rate of there 5 µL/s, flow rate of product of 20 µL/s, amount of flow reversal process of four times, and segment amount of three (picrate-creatinine -picrate) with each volume of 100 µL, were obtained. This method is successfully applied to the determination of creatinine in urine with the detection limit of 1.7 µg/g

Temperature and pollution control in flames

We apply control theory for PDEs to flame control. The targeted flame is calculated with complex chemistry. For pollutant control in flames we study both the control of temperature distribution in the flame and flame length at given fuel rate in the flow. Approximate state and sensitivity evaluations as well as mesh adaptation are used to keep the complexity as low as possible and get mesh independent results. In addition, a new recursive semi-deterministic global optimization approach is tested

Multidomain Spectral Method for the Helically Reduced Wave Equation

We consider the 2+1 and 3+1 scalar wave equations reduced via a helical Killing field, respectively referred to as the 2-dimensional and 3-dimensional helically reduced wave equation (HRWE). The HRWE serves as the fundamental model for the mixed-type PDE arising in the periodic standing wave (PSW) approximation to binary inspiral. We present a method for solving the equation based on domain decomposition and spectral approximation. Beyond describing such a numerical method for solving strictly linear HRWE, we also present results for a nonlinear scalar model of binary inspiral. The PSW approximation has already been theoretically and numerically studied in the context of the post-Minkowskian gravitational field, with numerical simulations carried out via the "eigenspectral method." Despite its name, the eigenspectral technique does feature a finite-difference component, and is lower-order accurate. We intend to apply the numerical method described here to the theoretically well-developed post-Minkowski PSW formalism with the twin goals of spectral accuracy and the coordinate flexibility afforded by global spectral interpolation.Comment: 57 pages, 11 figures, uses elsart.cls. Final version includes revisions based on referee reports and has two extra figure

Initial experiments to assess short-term survival of discarded plaice (Pleuronectes platessa) caught in trammel nets during winter season

European plaice (Pleuronectes platessa) is a key species in commercial fisheries in the North Sea, Skagerrak, Kattegat, and Baltic Sea. The reformed European Union Common Fisheries Policy includes the possibility of exemptions from the landing obligation for “species for which scientific evidence demonstrates high survival rates”. Discard survival from set-net fisheries is poorly studied. Trials were conducted on two commercial fishing vessels over seven trips from November to February 2017–2018 in the Baltic Sea. The nylon trammel nets had a nominal bar size for the inner/outer wall of 75/350 mm and 85/400 mm. Soaking time was 23–47 h, water depth 7–18 m, and deck temperature was − 0.1–6.0 ◦C. Following commercial practice, the trammel nets were hauled back onto the vessel, after which netting and fish passed through a net hauler onto a steel sorting table where the entire fish catch were manually untangled by the fishers and plaice collected by scientists. We used a storage system for housing the captured fish inside fishing harbours during observations. Catch-damage-index (CDI) and Reflex Action Mortality Predictor (RAMP) scores were used to assess fish condition immediately after capture and at the end of observation periods. All plaice below 40 cm were sampled with a total number of 118 individuals from 13 fleets (several nets joined together). The fish were assessed for short-term survival for 4–10 days with full survival (100%). The majority of fish exhibited no reflex impairments. Minor bruises, fraying, and net marks were frequently observed on captured fish. The overall condition of the fish did not change during observation periods

Ring closing reaction in diarylethene captured by femtosecond electron crystallography

The photoinduced ring-closing reaction in diarylethene, which serves as a model system for understanding reactive crossings through conical intersections, was directly observed with atomic resolution using femtosecond electron diffraction. Complementary ab initio calculations were also performed. Immediately following photoexcitation, subpicosecond structural changes associated with the formation of an open-ring excited-state intermediate were resolved. The key motion is the rotation of the thiophene rings, which significantly decreases the distance between the reactive carbon atoms prior to ring closing. Subsequently, on the few picosecond time scale, localized torsional motions of the carbon atoms lead to the formation of the closed-ring photoproduct. These direct observations of the molecular motions driving an organic chemical reaction were only made possible through the development of an ultrabright electron source to capture the atomic motions within the limited number of sampling frames and the low data acquisition rate dictated by the intrinsically poor thermal conductivity and limited photoreversibility of organic materials

External validation of the HCM Risk-Kids model for predicting sudden cardiac death in childhood hypertrophic cardiomyopathy

Aims Sudden cardiac death (SCD) is the most common mode of death in childhood hypertrophic cardiomyopathy (HCM). The newly developed HCM Risk-Kids model provides clinicians with individualized estimates of risk. The aim of this study was to externally validate the model in a large independent, multi-centre patient cohort. Methods and results A retrospective, longitudinal cohort of 421 patients diagnosed with HCM aged 1-16 years independent of the HCM Risk-Kids development and internal validation cohort was studied. Data on HCM Risk-Kids predictor variables (unexplained syncope, non-sustained ventricular tachycardia, maximal left ventricular wall thickness, left atrial diameter, and left ventricular outflow tract gradient) were collected from the time of baseline clinical evaluation. The performance of the HCM Risk-Kids model in predicting risk at 5 years was assessed. Twenty-three patients (5.4%) met the SCD end-point within 5 years, with an overall incidence rate of 2.03 per 100 patient-years [95% confidence interval (CI) 1.48-2.78]. Model validation showed a Harrell's C-index of 0.745 (95% CI 0.52-0.97) and Uno's C-index 0.714 (95% 0.58-0.85) with a calibration slope of 1.15 (95% 0.51-1.80). A 5-year predicted risk threshold of >= 6% identified 17 (73.9%) SCD events with a corresponding C-statistic of 0.702 (95% CI 0.60-0.81). Conclusions This study reports the first external validation of the HCM Risk-Kids model in a large and geographically diverse patient population. A 5-year predicted risk of >= 6% identified over 70% of events, confirming that HCM Risk-Kids provides a method for individualized risk predictions and shared decision-making in children with HCM.Peer reviewe

Tuberculosis incidence correlates with sunshine : an ecological 28-year time series study

Birmingham is the largest UK city after London, and central Birmingham has an annual tuberculosis incidence of 80 per 100,000. We examined seasonality and sunlight as drivers of tuberculosis incidence. Hours of sunshine are seasonal, sunshine exposure is necessary for the production of vitamin D by the body and vitamin D plays a role in the host response to tuberculosis. Methods: We performed an ecological study that examined tuberculosis incidence in Birmingham from Dec 1981 to Nov 2009, using publicly-available data from statutory tuberculosis notifications, and related this to the seasons and hours of sunshine (UK Meteorological Office data) using unmeasured component models. Results: There were 9,739 tuberculosis cases over the study period. There was strong evidence for seasonality, with notifications being 24.1% higher in summer than winter (p<0.001). Winter dips in sunshine correlated with peaks in tuberculosis incidence six months later (4.7% increase in incidence for each 100 hours decrease in sunshine, p<0.001). Discussion and Conclusion: A potential mechanism for these associations includes decreased vitamin D levels with consequent impaired host defence arising from reduced sunshine exposure in winter. This is the longest time series of any published study and our use of statutory notifications means this data is essentially complete. We cannot, however, exclude the possibility that another factor closely correlated with the seasons, other than sunshine, is responsible. Furthermore, exposure to sunlight depends not only on total hours of sunshine but also on multiple individual factors. Our results should therefore be considered hypothesis-generating. Confirmation of a potential causal relationship between winter vitamin D deficiency and summer peaks in tuberculosis incidence would require a randomized-controlled trial of the effect of vitamin D supplementation on future tuberculosis incidence