Highly sensitive and stable probe refractometer based on configurable plasmonic resonance with nano-modified fiber core

A dispersion model is developed to provide a generic tool for configuring plasmonic resonance spectral characteristics.The customized design of the resonance curve aiming at specific detection requirements can be achieved.According to the model,a probe-type nano-modified fiber optic configurable plasmonic resonance(NMF-CPR)sensor with tip hot spot enhancement is demonstrated for the measurement of the refractive index in the range of 1.3332-1.3432 corresponding to the low-concentration biomarker solution.The new-type sensing structure avoids excessive broadening and redshift of the resonance dip,which provides more possibilities for the surface modification of other functional nanomaterials.The tip hot spots in nanogaps between the Au layer and Au nanostars(AuNSs),the tip electric field enhancement of AuNSs,and the high carrier mobility of the WSe_(2)layer synergistically and significantly enhance the sensitivity of the sensor.Ex-perimental results show that the sensitivity and the figure of merit of the tip hot spot enhanced fiber NMF-CPR sensor can achieve up to 2995.70 nm/RIU and 25.04 RIU^(−1),respectively,which are 1.68 times and 1.29 times higher than those of the conventional fiber plasmonic resonance sensor.The results achieve good agreements with numerical simulations,demonstrate a better level compared to similar reported studies,and verify the correctness of the dispersion model.The detection resolution of the sensor reaches up to 2.00×10^(−5)RIU,which is obviously higher than that of the conventional side-polished fiber plasmonic resonance sensor.This indicates a high detection accuracy of the sensor.The dense Au layer effectively prevents the intermediate nanomaterials from shedding and chemical degradation,which enables the sensor with high stability.Furthermore,the terminal reflective sensing structure can be used as a practical probe and can allow a more convenient operation.

Flexible broadband WS_(2)/Si optical position-sensitive detector with high sensitivity and fast speed

Si-based optical position-sensitive detectors(PSDs)have stimulated the interest of researchers due to their wide range of practical applications.However,due to the rigidity and fragility of Si crystals,the applications of flexible PSDs have been limited.Therefore,we presented a flexible broadband PSD based on a WS_(2)/Si heterostructure for the first time.A scalable sputtering method was used to deposit WS_(2)thin films onto the etched ultrathin crystalline Si surface.The fabricated flexible PSD device has a broad spectral response in the wavelength range of 450-1350 nm,with a high position sensitivity of~539.8 mV·mm^(−1)and a fast response of 2.3μs,thanks to the strong light absorption,the built-in electrical field at the WS_(2)/Si interface,and facilitated transport.Furthermore,mechanical-bending tests revealed that after 200 mechanical-bending cycles,the WS_(2)/Si PSDs have excellent mechanical flexibility,stability,and durability,demonstrating the great potential in wearable PSDs with competitive performance.

Archean Basement and a Paleoproterozoic Collision Orogen in the Huoqiu Area at the Southeastern Margin of North China Craton: Evidence from Sensitive High Resolution Ion Micro-Probe U-Pb Zircon Geochronology

This paper reports sensitive high resolution ion micro-probe U-Pb zircon ages for the ＂Huoqiu Group＂ and granitoids of the Early Precambrian basement in the Huoqiu area, southeastern margin of the North China Craton. The ＂Huoqiu Group＂ is similar in rock association and metamorphism to the khondalite series, apart from it containing considerable amounts of banded iron formation. All detrital zircons from the ＂Huoqiu Group＂ meta-sedimentary rocks are 3.0 Ga and 2.75 Ga, without any 2.5 Ga and younger ones, as is commonly found in Paleoproterozoic khondalite series in other areas of the North China Craton. In the Huoqiu area, 2.75 Ga and 2.56 Ga granitoids have also been identified. This basement assemblage underwent strong metamorphism during the late Paleoproterozoic （-1.84 Ga） tectonothermal event that is widely developed in the North China Craton. Thus the formation time of the ＂Huoqiu Group＂ can be constrained between 2.75 and 1.84 Ga in terms of detrital and metamorphic zircon ages. It is considered, combined with regional data, that there may be a Paleoproterozoic collision orogen extending in a NWW-SEE direction to the southern margin of the North China Craton.

Association between preoperative high sensitive troponin I levels and cardiovascular events after hip fracture surgery in the elderly

Objective Cardiovascular complications contribute to postoperative morbidity and mortality in elderly hip fracture patients. Limited data are available regarding which preoperative risk factors predict cardiovascular course following hip fracture surgery （HFS）. We used high sensitive troponin I （hs-TnI） assays and clinical parameters to identify preoperative risk factors associated with major adverse cardiac events （MACE） in elderly hip frac^u＇e patients. Method From August 2014 to November 2016, 575 patients with hip fracture were enrolled in a retrospective, single-center registry. A total of 262 of these patients underwent HFS and hs-TnI assays. MACE was defined as postoperative all-cause deaths, heart failure （HF）, new-onset atrial fibrillation （AF）, myocardial infarction （MI） and cardiovascular re-hospitalization that occurred within 90 days postoperative. Results Of 262 HFS patients, MACE developed following HFS in 65 （24.8%）. Patients with MACE were older and had higher rates of renal insufficiency, coronary artery disease, prior HF, low left ventricular ejection fraction and use of beta blockers; higher levels of hs-Tnl and N-terminal pro-brain natriuretic peptide （NT-proBNP） and higher revised cardiac risk index. A preoperative hs-TnI≥ 6.5 ng/L was associated with high risk of postoperative HF, new-onset AF and MACE. In multivariable analysis, pre-operative independent predictors for MACE were age 〉 80 years [adjusted hazard ratio （HR）： 1.79, 95% confident interval （CI）： 1.03-3.13, P = 0.04], left ventricular ejection fraction （LVEF） 〈 50% （adjusted HR： 3.17, 95% CI： 1.47-5.82, P 〈 0.01） and hs-TnI 〉 6.5 ng/L （adjusted HR： 3.75, 95% CI： 2.09~5.17, P 〈 0.01）. Conclusion In elderly patients with hip fracture who undergo HFS, a preoperative assessment of hs-TnI may help the risk refinement of cardiovascular complications.

Highly sensitive digital optical sensor with large measurement range based on the dual-microring resonator with waveguide-coupled feedback

We propose a novel high-performance digital optical sensor based on the Mach-Zehnder interferential effect and the dual-microring resonators with the waveguide-coupled feedback. The simulation results show that the sensitivity of the sensor can be orders of magnitude higher than that of aconventional sensor, and high quality factor is not critical in it. Moreover, by optimizing the length of the feedback waveguide to be equal to the perimeter of the ring, the measurement range of the proposed sensor is twice as much as that of the conventional sensor in the weak coupling case.

Correlation of Enhancement Degree on Contrast-enhanced Ultrasound with Histopathology of Carotid Plaques and Serum High Sensitive C-Reactive Protein Levels in Patients Undergoing Carotid Endarterectomy

This study was undertaken to investigate the correlation of the enhancement degree on contrast-enhanced ultrasound(CEUS) with the histopathology of carotid plaques and the serum high sensitive C-reactive protein(hs-CRP) levels in patients undergoing carotid endarterectomy(CEA). Carotid CEUS was performed preoperatively in 115 patients who would undergo CEA, and the enhancement degree of the carotid plaques was evaluated by both the visual semiquantitative analysis and the quantitative time-intensity curve analysis. Serum hs-CRP levels were detected using the particle-enhanced immunoturbidimetric assay also before the operation. Additionally, the carotid plaque samples were subjected to histopathological examination postoperatively. The density of neovessels and the number of macrophages in the plaques were assessed by immunohistochemistry. The results showed that among the 115 patients, grade 0 plaque contrast enhancement was noted in 35 patients, grade 1 in 48 patients and grade 2 in 32 patients. The degree of plaque enhancement, the density of neovessels, the number of macrophages, and the hs-CRP levels were highest in the grade 2 patients. Correlation analysis showed that the enhancement degree of the carotid plaques was closely related to the immunohistochemical parameters of the plaques and the serum hs-CRP levels. It was suggested that the carotid plaque enhancement on CEUS can be used to evaluate the vulnerability of carotid plaques.

Relationship of High Sensitivity C-Reactive Protein with Cardiovascular, Diabetic, and Hepatic Biomarkers

Biomarkers are early predictors of various disorders, circulating level of C-reactive protein is a sensitive biomarker of systemic inflammation and may also be associated with the development of diabetic, hepatic, and cardiovascular diseases. In the present study, we aimed to investigate the association between circulating levels of high sensitive C-reactive protein (hs-CRP) and various biomarkers for hepatic, diabetic, and cardiovascular health. The retrospective analysis included 438 individuals who were tested for these panels simultaneously at Vibrant America Clinical Laboratory. The study population included free-living individuals without any preexisting clinical conditions. Among the cardiovascular markers, a positive correlation and significant association was found between high levels of hs-CRP and serum levels of triglycerides (r = 0.0964, p −0.1423, p −0.1216, p < 0.0105) with circulating levels of hs-CRP. Among all the diabetic markers, glucose (r = 0.1547, p < 0.0011) and glycated serum protein (r = 0.1725, p < 0.0003) were positively correlated with circulating hs-CRP. In the hepatic panel, AST, a transaminase that plays a vital role in amino acid metabolism, was found to have a strong positive correlation with hs-CRP (r = 0.2139, p < 0.0001). In conclusion, the results clearly show the association of hs-CRP with diabetic, hepatic, and cardiovascular risk factors indicating its central value as a key marker for several lifestyle-associated disorders.

Highly sensitive and stretchable piezoelectric strain sensor enabled wearable devices for real-time monitoring of respiratory and heartbeat simultaneously

The World Health Organization has declared COVID-19 a pandemic.The demand for devices or systems to diagnose and track COVID-19 infections noninvasively not only in hospitals but also in home settings has led to increased interest in consumer-grade wearables.A common symptom of COVID-19 is dyspnea,which may manifest as an increase in respiratory and heart rates.In this paper,a novel piezoelectric strain sensor is presented for real-time monitoring of respiratory and heartbeat signals.A highly sensitive and stretchable piezoelectric strain sensor is fabricated using a piezoelectric film with a serpentine layout.The thickness of the patterned PVDF flexible piezoelectric strain sensor is only 168μm,and the voltage sensitivity reaches 0.97 mV/με.The effective modulus is 13.5 MPa,which allows the device to fit to the skin and detect the small strain exhibited by the human body.Chest vibrations are captured by the piezoelectric sensor,which produces an electrical output voltage signal conformally mapped with respiratory–cardiac activities.The separate heart activity and respiratory signals are extracted from the mixed respiratory–cardiac signal by an empirical mode decomposition data processing algorithm.By detecting vital signals such as respiratory and heart rates,the proposed device can aid early diagnosis and monitoring of respiratory diseases such as COVID-19.

EFFECTS OF SIMVASTAIN COMBINED WITH OMEGA-3 FATTY ACIDS ON HIGH SENSITIVE C-REACTIVE PROTEIN, LIPIDEMIA, ANDFIBRINOLYSIS IN PATIENTS WITH MIXED DYSLIPIDEMIA

Objective To evaluate the effects of simvastatin combined with omega-3 fatty acids on high sensitive C-reactive protein(HsCRP), lipidemia, and fibrinolysis in coronary heart disease (CHD) and CHD risk equivalent patients with mixed dyslipi-demia. Methods A randomized, double-blind placebo controlled and parallel group trial was conducted. Patients with CHD and CHD risk equivalents with mixed dyslipidemia were treated with 10 or 20 mg simvastatin for 6-12 weeks. Following with the treatment of patients whose low-density lipoprotein cholesterol (LDL-ch) reaching goal level (< 100 mg/dL) or close to the goal (< 130 mg/dL), while triglyceride (TG) ≥200 mg/dL and < 500 mg/dL, was combined with omega-3 fatty acids (3 g/d) or a placebo for 2 months. The effects of the treatment on HsCRP, total cholesterol (TC), LDL-ch, high-density lipoprotein cholesterol (HDL-ch), TG, lipoprotein (a) [LP (a)], apolipoprotein A1 (apoA1), apolipoprotein B (apoB), plasminogen activator inhibitor-1 (PAI-1), and tissue plasminogen activator (tPA) were investigated. Forty patients finished the study with each group consisting of twenty patients. Results (1) There were significant reductions of HsCRP, TG, TC, and TC/HDL-ch, which decreased by 2.16 ±2.77 mg/L (38.5%), 94.0 ±65.4 mg/dL (31.1%), 13.3 ±22.3 mg/dL (6.3%), 0.78 ±1.60 respectively in the omega-3 fatty acids group (P< 0.01, < 0.001, < 0.05, < 0.05) compared to the baseline. HsCRP and triglyceride reduction were more significant in omega-3 fatty acids group compared to the placebo group (P=0.021 and 0.011 respectively). (2) In the omega-3 fatty acids group, the values and percentage of TG reduction had a significantly positive relation with HsCRP reduction (r=0.51 and 0.45, P=0.021 and 0.047 respectively). Conclusion In CHD and CHD risk equivalent patients with mixed dyslipidemia, dyslipidemia’s therapeutic effect using simvastatin and omega-3 fatty acids may result from not only the combination of lipid adjustment, but also enhancement of their own nonlipid influences.

Evaluation of the Key Mechanism Justifying the High Sensitivity of Obese Rodents to Treptozotocin (STZ)

Diabetes mellitus (DM) is a metabolic disease caused by the absence or dysfunction of insulin;a hormone secreted by the pancreatic beta cell (β-cell) whenever blood glucose exceeds the normal physiological value. The long-term effects of the disease on the body’s organs are one of the leading causes of death in the world. To alleviate this global burden of DM, a number of studies have been conducted to lower blood glucose levels in patients. For genetic and ethical reasons, humans are far from being appropriate subjects in such investigations and the use of animal models has therefore been the way forward. Streptozotocin (STZ) is a glucosamine-nitrosourea compound that selectively destroys β-cells and has been widely used to induce Type I diabetes in several animal species. Recent literature has shown that a non-diabetic dose of STZ, combined with a high-fat diet (HFD), can mimic Type II diabetes. Yet, researchers seldom provide data to corroborate the high sensitivity of STZ on these animal models. In addition, there are few reports of potentially fatal effects of the use of STZ as a supplement in obese HFD animals when attempting to induce Type II diabetes. The present review article highlights the parameters that could be at the origin of the extreme sensitivity and vulnerability of obese animals to STZ.

Tunable and highly sensitive temperature sensor based on graphene photonic crystal fiber

Optical fiber temperature sensors have been widely employed in enormous areas ranging from electric power industry,medical treatment,ocean dynamics to aerospace.Recently,graphene optical fiber temperature sensors attract tremendous attention for their merits of simple structure and direct power detecting ability.However,these sensors based on transfer techniques still have limitations in the relatively low sensitivity or distortion of the transmission characteristics,due to the unsuitable Fermi level of graphene and the destruction of fiber structure,respectively.Here,we propose a tunable and highly sensitive temperature sensor based on graphene photonic crystal fiber(Gr-PCF)with the non-destructive integration of graphene into the holes of PCF.This hybrid structure promises the intact fiber structure and transmission mode,which efficiently enhances the temperature detection ability of graphene.From our simulation,we find that the temperature sensitivity can be electrically tuned over four orders of magnitude and achieve up to~3.34×10^(-3) dB/(cm·℃)when the graphene Fermi level is~35 meV higher than half the incident photon energy.Additionally,this sensitivity can be further improved by~10 times through optimizing the PCF structure(such as the fiber hole diameter)to enhance the light–matter interaction.Our results provide a new way for the design of the highly sensitive temperature sensors and broaden applications in all-fiber optoelectronic devices.

HIGHLY SENSITIVE SPECTROPHOTOMETRY OF NIOBIUM

In pH 2.0-3.0 medium,niobium(v)forms molybdoniobic acid with sodium molybdate.A spectrophotometric method has been developed for the determination of niobium based on the formation of ion-associate compound of molybdoniobate with butyl Rhodamine B in aqueous solution in the presence of polyvinyl alcohol and 0.4-0.7 mol/L H_2SO_4.The molar absorptivity is 7.5×10~5 L.mol^(-1).cm^(-1) for niobium at 585 nm.

Highly Sensitive Detection of Deoxyribonucleic Acid Hybridization Using Au-Gated AlInN/GaN High Electron Mobility Transistor-Based Sensors

Gallium nitride- （GaN） based high electron mobility transistors （HEMTs） provide a good platform for biological detection. In this work, both Au-gated AlInN/GaN HEMT and AlGaN/GaN HEMT biosensors are fabricated for the detection of deoxyribonucleic acid （DNA） hybridization. The Au-gated AIInN/GaN HEMT biosensor exhibits higher sensitivity in comparison with the AlGaN/GaN HEMT biosensor. For the former, the drain-source current （VDS = 0.5 V） shows a clear decrease of 69μA upon the introduction of 1μmolL^-1 （μM） complimentary DNA to the probe DNA at the sensor area, while for the latter it is only 38 μA. This current reduction is a notable indication of the hybridization. The high sensitivity can be attributed to the thinner barrier of the AlInN/GaN heterostructure, which makes the two-dimensional electron gas channel more susceptible to a slight change of the surface charge.

Highly Sensitive Fiber-Optic Faraday-Effect Magnetic Field Sensor Based on Yttrium Iron Garnet

The principle and performance of a fiber-optic Faraday-effect magnetic-field sensor based on an yttrium iron garnet (YIG) and two flux concentrations are described. A single polarization-maintaining optical fiber links the sensor head to the source and detection system, in which the technique of phase shift cancellation is used to cancel the phase shift that accumulatein the optical fiber. Flux concentrators were exploited to enhance the YIG crystal magneto-optic sensitivity .The sensor system exhibited a noise-equivalent field of 8 pT/√Hz and a 3 dB bandwidth of ～10 MHz.

The Influence of Regular Hemodialysis on the Highly Sensitive Troponin-I Level in Children without Any Symptoms

Backgrounds: Cardiovascular diseases are still the prominent cause of death in cases of end-stage renal disease, cardiac troponin I (cTnI) can be used for detecting cardiac involvement in asymptomatic cases of end-stage renal disease on hemodialysis. Aim: Determine the direct cardiac consequence of dialysis treatments in children on hemodialysis by measuring high-sensitive troponin-I as a marker of myocardial injury. Subjects and Methods: This case-control study included thirty children with end-stage renal disease on regular hemodialysis;the study group was selected from the nephrology hemodialysis unit of Al-Zahraa Hospital, Al-Azhar University. Another group of thirty healthy children matches age and sex with the patient’s group as a control. Highly Sensitive cTnI (hsTnI) was measured pre and post hemodialysis with a sensitive assay;moreover, ECG, lipid profile including cholesterol, triglyceride, low and high-density lipoprotein (HDL) in the same line with routine investigations for those patients, we used bioimpedance for dry weight assessment in the hemodialysis (HD) group. Results: Children on (HD) have a significantly higher (hsTnI) pre-dialysis (0.250 ± 0.069 ng/ml) compared to post-dialysis (0.187 ± 0.004 ng/ml) with (p, 0.001). With no significant difference between post HD (0.187 ± 0.004 ng/ml) and the control group (0.189 ± 0.005) with (p, 0.090). cTnI is detected in (73.3%) of children pre-dialysis above the cut-off value compared to (3.31%) had a high-level post-dialysis. cTnI is positively correlated with systolic, diastolic blood pressure and heart rate with (r. 0.333, p, 0.001: r. 0.343, p, 0.001: r. 0.276, p, 0.033) respectively and (hsTnI) is negatively correlated with Hb and HDL (r. -0.333, p, 0.009: r. 0.324, p, 0.011). Meanwhile (hsTnI) is positively correlated with serum urea, creatinine, ph, PTH, serum ferritin and positively correlated with QT interval and QTC. Conclusion: cTnI levels rise significantly before hemodialysis, so those patients are exposed to silent myocardial injury pre HD, and fortunately, it is not persistent after hemodialysis except for a few of them had a high level. We strongly advised not to delay dialysis appointments;the nephrology team should aggressively treat those patients to prevent further myocardial damage.

HIGHLY SENSITIVE SPECTROPHOTOMETRY OF NIOBIUM

In pH2.0-3.0,niobium(V)forms molybdonlobic acid with sodium molybdate.A spectrophotometric method has been developed for the deter- mination of niobium based on the formation of ion-associate compound of molybdoniobate with Butyl Rhodamine B in aqueous solution in the presence of polyvinyl alcohol and 0.4-0.7 mol/L H_2SO_4.The maximum absorption of ion-associate compound exhioits at 85 nm and the molar absorptivity is 7.5×1.0~5 L.mol^(-1).cm^(-1)for niobium.The new method has been applied to the determination of microamounts niobium in silicate rock,when niobium content is at the level of 8×10^(-3)%,with the relative standard deviation of about 3%.

A Photonic Crystal Fiber Based Asymmetric Slotted Structured Highly Sensitive Refractive Index Plasmonic Biosensor

Surface plasmon resonance (SPR) sensors have grown in popularity owing to their sensitivity, precision, and capacity for a variety of applications, including detection, monitoring, and sensing, among others. Sensitivity and resolution are two areas where this technology has room for development. A plasmonic biosensor based on an asymmetric slotted PCF structure with extremely high sensitivity has been described and theoretically investigated. This high performance sensor is constructed and completely characterized using finite element method in COMSOL Multiphysics software environment. Sensitivity and resolution are analyzed as performance parameters for the proposed sensor. Numerical simulation exhibits the maximum wavelength-sensitivity of 1100 nm/RIU with 9.09 × 10-6 RIU resolution in the broad measurement range of refractive index from 1.30 to 1.44. A polarization controller can be used to fine-tune this extremely sensitive and wide-ranging refractive index sensor to fulfil a variety of practical needs. This is performed with the consideration of the variation in the refractive index (RI) of the analyte channels. In comparison with earlier PCF-based sensors, the fiber design structure is basic, symmetrical, simple to produce, and cost-effective. Because of the asymmetric air holes and higher sensitivities of the refractive index detector, it is possible to identify biomolecules, biochemicals and other analytes.

Clinical application of neutrophil/lymphocyte ratio combined with high sensitive C reactive protein in evaluation of community acquired pneumonia

Objective:To explore the application value of neutrophil/lymphocyte ratio (NLR) combined with high sensitive C reactive protein (hs-CRP) in the evaluation of community acquired pneumonia (CAP). Methods:From November 2015 to October 2016, 58 cases of CAP patients admitted in our department were selected as research objects and were divided into low risk group and high risk group according to the PSI score and CURB-65 standard for evaluation. They were divided into improved group (48 cases) and death group (10 cases) according to prognosis. Hs-CRP was determined by immunoturbidimetric assay, procalcitonin (PCT) by immunofluorescence, NLR by count method of laser scattering, and white blood (WBC) was counted. The differences in WBC, PCT, NLR and hs-CRP between different risk groups were compared, and the correlation was evaluated using Spearman's rank correlation analysis method. The changes in indexes were observed in the improved and death cases. Results:The high risk group had higher NLR, PCT and hs-CRP than low risk group (P<0.05), while no significant difference was found in WBC (P>0.05). No correlation was found between NLR and WBC, while a strong correlation was found between hs-CRP and PCT. The WBC, PCT, NLR and hs-CRP levels were significantly lower in the improved group than the death group (P<0.05). Conclusions:NLR combined with hs-CRP, WBC, and PCT has a good assessment of the severity of CAR, and high levels of NLR, hs-CRP, WBC, and PCT predict the severity of the disease and poor prognosis.

Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): I. Mathematical Framework

This work presents the “nth-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “nth-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the nth-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the nth-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the nth-FASAM-N methodology becomes identical to the extant nth CASAM-N (“nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the nth-FASAM-N and the nth-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the nth-FASAM-N and the nth-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.

Introducing the nth-Order Features Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-FASAM-N): II. Illustrative Example

This work highlights the unparalleled efficiency of the “nth-Order Function/ Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (nth-FASAM-N) by considering the well-known Nordheim-Fuchs reactor dynamics/safety model. This model describes a short-time self-limiting power excursion in a nuclear reactor system having a negative temperature coefficient in which a large amount of reactivity is suddenly inserted, either intentionally or by accident. This nonlinear paradigm model is sufficiently complex to model realistically self-limiting power excursions for short times yet admits closed-form exact expressions for the time-dependent neutron flux, temperature distribution and energy released during the transient power burst. The nth-FASAM-N methodology is compared to the extant “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (nth-CASAM-N) showing that: (i) the 1st-FASAM-N and the 1st-CASAM-N methodologies are equally efficient for computing the first-order sensitivities;each methodology requires a single large-scale computation for solving the “First-Level Adjoint Sensitivity System” (1st-LASS);(ii) the 2nd-FASAM-N methodology is considerably more efficient than the 2nd-CASAM-N methodology for computing the second-order sensitivities since the number of feature-functions is much smaller than the number of primary parameters;specifically for the Nordheim-Fuchs model, the 2nd-FASAM-N methodology requires 2 large-scale computations to obtain all of the exact expressions of the 28 distinct second-order response sensitivities with respect to the model parameters while the 2nd-CASAM-N methodology requires 7 large-scale computations for obtaining these 28 second-order sensitivities;(iii) the 3rd-FASAM-N methodology is even more efficient than the 3rd-CASAM-N methodology: only 2 large-scale computations are needed to obtain the exact expressions of the 84 distinct third-order response sensitivities with respect to the Nordheim-Fuchs model’s parameters when applying the 3rd-FASAM-N methodology, while the application of the 3rd-CASAM-N methodology requires at least 22 large-scale computations for computing the same 84 distinct third-order sensitivities. Together, the nth-FASAM-N and the nth-CASAM-N methodologies are the most practical methodologies for computing response sensitivities of any order comprehensively and accurately, overcoming the curse of dimensionality in sensitivity analysis.