Nonlinear Least-squares Curve Fitting Research Articles

Characteristic-constrained accelerating MR T1rho mapping with blockwise infimal convolution of matrix elastic-net regularization.

Magnetic resonance parameter mapping (MRPM) plays an important role in clinical applications and biomedical researches. However, the acceleration of MRPM remains a major challenge for achieving furtherimprovements. In this work, a new undersampled k-space based joint multi-contrast image reconstruction approach named CC-IC-LMEN is proposed for accelerating MR T1rhomapping. The reconstruction formulation of the proposed CC-IC-LMEN method imposes a blockwise low-rank assumption on the characteristic-image series (c-p space) and utilizes infimal convolution (IC) to exploit and balance the generalized low-rank properties in low-and high-order c-p spaces, thereby improving the accuracy. In addition, matrix elastic-net (MEN) regularization based on the nuclear and Frobenius norms is incorporated to obtain stable and exact solutions in cases with large accelerations and noisy observations. This formulation results in a minimization problem, that can be effectively solved using a numerical algorithm based on the alternating direction method of multipliers (ADMM). Finally, T1rho maps are then generated according to the reconstructed images using nonlinear least-squares (NLSQ) curve fitting with an established relaxometrymodel. The relative l2 -norm error (RLNE) and structural similarity (SSIM) in the regions of interest (ROI) show that the CC-IC-LMEN approach is more accurate than other competing methods even in situations with heavy undersampling or noisyobservation. Our proposed CC-IC-LMEN method provides accurate and robust solutions for accelerated MR T1rhomapping.

A major outbreak of the COVID-19 on the Diamond Princess cruise ship: Estimation of the basic reproduction number.

The COVID-19 pandemic, which broke out in Wuhan, China, in 2019, was declared an international public health emergency by the World Health Organization on January 31, 2020. The outbreak on the Diamond Princess cruise ship had appeared first as a cluster infection outside China during the early pandemic. The incident occurred on February 1, 2020, involved an 80-year-old Hong Kong man who was diagnosed with COVID-19. The cruise ship docked in Yokohama, Japan, for 14 days of onboard quarantine; however, cluster infection outbroke rapidly. We constructed a SIR mathematical model and conducted an epidemiological study of the COVID-19 outbreak on the Diamond Princess cruise ship, covering the period from February 5 (start of quarantine) to February 20 (completion of 14-day quarantine). We estimated the basic reproduction number (R 0 ) using a novel method of nonlinear least-squares curve fitting under Microsoft Excel Solver. The 95% confidence interval (CI) values were estimated by the jackknife procedures. Six hundred thirty-four (17.1%) cases were diagnosed in a total population of 3711 cruise passengers, and 328 (51.7%) cases were asymptomatic. As of April 24, 2020, 712 cases had been diagnosed and 14 (1.96%) deaths had occurred. The R 0 with 95% CI of the COVID-19 outbreak was 3.04 (2.72-3.36). Without an evacuation plan for passengers and crew, we estimated the total number of cumulative cases would reach 3498 (CI, 3464-3541). If the R 0 value was reduced by 25% and 50%, the cumulative cases would be reduced to 3161 (CI, 3087-3254) and 967 (CI, 729-1379), respectively. The abovementioned R 0 value was estimated from the original Wuhan strain. Cruise conditions would accelerate the spread of infectious diseases and were not suitable for onboard quarantine. Early evacuation and isolation of all passengers and crew members would reduce the R 0 value and avoid further infections.

Estimation of the Output Characteristic of a Photovoltaic Generator under Power Curtailment and Considering Converter Losses

Power curtailment methods contribute to the frequency stability of power systems with a high share of photovoltaic generation. This paper focuses on an online strategy that estimates the output characteristic of a photovoltaic generator while operating in power curtailment mode by using voltage and current measurements and the nonlinear least-squares curve-fitting. In contrast to previously reported methods, this work introduces an improvement consisting of the estimation of the power losses of the electronic converter that connects the photovoltaic panel with the grid. Thus, the impact of a mismatch between the dc-side and the ac-side is reduced. The procedure is tested at different power levels and with fluctuations of irradiance and temperature. The results show that the converter efficiency, expressed as an exponential function with two quadratic equations, is associated with irradiance and temperature. It is also found that the two-stage converter efficiency is mainly affected by the irradiance level when the photovoltaic system operates on the left side of the power-voltage characteristic. In contrast, the temperature level influences the converter efficiency significantly when working on the right side of the maximum power point. The estimated efficiency curves can improve the accuracy of the power curtailment method and can be used for designing the two-stage converter. The effectiveness of the proposed power curtailment method has been tested in a two-stage photovoltaic system through MATLAB/Simulink.

A novel kinetic model for a cocoa waste fermentation to ethanol reaction and its experimental validation

A non-segregated kinetic model is proposed to describe a fermentation process of agro-industrial residues derived via cocoa (mucilage juice) by Pichia kudriavzevii. The novel proposed hybrid model is based on a multiple coupling reaction mechanisms (structured) to describe the kinetics of substrate consumption, biomass, carbon dioxide, and ethanol, coupled to an unstructured model for the activity enzyme. The parameters of the kinetic model are estimated by non-linear least-squares curve fitting using the Marquardt-Levenberg algorithm. In addition, numerical simulations were compared with the experimental data via residual graphs. The effectiveness of the model was statistically evaluated using dimensionless efficiency coefficients under different initial conditions. A global sensitivity analysis was applied (Fisher's information matrix). The experimental results of the batch reactor showed a maximum ethanol concentration of 29 g/L, with a yield of 0.48 g-ethanol/g-glucose and a productivity of 0.30 g/L h. The method determined that the cell formation coefficient and the specific substrate consumption rate ( and ) directly influence most of the states of our system. The proposed scheme is particularly suitable to assist in the rational design of cell factory properties or fermentation processes because it can represent the complex biochemistry in more detail and under different initial experimental conditions; the above reveals that the generated model is robust and can be considered for control and optimization purposes.

Characterising the linear viscoelastic behaviour of an injection moulding grade polypropylene polymer

The linear viscoelastic behaviour of an injection moulding grade polypropylene is studied using theoretical and computational methods. Polypropylene has a variety of engineering applications as a component. However, it commonly exhibits viscoelastic deformations. This paper analyses the creep and recovery responses of the BJ368MO polypropylene copolymer using the Burgers and generalised Maxwell models. Within the linear viscoelastic regime, an experimental creep strain at 20 text{MPa} is used to determine the rheological constants of the models. These constants (springs and dashpots) are determined using a nonlinear least-squares curve fitting of the experimental creep. Then they are used to predict the creep and recovery responses of the polymer at three different stresses, 10 text{MPa}, 12.5 text{MPa} and 15 text{MPa}. The experiments are made using tensile specimens designed according to the ASTM D638-14standard. The theoretical evaluations are made using the creep and recovery equations derived from their constitutive. Whereas COMSOL Multiphysics software is used during the finite element (FE) analyses. The results of the theoretical and FE calculations are verified using creep and recovery experiments. Based on the validation analyses, both viscoelastic models showed lower deviations from the experimental results when a computational approach is used. In addition, the viscoelastic models are compared by evaluating the residuals of the creep and recovery strain predictions. The theoretical analyses showed better predictions at 12.5 text{MPa} and 15 text{MPa} stresses when the generalised Maxwell model is used. However, the improvements are attributed to the recovery predictions. When FE is used, the Burgers model showed lower mean absolute percentage errors (MAPEs) in all creep and recovery predictions. The model has a minimum of 6.37% error at the 10 text{MPa} stress and a maximum of 8.23% error at the 15 text{MPa}. By comparison, the generalised Maxwell model showed a minimum of 9.24% error at 12.5 text{MPa} and a maximum of 12.8% error at 15 text{MPa} stresses. The novelty of this paper is on predicting the creep and recovery behaviour of the polymer using the FE and theoretical approaches in the linear viscoelastic regime. The findings suggest that the FE analyses using the Burgers viscoelastic material model provide better predictions, with all calculated errors falling below 10%.

Optimal Control Applied to a Fractional-Order Foot-and-Mouth Disease Model

In this paper, we propose a nonlinear fractional-order model in order to explain and understand the outbreaks of foot-and-mouth disease. The proposed model rely on the Caputo operator. We computed the basic reproduction number and demonstrated that it is an important metric for extinction and persistence of the disease. Utilizing reported foot-and-mouth disease data for Zimbabwe and the nonlinear least-squares curve fitting method we estimated the model parameters. Meanwhile, we performed an optimal control study on the use of animal vaccination and culling of infectious animals as disease control measures against foot-and-mouth disease. Our findings showed combinations of optimal vaccination and culling rates that could lead to the effective management of the disease.

Caputo SIR model for COVID-19 under optimized fractional order

Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam–Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case (nu =1). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.

Effects of Pump-Pulse Width and Temperature on Experimental Brillouin Gain Spectrum Obtained from Brillouin Optical Time-Domain Analysis Sensors

In this paper, the characteristics of Brillouin gain spectrum (BGS) obtained from a Brillouin optical time-domain analysis (BOTDA) sensor are investigated and analyzed experimentally. The measured BGSs obtained for various pump-pulse widths and temperatures are fitted with different spectrum profiles using nonlinear least-squares curve fitting technique. The fitting performances of used profiles are presented and analyzed. Based on such performances, the proper spectrum profile to be used in the fitting process is determined and used to extract key parameters of the measured BGSs accurately. The variations of such key parameters with pump-pulse widths and temperatures are also investigated and analyzed. The results reveal that pump-pulse widths and temperatures have significant effects on the extracted key parameters of the measured BGSs obtained from BOTDA sensors.
 Bangladesh Journal of Physics, 27(1), 69-80, June 2020

A Multi-Layer Perceptron Network for Perfusion Parameter Estimation in DCE-MRI Studies of the Healthy Kidney

Background: Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an imaging technique which helps in visualizing and quantifying perfusion—one of the most important indicators of an organ’s state. This paper focuses on perfusion and filtration in the kidney, whose performance directly influences versatile functions of the body. In clinical practice, kidney function is assessed by measuring glomerular filtration rate (GFR). Estimating GFR based on DCE-MRI data requires the application of an organ-specific pharmacokinetic (PK) model. However, determination of the model parameters, and thus the characterization of GFR, is sensitive to determination of the arterial input function (AIF) and the initial choice of parameter values. Methods: This paper proposes a multi-layer perceptron network for PK model parameter determination, in order to overcome the limitations of the traditional model’s optimization techniques based on non-linear least-squares curve-fitting. As a reference method, we applied the trust-region reflective algorithm to numerically optimize the model. The effectiveness of the proposed approach was tested for 20 data sets, collected for 10 healthy volunteers whose image-derived GFR scores were compared with ground-truth blood test values. Results: The achieved mean difference between the image-derived and ground-truth GFR values was 2.35 mL/min/1.73 m2, which is comparable to the result obtained for the reference estimation method (−5.80 mL/min/1.73 m2). Conclusions: Neural networks are a feasible alternative to the least-squares curve-fitting algorithm, ensuring agreement with ground-truth measurements at a comparable level. The advantages of using a neural network are twofold. Firstly, it can estimate a GFR value without the need to determine the AIF for each individual patient. Secondly, a reliable estimate can be obtained, without the need to manually set up either the initial parameter values or the constraints thereof.

Fractional modeling for the spread of Hookworm infection under Caputo operator

Abstract It is estimated that, about one billion people mostly from Asia, Sub-Saharan Africa and Latin America are infected with the Hookworm infection. In this paper, we developed and analyzed a model for the transmission dynamics of Hookworm infection in a human population using Caputo fractional order differential operator. Under Caputo operator, existence and uniqueness for the solutions of the new Hookworm infection model have been analyzed using fixed point theorems. Parameters of the model are estimated with the help of real statistics available for the Hookworm infection from a city of Ghana and the best fit is obtained under the nonlinear least-squares curve fitting technique. Further analysis of the proposed model shows that the disease free (infection-absent) equilibrium is locally asymptotically stable whenever a certain reproduction number R 0 1 and the endemic (infection-present) equilibrium point is globally asymptotically stable whenever R 0 1 and unstable if R 0 > 1 . Using forward normalized sensitivity index, the most sensitive parameters are identified that are essential for control of the infection and we obtained different types of simulations for the proposed Hookworm transmission system with the best fitted fractional order parameter (χ). The modelling results show that the chemotherapy treatment, awareness and improvement of personal hygiene are the best measures to be taken for control of the Hookworm infection among vulnerable community.

Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system

Abstract Various infectious diseases primarily contain the characteristics of memory and non-locality. Keeping this in view; we have, in the present paper, proposed a new epidemiological system for the measles epidemic via Caputo fractional order operator which is not only a non-local operator but also contains all characteristics concerned with memory of the epidemic. The proposed system is autonomous in nature which has been made physically meaningful by dimensional homogeneity among the fractional order Caputo derivative and the biological parameters used in the system. Caputo fractional order parameter “τ” and the disease transmission rate “β” are fitted with nonlinear least-squares curve fitting technique while using real confirmed measles incidence cases for May-December, 2018 in Pakistan as reported by World Health Organization (WHO). Coming to mathematical analysis, the system is found to have unique solution under fixed point theory with biologically feasible region which is shown as positively invariant. Steady-states are determined to be locally asymptotically stable under different conditions on the basic reproduction number whereas the least and the most influential parameters for the system are computed via forward sensitivity index analysis. Finally, the Caputo system is simulated using Adams technique devised for finding approximate solutions of fractional Caputo ordinary differential equations. Comparative analysis is carried out and effects of different biological parameters on dynamics and transmission of the measles epidemic have been thoroughly investigated.

The effect of different inorganic anions on mineralization of acrylic acid in wet air oxidation.

Wet Air Oxidation (WAO) process is being developed as a very promising technique for efficient removal of high-concentration organic pollutants. However, because of the technical constraints, many chemical wastewater contain inorganic anions (e.g., Cl-, SO42-, PO43- and NO3-). These inorganic salts can cause equipment corrosion and also affect WAO reactivity. But very limited studies of the effect of inorganic anions on WAO in chemical wastewater have been performed. Here we for the first time intensively investigate the effect of different inorganic anions on kinetics and pathways of WAO reaction, acrylic acid was selected as substrate. We used a nonlinear least-squares curve fitting method using Matlab 2014® to obtain the kinetic model. Importantly, it was demonstrated that this proposed kinetic model represented the experimental data well, and acetic acid was the only residual short-chain carboxylic acid. Moreover, the higher concentration anions the higher selectivity of WAO of CO2 by acrylic acid. And the selectivity order of WAO to acetic acid is PO43->NO3->Cl->SO42- at low concentration (100mmolL-1). Finally, the theory calculation disclosed the feasibility of the reactions between these anions and acrylic acid, calculation results revealed that atoms 1#, 7# and 8# have the strongest chargeability and are more vulnerable to oxidant attack because of their high charge density. And the Total Organic Carbon (TOC) removal was positively correlated with the electronegativity of the central atom of oxidizing acid.

Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan

Abstract Epidemics have memory characteristics and the deterministic systems in mathematical epidemiology based upon ordinary differential equations are the most suitable tools when modeled under differential operators possessing such memory effects. This paper proposes a new four compartmental based system under the Atangana–Baleanu–Caputo (ABC) fractional order operator for measles epidemic. The mutually exclusive compartments containing susceptible, exposed, infectious and recovered individuals are fractionalyzed with ABC operator while balancing dimension for each parameter of the system. The real measles monthly incidence data of Pakistan from May-December, 2018 reported by WHO is used for parameter estimation thereby getting fitted values for transmission coefficient rate β and the fractional order parameter α via nonlinear least-squares curve fitting technique. The error norm obtained in the ABC case is about 50% smaller than the classical case, that is, when α = 1 . Fixed point theory proves existence of the unique solution for the fractional order measles system with positive invariant region. Stability analysis of the fractional system shows that both measles-free and endemic equilibria are locally asymptotically stable whenever the basic reproductive number R 0 is less and greater than unity, respectively. Later, the least (λ) and the most (α) sensitive parameters are determined using the normalized sensitivity indices for R 0 . Numerical simulations for the classical and fractional measles epidemiological systems illustrate the better fit for the real data about the infected individuals with the solution obtained via fractional order ABC operator. Various values of the biological parameters are taken to observe their effects on the proposed fractional system thereby suggesting the reduction in the contact rate of measles infected individuals with susceptible population.

Characterization of Material Properties Based on Inverse Finite Element Modelling

This paper describes a new approach that can be used to determine the mechanical properties of unknown materials and complex material systems. The approach uses inverse finite element modelling (FEM) accompanied with a designed algorithm to obtain the modulus of elasticity, yield stress and strain hardening material constants of an isotropic hardening material model, as well as the material constants of the Drucker–Prager material model (modulus of elasticity, cap yield stress and angle of friction). The algorithm automatically feeds the input material properties data to finite element software and automatically runs simulations to establish a convergence between the numerical loading–unloading curve and the target data obtained from continuous indentation tests using common indenter geometries. A further module was developed to optimise convergence using an inverse FEM analysis interfaced with a non-linear MATLAB algorithm. A sensitivity analysis determined that the dual spherical and Berkovich (S&B) approach delivered better results than other dual indentation methods such as Berkovich and Vickers (B&V) and Vickers and spherical (V&S). It was found that better convergence values can be achieved despite a large variation in the starting parameter values and/or material constitutive model and such behaviour reflects the uniqueness of the dual S&B indentation in predicting complex material systems. The study has shown that a robust optimization method based on a non-linear least-squares curve fitting function (LSQNONLIN) within MATLAB and ABAQUS can be used to accurately predict a unique set of elastic plastic material properties and Drucker–Prager material properties. This is of benefit to the scientific investigation of properties of new materials or obtaining the material properties at different locations of a part which may be not be similar because of manufacturing processes (e.g., different heating and cooling rates at different locations).

An Open-Source, Cross-Platform Resource for Nonlinear Least-Squares Curve Fitting

The quantitative evaluation of experimental data and their graphical presentation are integral to teaching and research in chemistry and the life sciences. Data are commonly fitted to physical models, which in all but the simplest cases are expressed as nonlinear mathematical functions. To facilitate data evaluation in both teaching and research contexts, the Fit-o-mat program, implemented in Python, offers versatile nonlinear least-squares curve fitting through a graphical user interface. Fit-o-mat supports near-arbitrary fitting functions, including numerical and discontinuous ones, produces vectorized graphics, runs on different operating systems, and is free of charge, thus promoting the adoption of the program by students and instructors in the classroom and beyond. An embedded tutorial mode facilitates integration of Fit-o-mat into teaching curricula at the undergraduate and graduate levels.

Synthesis and Cell Interaction of Statistical l-Arginine-Glycine-l-Aspartic Acid Terpolypeptides.

Copolymerizations and terpolymerizations of N-carboxyanhydrides (NCAs) of glycine (Gly), Nδ-carbobenzyloxy-l-ornithine (Z-Orn), and β-benzyl-l-aspartate (Bz-Asp) were investigated. In situ 1H NMR spectroscopy was used to monitor individual comonomer consumptions during binary and ternary copolymerizations. The six relevant reactivity ratios were determined from copolymerizations of the NCAs of amino acids via nonlinear least-squares curve fitting. The reactivity ratios were subsequently used to maximize the occurrence of the Asp-Gly-Orn ( DGR') sequence in the terpolymers. Terpolymers with variable probability of occurrence of DGR' were prepared in the lab. Subsequently, the ornithine residues on the terpolymers were converted to l-arginine (R) residues via guanidination reaction after removal of the protecting groups. The resulting DGR terpolymers translate to traditional peptides and proteins with variable RGD content, due to the convention in nomenclature that peptides are depicted from N- to C-terminus, whereas the NCA ring-opening polymerization is conducted from C- to N-terminus. The l-arginine containing terpolymers were evaluated for cell interaction, where it was found that neuronal cells display enhanced adhesion and process formation when plated in the presence of statistical DGR terpolymers.

19F-nuclear magnetic resonance spectroscopy as a tool to investigate host-guest complexation of some antidepressant drugs with natural and modified cyclodextrins

Purpose: 19 F-Nuclear magnetic resonance spectroscopy ( 19 F-NMR) was used to study host-guest complexation of three fluorine containing antidepressant drugs, viz, fluoxetine hydrochloride, citalopram hydrobromide and fluvoxamine maleate, with various cyclodextrins (CD), including α-, β-cyclodextrin, methylated α-cyclodextrin (M-α-CD), diamino derivative of methylated α-cyclodextrin, (DAM-α-CD) and tetramino derivative of methylated α-cyclodextrin (TAM-α-CD). Methods: Using the mole ratio method, a 1:1 stoichiometry was determined for the resulting inclusion complexes. 19 F chemical shifts were used to determine the formation constant of the complexes. Experiments were performed with solutions containing 0.001 M drug and various concentrations of CDs. NMR data were plotted as 19 F chemical shift versus CD/drug mole ratio, and fitted using the nonlinear least-squares curve fitting program, KINFIT, to obtain the formation constant of CD-drug complex. Molecular modeling (MM) calculations were used to predict the geometry of the complex of fluvoxamine and β-CD. Molecular modeling studies were performed in vacuum phase, employing empirical force fields and semi-empirical quantum theory using AM1 Hamiltonian. Results: Complex formation caused separation of the fluorine peaks that can be assigned to the two enantiomers of fluoxetine hydrochloride. Molecular modeling data suggest that fluvoxamine/β-CD inclusion complexes have a 1:1 stoichiometry and that the CF3-substituted ring of fluvoxamine is embedded in the cavity of β-CD, indicating a good agreement between molecular modeling calculation and experimental data (NMR data). Conclusion: One-dimensional 19 F-NMR is a fast and convenient method for the determination of complex stoichiometry and complexation constants of natural and modified CDs and fluorinated drugs. Keywords: Antidepressant drugs, Cyclodextrins, Complexation, Inclusion complex, Formation constant, 19 F-NMR

Spectroscopic line parameters of 12CH4 for atmospheric composition retrievals in the 4300–4500 cm−1 region

Due to the importance of methane as a trace atmospheric gas and a greenhouse gas, we have carried out a precise line-shape study to obtain the CH4–CH4 and CH4–air half-width coefficients, CH4–CH4 and CH4–air shift coefficients and off-diagonal relaxation matrix element coefficients for methane transitions in the spectral range known as the “methane Octad”. In addition, the associated temperature dependences of these coefficients have been measured in the 4300–4500cm−1 region of the Octad. The high signal to noise ratio spectra of pure methane and of dilute mixtures of methane in dry air with high resolution have been recorded at temperatures from 148K to room temperature using the Bruker IFS 125 HR Fourier transform spectrometer (FTS) at the Jet Propulsion Laboratory, Pasadena, California. The analysis of spectra was done using a multispectrum non-linear least-squares curve fitting technique. Theoretical calculations have been performed and the results are compared with the previously published line positions, intensities and with the line parameters available in the GEISA and HITRAN2012 databases.

Effects of glutathione, l-cysteine, and l-methionine on the kinetics and mechanism of the peroxyoxalate–rubrene–H2O2 chemiluminescence system

The quenching effect of glutathione, l-cysteine, and l-methionine on the strong chemiluminescence (CL) intensity of bis(2,4,6-trichlorophenyl)oxalate (TCPO)–H2O2 in the presence of rubrene (5,6,11,12-tetraphenylnaphthacene) as a fluorescer was investigated. Kinetic parameters for the peroxyoxalate chemiluminescence (PO–CL) including the intensity at maximum CL, time at maximum intensity, total light yield, theoretical maximum level of intensity and pseudo-first order rate constants for the rise and fall of the CL burst (k r and k f ) were also calculated using the pooled intermediate model by a computerized non-linear least-squares curve fitting program (KINFIT). These systems resulted in Stern–Volmer plots in the quencher concentration range of 2.5 × 10−5 to 2.25 × 10−4 M, with k Q values of 2.5 × 104, 2.1 × 104 and 1.1 × 104 M−1, for glutathione, l-cysteine, and l-metionine, in order.

Model Membrane-Free Li-S Batteries for Enhanced Performance and Cycle Life.

The success of the rechargeable Li-S cell is limited in part by the dissolution of lithium-polysulfide in the electrolyte. Remarkably, it is found that removal of the conventional membrane separator in a Li-S cell improves sulfur utilization and cycling performance, whether the sulfur is initially contained in the cathode or electrolyte. An optimized cell design yields discharge capacities as high as 980 mA h g-1 after 100 cycles.