Some biomedical applications of a non-linear curve fit method
Nonlinear curve fit method for estimating parameters of equations for biological models
BIOLOGICAL MODEL↗
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Flight transition data for angles of attack at Mach 22 with correlations of the data
Boundary-layer transition data for angles of attack from 2.5 to 47 deg from a flight experiment with a cone that reentered at angles of attack up to 75 deg were analyzed and their local flow conditions are presented. The transition data were obtained from both acoustic and electrostatic sensors. The data from the acoustic and electrostatic sensors were correlated by use of three different sets of correlating parameters. For each set of correlating parameters, the transitional and turbulent data from the acoustic and electrostatic sensors were plotted separately. Each of the correlations was compared with a linear curve fit of previous cone-flight data at near zero angle of attack. Results indicate that the data from acoustic sensors falls below the linear curve fits to the flight data and indicates the sensitivity of the sensors. It is shown that the transition data from the electrostatic sensors tends to scatter much more than the data from the acoustic sensors. However, the data from the electrostatic sensors tends to scatter about the linear curve fits based on previous flight data.
Johnson, C. B.↗
Method for Making Measurements of the Post-Combustion Residence Time in a Gas Turbine Engine
A system and method of measuring a residence time in a gas-turbine engine is provided, whereby the method includes placing pressure sensors at a combustor entrance and at a turbine exit of the gas-turbine engine and measuring a combustor pressure at the combustor entrance and a turbine exit pressure at the turbine exit. The method further includes computing cross-spectrum functions between a combustor pressure sensor signal from the measured combustor pressure and a turbine exit pressure sensor signal from the measured turbine exit pressure, applying a linear curve fit to the cross-spectrum functions, and computing a post-combustion residence time from the linear curve fit.
Miles, Jeffrey H↗
Studies of the Magnetocaloric and Electrical Properties of La{sub 0.7}Er{sub 0.05}Sr{sub 0.15}Ca{sub 0.1}Mn{sub 1−x}In{sub x}O{sub 3} (0 ≤ x ≤ 0.30)
We report on the study of In substitution for Mn on the magnetic and transport properties of layered manganese oxides La{sub 0.7}Er{sub 0.05}Sr{sub 0.15}Ca{sub 0.1}Mn{sub 1−x}In{sub x}O{sub 3} (0 ≤ x ≤ 0.30) synthesized via sol-gel method. For all the samples, all peaks are satisfactorily indexed in the rhombohedra structure with R 3-bar c space group. Magnetic data, under a magnetic field of 0.05 T, revealed that our compounds exhibit a continuous (second-order) transition from a ferromagnetic (FM) to a paramagnetic (PM) state upon decreasing the temperature. Also, magnetic entropy change and relative cooling power for magnetic field variation were predicted. Then, we have fitted the experimental data of resistivity using non-linear curve fitting, a typical mathematical function (Gauss function). This function can describe the carrier transport behavior of manganites as a function of temperature around the electrical phase transition. The obtained results were discussed. These predicted parameters agree with the experimental data.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Energy from Redox Disproportionation of Sugar Carbon Drives Biotic and Abiotic Synthesis
To identify the energy source that drives the biosynthesis of amino acids, lipids, and nucleotides from glucose, we calculated the free energy change due to redox disproportionation of the substrate carbon of: (1) 26-carbon fermentation reactions and (2) the biosynthesis of amino acids and lipids of E. coli from glucose. The free energy (cal/mmol of carbon) of these reactions was plotted as a function of the degree of redox disproportionation of carbon (disproportionative electron transfers (mmol)/mmol of carbon). The zero intercept and proportionality between energy yield and degree of redox disproportionation exhibited by this plot demonstrate that redox disproportionation is the principal energy source of these redox reactions (slope of linear fit = -10.4 cal/mmol of disproportionative electron transfers). The energy and disproportionation values of E. coli amino acid and lipid biosynthesis from glucose lie near this linear curve fit with redox disproportionation accounting for 84% and 96% (and ATP only 6% and 1 %) of the total energy of amino acid and lipid biosynthesis, respectively. These observations establish that redox disproportionation of carbon, and not ATP, is the primary energy source driving amino acid and lipid biosynthesis from glucose. In contrast, we found that nucteotide biosynthesis involves very little redox disproportionation, and consequently depends almost entirely on ATP for energy. The function of sugar redox disproportionation as the major source of free energy for the biosynthesis of amino acids and lipids suggests that sugar disproportionation played a central role in the origin of metabolism, and probably the origin of life.
Weber, Arthur L.↗
Energy from Redox Disproportionation of Sugar Carbon Drives Biotic and Abiotic Synthesis
To identify the energy source that drives the biosynthesis of amino acids, lipids, and nucleotides from glucose, we calculated the free energy change due to redox disproportionation of the substrate carbon of: (1) 26-carbon fermentation reactions and (2) the biosynthesis of amino acids and lipids of E. coli from glucose. The free energy (cal/mmol of carbon) of these reactions was plotted as a function of the degree of redox disproportionation of carbon (disproportionative electron transfers (mmol)/mmol of carbon). The zero intercept and proportionality between energy yield and degree of redox disproportionation exhibited by this plot demonstrate that redox disproportionation is the principal energy source of these redox reactions (slope of linear fit = -10.4 cal/mmol of disproportionative electron transfers). The energy and disproportionation values of E. coli amino acid and lipid biosynthesis from glucose lie near this linear curve fit with redox disproportionation accounting for 84% and 96% (and ATP only 6% and 1%) of the total energy of amino acid and lipid biosynthesis, respectively. These observations establish that redox disproportionation of carbon, and not ATP, is the primary energy source driving amino acid and lipid biosynthesis from glucose. In contrast, we found that nucleotide biosynthesis involves very little redox disproportionation, and consequently depends almost entirely on ATP for energy. The function of sugar redox disproportionation as the major source of free energy for the biosynthesis of amino acids and lipids suggests that sugar disproportionation played a central role in the origin of metabolism, and probably the origin of life.
Weber, Arthur L.↗
Real-time Exponential Curve Fits Using Discrete Calculus
This paper presents an improved solution for curve fitting data to an exponential equation (Y = AeBt + C). This improvement is in four areas ? speed, stability, determinant processing time, and the removal of limits. The solution presented in this paper avoids iterative techniques and their stability errors by using three mathematical ideas ? discrete calculus, a special relationship (between exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation Y = AxB + C and the general geometric growth equation Y = AkBt + C.
Rowe, Geoffrey K.↗
Real-Time Exponential Curve Fits Using Discrete Calculus
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Rowe, Geoffrey↗
Geographically distributed real-time digital simulations using linear prediction
Not Available
24 POWER TRANSMISSION AND DISTRIBUTION↗
A method for nonlinear exponential regression analysis
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
Junkin, B. G.↗
Spectral moment estimation in MST radars
Signal processing techniques used in Mesosphere-Stratosphere-Troposphere (MST) radars are reviewed. Techniques which produce good estimates of the total power, frequency shift, and spectral width of the radar power spectra are considered. Non-linear curve fitting, autocovariance, autocorrelation, covariance, and maximum likelihood estimators are discussed.
Woodman, R. F.↗
Turbulence in a convective marine atmospheric boundary layer
The structure and kinetic energy budget of turbulence in the convective marine atmospheric boundary layer as observed by aircraft during a cold air outbreak have been studied using mixed layer scaling. The results are significantly different from those of previous studies under conditions closer to free convection. The normalized turbulent kinetic energy and turbulent transport are about twice those found during the Air Mass Transformation Experiment (AMTEX). This implies that for a given surface heating the present case is dynamically more active. The difference is mainly due to the greater importance of wind shear in the present case. This case is closer to the roll vortex regime, whereas AMTEX observed mesoscale cellular convection which is closer to free convection. Shear generation is found to provide a significant energy source, in addition to buoyancy production, to maintain a larger normalized turbulent kinetic energy and to balance a larger normalized dissipation. The interaction between turbulent pressure and divergence (i.e., pressure scrambling) is also found to transfer energy from the vertical to the horizontal components, and is expected to be stronger in roll vortices than in m esoscale cells. The sensible heat flux is found to fit well with a linear vertical profile in a clear or subcloud planetary boundary layer (PBL), in good agreement with the results of Lenschow et al., (1980). The heat flux ratio between the PBL top and the surface, derived from the linear fitted curve, is approximately -0.14, in good agreement with that derived from the lidar data for the same case. Near the PBL top, the heat flux profiles are consistent with those of Deardoff (1979) and Deardorff et al. (1980).
Chou, S.-H.↗
Use of Vertically Integrated Ice in WRF-Based Forecasts of Lightning Threat
Previously reported methods of forecasting lightning threat using fields of graupel flux from WRF simulations are extended to include the simulated field of vertically integrated ice within storms. Although the ice integral shows less temporal variability than graupel flux, it provides more areal coverage, and can thus be used to create a lightning forecast that better matches the areal coverage of the lightning threat found in observations of flash extent density. A blended lightning forecast threat can be constructed that retains much of the desirable temporal sensitivity of the graupel flux method, while also incorporating the coverage benefits of the ice integral method. The graupel flux and ice integral fields contributing to the blended forecast are calibrated against observed lightning flash origin density data, based on Lightning Mapping Array observations from a series of case studies chosen to cover a wide range of flash rate conditions. Linear curve fits that pass through the origin are found to be statistically robust for the calibration procedures.
McCaul, E. W., jr.↗
THEMIS signal analysis statistics research program - Development and analysis of modified paired comparisons by use of linearized nonlinear regression
Curve fitting for modified paired comparisons using linearized nonlinear regression
Walsh, J. E.↗
On the cost of approximating and recognizing a noise perturbed straight line or a quadratic curve segment in the plane
Approximation of noisy data in the plane by straight lines or elliptic or single-branch hyperbolic curve segments arises in pattern recognition, data compaction, and other problems. The efficient search for and approximation of data by such curves were examined. Recursive least-squares linear curve-fitting was used, and ellipses and hyperbolas are parameterized as quadratic functions in x and y. The error minimized by the algorithm is interpreted, and central processing unit (CPU) times for estimating parameters for fitting straight lines and quadratic curves were determined and compared. CPU time for data search was also determined for the case of straight line fitting. Quadratic curve fitting is shown to require about six times as much CPU time as does straight line fitting, and curves relating CPU time and fitting error were determined for straight line fitting. Results are derived on early sequential determination of whether or not the underlying curve is a straight line.
Cooper, D. B.↗
Estimating sunspot number
An empirical method is developed to predict certain parameters of future solar activity cycles. Sunspot cycle statistics are examined, and curve fitting and linear regression analysis techniques are utilized.
Wilson, R. M.↗
Non-Contact Thrust Stand Calibration Method for Repetitively-Pulsed Electric Thrusters
A thrust stand calibration technique for use in testing repetitively-pulsed electric thrusters for in-space propulsion has been developed and tested using a modified hanging pendulum thrust stand. In the implementation of this technique, current pulses are applied to a solenoidal coil to produce a pulsed magnetic field that acts against the magnetic field produced by a permanent magnet mounted to the thrust stand pendulum arm. The force on the magnet is applied in this non-contact manner, with the entire pulsed force transferred to the pendulum arm through a piezoelectric force transducer to provide a time-accurate force measurement. Modeling of the pendulum arm dynamics reveals that after an initial transient in thrust stand motion the quasisteady average deflection of the thrust stand arm away from the unforced or zero position can be related to the average applied force through a simple linear Hooke s law relationship. Modeling demonstrates that this technique is universally applicable except when the pulsing period is increased to the point where it approaches the period of natural thrust stand motion. Calibration data were obtained using a modified hanging pendulum thrust stand previously used for steady-state thrust measurements. Data were obtained for varying impulse bit at constant pulse frequency and for varying pulse frequency. The two data sets exhibit excellent quantitative agreement with each other as the constant relating average deflection and average thrust match within the errors on the linear regression curve fit of the data. Quantitatively, the error on the calibration coefficient is roughly 1% of the coefficient value.
Wong, Andrea R.↗
Molecular Mass Growth Processes to Polycyclic Aromatic Hydrocarbons through Radical–Radical Reactions Exploiting Photoionization Reflectron Time-of-Flight Mass Spectrometry
Polycyclic aromatic hydrocarbons (PAHs) represent critical building blocks in molecular mass growth processes to carbonaceous nanoparticles, referred to as interstellar and circumstellar grains along with soot particles in astrophysical environments and combustion systems, respectively. Recent advancements on elucidating elementary steps to PAHs have utilized reactions of aromatic radicals, resonantly stabilized free radicals, and aliphatic radicals with closed shell hydrocarbons. However, the role of radical–radical reactions (RRRs) leading to PAHs has remained largely unexplored on the molecular level due to preceding experimental challenges in producing sufficiently high number densities of radical reactants for isomer-selective detection of products from bimolecular and termolecular reactions. This Account offers the latest developments in our knowledge on the mechanisms and pathways to PAHs via RRRs probed in a chemical microreactor at temperatures as high as 1600 K. Product preservation in a molecular beam coupled with synchrotron vacuum ultraviolet photoionization reflectron time-of-flight mass spectrometry and photoelectron photoion coincidence spectroscopy enabled isomer-selective detection of PAHs of up to three rings by their photoionization efficiency curves, which were fit with a linear combination of reference curves for identification. Experiments were combined with computational fluid dynamics modeling of the physicochemical processes in the microreactor, as well as high-level electronic structure calculations to reveal the reaction pathways of each system. Six distinct reaction mechanisms were discovered in this work: propargyl addition─benzannulation (PABA), methyl addition─ring expansion (MARE), cyclopentadienyl addition─naphthylization (CPAN), fulvenallenyl addition─cyclization─aromatization (FACA), benzyl addition─aromatization (BAA), and phenyl addition─pentacyclization (PAP). By systematically varying the number of carbon atoms in the radical reactants, molecular mass growth processes involving reactions between radicals with odd numbers of carbon atoms access aromatics carrying one, two, or three six-membered rings, whereas reactions between even- and odd-carbon-numbered radicals produce aromatics combining five- and six-membered rings. Our investigations reveal unconventional cycloadditions on excited state triplet surfaces, additions of radicals to low spin density carbon-centered radicals, spiroaromatic and fulvene-type intermediates, and highly strained bicyclic reaction intermediates, challenging current perceptions of PAH molecular mass growth processes. All of the listed mechanisms, except for FACA, feature endoergic reactions or barriers which lie above the separated reactants and therefore might be central to circumstellar environments of carbon-rich stars and planetary nebulae as their descendants, but they play no role in the gas phase of cold molecular clouds where temperatures as low as 10 K dominate. Altogether, this work provides detailed reaction mechanisms of PAH growth processes, advancing our knowledge of the chemistry of carbonaceous matter in the universe.
Addition reactions↗