PyTheis—A Python Tool for Analyzing Pump Test Data

The Theis equation is an important mathematical model used for analyzing drawdown data obtained from pumping tests to estimate aquifer parameters. Since the Theis model is a nonlinear equation, a complex graphical procedure is employed for fitting this equation to pump test data. This graphical method was originally proposed by Theis in the late 1930s, and since then, all the groundwater textbooks have included this fitting method. Over the past 90 years, every groundwater hydrologist has been trained to use this tedious procedure for estimating the values of aquifer transmissivity (T) and storage coefficient (S). Unfortunately, this mechanical procedure does not provide any intuition for understanding the inherent limitations in this manual fitting procedure. Furthermore, it does not provide an estimate for the parameter error. In this study, we employ the public domain coding platform Python to develop a script, namely, PyTheis, which can be used to simultaneously evaluate T and S values, and the error associated with these two parameters. We solve nine test problems to demonstrate the robustness of the Python script. The test problems include several published case studies that use real field data. Our tests show that the proposed Python script can efficiently solve a variety of pump test problems. The code can also be easily adapted to solve other hydrological problems that require nonlinear curve fitting routines.

Analysis and forecast of COVID-19 spreading in India using Nonlinear curve fitting model with machine learning

In this paper, an analysis and forecasting of Indian COVID-19 data is discussed by using scipy optimize curve fitting model of machine learning. We demonstrates the month wise analysis of coming cases, daily recovered cases, death cases and test cases conducted by the Government of India, of COVID-19 from 01st March 2020 to 02nd August 2020, and also forecast for the new cases, recover cases & death cases from 03rd August 2020 to 01st November 2020. Our study show that the total numbers of affected persons due to COVID-19 up to 01st November 2020 will be total cases 13,690,491, recover cases 10,499,593 and death of 129,271.

Prediction of the “Tipping Point” to Widespread Uptake of Battery Electric Vehicles in China via Nonlinear Curve-Fitting Method

<p>The “Tipping Point” is a term that is widely used today to describe that a time or threshold once being surpassed would result in exponential growth in technology adoption or product sales in a specific industry. China’s BEV industry has grown tremendously in the past 10 years and recently, and China has been leading both BEV sales and manufacturing in the world. Thus, this paper aims to investigate the “Tipping Point” timeframe for Battery Electric Vehicles (BEVs) penetration in China. The major work is conducted in 3 steps. 1. This paper firstly defined the exactitude of “Tipping Point” as a 16% market penetration rate from Roger’s technology adoption model. 2. Then this paper used a simple exponential curve formula using the Levenberg–Marquardt Algorithm (LMA) calculation method to conduct nonlinear curve fitting modeling for various nations and testify the validity of our formula used. 3. Finally, after getting a positive result from these sample countries, this paper continues using this method to predict the 16% “Tipping Point” from several current predictions reports. It concludes with a calculated assumption that this 16% BEV market penetration rate would most likely occur by the end of 2024.</p>

Determination of Wall Friction Velocity of the Turbulent Boundary Layer by Two-Parameter Nonlinear Curve Fitting

Hot-wire anemometer is a fundamental tool for flow field measurement, and has been widely adopted in research of turbulent flow. A turbulent boundary layer was generated by a trip wire and a piece of sandpaper in the low-speed wind tunnel, and the time-averaged velocity profiles at three different streamwise stations in the boundary layer were measured with IFA-300 constant temperature anemometer. Targeting the dimensionless velocity profile model White Law of the turbulent boundary layer, a nonlinear curve fitting MATLAB program for two parameters, which were theoretical original point of wall coordinate y0 and wall friction velocity uτ, was developed. Based on the measured time-averaged velocity profiles, the program was adopted to determine y0 and uτ of the three streamwise stations. It is found that the initial search domain and search step size of y0 and uτ have no effect on the fitting results if the physical solutions are included in the domain. It is also found that the selected fitting velocities data are closely related to the results. The value of the friction velocity with high precision will be obtained by this nonlinear curve fitting method if the highest fitting velocity data point dose not fall into the wake region. The method given in this paper is simple in programming and reliable in fitting results, and it is of practical to obtain the wall friction velocity of the turbulent boundary layer.

A New Nonlinear Sparse Component Analysis for a Biologically Plausible Model of Neurons

It is known that brain can create a sparse representation of the environment in both sensory and mnemonic forms (Olshausen & Field, 2004 ). Such sparse representation can be combined in downstream areas to create rich multisensory responses to support various cognitive and motor functions. Determining the components present in neuronal responses in a given region is key to deciphering its functional role and connection with upstream areas. One approach for parsing out various sources of information in a single neuron is by using linear blind source separation (BSS) techniques. However, applying linear techniques to neuronal spiking activity is likely to be suboptimal due to inherent and unknown nonlinearity of neuronal responses to inputs. This letter proposes a nonlinear sparse component analysis (SCA) method to separate jointly sparse inputs to neurons with post summation nonlinearity, or SCA for post-nonlinear neurons (SCAPL). Specifically, a linear clustering approach followed by principal curve regression (PCR) and a nonlinear curve fitting are used to separate sources. Analysis using simulated data shows that SCAPL accuracy outperforms ones obtained by linear SCA, as well as other separating methods, including linear independent and principal component analyses. In SCAPL, the number of derived sparse components is not limited by the number of neurons, unlike most BSS methods. Furthermore, this method allows for a broad range of post-summation nonlinearities that could differ among neurons. The sensitivity of our method to noise, joint sparseness, degree, and shape of nonlinearity and mixing ill conditions is discussed and compared to existing methods. Our results show that the proposed method can successfully separate input components in a population of neurons provided that they are temporally sparse to some degree. Application of SCAPL should facilitate comparison of functional roles across regions by parsing various elements present in a region.