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16 results for “analytical solutions”
A semi-analytical solution for heat transport in rock with parallel fractures and a heat source in both fracture and matrix
<p>In this study, we propose a two-dimensional semi-analytical solution framework based on a Green’s function approach for a flexible heat source definition, including source dimensions, energy delivery strength and duration, and the presence of a heat source in the matrix and/or fracture. The solution fully accounts for heat conduction, advection, dispersion and transient heat exchange between the mobile and immobile phases in a system of parallel fractures. The solution having a strip heat source extending from a fracture into the matrix indicates that one-dimensional heat conduction in the matrix underestimates and overestimates temperature responses at early and later times, respectively.</p> <p>The dataset is for the figures 2-7 in the journal paper. </p>
Supplemental materials for "Benchmarking magnetized three-wave coupling for laser backscattering: Analytic solutions and kinetic simulations"
<p>Place the unzipped Data and Programs folders in the same directory. The contents of these folders are as follows:</p> <ul> <li>Data<br> Post processed data underlying each figure in the paper. The data files are .txt files with self-contained explanations. The files are organized in subfolders according to their purposes.<br> </li> <li>Programs <ul> <li>./PlotFigures<br> Contains python scripts for reading and plotting Data</li> <li>input.deck<br> Example input for EPOCH PIC code that generates raw data </li> <li>setup_batch.csh<br> Linux/Unix shell script for setting up batch simulations</li> <li>submit_batch<br> Slurm script for submitting jobs on computing clusters</li> </ul> </li> </ul>
Line-by-line coefficients for an analytical solution of spectrally resolved outgoing longwave radiation
<p>Following <strong>Feng et al., 2023</strong> , the change in spectrally-resolved outgoing longwave radiance <span class="math-tex">\(R\)</span> is:</p> <p><span class="math-tex">\(\pi \frac{R_{\text{trop}}}{R} [B(rT_e) - B(T_e)]\)</span></p> <p>In this equation, B(T_e) refers to Planck Function at temperature T_e, <span class="math-tex">\(R_{trop}\)</span> is the radiance contributed by troposphere, and <span class="math-tex">\(r\)</span> is an emission temperature shift ratio, computed using <strong>Eq. 10</strong> of <strong>Feng et al., 2023 </strong>with line-by-line regression coefficients <span class="math-tex">\(k\)</span> contained in the netCDF file 'lbl_regression_coeff.nc' for each major greenhouse gas. This set of coefficients is derived using an open-source line-by-line radiation code PyLBL (<a href="https://pylbl-1.readthedocs.io/en/latest/">https://pylbl-1.readthedocs.io</a>) following the Appendix of Feng et al., 2023 via Eq. B2, B4, and B6.</p> <p>An example matlab script is included to compute the emission temperature shift ratio based on the line-by-line coefficients and to further predict the spectrally-resolved feedback parameter based on Feng et al., 2023.</p>
The conductivity profile of Earth-ionosphere cavity used in the paper "Finite-difference time-domain analysis of ELF radio wave propagation in the spherical Earth-ionosphere waveguide and its validation based on analytical solutions" by Volodymyr Marchenko, Andrzej Kulak, Janusz Mlynarczyk
<p>The file "Marchenko_FDTD_Paper_Conductivity_Profile.dat" contains the conductivity profile of Earth-ionosphere cavity. The first column provides the altitude (in km) and the second column provides the conductivity (in S/m).</p>
A semi-analytical solution for heat transport in rock with parallel fractures and a heat source in both fracture and matrix
<p>In this study, we propose a two-dimensional semi-analytical solution framework based on a Green’s function approach for a flexible heat source definition, including the heat source dimensions, energy delivery strength and duration, and the presence of a heat source in the matrix and/or fracture. The solution fully accounts for heat conduction, advection, dispersion, and transient heat exchange between the fracture fluid and rock matrix in a system of parallel fractures. </p> <p>The dataset is for the figures 2-9 in the journal paper. </p> <p>The computation code is available to generate the temperature in rock matrix or fracture using Matlab. </p>
VORTEX 01: Analytic solution of the flow, aeroacoustic source and acoustic field from a co-rotating vortex pair
<div>This aeroacoustic reference example (often referred in literature as "Co-rotating vortex pair") provides the analytic solution of the flow, aeroacoustic source and acoustic field. Details on the example and derivation can be found in the article "Analysis of the co-rotating vortex pair as a test case for computational aeroacoustics" on which the analytic functions are based on can be found here: <a title="Persistent link using digital object identifier" href="https://doi.org/10.1016/j.jsv.2024.118496" target="_blank" rel="noopener">10.1016/j.jsv.2024.118496</a>. The following Matlab functions can be used for computing the aero-acoustic radiation of a co-rotating vortex pair:</div> <div> </div> <div><strong>Main script:</strong></div> <div>compute_pfar - Computes the radiated acoustic field. Use the "method" variable to change the aeroacoustic model</div> <div> </div> <div><strong>Computing the source terms:</strong></div> <div>vpair_pic - Incompressible pressure field p_ic and Dp_ic / Dt at a given time instance</div> <div>vpair_u - Velocity field u, and its first and second spatial derivatives at a given time instance</div> <div> </div> <div>plot_source_terms - Create a plot of the source terms of both Lighthill and PCWE</div> <div>plot_quadrupole_field - Plots the analytical quadrupole field solution</div> <div> </div> <div><strong>Utility functions used by the main script:</strong></div> <div>gaussquad - Gauss-Legendre quadrature in 1D (original version from Mathworks FTP)</div> <div>subdiv_graded - Graded subdivision of one or more sections in 1D</div> <div>vpair_quadrature - Quadrature base points and weights for numerical convolution</div> <div> </div> <div><strong>Resource:</strong></div> <div>colormap.png - Blue -> Gray -> Red color scale</div> <div> </div> <div>All functions and scripts, except gaussquad.m were created by the authors:</div> <div>P. Rucz, M. Á. Ulveczki, J. Heinz, S. Schoder</div>
Hard Rod Fluid Analytical Solution in .npy (For Operator learning)
<p>Hard rod fluid with diameter of 1.0 between 2 walls with distance L+2d=10.0,<br>under different chemical potential (mu) and external potential (V_ext(x)), with a sampling distance dz=0.1.</p> <p>Data are stored as numpy structured ndarrays, each npy file store one type of data. <br>The ndarrays has the shape of (n_sample,n_grid), with 4 fields:<br>the position "z", <br>the density profile "rho", <br>the local chemical potential "muloc"<br>the one-body direct correlation function "c1".<br>Where muloc(z)=mu-V_ext(z)</p> <p>In Operator Learning, I've tried the mapping of rho to c1 as well as muloc to rho.</p> <p>dataload.py contains some functions used for loading data<br>data_model_train.py contains the read-in function for model-training data.</p> <p>data_4groups.npy saves 8000 data, with 2000 in each group, generated from the following external potentials:<br>group 1: V_ext=0 <br>group 2: V_binary[z] = -epsilon*((a/(z+a/2))^3+(a/(L+a/2-z))^3)<br>group 3: V_binary[z] = -mg*z<br>group 4: V_binary[z] = -u0*(abs(z/z0))^a0<br>with mu, epsilon, a, mg, u0, z0, a0 are adjustable constants of the potential </p> <p>data_mixed23.npy saves 2000 data, generated from the following external potentials:<br> V_binary[z] = -epsilon*((a/(z+a/2))^3+(a/(L+a/2-z))^3) -mg*z</p> <p>Folders are taped in .zip files.</p> <p>Folder "~/R_data_generator" stores the generator of the data, analytical solution of 1D hard rod fluid.<br>Folder "~/Rdata" contains same data in .Rdata file, as R matrixs<br>Folder "~/R2py" contains the script to generate .npy file from .Rdata file</p>
Simplified Analytical Solutions for Martian Nighttime OH* Layer
<p>Article dataset</p>
Dataset supporting publication: "Development and Validation of Analytical Solutions for Earth Basket (Spiral) Heat Exchangers"
<p>Dataset supporting publication: “Development and Validation of Analytical Solutions for Earth Basket (Spiral) Heat Exchangers” (publication available for download:<a href="https://zenodo.org/record/7274096#.Y2JpLnbMJPY">GEOFIT Zenodo</a>).</p> <p>This paper presents an analytical solution and its validation for earth basket (vertical spiral) ground heat<br> exchangers. The model, based on the well known Finite Line Source Equation, accounts for the heat exchanger pipe diameter and seasonally varying near surface temperature. For computational efficiency the standard approach of using G-functions has been implemented as well. The analytical model is validated based on laboratory experiments and extensive CFD analysis.</p>
Models and data for "Guaranteed safe controller synthesis for switched systems using analytical solutions"
<p>Models and data for the paper "Guaranteed safe controller synthesis for switched systems using analytical solutions" presented at the 7th IEEE Conference on Control Technology and Applications, Barbados, August 16-18, 2023.</p> <p> </p>
A Benchmark Analytical Solution for Variable Viscosity Flow in Fractured Media: Development and Comparative Analysis with Numerical Simulations
<p>This data is associated with <strong>(a) Figure 3.</strong> Comparison between the velocities obtained through analytical calculations and those estimated numerically, and <strong>(b) Figure 4.</strong> Comparison of the BTCs obtained through analytical calculations and those estimated numerically.</p>
Supplemental figures for "An analytic solution for evaluating the magnetic field induced from an arbitrary, asymmetric ocean world"
<p>Supplemental figures referenced in the text of "An analytic solution for evaluating the magnetic field induced from an arbitrary, asymmetric ocean world," submitted to Icarus.</p>
Modeling the Organic Carbon Oxidation and Redox Sequence under the Partial- Equilibrium Approach: a Discussion by means of a Semi-Analytical Solution
<p>Filename: Analytical_solution.xls<br> File format: Excel<br> Description: It contains the calculation of the analytical model, programmed by means of excel. The sheet "advection" contains the calculation of the advection model and the sheet "diffusion" that of the diffusion model. The sheet "Phreeqc results" contains the results of the Phreeqc batch model (see Batch.pqi). Input data are highlighted in yellow.</p> <p>Filename: Batch.pqi<br> File format: Phreeqc<br> Description: It contains the input file for the calculation of the batch model by Phreeqc. It requires the Phreeqc database file Phreeqc.dat</p> <p>Filename: PEA_om_adv.pqi<br> File format: Phreeqc<br> Description: It contains the input file for the numerical calculation of the advection model by Phreeqc using the PEA (Partial Equilibrium Assumption). It requires the Phreeqc database file Phreeqc.dat</p> <p>Filename: PEA_om_dif.pqi<br> File format: Phreeqc<br> Description: It contains the input file for the numerical calculation of the diffusion model by Phreeqc using the PEA (Partial Equilibrium Assumption). It requires the Phreeqc database file Phreeqc.dat</p> <p>Filename: KIN_om_adv.pqi<br> File format: Phreeqc<br> Description: It contains the input file for the numerical calculation of the advection model by Phreeqc using the fully kinetic approach. It requires the Phreeqc database file PhreeqcKIN.dat</p> <p>Filename: KIN_om_dif.pqi<br> File format: Phreeqc<br> Description: It contains the input file for the numerical calculation of the diffusion model by Phreeqc using the fully kinetic approach. It requires the Phreeqc database file PhreeqcKIN.dat</p> <p>Filename: phreeqc.dat<br> File format: Phreeqc database<br> Description: It contains thermodynamic data for the batch model (see Batch.pqi) and the PEA models (see PEA_om_adv.pqi and PEA_om_dif.pqi). It is the default thermodynamic database of Phreeqc, dat), from which we removed ammonium to avoid the unrealistic reduction of NO3- and N2 to NH4+</p> <p>Filename: phreeqcKIN.dat<br> File format: Phreeqc database<br> Description: It contains thermodynamic data for the fully kinetic models (see KIN_om_adv.pqi and KIN_om_dif.pqi). It is the default thermodynamic database of Phreeqc, dat), from which we removed the relevant equilibrium redox reaction, so that they can be treated kinetically.</p> <p> </p> <p> </p>
Data sets for the Publication 'Analytical solution of gas flow in rough-walled micro-fracture at in-situ state' in Water Resources Research.
<p>Data sets for the Publication 'Analytical solution of gas flow in rough-walled micro-fracture at in-situ state' in Water Resources Research.</p>
Analytical solution of apparent permeability of a laminated structure with cross flow in the transient flow process-data
<p>This file is the data used in the aritcle "Analytical solution of apparent permeability of a laminated structure with cross flow in the transient flow process"</p>
Datasets and Supporting Information for "A novel semi-analytical (inertial) solution for determining permeability of highly pervious porous materials using the two-reservoir laboratory setup"
<p>The uploaded datasets represent the experimental data of the Two-Reservoirs test and the Constant Head Permeability Test, both described in details in the paper "A novel semi-analytical (inertial) solution for determining permeability of highly pervious porous materials using the two-reservoir laboratory setup" and in the corresponding uploaded pdf document "FStanic_et_al_SupportingInformation2.pdf". Data for the Two-Reservoirs test contain information about the water level values <em>Π</em><em><sub>1</sub></em> and <em>Π</em><em><sub>2 </sub></em>in connected Reservoirs 1 and 2, respectively, and times when the corresponding values are captured, while data for the Constant Head Permeability test contain water level values recorded in Piezometer (<em>Π</em><em><sub>12</sub></em>)<em> </em>and the corresponding water flux values<em> v<sub>s</sub>. </em></p> <p>Also, in the document "FStanic_et_al_SupportingInformation1.pdf" are presented some technical details related to the experimental apparatus developed in this work, that can be helpful for researchers trying to conduct similar test. </p>
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