Fortran Code Research Articles

PDFO: a cross-platform package for Powell’s derivative-free optimization solvers

AbstractThe late Professor M. J. D. Powell devised five trust-region methods for derivative-free optimization, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. He carefully implemented them into publicly available solvers, renowned for their robustness and efficiency. However, the solvers were implemented in Fortran 77 and hence may not be easily accessible to some users. We introduce the PDFO package, which provides user-friendly Python and MATLAB interfaces to Powell’s code. With PDFO, users of such languages can call Powell’s Fortran solvers easily without dealing with the Fortran code. Moreover, PDFO includes bug fixes and improvements, which are particularly important for handling problems that suffer from ill-conditioning or failures of function evaluations. In addition to the PDFO package, we provide an overview of Powell’s methods, sketching them from a uniform perspective, summarizing their main features, and highlighting the similarities and interconnections among them. We also present experiments on PDFO to demonstrate its stability under noise, tolerance of failures in function evaluations, and potential to solve certain hyperparameter optimization problems.

Impact of geometric variables on the functionality of downdraft biomass gasifiers across diverse dimensions

This study offers an extensive examination of the fundamental design parameters that influence the performance of biomass downdraft gasifiers. The impact of design parameters such as reactor dimensions, throat diameter, length of converging and diverging section and ratio of maximum to minimum diameter (dmax/dmin) were analysed using FORTRAN code, which was initially developed for 4 kW Imbert gasifier. Simulation results highlight that the optimal range of hearth loads for gasifier operation is influenced by both the gasifier’s size and the particle size of the feedstock. Increasing gasifier size from 20 mm to 100 mm throat diameter, while maintaining the same superficial air velocity (SAV), escalates hearth load and superficial velocity due to heightened biomass consumption, leading to higher hearth temperature and improved gas calorific value. Similar trends are observed across varying SAV values (0.35 m/s to 1.8 m/s), suggesting a need for lower SAV values in larger gasifiers, possibly with larger particle sizes. Additionally, altering the length of the converging and diverging sections impacts gas quality, with deviations from recommended values affecting ignition and overall performance, while dmax/dmin variations show no significant impact.

Magnetohydrodynamic double diffusion natural convection of power-law Non-Newtonian Nano-Encapsulated phase change materials in a trapezoidal enclosure

PurposeThe present numerical investigation examines the magnetohydrodynamic (MHD) double diffusion natural convection of power-law non-Newtonian nano-encapsulated phase change materials (NEPCMs) in a trapezoidal cavity.Design/methodology/approachThe governing Navier-Stokes, energy and concentration equations based on the Cartesian curvilinear coordinates are solved using the collocated grid arrangement’s finite volume method. The in-house FORTRAN code is validated with the different benchmark problems. The NEPCM nanoparticles consist of a core-shell structure with Phase Change Material (PCM) at the core. The enclosure, shaped as a trapezoidal hollow, features a warmed (Th) left wall and a cold (Tc) right wall. Various parameters are considered, including the power law index (0.6 ≤ n ≤ 1.4), Hartmann number (0 ≤ Ha ≤ 30), Rayleigh number (104 ≤ Ra ≤ 105) and fixed variables such as buoyancy ratio (Br = 0.8), Prandtl number (Pr = 6.2), Lewis number (Le = 5), fusion temperature (Θf = 0.5) and volume fraction (ϕ = 0.04).FindingsThe findings indicate a decrease in local Nusselt (Nu) and Sherwood (Sh) numbers with increasing Hartmann numbers (Ha). Additionally, for a shear-thinning fluid (n = 0.6) results in the maximum local Nu and Sh values. As the Rayleigh number (Ra) increases from 104 to 105, the structured vortex in the streamline pattern is disturbed. Furthermore, for different Ra values, an increase in n from 0.6 to 1.4 leads to a 67.43% to 76.88% decrease in average Nu and a 70% to 77% decrease in average Sh.Research limitations/implicationsThis research is for two-dimensioal laminar flow only.Practical implicationsPCMs represent a class of practical substances that behave as a function of temperature and have the innate ability to absorb, release and store heated energy in the form of hidden fusion enthalpy, or heat. They are valuable in these systems as they can store significant energy at a relatively constant temperature through their latent heat phase change.Originality/valueAs per the literature review and the authors’ understanding, an examination has never been conducted on MHD double diffusion natural convection of power-law non-Newtonian NEPCMs within a trapezoidal enclosure. The current work is innovative since it combines NEPCMs with the effect of magnetic field Double diffusion Natural Convection of power-law non-Newtonian NEPCMs in a Trapezoidal enclosure. This outcome can be used to improve thermal management in energy storage systems, increasing safety and effectiveness.

Accelerating Fortran codes: A method for integrating Coarray Fortran with CUDA Fortran and OpenMP

Fortran's prominence in scientific computing requires strategies to ensure both that legacy codes are efficient on high-performance computing systems, and that the language remains attractive for the development of new high-performance codes. Coarray Fortran (CAF), part of the Fortran 2008 standard introduced for parallel programming, facilitates distributed memory parallelism with a syntax familiar to Fortran programmers, simplifying the transition from single-processor to multi-processor coding. This research focuses on innovating and refining a parallel programming methodology that fuses the strengths of Intel Coarray Fortran, Nvidia CUDA Fortran, and OpenMP for distributed memory parallelism, high-speed GPU acceleration and shared memory parallelism respectively. We consider the management of pageable and pinned memory, CPU-GPU affinity in NUMA multiprocessors, and robust compiler interfacing with speed optimisation. We demonstrate our method through its application to a parallelised Poisson solver and compare the methodology, implementation, and scaling performance to that of the Message Passing Interface (MPI), finding CAF offers similar speeds with easier implementation. For new codes, this approach offers a faster route to optimised parallel computing. For legacy codes, it eases the transition to parallel computing, allowing their transformation into scalable, high-performance computing applications without the need for extensive re-design or additional syntax.

The 2024 KIDA network for interstellar chemistry

Context. The study of the chemical composition of the interstellar medium (ISM) requires a strong synergy between laboratory astrophysics, modeling, and observations. In particular, astrochemical models have been developed for decades now and include an increasing number of processes studied in the laboratory or theoretically. These models follow the chemistry both in the gas phase and at the surface of interstellar grains. Since 2012, we have provided complete gas-phase chemical networks for astrochemical codes that can be used to model various environments of the ISM. Aims. Our aim is to introduce the new up-to-date astrochemical network kida.uva.2024 together with the ice chemical network and the fortran code to compute time dependent compositions of the gas, the ice surface, and the ice mantles under physical conditions relevant for the ISM. Methods. The gas-phase chemical reactions, as well as associated rate coefficients, included in kida.uva.2024 were carefully selected from the KIDA online database and represent the most recent values. The model predictions for cold core conditions and for when considering only gas-phase processes were computed as a function of time and compared to the predictions obtained with the previous version, kida.uva.2014. In addition, key chemical reactions were identified. The model predictions, including both gas and surface processes, were compared to the molecular abundances as observed in the cold core TMC1-CP. Results. Many gas-phase reactions were revised or added to produce kida.uva.2024. The new model predictions are different by several orders of magnitude for some species. The agreement of this new model with observations in TMC-1 (CP) is, however, similar to the one obtained with the previous network.

Advancing Fixed-Source Reactor Analysis Through OpenNode Implementation

OpenNode, a new open-source Fortran code, enables the simulation of fixed-source reactors. Powered by the nodal expansion method (NEM) and seamless Python integration, OpenNode competes with existing nuclear reactor simulation tools. The fixed-source problem plays a crucial role in radioprotection, providing flux calculations and detailed insights into heating effects and dose rates. Users can define and configure reactor models via a JSON input file, specifying critical parameters like geometry, materials, cross-section data, boundary conditions, and fixed sources. OpenNode further empowers users with a Python interface for preprocessing and postprocessing, streamlining result analysis. Distinguishing itself from conventional NEM codes, OpenNode supports three-dimensional (3D) Cartesian geometries, facilitating intricate reactor design simulations. Customization options, including mesh sizes, polynomial orders, and calculation modes, enhance precision and efficiency. In our comprehensive study, we verified OpenNode’s fixed-source mode using the 3D-IAEA reactor, comparing it with the SANM code KOMODO. The results underscore OpenNode’s exceptional accuracy in computing critical parameters, like the effective multiplication factor, power distribution, and nodal flux, within fixed-source reactors. OpenNode stands as a reliable, user-friendly tool poised to advance nuclear reactor simulations.

Estimation of vibrational spectra of Trp-cage protein from nonequilibrium metadynamics simulations

The development of methods that allow a structural interpretation of linear and nonlinear vibrational spectra is of great importance, both for spectroscopy and for optimizing force field quality. The experimentally measured signals are ensemble averages over all accessible configurations, which complicates spectral calculations. To account for this, we present a recipe for calculating vibrational amide-I spectra of proteins based on metadynamics molecular dynamics simulations. For each frame, a one-exciton Hamiltonian is set up for the backbone amide groups, in which the couplings are estimated with the transition-charge coupling model for nonnearest neighbors, and with a parametrized map of ab initio calculations that give the coupling as a function of the dihedral angles for nearest neighbors. The local-mode frequency variations due to environmental factors such as hydrogen bonds are modeled by exploiting the linear relationship between the amide C-O bond length and the amide-I frequency. The spectra are subsequently calculated while taking into account the equilibrium statistical weights of the frames that are determined using a previously published reweighting procedure. By implementing all these steps in an efficient Fortran code, the spectra can be averaged over very large amounts of structures, thereby extensively covering the phase space of proteins. Using this recipe, the spectral responses of 2.5 million frames of a metadynamics simulation of the miniprotein Trp-cage are averaged to reproduce the experimental temperature-dependent IR spectra very well. The spectral calculations provide new insight into the origin of the various spectral signatures (which are typically challenging to disentangle in the congested amide-I region), and allow for a direct structural interpretation of the experimental spectra and for validation of the molecular dynamics simulations of ensembles.

Determining beta radiation doses from Y-90 microsphere for the treatment of hepatic tumors by using Monte Carlo and analytical methods

The very short range of beta radiation is a potential radiation treatment for tumor, which can preserve sensitive structures. However, due to the limited range of beta radiation, practical dosimetry of beta sources may be a point of concern, and theoretical dosimetry methods play an important role. A resin microsphere loaded with the Yttrium-90 (Y-90) radionuclide can be applied in the radioembolization of hepatic tumors. In this work, we present initial calculations of dose rates around a microsphere loaded with the Y-90 radionuclide uniformly distributed on its exterior surface. Two approaches were used to carry out the estimations: the first one by means of Monte Carlo simulations using the PENELOPE code and the second one by means of the beta-point dose function formalism. A Fortran code was developed to handle with the various quantities necessary to perform the numerical integration of the beta-point dose function. A comparison between results obtained by means of both methods indicated a maximum difference of ~5% up to the 0.3 cm distance from the center of the sphere.

Re-patterning of cylindrical packing of diblock copolymers under confinement and curvature effects by using approximations of PDE’s involved in the CDS model on polar mesh system

Soft materials, including diblock copolymers, are advancing nanotechnology due to their unique properties, applications materials include energy harvesting, water sanitation, environmental treatment, nanosensors, drug delivery and nanolithography. These materials are light, cheap, efficient, sensitive, durable and more functional, whose new morphologies have been predicted by mathematicians through simulation. This work produces and predicts the pattern of packing of nano-cylinders by using confinement to appreciate the frustration in the packing of nano-cylinders under the influence of curvature. In this contribution, the cell dynamic simulations model is used to examine the impact of circular annular pore confinement on system orientation toward cylindrical morphologies. A 9-point stencil approximates the isotropic Laplacian by finite-difference discretization on a polar grid to meet the requirement of a cell dynamic simulation model. FORTRAN codes are generated for the set of PDEs included in the CDS model. OPEN DX is used to visualise the predicted cylindrical patterns. The consistency of our results with experimental observations makes our research valid and significant.

Entropy production associated with magnetohydrodynamics (MHD) thermo-solutal natural convection of non-Newtonian MWCNT-SiO2-EG hybrid nano-coolant

This article investigates the convective thermal and solutal exchange from the active walls of a trapezium chamber which is filled with multi-walled carbon nanotubes (MWCNT)-silicon dioxide (SiO2)-ethylene glycol-water hybrid nano-coolant. The hybrid nano-coolant exhibits non-Newtonian shear-thinning rheology and is modeled by the power-law viscosity as per an exploratory report. The convection is generated by both the thermal and solutal buoyancy forces in the presence of a magnetic field. Thermophysical properties of the particular nano-coolants are estimated from the temperature-dependent empirical correlation. An in-house FORTRAN code based on the finite volume method (FVM) has been utilized to simulate the non-dimensional controlling equations representing the physical model. By systematically varying the strength of the magnetic field (Ha=0−50) and its direction (δ1=0−90), the volume fraction of nano-coolant (ϕ=0−0.04) and solutal-to-thermal buoyancy ratio (N=−2 to 2), we thoroughly analyzed their impact on the flow field, thermal, and solutal transmission behavior. Significant impacts arising from the shear-thinning nature (n<1) of the nano-coolant were observed, influencing both thermal and solutal transfer rates as reflected in the Nusselt number (Nu) and Sherwood number (Sh). The impact of Ha on Nu and Sh is more substantial for n<1 than the case n=1. The investigation exposed that when Ha=30,δ1=30∘ the average Nu (Nu‾) for nano-ccolants (ϕ=2%) is maximally enhanced by 80% for n=0.6 compared to the case n=1.0. For the same nano-coolant with Ha=30 and δ1=90∘, there is a 128% elevation in the average Sherwood number (Sh‾) when n=0.6 compared to n=1.0. The entropy generation (S‾) inherent to the heat and mass transfer process and hence a criterion (ξ=S‾/Nu‾) is computed to address the system thermal performance from the thermodynamics second law. S‾ increased as n was reduced, indicating that the shear-thinning effect contributed strongly to the entropy generation.

Element-based finite volume method applied to autogenous bead-on-plate GTAW process using the enthalpy energy equation

The welding process is the most used technique for metal joining. Understanding the temperature variation along the welded part during the process can prevent the appearance of failures. The experimental investigation process is quite time-consuming and costly. Therefore, numerical simulation processes based on the finite difference method, finite element method, finite volume method, or meshless Element-Free Galerkin (EFG) methods are important tools to optimize the welding process. The main goal of the present study is to show the feasibility of the Element-based Finite-Volume Method (EbFVM) approach for actual engineering applications. To solve the unsteady 2D and 3D thermal energy equation using enthalpy as an independent variable, an in-house Fortran code has been developed based on the EbFVM approach in conjunction with unstructured and structured meshes. The numerical simulations, with four types of different heat sources, were performed for applications of real welding processes with variations in density and enthalpy as a function of temperature. The results are presented in terms of thermal cycles and temperature fields. Furthermore, the developed code was confronted against experimental works from the literature, simulated and lab-controlled experiments with AISI 409 ferritic workpieces, and exact analytical solutions with thermocouples fixed in different positions. In general, the numerical results from the current investigation are in close agreement with the results from the literature and the experimental results performed by the authors. The numerical results also highlighted the differences between the 2D and 3D models for thermal cycles near the bead weld.

Version [1.1] - [2D-xtDCR-LTBEM: A Fortran code for numerical solutions to the unsteady anisotropic-DCR equation of spatio-temporal coefficients]

Variable coefficient equations are usually used as governing equations for modeling problems which are associated with Functionally Graded Materials (FGM). Version 1.1 - 2D-xtDCR-LTBEM is a Fortran code that can be used to find numerical solutions of two-dimensional (2D) initial–boundary value problems which are governed by the unsteady anisotropic-diffusion convection reaction (DCR)-type and the anisotropic-diffusion reaction (DR)-type equations with a class of space–time dependent coefficients, by utilizing a combined Laplace Transform-Boundary Element Method (LTBEM). This code may provide valuable help for simulation of problems of FGM.

TTEP: A code for efficient calculation of the thermal transport from constant electron-phonon coupling approximation

A Fortran code named TTEP (Thermal Transport from constant Electron-Phonon coupling approximation) is presented in this work. Within the framework of first-principles calculation, this code utilizes the deformation potential approximation to replace the electron–phonon (EP) coupling matrix element in the phonon scattering due to EP interaction. By adopting this approximation, our method achieves a balance between computational efficiency and accuracy, enabling the exploration of the thermal transport from EP interaction with much reduced computational consumption. One of the key features of TTEP is its versatility in handling a broad range of carrier concentration, including both hole and electron doping. We also extend the applicability of TTEP to actual doping case and capture EP effect over a wide temperature range. Other scattering mechanisms, such as grain boundary scattering and phonon–phonon interaction, have been included in the calculation of lattice thermal conductivity through the Matthiessen’s rule. Several test cases are presented in this work to demonstrate the above features.

Effect of an Adiabatic Obstacle on the Symmetry of the Temperature, Flow, and Electric Charge Fields during Electrohydrodynamic Natural Convection

This study explores the impact of an adiabatic obstacle on the symmetry of temperature, flow, and electric charge fields during electrohydrodynamic (EHD) natural convection. The configuration studied involves a square, differentially heated cavity with an adiabatic obstacle subjected to a destabilizing thermal gradient and a potential difference between horizontal walls. A numerical analysis was performed using the finite volume method combined with Patankar’s “blocked-off-regions” technique, employing an in-house FORTRAN code. The study covers a range of dimensionless electrical Rayleigh numbers (0 to 700) and thermal Rayleigh numbers (102 to 105), with various obstacle positions. Key findings indicate that while the obstacle reduces heat transfer, this can be counterbalanced by electric field effects, achieving up to 165% local heat transfer improvement and 100% average enhancement. Depending on the obstacle’s position and size, convective transfer can increase by 27% or decrease by 21%. The study introduces five multiparametric mathematical correlations for rapid Nusselt number determination, applicable to numerous engineering scenarios. This work uniquely combines passive (adiabatic obstacle) and active (electric field) techniques to control heat transfer, providing new insights into the flow behaviour and charge distribution in electro-thermo-hydrodynamic systems.

Analysis of Laminated Composite Porous Plate under Sinusoidal Load with Various Boundary Conditions.

Bending analysis was carried out for a laminated composite porous plate due to sinusoidal loading with various boundary conditions using improved third-order theory. Zero transverse shear stress provided a free surface at the top and bottom of the plate. Also, the authors developed a finite element formulation based on improved third-order shear deformation theory. To circumvent the C1 continuity requirement associated with improved third-order shear deformation theory, a C0 FE formulation was developed by replacing the out-of-plane derivatives with independent field variables. An in-house FORTRAN code was developed for the bending analysis of the laminated porous plate considering a 2D finite element model. The complete thickness of the plate was covered with different porosity patterns. The impacts of various modulus ratios, boundary conditions, thickness ratios, fiber orientation angles, and material parameters were examined for laminated porous plates. There was an 18.8% reduction in deflection in the case of the square plate as compared to rectangular plates, with a porosity value of 0.1, a thickness ratio of 10, and an orientation angle of 0°/90°/0°. According to the current research, adding porosities causes a relatively greater change in deflection rather than stress, thereby aiding in the development of a lightweight structure.

H-COUP Version 3: A program for one-loop corrected decays of any Higgs bosons in non-minimal Higgs models

The H-COUP program is provided as a package of Fortran codes, which can compute observables related to Higgs bosons including radiative corrections in various extended Higgs sectors. We give a manual for the latest version of H-COUP (H-COUP_3.0), in which decay rates and branching ratios of all the Higgs bosons can be calculated at one-loop level in EW and Higgs interactions with QCD corrections in the Higgs singlet model, four types of the two Higgs doublet model with a softly-broken Z2 symmetry, and the inert doublet model. The previous version (H-COUP_2.0) can evaluate those only for the standard model like Higgs boson with the mass of 125 GeV (h). In H-COUP_3.0, renormalized quantities are computed based on the gauge-independent on-shell renormalization scheme. The source code of H-COUP_3.0 can be downloaded via the following link: http://www-het.phys.sci.osaka-u.ac.jp/~hcoup. By using H-COUP_3.0, we can compare the precise measurements of the properties of h and direct searches for additional Higgs bosons with their predictions at one-loop level, by which we can reconstruct the structure of the Higgs sector. New version program summaryProgram Title: H-COUP Version 3 5CPC Library link to program files:https://doi.org/10.17632/f88szmrj5x.3Developer's repository link:http://www-het.phys.sci.osaka-u.ac.jp/~hcoupLicensing provisions: GPLv3Programming language: Fortran90Journal reference of previous version: Comput. Phys. Commum. 257 (2020) 107512Does the new version supersede the previous version?: YesReasons for the new version: The previous version (H-COUP version 2) is a package of Fortran codes to provide one-loop corrected couplings, decay rates and branching ratios of the 125 GeV Higgs boson in the Higgs Singlet Model (HSM), the Two Higgs doublet models (THDMs) with a softly-broken Z2 symmetry, and the Inert Doublet Model (IDM). In the new version (H-COUP version 3), the H-COUP program has been improved to calculate the decay rates and the branching ratios of all the Higgs bosons including one-loop corrections in the above models. These calculations are performed based on the gauge independent on-shell renormalization scheme.Summary of revisions: We have added radiatively corrected decay rates and branching ratios for all the additional Higgs bosons, not only for the 125 GeV Higgs boson, in the extended Higgs models. Furthermore, several choices are provided for renormalization schemes used to evaluate electroweak corrections. The scalar two-point functions are renormalized by on-shell scheme as in the previous version, while the renormalization for the tadpole is performed by either the standard tadpole scheme or the alternative tadpole scheme. The users can choose these renormalization schemes.Nature of problem: Decay rates and branching ratios of all the Higgs bosons can be calculated with one-loop electroweak corrections and QCD corrections in the HSM, four types of the THDMs with the softly-broken Z2 symmetry, and the IDM. In the calculations of additional Higgs boson decays, for the three-body decay processes and loop induce processes of additional Higgs bosons, electroweak corrections are not included. As for the QCD correction, next-to-leading order or next-to-next-to-leading order corrections are included, depending on the decay process.Solution method: Electroweak corrections are evaluated based on the gauge independent on-shell renormalization scheme, while some parameters are renormalized by the MS‾ scheme. QCD corrections are evaluated with the MS‾ scheme.Additional comments including restrictions and unusual features: All functions up to the previous version are included in H-COUP version 3.

Techno-economic feasibility of integrating hybrid battery-hydrogen energy storage system into an academic building

Green hydrogen production and storage are vital in mitigating carbon emissions and sustainable transition. However, the high investment cost and management requirements are the bottleneck of utilizing hybrid hydrogen-based systems in microgrids. Given the necessity of cost-effective and optimal design of these systems, the present study examines techno-economic feasibility of integrating hybrid hydrogen-based systems into an outdoor test facility. With this perspective, several solar-driven hybrid scenarios are introduced at two energy storage levels, namely the battery and hydrogen energy storage systems, including the high-pressure gaseous hydrogen and metal hydride storage tanks. Dynamic simulations are carried out to address subtle interactions in components of the hybrid system by establishing a TRNSYS model coupled to a Fortran code simulating the metal hydride storage system. The OpenStudio-EnergyPlus plugin is used to simulate the building load, validate against experimental data, according to the measured data and monitored operating conditions. Aimed at enabling efficient integration of energy storage systems, a techno-enviro-economic optimization algorithm is developed to simultaneously minimize the levelized cost of the electricity and maximize the CO2 mitigation in each proposed hybrid scenario. The results indicate that integrating the gaseous hydrogen and metal hydride storages into the photovoltaic-alone scenario enhances 22.6% and 14.4% of the annual renewable factor. Accordingly, the inclusion of battery system to these hybrid scenarios gives a 30.4% and 20.3 % boost to the renewable factor value, respectively. Although the inclusion of battery energy storage into the hybrid systems increases the renewable factor, the results imply that it reduces the hydrogen production rate via electrolysis. The optimized values of the levelized cost of electricity and CO2 emission for different scenarios vary in the range of 0.376–0.789 $/kWh and 6.57–9.75 ton, respectively. The multi-criteria optimizations improve the levelized cost of electricity and CO2 emission by up to 46.2% and 11.3%, with respect to their preliminary design.

Patterns of Nanoporous Spherical Packing Emerging under Influence of Curvature and Confinement

Nanoporous membranes are popular in nanotechnology due to biomedical and industrial applications. During the past decade, experimental, theoretical and computational research into porous membranes and soft materials has opened up new mathematical dimensions. In bulk, diblock copolymers exhibit ordered morphologies such as parallel matrices of lamellae, bicontinuous matrices of gyroids, hexagonal matrices of cylinders and body-centred cubic matrices of spheres. In melt, confinement plays an essential role in tuning the frustration of the diblock copolymer system to predict more nanostructures. These nanostructures depend on the composition of the copolymers, their confining geometries and the degree of structural frustration. An isotropic 9-point stencil for Laplacian is constructed. The discrete finite-difference technique is used in polar grids to discretize the macromolecule of the diblock copolymer system to study spherical patterns to study the effect of curvature and confinement with a well-known and efficient cell dynamic simulation model. Intel FORTRAN (IFORT) codes are generated to run the CDS model and visualisation of simulation results is observed with the help of OPENDX. A comparison of the proposed study with existing experimental and computational studies is also presented.

ReMKiT1D - A framework for building reactive multi-fluid models of the tokamak scrape-off layer with coupled electron kinetics in 1D

In this manuscript we present the recently developed flexible framework for building both fluid and electron kinetic models of the tokamak Scrape-Off Layer in 1D - ReMKiT1D (Reactive Multi-fluid and Kinetic Transport in 1D). The framework can handle systems of non-linear ODEs, various 1D PDEs arising in fluid modelling, as well as PDEs arising from the treatment of the electron kinetic equation. As such, the framework allows for flexibility in fluid models of the Scrape-Off Layer while allowing the easy addition of kinetic electron effects. We focus on presenting both the high-level design decisions that allow for model flexibility, as well as the most important implementation aspects. A significant number of verification and performance tests are presented, as well as a step-by-step walkthrough of a simple example for setting up models using the Python interface. Program summaryProgram title: ReMKiT1DCPC Library link to program files:https://doi.org/10.17632/j47ym66xzj.1Developer's repository link:https://github.com/ukaea/ReMKiT1D and https://github.com/ukaea/ReMKiT1D-PythonLicensing provisions: GPLv3Programming language: Fortran, PythonSupplementary material:https://doi.org/10.14468/fdq7-z869Nature of problem: The flexible generation and modification of 1D models pertaining to multi-fluid simulations of the tokamak Scrape-Off Layer (SOL) with electron kinetics and reaction support. This would then allow both for rapid iteration on reduced models as well as the evaluation of kinetic electron effects in equilibria and during transients, following the formalism previously developed for SOL-KiT [1]. The framework was not only envisioned as the successor to SOL-KiT, but a tool that would allow users to construct their own models coupled with electron kinetics capabilities.Solution method: The framework is written heavily utilizing Object-Oriented design principles, in particular using an extended version of the puppeteer pattern as presented by Rouson et al. [2], as well as the heavy use of the strategy pattern/dependency injection. The Fortran code is MPI parallel and utilizes the PETSc library for implicit time-stepping. MPI parallelization is extended to distribution function Legendre harmonics, allowing for improved strong scaling. Initialization of the Fortran framework is done using JSON configuration files generated by an accompanying Python interface, and data analysis is standardized using widely used data formats such as HDF5.Additional comments including restrictions and unusual features: The present manuscript focuses on the design and high-level implementation of the framework, as well as the demonstration of the workflow and various verification and performance benchmarking tests. Some details are avoided for the sake of brevity at various points, and these are meant to be available as part of the general code documentation or tutorials offered on the main repositories.

Elasto-plasticity theory for large plastic deformation and its use for the material stiffness determination

In this paper, we present a finite elasto-plasticity theory for large plastic deformations. For the elastic part of the model, we use the St. Venant–Kirchhoff elasticity. The plastic part is described by the isomorphy concept, the yield condition is covered by the isotropic J2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_2$$\\end{document} theory of (Huber in Czas Techn 22:34,1904; von Mises in Math Phys 4:582–592, 1913) and (Hencky in ZAMM 9:215–220, 1924), and the yield condition uses the principle of maximum plastic dissipation. The numeric of this theory is discussed and finally implemented in a Fortran code to use it as material law in the UMAT subroutine of the finite element program Abaqus. The material law is validated using different test calculations like tensile and shear tests as well as a large deformation simulation compared to the Abaqus internal material law. Further, we apply this material model to determine the effective material stiffness tetrad of large deformed inhomogeneous materials. For these purposes, we additionally present an automated method for determining material stiffnesses of an arbitrary material in Abaqus.