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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,495 records · Page 83
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Thin Film Morphological Characteristics of a Perfluorinated Anion Exchange Membrane

Anion exchange membranes (AEMs) are a promising technology for fuel cell applications. Most of the research done to date was focused on membrane development, electrode fabrication, or cell performance. Studies of the polymer catalyst interface are needed in order to advance the science of these devices and achieve further improvements. In this work we have studied these interfacial properties using grazing-incidence small-angle x-ray scattering (GISAXS). Thin films of a perfluorinated anion exchange polymer were spin cast onto bare, or silver or platinum coated flat silicon substrates. From the GISAXS data, we can conclude that the polymer chains align parallel to the plain silicon or silver coated substrate at higher thicknesses, >17 nm and, >13 nm respectively. However, on the coated platinum substrate the alignment is somewhere between parallel and perpendicular. The in-plane alignment of ionomer on the surface constrains the swelling of water channels which affects the transport of reactants and products.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2015

Cable Braid Electromagnetic Penetration Model

The model for penetration of a wire braid is rigorously formulated. Integral formulas are developed from energy principles and reciprocity for both self and transfer immittances in terms of potentials for the fields. The detailed boundary value problem for the wire braid is also setup in a very efficient manner; the braid wires act as sources for the potentials in the form of a sequence of line multipoles with unknown coefficients that are determined by means of conditions arising from the wire surface boundary conditions. Approximations are introduced to relate the local properties of the braid wires to a simplified infinite periodic planar geometry. This is used in a simplified application of reciprocity to be able to treat nonuniform coaxial geometries including eccentric interior coaxial arrangements and an exterior ground plane.

42 ENGINEERING↗
DOE OSTI2019

Experimental Studies of Anisotropy on Borehole Breakouts in Mancos Shale

Calculating the size and orientation of borehole breakouts is one of the key methods for determining the orientation and magnitudes of the in situ stresses in the subsurface. To better understand the effects of anisotropy on borehole breakouts, experiments were conducted on Mancos Shale, a finely laminated mudrock. A novel testing configuration was developed to conduct borehole breakout experiments in a standard triaxial vessel and load frame. Samples were prepared at three different orientations and deformed under 6.9 to 20.7 MPa confining pressure. The results show a variation of peak strength and breakout geometry depending on the lamination orientation. Samples deformed parallel to laminations failed at a higher maximum compressive stress than samples deformed perpendicular to laminations, which were stronger than inclined samples. These relationships are quantified by a cosine-based failure envelope. Observed breakout shapes in perpendicular samples are V-shaped and symmetric around the borehole, which advance as a series of fractures of increasing size into the sidewalls. In inclined samples, fractures form along weaker laminations planes and grow in an en echelon pattern towards the axial stress direction. In parallel samples, long fractures grow from the wellbore towards the axial stress direction. The observed geometries point to potential sources of error in calculating in situ stresses from borehole breakouts.

58 GEOSCIENCES↗
DOE OSTI2021

Interplay Between Crustal‐Scale Thrusting, High Metamorphic Heating Rates, and the Development of Inverted Thermal‐Metamorphic Gradients: Numerical Models and Examples From the Caledonides of Northern Scotland

Abstract Understanding the processes that produce high prograde metamorphic heating rates and the development of inverted metamorphic sequences in collisional thrust belts remains a fundamental challenge for tectonics and metamorphic petrology. New 2D finite element models of crustal‐scale thrusts with variable slip rates (10, 20, 35, 50 km Myr −1 ) are used to examine how thrust sheet emplacement contributes to these processes. In the models, average prograde heating rates of 31–118 °C Myr −1 are observed in the footwall, with maximum transient heating rates of ∼167 °C Myr −1 occurring at the highest slip rate. Also, thrust sheet emplacement produces an inverted thermal gradient in the model footwall. At slip rates of 10 km Myr −1 , heating magnitudes >200 °C are observed >7 km structurally beneath the thrust plane. At slip rates of 20–50 km Myr −1 , models produce thermal penetration depths of 4–5 km for similar heating magnitudes. Petrologically determined heating rates for thrust footwalls in the Scandian orogenic wedge of northern Scotland mostly yield rates consistent with model results (10–230 °C Myr −1 ). The model‐derived magnitude of inverted thermal gradients is also similar to those indicated in texturally determined deformation temperature transects across the Scandian orogenic wedge (100 °C–180 °C). Combined, these results indicate that high heating rates can be produced by fault slip at typical plate velocities. Additionally, this implies that crustal‐scale thrusts are likely to produce inverted metamorphic sequences in most systems, provided that P‐T conditions during slip allow for metamorphic or recrystallization processes that would preserve evidence for such features.

Thigpen, J. Ryan↗
DOE OSTI2021

Field validation of an actuated convergent-beam acoustic Doppler profiler for high resolution flow mapping

Abstract Energetic river and tidal flow environments feature complex hydrodynamic conditions. Conventional acoustic Doppler profiling instrumentation typically requires assumptions of flow homogeneity over the spatial scales of the divergent beam separation. This removes the ability to measure spatio-temporal variability within the flow. However, velocity variability within these spatial scales is often important in the design of structures and devices exposed to such flow, informing dynamic and peak hydrodynamic load predictions. The research presented outlines the development and testing of a flow measurement instrument consisting of multiple spatially-separated single beam acoustic Doppler profilers converging on a remote focal point, the location of which can be programmatically adjusted through actuation. This increases the spatial resolution at which remote field measurements can be made in energetic flow environments. Field testing of the instrument was conducted in a tidal channel at Sequim Bay Inlet, WA, USA. Results are compared with independent reference measurements made by a co-located, motion-corrected acoustic Doppler velocimeter. This comparison, across tidal velocities of 0.4–0.7 m s −1 , showed a mean velocity error of 0.5%–13.2% across nine sample locations within a 3.00 m × 2.25 m plane. To the authors’ knowledge, this is the first publication of flow velocity results from non-intrusive acoustic measurements at an off-axis, focal point location that features 3D positional control.

13 HYDRO ENERGY↗
DOE OSTI2018

Configurational forces in electronic structure calculations using Kohn-Sham density functional theory

Here we derive the expressions for configurational forces in Kohn-Sham density functional theory, which correspond to the generalized variational force computed as the derivative of the Kohn-Sham energy functional with respect to the position of a material point x. These configurational forces that result from the inner variations of the Kohn-Sham energy functional provide a unified framework to compute atomic forces as well as stress tensor for geometry optimization. Importantly, owing to the variational nature of the formulation, these configurational forces inherently account for the Pulay corrections. The formulation presented in this work treats both pseudopotential and all-electron calculations in a single framework, and employs a local variational real-space formulation of Kohn-Sham density functional theory (DFT) expressed in terms of the nonorthogonal wave functions that is amenable to reduced-order scaling techniques. We demonstrate the accuracy and performance of the proposed configurational force approach on benchmark all-electron and pseudopotential calculations conducted using higher-order finite-element discretization. To this end, we examine the rates of convergence of the finite-element discretization in the computed forces and stresses for various materials systems, and, further, verify the accuracy from finite differencing the energy. Wherever applicable, we also compare the forces and stresses with those obtained from Kohn-Sham DFT calculations employing plane-wave basis (pseudopotential calculations) and Gaussian basis (all-electron calculations). Finally, we verify the accuracy of the forces on large materials systems involving a metallic aluminum nanocluster containing 666 atoms and an alkane chain containing 902 atoms, where the Kohn-Sham electronic ground state is computed using a reduced-order scaling subspace projection technique

36 MATERIALS SCIENCE↗
DOE OSTI2015

Quantum Electronic Matter in Two Dimensions

Most often, the electrical properties of a material are described as either "conducting" or "insulating". Copper, everyone knows, is a good conductor. It is the foundation of the electrical infrastructure of the nation. Glass, on the other hand, is an excellent insulator. But do these two words describe all the possibilities? The answer is emphatically no, and the basic subject of the research funded by this grant is aimed at fleshing out a more complete description of the electrical properties of materials. Many people are aware that there are also special materials called superconductors. A superconductor (e.g. aluminum when cooled to very low temperatures) is like a regular conductor except that it conducts electricity with no energy loss at all. Ordinary metals get hot when current flows through them; witness the toaster in your kitchen. In a superconductor something very special is going on: The electrons in the metal don't behave individually as they do in an ordinary conductor. Instead they act collectively. It is this collective aspect that makes superconductors so interesting to physicists. So now we have metals, insulators and superconductors. Is there anything else? We now know the answer is yes. In this research we examine special conducting materials, ones in which the mobile electrons are confined to move on a plane surface (as opposed to motion in all three directions). Examples of such "2D" materials include electrons confined to the interface between two otherwise insulating materials (as in the so-called "semiconductor heterostructures" used here) and the single atomic layer of carbon atoms now known as "graphene". Materials like these are not just museum curiosities; each of the billions of transistors in every smart-phone has a 2D electron system in it. In the work supported by this grant, the focus is on both collective conducting states in semiconductor heterostructures and on the conducting properties of graphene and its few-layer cousins. In particular, the exotic collective (and deeply quantum mechanical) electronic phases which develop when a large magnetic field is applied have been a major focus of effort. Significant results have been obtained from both ordinary electrical measurements and from more sophisticated thermoelectric studies of such systems. Related studies of few-layer graphenes have elucidated the transition from the two- to three-dimensional electrical properties of carbon-based conductors. Investigations like these expand our understanding of electronic materials general. While there are certainly immediate fundamental scientific pay-offs, it is also true that research of this kind ultimately leads to technological breakthroughs in the long term. By way of example, superconductivity was undoubtedly regarded as a useless novelty when it was discovered in 1911. Who could have known then that it would become crucial to the medical revolution brought about by magnetic resonance imaging decades later?

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

FY23 Progress Report: SRNL Analysis of ICCWR LCM and WAMS data for Corrosion and Cracking

Algorithms for Machine Learning (ML) and data analysis for the 3013 Surveillance Program have been developed in an ongoing collaborative effort by the Savannah River National Laboratory (SRNL) and the University of South Carolina (USC). The objective of the algorithms is to automate the identification of corrosion and crack formation in the Inner Container Closure Weld Region (ICCWR) of the canister system used to store Pu-bearing material. Data for corrosion and cracking is collected from large binary files generated by a Laser Confocal Microscope (LCM), the Wide Area 3D Measurement System (WAMS), and in a recent proposal, by a Scanning Electron Microscope (SEM). The ML software uses the physical attributes in the data files (e.g., one or all of: height, color, and grayscale values as functions of position in a plane projection) to detect the presence of surface corrosion and cracking after being trained on similar data with the features to be detected labeled.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2014

Augmented Lagrangian formulation of orbital-free density functional theory

We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Femtosecond photoemission electron microscopy of surface plasmon polariton beam steering via nanohole arrays

Directional control over surface plasmon polariton (SPP) waves is a prerequisite for the development of miniaturized optical circuitry. Here, the efficacy of single and dual component SPP steering elements is explored through photoemission electron microscopy. Our imaging scheme relies on two-color photoemission and counter-propagating SPP generation, which collectively allow SPPs to be visualized in real space. Wave-vector difference mixing between two-dimensional arrays of nanoholes and photon momenta enables SPP steering with directionality governed by the array lattice constant. The magnitude of grating momentum required to achieve counter-propagation guarantees efficient steering over the full range of the negative half-space. In our dual component configuration, separate SPP generation and Bragg diffraction based steering optics are employed. We find that array Bragg planes principally influence the SPP angles through the array band structure, which allows us to visualize both positive and negative refractory waves.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Model-based PSF and MTF estimation and validation from skeletal clinical CT images

Purpose: A method was developed to correct for systematic errors in estimating the thickness of thin bones due to image blurring in CT images using bone interfaces to estimate the point-spread-function (PSF). This study validates the accuracy of the PSFs estimated using said method from various clinical CT images featuring cortical bones. Methods: Gaussian PSFs, characterized by a different extent in the z (scan) direction than in the x and y directions were obtained using our method from 11 clinical CT scans of a cadaveric craniofacial skeleton. These PSFs were estimated for multiple combinations of scanning parameters and reconstruction methods. The actual PSF for each scan setting was measured using the slanted-slit technique within the image slice plane and the longitudinal axis. The Gaussian PSF and the corresponding modulation transfer function (MTF) are compared against the actual PSF and MTF for validation. Results: The differences (errors) between the actual and estimated full-width half-max (FWHM) of the PSFs were 0.09 ± 0.05 and 0.14 ± 0.11 mm for the xy and z axes, respectively. The overall errors in the predicted frequencies measured at 75%, 50%, 25%, 10%, and 5% MTF levels were 0.06 ± 0.07 and 0.06 ± 0.04 cycles/mm for the xy and z axes, respectively. The accuracy of the estimates was dependent on whether they were reconstructed with a standard kernel (Toshiba's FC68, mean error of 0.06 ± 0.05 mm, MTF mean error 0.02 ± 0.02 cycles/mm) or a high resolution bone kernel (Toshiba's FC81, PSF FWHM error 0.12 ± 0.03 mm, MTF mean error 0.09 ± 0.08 cycles/mm). Conclusions: The method is accurate in 3D for an image reconstructed using a standard reconstruction kernel, which conforms to the Gaussian PSF assumption but less accurate when using a high resolution bone kernel. The method is a practical and self-contained means of estimating the PSF in clinical CT images featuring cortical bones, without the need phantoms or any prior knowledge about the scanner-specific parameters.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Motion as perturbation. II. Development of the method for dosimetric analysis of motion effects with fixed-gantry IMRT

Purpose: In this work, the feasibility of implementing a motion-perturbation approach to accurately estimate volumetric dose in the presence of organ motion—previously demonstrated for VMAT-–is studied for static gantry IMRT. The method's accuracy is improved for the voxels that have very low planned dose but acquire appreciable dose due to motion. The study describes the modified algorithm and its experimental validation and provides an example of a clinical application. Methods: A contoured region-of-interest is propagated according to the predefined motion kernel throughout time-resolved 4D phantom dose grids. This timed series of 3D dose grids is produced by the measurement-guided dose reconstruction algorithm, based on an irradiation of a staticARCCHECK (AC) helical dosimeter array (Sun Nuclear Corp., Melbourne, FL). Each moving voxel collects dose over the dynamic simulation. The difference in dose-to-moving voxel vs dose-to-static voxel in-phantom forms the basis of a motion perturbation correction that is applied to the corresponding voxel in the patient dataset. A new method to synchronize the accelerator and dosimeter clocks, applicable to fixed-gantry IMRT, was developed. Refinements to the algorithm account for the excursion of low dose voxels into high dose regions, causing appreciable dose increase due to motion (LDVE correction). For experimental validation, four plans using TG-119 structure sets and objectives were produced using segmented IMRT direct machine parameters optimization in Pinnacle treatment planning system (v. 9.6, Philips Radiation Oncology Systems, Fitchburg, WI). All beams were delivered with the gantry angle of 0°. Each beam was delivered three times: (1) to the static AC centered on the room lasers; (2) to a static phantom containing a MAPCHECK2 (MC2) planar diode array dosimeter (Sun Nuclear); and (3) to the moving MC2 phantom. The motion trajectory was an ellipse in the IEC XY plane, with 3 and 1.5 cm axes. The period was 5 s, with the resulting average motion speed of 1.45 cm/s. The motion-perturbed high resolution (2 mm voxel) volumetric dose grids on the MC2 phantom were generated for each beam. From each grid, a coronal dose plane at the detector level was extracted and compared to the corresponding moving MC2 measurement, using gamma analysis with both global (G) and local (L) dose-error normalization. Results: Using the TG-119 criteria of (3%G/3 mm), per beam average gamma analysis passing rates exceeded 95% in all cases. No individual beam had a passing rate below 91%. LDVE correction eliminated systematic disagreement patterns at the beams’ aperture edges. In a representative example, application of LDVE correction improved (2%L/2 mm) gamma analysis passing rate for an IMRT beam from 74% to 98%. Conclusions: The effect of motion on the moving region-of-interest IMRT dose can be estimated with a standard, static phantom QA measurement, provided the motion characteristics are independently known from 4D CT or otherwise. The motion-perturbed absolute dose estimates were validated by the direct planar diode array measurements, and were found to reliably agree with them in a homogeneous phantom.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Collision of plane thermonuclear detonation waves in a preliminarily compressed DT mixture

The paper deals with a one-dimensional problem on symmetric irradiation of a plane DT fuel layer with a thickness 2H and density ρ{sub 0} ⩽ 100ρ{sub s} (where ρ{sub s} is the density of the DT fuel in the solid state at atmospheric pressure and a temperature of 4 K) by two identical monoenergetic proton beams with a kinetic energy of 1 MeV, an intensity of 10{sup 19} W/cm{sup 2}, and a duration of 50 ps. The problem is solved in the framework of one-fluid two-temperature hydrodynamic model that takes into account the equation of state for hydrogen, electron and ion heat conductivities, kinetics of the DT reaction, plasma self-radiation, and plasma heating by α-particles. The irradiation of the fuel results in the appearance of two counterpropagating detonation waves to the fronts of which rarefaction waves are adjacent. The efficiency of the DT reaction after the collision (reflection from the plane of symmetry) of the detonation waves depends on the spatial homogeneity of thermodynamic functions between the fronts of the reflected detonation waves. At Hρ{sub 0} ≈ 1 g/cm{sup 2}, the gain factor is G ≈ 200, whereas at Hρ{sub 0} ≈ 5 g/cm{sup 2}, it is G > 2000. As applied to a cylindrical target that is ignited from ends and in which the cylinder with the fuel is surrounded by a heavy magnetized shell, the obtained values of the burn-up and gain factors are maximum possible. To estimate the ignition energy E{sub ig} of a cylindrical target by using solutions to the one-dimensional problem, a quasi-one-dimensional model is developed. The model assumes that the main mechanism of target ignition is fuel heating by α-particles. The trajectories of α-particles are limited by a cylindrical surface with a given radius, which is a parameter of the model and is identified with the fuel radius in the target and the radii of the irradiating proton beams. This model reproduces the well-known theoretical dependence E{sub ig} ∼ ρ{sub 0}{sup −2} and yields E{sub ig} = 160 kJ as a lower estimate of the ignition energy for ρ{sub 0} = 100ρ{sub s} ≈ 22 g/cm{sup 3}.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

FY25 Progress Report: SRNL Analysis of ICCWR LCM and WAMS data for Corrosion and Cracking

Algorithms for Machine Learning (ML) and image analysis for the 3013 Surveillance Program have been developed in an ongoing collaborative effort by the Savannah River National Laboratory (SRNL) and the University of South Carolina (USC). The objective of the algorithms is to automate the identification of corrosion and cracks in the Inner Container Closure Weld Region (ICCWR) of the canister system used to store Pu-bearing material. Data for corrosion and cracking is collected from large binary files generated by a Laser Confocal Microscope (LCM), the Wide Area 3D Measurement System (WAMS), or, in a recent proposal, by a Scanning Electron Microscope (SEM). The ML software uses the physical attributes in the data files (e.g., one or more of: height, color, and 16-bit grayscale values as functions of position in a plane projection) to detect signs of surface corrosion and cracking after being trained on similar data with the features to be detected. Although the initial scope included screening for broader indicators of corrosion, e.g., pitting, the identification of potential cracks was prioritized for the past several years at the request of program leadership.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Developing a GUI for the Robotic Test Stand

The introduction of this poster explains the technology behind DUNE’s far and near detectors and how passing neutrinos generate electrons that drift into a wire grid. I then explain how 3 ASICs manage signals received from electron interception. Next, the poster states how COLDATA chips are undergoing quality control by a Robotic Test Stand using a state machine. I further explained how earlier tests were done via a command line script and the necessity to implement a user-friendly Graphical User Interface with new features a command line can’t implement. For the implementation section, tools and methods for implementation are listed such as Python, tkinter, and GitHub as well as how multithreading and queue implementation was necessary for GUI functionality. Then, I elaborated on the GUIs new features. Finally, I explain how the GUI will be distributed across multiple institutions and future changes planned for the GUI. Photos of the RTS, far detector cave, diagram of anode assembly plane, COLDATA chips, set up tab, result tab, and legacy command line interface are shown.

Gutierrez Villanueva, Jaziel [DuPage Coll.]↗
DOE OSTI2023

Face‐on Orientation Matches Vertical Organic Electrochemical Transistors for High Transconductance and Superior Non‐Volatility

Abstract The recently developed vertical structure of organic electrochemical transistors (OECTs) can integrate volatile and non‐volatile functions into one reconfigurable device, making it highly promising. However, comparing with the conventional planar OECT (c‐OECT), the understanding of vertical OECT (v‐OECT) working principles and device engineering strategies is still lacking, impeding rational optimization. Since a major difference between c‐ and v‐OECTs is their charge transport directionality, which is highly influenced by crystallite orientations, the orientation–device structure match thus becomes an important yet outstanding topic for OECTs. Herein, using ann‐type small molecule IDIC‐MEG, investigate how much impact such match can have on OECT performance. The IDIC‐MEG c‐OECT fails to work due to the seriously hindered in‐plane electron transport by face‐on orientation. Surprisingly, simply changing the device structure from planar to vertical allows the resultant v‐OECT to exhibit the highest reported transconductance (46.3 mS) among all small‐molecule OECTs, thanks to the match between face‐on orientation and the vertical structure. Such match also leads to excellent non‐volatility, including highly predictable programmability and good operational stability. This work, for the first time, explicitly demonstrates the significance of orientation–device structure match for OECT optimization, establishing new guidelines for achieving high‐performance volatile and non‐volatile OECTs.

Chemistry↗
DOE OSTI2018

The conformal bootstrap at finite temperature

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O(N) model at leading order in 1/N. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Efficient computation of basic sums for random polydispersed composites

The main goal of the paper was to develop algorithms and methods for computation of basic sums, the mathematical objects of great importance in computational materials science having applications to description of the representative volume element (RVE) and to the effective properties of 2D composites. The previously used algorithm had the exponential complexity. We propose a linearly complex algorithm. All the presented algorithms can be easily implemented in modern scientific computing packages, while maintaining both efficient calculations and a high level of abstraction. The proposed approach is applied to derivation of a polynomial approximation of the effective conductivity formula for 2D random material with non-overlapping circular inclusions with normally distributed radii. The obtained formulas are applied to the optimal packing problem of disks on the plane.

97 MATHEMATICS AND COMPUTING↗