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At least 631 records · Page 35

Autonomous Intelligent Charging/Discharging of Electric Vehicles using Distributed Multi-Agent ADMM Framework for Grid Ancillary Services

The increasing popularity of Electric Vehicles (EVs) in the distribution grid along with technological advancement in EV electronics such as vehicle to grid (V2G) technique has enabled them to participate in grid ancillary services. To achieve this, the EVs need to establish a contract with third-party aggregators and connect to a charging unit, either residential or commercial. At any time they are connected, the EVs can decide to take part in the ancillary services program offered to them by the aggregators. If agreed, the aggregators will use the EVs as a power source capable of charging/discharging power according to the input signal, and in return, they will be compensated. This inter-temporal nature of charging/discharging is also transforming the traditional optimal power flow (OPF) problem into a dynamic OPF problem. This chapter aims at developing a multi-layer time-dependent optimization algorithm to utilize EV potential and provide ancillary services while maximizing its utilization function. Specifically, in the upper layer, an autonomous distributed ADMM algorithm is developed to optimize the cost for charging/discharging EVs while using them to regulate the voltage at each bus in the distribution grid. The distributed ADMM algorithm is also expanded to the lower layer where the individual EVs active and reactive power is controlled for voltage regulation while maintaining the desired state of the charge of the vehicle at the end of the charging period. The effectiveness and performance improvement of the proposed multi-layer algorithm is illustrated through analytical analysis and simulation results.

Rahman, Towfiq↗

Advances in 3D Gel Printing for Enzyme Immobilization

Incorporating enzymes with three-dimensional (3D) printing is an exciting new field of convergence research that holds infinite potential for creating highly customizable components with diverse and efficient biocatalytic properties. Enzymes, nature’s nanoscale protein-based catalysts, perform crucial functions in biological systems and play increasingly important roles in modern chemical processing methods, cascade reactions, and sensor technologies. Immobilizing enzymes on solid carriers facilitates their recovery and reuse, improves stability and longevity, broadens applicability, and reduces overall processing and chemical conversion costs. Three-dimensional printing offers extraordinary flexibility for creating high-resolution complex structures that enable completely new reactor designs with versatile sub-micron functional features in macroscale objects. Immobilizing enzymes on or in 3D printed structures makes it possible to precisely control their spatial location for the optimal catalytic reaction. Combining the rapid advances in these two technologies is leading to completely new levels of control and precision in fabricating immobilized enzyme catalysts. The goal of this review is to promote further research by providing a critical discussion of 3D printed enzyme immobilization methods encompassing both post-printing immobilization and immobilization by physical entrapment during 3D printing. Especially, 3D printed gel matrix techniques offer mild single-step entrapment mechanisms that produce ideal environments for enzymes with high retention of catalytic function and unparalleled fabrication control. Examples from the literature, comparisons of the benefits and challenges of different combinations of the two technologies, novel approaches employed to enhance printed hydrogel physical properties, and an outlook on future directions are included to provide inspiration and insights for pursuing work in this promising field.

3D printing↗

Accelerating the development of new solar absorbers by photoemission characterization coupled with density functional theory

Abstract The expectation to progress towards Terawatts production by solar technologies requires continuous development of new materials to improve efficiency and lower the cost of devices beyond what is currently available at industrial level. At the same time, the turnaround time to make the investment worthwhile is progressively shrinking. Whereas traditional absorbers have developed in a timeframe spanning decades, there is an expectation that emerging materials will be converted into industrially relevant reality in a much shorter timeframe. Thus, it becomes necessary to develop new approaches and techniques that could accelerate decision-making steps on whether further research on a material is worth pursuing or not. In this review, we will provide an overview of the photoemission characterization methods and theoretical approaches that have been developed in the past decades to accelerate the transfer of emerging solar absorbers into efficient devices.

14 SOLAR ENERGY↗

5.1.6 Demo #6: NanoStitch (NAWAStitch) Multifunctional Composites Trade Validation

The overall objective of the NanoStitch Multifunctional Composites Trade Validation Demonstration project was to determine the value proposition of adding NanoStitch to rapid-cure composite systems for structures used in the expanding sector of advanced air mobility (AAM) and specifically electric vertical take-off and landing (eVTOL) aircraft. The expected value proposition was stronger composite parts, with new multifunctional attributes, that are lower cost to fabricate and maintain. NanoStitch is a new composite innovation where a contiguous vertically aligned carbon nanotube (VACNT) forest is located between each ply of a laminate composite resulting in improved mechanical properties as well as other multifunctional properties such as enhanced thermal and electrical conductivity. NanoStitch was originally distributed by N12, later acquired by NAWA Technologies, now called NAWAStitch, and henceforth referred to in this document as NAWAStitch. Two significant evaluations were framed to help meet the overall objective. First, was Task 1 to evaluate the effects that adding NAWAStitch to a rapid cure material system would have on the mechanical and processing properties of the material. Second, was Task 2 to evaluate the workability of adding NAWAStitch to practical flight demonstration articles. From previous research, it was already known that the application of NAWAStitch to a composite structure can enhance the mechanical properties of that structure. However, this project will help the engineering community understand those benefits and the basic structural strength values to apply when incorporating NAWAStitch material into composite structure that utilizes a rapid-cure resin system, which is novel. Testing showed that by adding NAWAStitch to the prepreg, most material properties were improved because the VACNTs strengthened the resin to fiber interface, and the interface itself, between plies. For example compression strength improved by more than 20%, and erosion resistance by more than 50%. The UDRI team identified two flight demonstration articles through discussions with Aurora Flight Sciences (Aurora) and reviewing literature on air mobility and the eVTOL market. The demonstration articles were a thin skin honeycomb panel and a section from an eVTOL propeller blade. The manufacturing and testing trials of the demonstration articles were as follows: • NAWAStitch added no manufacturing complexity or detriment to the article physical qualities, while at the same time added multifunctional properties such as enhanced rain erosion and electrothermal de-icing besides enhanced mechanical properties • VACNTs did not increase or hurt the mechanical properties of the interface between honeycomb core materials and the thin skin face sheet • Demonstrated successful de-icing function in an eVTOL propeller meeting real-world specifications in uniformity and endurance • Multifunctional eVTOL propeller cost analysis showed a cost savings of at least 67 % for a single propeller blade with multifunctional de-icing capability and improved mechanical properties which equates to a potential savings of $10,116 per eVTOL aircraft with six three-bladed propellers Overall, the results of this project can provide additional tools for the composite industry to optimize energy efficiency through faster and stronger composite parts that are lower cost to fabricate and maintain. Additionally, the results of this effort can help US industry like NAWA America set the stage for rapid growth and establishment of a manufacturing facility in Ohio. The project has given NAWA America the basic understanding of how the addition of VACNTs to a composite structure can affect the mechanical properties and hence point them to potential commercial applications. The project has also provided Teijin Carbon US with another potential material application for their rapid cure materials that are manufactured at the Renegade facility in Miamisburg, OH.

36 MATERIALS SCIENCE↗

Applications of Decellularized Plant Tissues in Regenerative Medicine and Tissue Engineering

The development of biomaterials capable of supporting complex tissue growth remains a central challenge in regenerative medicine and tissue engineering, particularly in replicating the structural, mechanical, and transport functions of native extracellular matrices. While decellularized animal tissues have demonstrated significant success as scaffolds for tissue engineering, they are still constrained by cost, immunogenicity, and ethical concerns. In recent years, decellularized plant tissues have emerged as a compelling alternative scaffold platform due to their inherent vascular architectures, ethical sourcing, tunable mechanical properties, cytocompatibility, and sustainability. This review summarizes current strategies for the decellularization of plant tissues, including chemical, enzymatic, and physical approaches, and discusses how these methods preserve plant cell wall structure while removing immunogenic components. Advances in surface loading and functionalization, including protein coatings, oxidation, nanoparticle incorporation, peptide conjugation, and bioactive molecule loading, have further enhanced cell adhesion, differentiation, biodegradability, and immunomodulation. Recent applications of decellularized plant scaffolds in cardiac, skeletal muscle, bone, nerve, and wound healing contexts are reviewed, highlighting proof-of-concept successes and remaining challenges. Beyond therapeutic applications, plant-derived scaffolds have also enabled physiologically relevant in vitro models for vascular biology, mechanotransduction, cancer, metabolic tissues, and drug response studies. Collectively, these advances position decellularized plant tissues as versatile, low-cost, and ethically favorable biomaterials with growing relevance for both regenerative medicine and tissue modeling.

59 BASIC BIOLOGICAL SCIENCES↗

On the Impact of Income, Age, and Travel Distance on the Value of Time

The value of time (VOT) is a fundamental component used in transportation modeling, policy analysis, and economic appraisal. Decades of research and practice have empirically estimated the VOT across many factors (e.g., mode, purpose, time, comfort, etc.), yet little is known about its underlying form. Although it is well established that VOT can vary, it is still unclear whether patterns exist in this variation. The objective of this paper is not to merely estimate the VOT, but to model the VOT across multiple continuous and interacting variables. The purpose is to reveal its functional form with respect to mode, age, gender, purpose, income, and time of day to provide a generalizable understanding for future research and practice. Such an understanding can help develop simpler models and reduce the need for bespoke estimations for every conceivable variable perturbation. This research utilized a household travel survey containing 14,159 reported trips with imputed travel time and costs for the alternative mode choices. The average overall estimated VOT is 40.32 $/h, with results showing VOT varying log-linearly with income and trip distance, but following a Gaussian function (normal curve) with age. Overall, the results show that travel distance dominates VOT variation, which increases exponentially at a rate that is 3.61 times higher per mile of distance than per $10,000 of income, and that VOT by age peaks at age 54. This basic understanding of how the VOT varies sets the foundation for answering the subsequent question for why it might vary.

Engineering↗

Shape restricted additive hazards models: Monotone, unimodal, and U‐shape hazard functions

We consider estimation of the semiparametric additive hazards model with an unspecified baseline hazard function where the effect of a continuous covariate has a specific shape but otherwise unspecified. Such estimation is particularly useful for a unimodal hazard function, where the hazard is monotone increasing and monotone decreasing with an unknown mode. A popular approach of the proportional hazards model is limited in such setting due to the complicated structure of the partial likelihood. Our model defines a quadratic loss function, and its simple structure allows a global Hessian matrix that does not involve parameters. Thus, once the global Hessian matrix is computed, a standard quadratic programming method can be applicable by profiling all possible locations of the mode. However, the quadratic programming method may be inefficient to handle a large global Hessian matrix in the profiling algorithm due to a large dimensionality, where the dimension of the global Hessian matrix and number of hypothetical modes are the same order as the sample size. We propose the quadratic pool adjacent violators algorithm to reduce computational costs. The proposed algorithm is extended to the model with a time‐dependent covariate with monotone or U‐shape hazard function. In simulation studies, our proposed method improves computational speed compared to the quadratic programming method, with bias and mean square error reductions. We analyze data from a recent cardiovascular study.

Mathematical & Computational Biology↗

Smooth Dispersion Is Physically Appropriate: Assessing and Amending the D4 Dispersion Model

The addition of dispersion corrections to density functionals is essential for accurate energy and geometry predictions. Among them, the D4 scheme is popular due to its low computational cost and high accuracy. However, due to its design, the D4 correction can occasionally lead to anomalies, such as unphysical curvature and bumps in the potential energy surface. We find these anomalies are common in the D4 model, although observable consequences are rarer than in the D3 model for reasons we explain. Nevertheless, we uncover instances of unphysical local minima and stationary points with the D4 scheme and propose two solutions that yield smoother dispersion energy as a function of nuclear position. One is trivial to implement, based on a smoother reparametrization of Gaussian weighting (D4S) to find the effective coordination number. The other replaces Gaussian weighting with soft linear interpolation (D4SL). These new approaches usually remove artificial extremum points, while maintaining accuracy.

Tkachenko, Nikolay V↗

Development of neural network force fields for corrosion studies

To fully understand the chemistry and physics of corrosion, novel methods of simulation must be developed. One approach is designing machine learning (ML) algorithms integrated with density functional theory to develop adaptive force fields to gain insight into corrosion behavior namely at the surface of metal oxides. Current methods of modeling corrosion are slow due to the computational cost of resolving both reaction mechanics and mass transport processes. Machine learning methods can be implemented to obtain structure-activity relationships at both the molecular and bulk scale while still retaining the accuracy of density functional theory (DFT) and significantly decreasing the time needed for simulations of complex chemical processes in the various environments of corrosion. Multiscale models are needed for corrosion studies to fully understand its processes not only at the atomic length scale (chemical bonding, energies, and forces), but also at the nano and meso length scales (solid-state physics and material science processes). Current methods of study include DFT, molecular dynamics, and Monte Carlo. The limitation of DFT is that only a small number of atoms or molecules can be simulated at that level of theory. Density functional theory is used to study the electronic structure of atoms and molecules, and calculate the force component of each atom. However, these calculations are limited to about 1000 atoms. Custom periodic boundary conditions (PBC) can be used to describe the various environments and defects that affect the atomic forces to produce a large data set from which a training set can be derived. Machine learning can be utilized to overcome the barrier of modeling macroscopic and multi-scale processes from ab initio calculations through the development of adaptive force fields. Local environments determine the atomic forces of a given system, therefore adaptive force fields must be created to produce reliable quantum mechanical calculations. This can be achieved by developing a learning algorithm that uses the mapped atomic forces or fingerprint as an input to produce energies and magnetic moments as output. A systematic approach was used to begin to build a data set in order to accurately describe the atomic forces in various environments. In Figure 4 below, a simple PBC cell of Fe{sub 2}O{sub 3} was first optimized. A surface optimization was performed next, followed by a hydroxylated surface optimization. Once this calculation has converged, the adsorption of halide species to the hydroxylated surface will be investigated. TensorFlow is an open source platform for machine learning developed by Google. Using a high level application program interface (API) such as Keras allows for building and training ML models easily in a number of different environments and languages. For this project, a neural network was developed within Anaconda in Python. Future Work: Further development of reference data set; Refining neural network and learning algorithm; Fingerprinting atomic environment to enable mapping of atomic force components; Choosing appropriate training set from reference data; Learning from training set and enabling non-linear mapping of training set fingerprints and the atomic forces; Estimation of uncertainty to identify ranges of outside applicability; Testing and analysis of molecular dynamic simulations.

36 MATERIALS SCIENCE↗

$\mathrm{DRAGON}$: A multi-GPU orbital-free density functional theory molecular dynamics simulation package for modeling of warm dense matter

As progress in electronic structure theoretical methods is made, ab initio molecular dynamics (MD) based on orbital-free density functional theory (OF-DFT) is becoming increasingly more successful at substituting the traditional, very accurate but computationally costly Kohn–Sham (KS) approach for simulations of matter at the challenging warm dense matter (WDM) regime. However, despite the significant cost alleviation of eliminating the dependence on the KS orbitals, OF-DFT MD runs require ~10 2 to 10 3 CPU cores running for days, or even weeks, for simulations of systems comprised of 10 2 to 10 3 atoms, depending on thermodynamic conditions. Here we present DRAGON, a multi-GPU OF-DFT MD code for fast and efficient simulations of WDM. With a relatively small allocation of resources (4 to 8 GPU devices) it can provide an order of magnitude speedup for simulations containing $\mathscr{O}$(10 4 ) atoms and target systems composed of $\mathscr{O}$(10 5 ) atoms at conditions within the WDM regime, which is currently outside the capabilities of CPU codes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Meta-GGA performance in solids at almost GGA cost

A recent modification, r 2 SCAN, of the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (GGA) exchange-correlation functional mostly eliminates numerical instabilities and attendant integration grid sensitivities exhibited by SCAN. Here, we show that the successful deorbitalization of SCAN to SCAN-L (SCAN with density Laplacian dependence) carries over directly to yield r 2 SCAN-L. A major benefit is that the high iteration counts that hindered the use of SCAN-L are eliminated in r 2 SCAN-L. It therefore is a computationally much faster meta-GGA than its orbital-dependent antecedent. In this work, validation data for molecular heats of formation, bond lengths, and vibration frequencies (G3/99X, T96-R, and T82-F test sets, respectively) and on lattice constants, and cohesive energies (for 55 solids) and bulk moduli (for 40 solids) are provided. In addition, we show that the overmagnetization of bcc Fe, hcp Co, and fcc Ni persists in r 2 SCAN but does not appear in r 2 SCAN-L. Distinct from SCAN, both r 2 SCAN and r 2 SCAN-L give the correct nonmagnetic ground state for bcc V.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Applications to Materials for Catalysis and Electrochemistry

Modeling complex materials using high-fidelity, ab initio methods at low cost is a fundamental goal for quantum chemical software packages. The GW approximation and random phase approximation (RPA) provide a unified description of both electronic structure and total energies using the same physics in a many-body perturbative approach that can be more accurate than generalized-gradient density functional theory (DFT) methods. However, GW/RPA implementations have historically been limited to either specific materials classes or application toward small chemical systems. Here, the static subspace approximation allows for reduced cost full-frequency GW/RPA calculations and has previously been benchmarked thoroughly for GW calculations. Here, we describe our approach to including partial occupations of electronic orbitals in full-frequency GW and RPA calculations for the study of electrocatalysts. We benchmarked RPA total energy calculations using the subspace approximation across a diverse test suite of materials for a variety of computational parameters. The benchmarking quantifies the impact of different extrapolation procedures for representing the static polarizability at infinite screened cutoff, and shows that using screened cutoffs above 20-25 Ryd result in diminishing accuracy returns for predicting RPA total energies. Additionally, for moderately sized electrocatalytic models, 2-3 times fewer computational resources are used to compute RPA total energies by representing the static polarizability with 20-30% of the static subspace basis, with an error of approximately 0.01 eV or better in RPA adsorption energy calculations. Finally, we show that for these electrochemical models RPA can shift DFT adsorption energy shifts by up to 0.5 eV and that GW can frequently shift DFT eigenvalues of surface and adsorbate states by approximately 0.5-1 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Model Predictive Control for a Grid-interactive Efficient Thermal Storage-integrated Heat Pump System

Building heating and cooling systems can be used to overcome the mismatch between the intermittent supply of renewable power and the fluctuating demand for electricity. A novel underground thermal energy storage integrated with a dual-source heat pump has been proposed to mitigate the mismatch while meeting the thermal demand of buildings efficiently. Conventional thermostat control with heuristic rules cannot provide intelligent decisions to maximize the thermal efficiency and flexibility of the proposed system. Advanced control strategies like model predictive control (MPC) have provided a new paradigm for grid-interactive efficient building operation with the advancement of computation and sensing. This study developed an MPC for the proposed system to provide grid service for Demand Side Management and minimize the operating cost of building owners. A control-oriented dynamic model of the proposed system has been developed. Given an objective function and proper constraints, an optimization problem is formulated to determine the optimal control strategy of the system. Dynamic Programming is adopted to solve the optimization problem. A rule-based control (RBC) is also developed to achieve similar goals. Short-term simulations are conducted to compare the system performance resulting from the two controls. The simulation results indicate that the MPC performs more intelligently than the RBC in charging thermal energy storage and selecting heat pump sources by taking advantage of the predicted cooling demands of the building and the performance of the integrated system. As a result, the MPC could save energy and reduce operating costs compared with the RBC. A case study shows that, for a 3-day operation, the MPC saves 36.9% energy and reduces 38.5% operating cost compared with the RBC.

Shi, Liang↗

Realizing tunable Fermi level in SnTe by defect control

The tuning of the Fermi level in tin telluride, a topological crystalline insulator, is essential for accessing its unique surface states and optimizing its electronic properties for applications such as spintronics and quantum computing. In this study, we demonstrate that the Fermi level in tin telluride can be effectively modulated by controlling the tin concentration during chemical vapor deposition synthesis. By introducing tin-rich conditions, we observed a blue shift in the x-ray photoelectron spectroscopy core-level peaks of both tin and tellurium, indicating an upward shift in the Fermi level. Further, this shift is corroborated by a decrease in work function values measured via ultraviolet photoelectron spectroscopy, confirming the suppression of Sn vacancies. Our findings provide a low-cost, scalable method to achieve tunable Fermi levels in tin telluride, offering a significant advancement in the development of materials with tailored electronic properties for next-generation technological applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effects of MOF linker rotation and functionalization on methane uptake and diffusion

The flexible degrees of freedom in metal–organic frameworks (MOFs) can have significant effects on guest molecule behavior. However, in the majority of studies applying molecular simulations to MOFs, the framework is assumed to be rigid in order to minimize computational cost. Here, in this work, we assess the significance of this assumption on a representative example of methane uptake and diffusion in UiO-66. We introduce an open-source code to modify MOFs through functionalization and linker rotation and we perform Grand Canonical Monte Carlo and molecular dynamics simulations of methane in each of the functionalized and linker-rotated derivatives of UiO-66. We find that linker rotation moderately influences methane uptake and significantly influences methane diffusion. Our assessment provides ranges of property values that serve as measures of uncertainty of these two properties associated with linker rotation. We further determine that void volume fraction and minimum pore size are the features that govern methane uptake and diffusion, respectively. These findings illustrate the impact of linker rotation on MOFs and provide design principles to guide future investigations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Low-cost fin-tube heat exchanger design for building thermal energy storage using phase change material

Heat transfer in phase change materials (PCMs) is complex because the melting and freezing fronts change as functions of stored or released heat. In prior attempts to optimize heat exchangers (HXs) in one or two dimensions, complex geometry has often been used to maximize the melt and freeze front area. This complex geometry is difficult and hence expensive to construct. This paper proposes a multiple-scale 3D finite element modeling approach to design fin-tube HXs for low-cost latent thermal energy storage applications. Further, the optimal fin and tube designs were determined at three scales (unit-scale, medium-scale, and large-scale) by modeling the melt and freeze front in three dimensions and using measured bulk thermal properties. The finite element model was validated by comparing it with the experimental data for a referenced design of a similar type. The results indicate that commercially available organic PCMs with low conductivity (<0.3 W/m·K) can have charge and discharge times appropriate for building thermal energy storage (i.e., 4–5 h) with fin-tube HX designs at costs <$26/kWh, even when the temperature difference (5.56°C) between the heat transfer fluid and the PCM phase change temperature is small. However, as the HX increases in length, the temperature reduction along the tube limits some larger-scale designs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A low-cost and realistic noisy light system for studying photosynthesis

Unlike the light conditions commonly used to grow photosynthetic organisms in the research laboratory, the light intensity in real environments is dynamic. A simple and low-cost system is described in which a commercial dimmable LED panel is controlled to simulate a sinusoidal function representing daylight hours and overlaid with stochastic shading events. The output closely resembles light intensity measurements on Earth’s surface on partly cloudy days or in lower levels of plant canopies. Here, this tool may be useful to researchers studying photosynthetic acclimation responses.

59 BASIC BIOLOGICAL SCIENCES↗

Field validation of isotropic analytical models for simulating fabric shades

Fabric roller shades are common shading materials used in commercial and residential buildings. Accurately characterizing and modeling shades helps practitioners select the appropriate product and its control strategy based on climate and occupants' priorities, such as visual comfort and view to outdoors. Previous studies established a generalized method for modeling complex fenestration systems using data-driven tabulated bidirectional scattering distribution functions. However, deploying such a method at scale to all fabric shading products on the market is too costly and time-consuming. Analytical models that are based on a limited set of measurements (e.g., normal-normal and normal-hemispherical visible transmittance and reflectance, and directional cut-off angles) can be used to model the wide variety of shading products on the market. This study evaluates the performance of two isotropic analytical models, Roos-Wienold and Modified-Kotey, for modeling fabric roller shades, with a focus on the model's ability to predict occupant visual comfort. The performance evaluation was conducted through laboratory and field measurements and simulations. The results showed that both models are sufficient for predicting vertical illuminance at seated eye-level. Roos-Wienold model was able to predict binary visual comfort classification (glare/no-glare) under a wide range of luminance conditions, while Modified-Kotey model did not perform as well under high-contrast low-adaptation conditions. Both models are insufficient in predicting visual comfort at a four-point scale (e.g., imperceptible, perceptible, disturbing, intolerable). The two isotropic models become less accurate when the fabric exhibits high anisotropy.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗