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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Life cycle impact assessment of artisanal sandstone mining on the environment and health of mine workers

Highlights: • Life cycle assessment (LCA) of artisanal sandstone mining in South Africa • Impact assessment of sandstone mining activities on environment and health • Fossil fuel and coal generated electricity are major non-renewable energy sources • Diesel fuel combustion during transportation phase contributed to major emissions • Silicosis and musculoskeletal problems are most common health issues - Abstract: Artisanal and small scale mining (ASM) is considered as a means to support and improve the quality of rural life, and is often the only activity that local communities have to sustain themselves. It is important to understand the nature of ASM and associated environmental effects in order to make informed decisions on the management, licensing and policy formulation of the ASM sector. Compared to other mined commodities such as, gold or diamond, the studies focusing on environmental and health impacts of sandstone mining are limited. This study used life cycle assessment (LCA) tool to evaluate the overall impact of artisanal sandstone mining (ASAM) on the environment and human health. The impact categories assessed in the study included: resource depletion, global warming, ozone layer depletion and acidification. It was observed that the impact of ASAM on the environment was minimal, however the high physical demand of the work negatively affected the health of the miners. The most common health related issues with the miners was observed to be silicosis and musculoskeletal problems. Fossil fuel used during transportation was observed to be the highest contributor for most of the impact categories.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Dynamic Analysis of Hybrid Energy Systems under Flexible Operation and Variable Renewable Generation -- Part I: Dynamic Performance Analysis and Part II: Dynamic Cost

Dynamic analysis of hybrid energy systems (HES) under flexible operation and variable renewable generation is considered in order to better understand various challenges and opportunities associated with the high system variability arising from the integration of renewable energy into the power grid. Unique consequences are addressed by devising advanced HES solutions in which multiple forms of energy commodities, such as electricity and chemical products, may be exchanged. Dynamic models of various unit operations are developed and integrated within two different HES options. One HES option, termed traditional, produces electricity only and consists of a primary heat generator (PHG) (e.g., a small modular reactor), a steam turbine generator, a wind farm, and a battery storage. The other HES option, termed advanced, includes not only the components present in the traditional option but also a chemical plant complex to repurpose excess energy for non-electricity services, such as for the production of chemical goods (e.g., transportation fuel). In either case, a given HES is connected to the power grid at a point of common coupling and requested to deliver a certain electricity generation profile as dictated by a regional power grid operator based on a predicted demand curve. Dynamic analysis of these highly-coupled HES are performed to identify their key dynamical properties and limitations and to prescribe solutions for best managing and mitigating the high variability introduced from incorporating renewable energy into the energy mix. A comparative dynamic cost analysis is also conducted to determine best HES options. The cost function includes a set of metrics for computing fixed costs, such as fixed operations and maintenance (O&M) and overnight capital costs, and also variable operational costs, such as cost of variability, variable O&M cost, and cost of environmental impact, together with revenues. Assuming different options for implementing PHG (e.g., natural gas, coal, nuclear), preliminary results identify the level of renewable penetration at which a given advanced HES option (e.g., a nuclear hybrid) becomes increasingly more economical than a traditional electricity-only generation solution. Conditions are also revealed under which carbon resources may be better utilized as carbon sources for chemical production rather than as combustion material for electricity generation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2015

Scalable tuning of building models to hourly data

Energy models of existing buildings are unreliable unless calibrated so they correlate well with actual energy usage. Manual tuning requires a skilled professional, is prohibitively expensive for small projects, imperfect, non-repeatable, non-transferable, and not scalable to the dozens of sensor channels that smart meters, smart appliances, and cheap/ubiquitous sensors are beginning to make available today. A scalable, automated methodology is needed to quickly and intelligently calibrate building energy models to all available data, increase the usefulness of those models, and facilitate speed-and-scale penetration of simulation-based capabilities into the marketplace for actualized energy savings. The "Autotune'' project is a novel, model-agnostic methodology which leverages supercomputing, large simulation ensembles, and big data mining with multiple machine learning algorithms to allow automatic calibration of simulations that match measured experimental data in a way that is deployable on commodity hardware. This paper shares several methodologies employed to reduce the combinatorial complexity to a computationally tractable search problem for hundreds of input parameters. Furthermore, accuracy metrics are provided which quantify model error to measured data for either monthly or hourly electrical usage from a highly-instrumented, emulated-occupancy research home.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2016

Dynamic performance analysis of two regional Nuclear Hybrid Energy Systems

In support of more efficient utilization of clean energy generation sources, including renewable and nuclear options, hybrid energy systems (HES) can be designed and operated as flexible energy resources (FER) to meet both electrical and thermal energy needs in the electric grid and industrial sectors. These conceptual systems could effectively and economically be utilized, for example, to manage the increasing levels of dynamic variability and uncertainty introduced by variable energy resources (VER) such as renewable sources (e.g., wind, solar), distributed energy resources, demand response schemes, and modern energy demands (e.g., electric vehicles) with their ever changing usage patterns. HES typically integrate multiple energy inputs (e.g., nuclear and renewable generation) and multiple energy outputs (e.g., electricity, gasoline, fresh water) using complementary energy conversion processes. This work reports a preliminary dynamic analysis of two realistic HES including a nuclear reactor as the main baseload heat generator and to assess the local (e.g., HES owners) and system (e.g., the electric grid) benefits attainable by their application in scenarios with multiple commodity production and high renewable penetration. It is performed for regional cases - not generic examples - based on available resources, existing infrastructure, and markets within the selected regions. This study also briefly addresses the computational capabilities developed to conduct such analyses.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

Modeling, control, and dynamic performance analysis of a reverse osmosis desalination plant integrated within hybrid energy systems

An RO (reverse osmosis) desalination plant is proposed as an effective, FLR (flexible load resource) to be integrated into HES (hybrid energy systems) to support various types of ancillary services to the electric grid, under variable operating conditions. To study the dynamic (transient) analysis of such system, among the various unit operations within HES, special attention is given here to the detailed dynamic modeling and control design of RO desalination process with a spiral-wound membrane module. The model incorporates key physical phenomena that have been investigated individually into a dynamic integrated model framework. In particular, the solution-diffusion model modified with the concentration polarization theory is applied to predict RO performance over a large range of operating conditions. Simulation results involving several case studies suggest that an RO desalination plant, acting as a FLR, can provide operational flexibility to participate in energy management at the utility scale by dynamically optimizing the use of excess electrical energy. Here, the incorporation of additional commodity (fresh water) produced from a FLR allows a broader range of HES operations for maximizing overall system performance and profitability. For the purpose of assessing the incorporation of health assessment into process operations, an online condition monitoring approach for RO membrane fouling supervision is addressed in the case study presented.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

The European wood pellets for heating market - Price developments, trade and market efficiency

Competitive international markets imply adjustments towards competitive spatial equilibrium in which excess from one market is transferred to another and prices are equilibrated except for remaining differences that can be assigned to transfer costs. The European market for wood pellets used in small-scale heating systems has been expanding significantly over the past decade. Small scale pellet heating is arguably a mature technology, but whether the market is mature is another question. In this paper we analyse recent data on trade flows and price developments between Italy, Austria, Germany and France to understand the developments of wood pellet market efficiency and to draw conclusions about market function. The objective of this study is to establish a framework to test the European residential wood pellet market for competitive spatial equilibrium using modern trade theory. We find mainly inefficiently integrated markets with remaining positive marginal profits and detectable arbitrageurs’ activity. Based on a thorough discussion of these findings and the underlying data we outline possible methodology advancements and list policy recommendations to secure access and affordability of this renewable heating commodity in the long run.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Design and optimization of a modular hydrogen-based integrated energy system to maximize revenue via nuclear-renewable sources

Here, this paper demonstrates a novel modular distributed framework that uses optimal energy-dispatching strategies to enable greater flexibility and profitability in nuclear-renewable integrated energy systems (NR-IES). Hydrogen is used as a commodity in this framework since its production can improve grid stability and system operational flexibility, decarbonize heavy industry, and create an additional revenue stream for electricity generators, particularly nuclear power plants with high operational expenses. The proposed solution addresses the challenges associated with merging multiple software and services from various domains by using functional mock-up units (FMU) to co-simulate diverse subsystems designed in various platforms. The tightly coupled integrated energy system (IES) is optimized to maximize revenue by utilizing the deep reinforcement learning (DRL) technique to make smart dispatching decisions based on variable electricity prices and the availability of renewable energy. Proximal policy optimization (PPO) algorithm is used in training and testing the DRL agent. Over a period of 120 days, the proposed hydrogen-based IES framework showed about 10% revenue boost compared to a non-hydrogen generating baseline IES while also providing an easily-adoptable framework which can help to improve the flexibility of future generation nuclear power plants.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2014

Identification and characterization of the polyketide synthase involved in ochratoxin A biosynthesis in Aspergillus carbonarius

Ochratoxin A (OTA) is a potent mycotoxin produced by Aspergillus and Penicillium species and is a common contaminant of a wide variety of food commodities, with Aspergillus carbonarius being the main producer of OTA contamination in grapes and wine. The molecular structure of OTA is composed of a dihydroisocoumarin ring linked to phenylalanine and, as shown in different producing fungal species, a polyketide synthase (PKS) is a component of the OTA biosynthetic pathway. Similar to observations in other filamentous ascomycetes, the genome sequence of A. carbonarius contains a large number of genes predicted to encode PKSs. In this work a pks gene identified within the putative OTA cluster of A. carbonarius, designated as AcOTApks, was inactivated and the resulting mutant strain was unable to produce OTA, confirming the role of AcOTApks in this biosynthetic pathway. AcOTApks protein is characteristic of the highly reduced (HR)-PKS family, and also contains a putative methyltransferase domain likely responsible for the addition of the methyl group to the OTA polyketide structure. AcOTApks is different from the ACpks protein that we previously described which showed an expression profile compatible with OTA production. We performed phylogenetic analyses of the β-ketosynthase and acyl-transferase domains of the OTA PKSs which had been identified and characterized in different OTA producing fungal species. The phylogenetic results were similar for both the two domains analyzed and showed that OTA PKS of A. carbonarius, Aspergillus niger, and Aspergillus ochraceus clustered in a monophyletic group with 100% bootstrap support suggesting a common origin, while the other OTA PKSs analyzed were phylogenetically distant. A qRT-PCR assay monitored AcOTApks expression during fungal growth and concomitant production of OTA by A. carbonarius in synthetic grape medium. A clear correlation between the expression profile of AcOTApks and kinetics of OTA production was observed with AcOTApks which reached its maximum level of transcription before OTA accumulation in mycelium reached its highest level, confirming the fact that gene transcription always precedes phenotypic production.

fungi, Aspergillus, mycotoxin, ochratoxin, carbona↗
DOE OSTI2022

Growth and inactivation of Listeria monocytogenes in sterile extracts of fruits and vegetables: Impact of the intrinsic factors pH, sugar and organic acid content

Intrinsic characteristics of fresh produce, such as pH, water activity, acid content and nutrient availability are critical factors in determining the survival and growth of Listeria monocytogenes (Lm). In this study, sterile fresh produce juice was used to analyze Lm growth potential among 14 different commodities and to identify physicochemical characteristics in those juices that affect Lm growth. Significant growth of Lm was observed in juices with pH ≥5.6 and low acidity (0.04–0.07 % titratable acidity (TA)) (cantaloupe, carrot, celery, green pepper, parsley, and romaine lettuce), slight reduction of Lm was observed in juices with pH 4.1 (tomato) and pH 3.9 (mango), and no Lm counts were recovered from juices with pH ≤3.8 and high acidity (0.28–1.17 % TA) (apple, blueberry, grape, peach, and pineapple). Although these acidic fruit juices possessed a high sugar content, the pH and acidity of produce juice seemed to be the primary determinants for Lm growth. The neutralization of acidic juices (i.e., Fuji and Gala apple, blueberry, grape, mango, pineapple, peach, and tomato) enabled Lm growth at 37 °C in all juices except for Gala apple and peach. Strong decline in Lm populations in Gala apple, grape and peach juices might be linked to sensitivity to organic acids, such as malic acid. As a result, Lm populations significantly decreased in pH-neutral (7.6) cauliflower juice, suggesting that potential antilisterial substances may play a role in Lm decline in cauliflower juice.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Minimizing exposure to legacy wells and avoiding conflict between storage projects: Exploring area of review as a screening tool

Elevated pressure from large-volume injection is a key driver of risk and project cost. If transmissive features (e.g., non-isolating wells or fracture systems) are present, increased injection-zone pressure can drive fluids from depth toward protected freshwater resources. In US Carbon Capture and Storage (CCS) law, the area at risk is known as the Area of Review (AoR). The size and number of potentially transmissive features to be evaluated and possibly remediated or managed is a function of the size and location of the AoR. The size of the AoR depends on several variables, including properties of the injection zone, properties of protected resources, and injection rate and duration. Evaluation of the intersection of these variables across a portfolio of sites highlights the injection zone depth and boundary conditions as top-level controls. Deep injection, use of multiple stacked injection zones, reduced injection rate and choice of injection well location can all be used to minimize AoR and the number of potentially transmissive features within it. Here, we introduce the concept of pressure space (defined as connected pore volume times pressure) as the key subsurface commodity for CO 2 storage and we suggest that it forms a more robust basis for leasing and regulation than pore space alone.

58 GEOSCIENCES↗
DOE OSTI2025

Ultra-high efficiency hydrogen production using a large-scale solid oxide electrolysis cell system

Efficient and cost-effective production of clean hydrogen is key to decarbonizing the production of hard-to-abate industries, such as chemicals, fuels, steel, cement and many other commodities that form the basis of modern societies. High-temperature steam electrolysis (HTSE) has recently become commercially available and offers opportunities for producing hydrogen at higher efficiency and lower cost than competing low temperature technologies. In this work, we report world record setting hydrogen production efficiency from large-scale prototype HTSE systems based on solid oxide electrolysis cell (SOEC) technology. Independent tests performed at Idaho National Laboratory (INL) employed a Bloom Energy 100 kW SOEC system to achieve a hydrogen production direct current specific electric energy consumption as low as 36.7 kWh per kilogram of hydrogen. Remarkably, similar high efficiencies in the range of 36–39 kW/kg-H2 were obtained over a wide range of hydrogen production rates and even during dynamic ramping as the hydrogen production and electric power consumption of the system were varied between 20 % and 100 % of nominal conditions. Furthermore, these test results validate previous projections that commercial SOEC systems can produce clean hydrogen at efficiencies approaching 100 % for less than 2 U S. dollars per kilogram when located near sources of inexpensive, low-grade heat and clean electricity.

08 HYDROGEN↗
DOE OSTI2018

Fundamental catalytic challenges to design improved biomass conversion technologies

During the past ten years, there has been significant interest and investment in the study of catalytic conversion of biomass-derived feedstocks into renewable fuels and chemicals. In the United States, an estimated $25 billion has been spent by venture capitalists, industry, and government agencies during this period of time to commercialize “renewable technologies” including solar energy, wind power, batteries, and biofuels (e.g., cellulosic ethanol). Four societal factors are driving these investments including: (1) the increased price of crude oil; (2) concerns about global warming; (3) the desire to improve rural economies where biomass is produced, and; (4) national goals to become energy self-sufficient. Furthermore, underlying these efforts is the realization that lignocellulosic biomass is the only realistic, near-term and non-food-competitive source of renewable organic carbon. To this end, legislative efforts, such as the US Renewable Fuel Standards, have been implemented to create subsidies, tax credits, mandates, and loan guarantees to help bring renewable fuel technologies to market. However, the representative body of industrial efforts to this end has faced significant challenges, with several startup companies having commercialized biomass conversion technologies but having struggled to reach commercial scale; in fact, many of these companies have filed for bankruptcy. This situation is likely due to the challenges associated with scaling up unproven pioneer processes, as well as neophyte investors not understanding the decade-long time frames and the sheer amount of funding that is often required to bring chemical process technologies to market. Nevertheless, several emerging catalytic technologies have either entered the market place, or are currently demonstrating their technologies in fully integrated pilot plants. Commercial and near commercial technologies for second generation biomass conversion technologies to-date include, among others: biomass-derived jet and diesel fuel from both waste vegetable oils and ethanol; small scale production of renewable jet and diesel from landfill gases via Fischer-Tropsch synthesis; catalytic conversion of carbohydrates into gasoline and aromatics; hydropyrolysis of biomass into gasoline and diesel, and; catalytic conversion of wood into aromatics. To be successful, biomass conversion technologies must ultimately be able to compete economically with petroleum technologies, which are already operating at large commercial scales and have been practiced for decades. To this end, various factors must be considered when evaluating the potential for new processes to compete with incumbent technologies; factors such as regional variations in feedstock quality and availability, government policy, subsidies and tax rates, and the proprietary positions of the ancillary technologies that might support the process. By any measure, however, a critical metric of the economic potential of a process is its efficiency with respect to the yield of products from raw materials, and this metric of performance is directly related to atom efficiency of the underlying chemical reactions. Therefore, while promising biomass conversion technologies continue to demonstrate progress towards commercialization, there remains an important need for the catalysis community to aid in this effort by: (1) designing more active, selective and stable catalysts, and (2) elucidating a more detailed understanding of the catalytic chemistries underlying these processes. Indeed, the study of catalytic biomass conversion has grown tremendously during the past decade; and new or emerging technologies that are in the laboratory stage have allowed for biomass to be converted into a wider variety of commodity chemicals and the full range of liquid fuels that are produced from petroleum. The objective of this perspective is to highlight some of the ongoing, fundamental challenges with respect to the catalytic conversion of biomass into renewable products, and to provide insight as to how the catalysis community can overcome several of these challenges. It is our belief that, as an international academic community of catalysis researchers, we can (and must) work together to address these challenges, and to drive progress toward the production of next-generation renewable chemicals and fuels from biomass.

09 BIOMASS FUELS↗
DOE OSTI2021

Promoting Diels-Alder reactions to produce bio-BTX: Co-aromatization of textile waste and plastic waste over USY zeolite

Producing commodity aromatic hydrocarbons from textile waste is a promising approach to promote carbon neutrality and circular economy. Catalytic degradation of flax waste (FW) to generate furans and its subsequent Diels-Alder transformation to monocyclic aromatic hydrocarbons over USY zeolite were conducted. Experimental results indicated that USY catalyzed FW resulted in a 5.5-fold increase in furans production compared with the non-catalytic trial. The Si/Al molar ratio in USY played a determining role in furans formation, and a 5-fold increase was observed over USY with a Si/Al ratio of 5.3 as opposed to that with a Si/Al ratio of 11. Plastic waste, polyethylene (PE), co-fed with FW yielded 1.6 times higher aromatic hydrocarbons than polypropylene (PP). The selectivity to aromatic hydrocarbons reached 81.6% under 20% PE co-fed with 80% FW, in which benzene, toluene, and xylenes (BTX) were predominant products with the maximum selectivity of 68%. Furthermore, this study presents a cleaner approach for value-added resource recovery and sustainable management of textile and plastic waste.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Comparative life cycle analysis on ethylene production from electrocatalytic reduction of carbon dioxide

Ethylene is one of the largest greenhouse gas emitters and the most diversly used commodity chemicals globally. Electrocatalytic reduction of CO 2 to ethylene received great attention from the research society to decarbonize the ethylene production. Here, in this study, a life-cycle analysis is conducted using the Greenhouse Gases, Regulated Emissions, and Energy use in Technologies (GREET) model on the three electrocatalytic CO 2 -reduction pathways (or “e-ethylene” pathways): i) cascade conversion via carbon monoxide intermediate; ii) single-step conversion in membrane electrode assembly (MEA); and iii) single-step conversion in alkaline flow cell. The results showed that the electricity consumption is the lowest for the cascade pathway (164 MJ/kg), thus resulting in the lowest cradle-to-gate carbon intensity [18 kgCO 2 e/kg with United States (US) average grid)] among the three pathways followed by the single-step MEA (32 kgCO 2 e/kg) and then by the single-step alkaline (56 kgCO 2 e/kg). However, all three e-ethylene pathways were significantly more carbon-intensive than their fossil-based counterpart (1.1 kgCO 2 e/kg) due to their excessive energy consumption with the current state of technology. With renewable electricity, all three pathways yielded negative carbon intensity: from -3.1 kgCO 2 e/kg to -1.6 kgCO 2 e/kg depending on the source of CO 2 . The threshold carbon intensity of electricity (TCIE), defined as the upper bound of the carbon intensity of electricity to achieve lower carbon intensity for e-ethylene compared to fossil-based ethylene, is calculated for both current and future state of e-ethylene technologies. The cascade pathway had the highest TCIE out of the three e-ethylene pathways for both current (92 gCO 2 e/kWh) and future (124 gCO 2 e/kWh) state of technologies. However, the carbon intensity of average US grid (i.e., 467 and 303 gCO 2 e/kWh for current and future projections) were higher than the TCIEs of the corresponding timeline. Thus, reducing electricity requirement for e-ethylene pathways and bringing low-carbon generation mix in the United States (US) grid faster than the current projection are both essential to decarbonize ethylene and its downstream chemicals/polymers.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2026

Valorization of waste polyolefins to butene, unsaturated fatty alcohols, and branched alkenes using CO 2 and plasma catalyst

Butene, branched alkenes, and short-chain unsaturated fatty alcohols are among the chemicals that have a wide range of industrial applications in the production of fuels, chemicals, and polymers. In this work, we produced these valuable commodity chemicals from waste plastics using a single-step plasma-catalytic process at atmospheric pressure CO 2 . The study shows that combining non-thermal plasma and zeolite could convert polyolefins at a temperature of 200 °C within 15 minutes, producing liquids rich in C 5 and C 6 branched alkenes and C 6 -C 8 unsaturated fatty alcohols. Additionally, gaseous products include a high yield of butene. Comparative studies indicate that combining CO 2 plasma with zeolite synergistically increases reaction rates and alters product compositions. Product selectivity was strongly dependent on reaction conditions, including plasma power, gas flow rates, reactor temperature, and catalyst loading. Furthermore, this process was applicable to common polyolefins and post-consumer polyethylene, indicating that the plasma catalytic approach has promising potential to valorize waste plastics and greenhouse gas CO 2 into versatile chemicals.

42 ENGINEERING↗
DOE OSTI2012

Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs

This paper presents parallelization strategies for the radial basis function-finite difference (RBF-FD) method. As a generalized finite differencing scheme, the RBF-FD method functions without the need for underlying meshes to structure nodes. It offers high-order accuracy approximation and scales as O(N) per time step, with N being with the total number of nodes. To our knowledge, this is the first implementation of the RBF-FD method to leverage GPU accelerators for the solution of PDEs. Additionally, this implementation is the first to span both multiple CPUs and multiple GPUs. OpenCL kernels target the GPUs and inter-processor communication and synchronization is managed by the Message Passing Interface (MPI). We verify our implementation of the RBF-FD method with two hyperbolic PDEs on the sphere, and demonstrate up to 9x speedup on a commodity GPU with unoptimized kernel implementations. On a high performance cluster, the method achieves up to 7x speedup for the maximum problem size of 27,556 nodes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

97 MATHEMATICS AND COMPUTING↗