Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ordering transformation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15

Glass formation and structure of melt quenched mixed oxy-sulfide Na 4 P 2 S 7-x O x glasses for 0 ≤ x ≤ 5

The structures of Na 4 P 2 S 7-x O x , 0 ≤ x ≤ 5, glasses were investigated using melt quench (MQ) samples. The short-range order (SRO) structures of these glasses were examined using a combination of Raman, Fourier Transform Infrared (FT-IR), and 31 P Magic Angle Spinning NMR ( 31 P MAS NMR) spectroscopies to determine how oxygen is incorporated into the sulfide structure. Using vibrational spectroscopy, semi-quantitative 31 P MAS NMR, and charge balancing, a complete compositional map of all the SRO structures present in these glasses has been generated. From these findings, full incorporation of the oxygen into the sulfide melt was found to occur across the compositional series through a structural disproportionation reaction where oxygen systematically replaces bridging sulfurs (BSs), before replacing the remaining non-bridging sulfurs (NBSs). Under the melting and quenching conditions used in this study, it was found that the melts crystallize too quickly to form homogeneous crystallite-free glasses for x > 5.

36 MATERIALS SCIENCE↗

Irradiation effects on Al 0.3 CoCrFeNi and CoCrMnFeNi high-entropy alloys, and 316H stainless steel at 500 °C

To evaluate the potential of high entropy alloys (HEAs) for nuclear applications, two HEAs, Al 0.3 CoCrFeNi and CoCrFeMnNi, and a conventional Type 316H stainless steel (SS) were irradiated with 1 MeV krypton ions at 500 degrees C up to 1 dpa, and examined in-situ with a transmission electron microscope (TEM). After irradiation, a high density of ordered L1 2 nanoparticles was observed in Al 0.3 CoCrFeNi. In contrast, no phase transformation was observed in CoCrFeMnNi and 316H SS. In the thin foil regions of TEM samples, stacking-fault tetrahedra were observed in the HEAs. In the thick foil regions, interstitial dislocation loops were observed for all alloys, and the areal loop density increased linearly with foil thickness. The Al 0.3 CoCrFeNi had the largest loop size (the lowest density), followed by the CoCrFeMnNi and then the 316H SS. The higher loop nucleation rate in the 316H SS was attributed to carbon content. Finally, the degree of irradiation hardening was slightly lower for the HEAs than for the 316H SS, which is a promising sign for the nuclear application of HEAs at high temperatures.

36 MATERIALS SCIENCE↗

A discrete integral transform for rapid spectral synthesis

Accurate synthetic spectra that rely on large Line-By-Line (LBL)-databases are used in a wide range of applications such as high temperature combustion, atmospheric re-entry, planetary surveillance and laboratory plasmas. Conventionally synthetic spectra are calculated by computing a lineshape for every spectral line in the database and adding those together, which may take multiple hours for large databases. In this paper we propose a new approach for spectral synthesis based on an integral transform: the synthetic spectrum is calculated as the integral over the product of a Voigt profile and a newly proposed three-dimensional “lineshape distribution function”, which is a function of spectral position and Gaussian- & Lorentzian width coordinates. A fast discrete version of this transform based on the Fast Fourier Transform (FFT) is proposed, which improves performance compared to the conventional approach by several orders of magnitude while maintaining accuracy. Strategies that minimize the discretization error are discussed. A Python implementation of the method is compared against state-of-the-art spectral code RADIS, and is since adopted as RADIS's default synthesis method. The synthesis of a benchmark CO2 spectrum consisting of 1.8 M spectral lines and 200k spectral points took only 3.1 s using the proposed method (1011 lines × spectral points/s), a factor ~300 improvement over the state-of-the-art, with the relative improvement generally increasing for higher number of lines and/or number of spectral points. Finally, an experimental GPU-implementation of the method was also benchmarked, which demonstrated another 2~3 orders performance increase, achieving up to 5 ∙ 10 14 lines × spectral points/s.

42 ENGINEERING↗

Power-transfer and fixed-point analysis of sawtooth simulations of a current-carrying stellarator

Power-transfer and fixed-point analysis of previous NIMROD simulations (Roberds et al. , Phys. Plasmas , vol. 23, issue 9, 2016, 092513) improved the understanding of the effect of 3D (non-axisymmetric equilibrium) magnetic fields on sawtooth oscillations in the Compact Toroidal Hybrid (CTH) experiment. Computing the locations of order-1 fixed points, their Greene's residues, and local values for the rotational transform results in a description of CTH sawteeth consistent with Kadomtsev's model. A power-transfer analysis quantifies the distribution of energy among toroidal Fourier modes and their nonlinear interactions. The Lorentz power transfer drives sawtooth growth, and it is unambiguously interpreted as the flow of energy from toroidal mode $n'$ to mode $n$ , catalysed by $\boldsymbol {B}_{n-n'}$ . It has been reported previously that the CTH sawtooth frequency increases with the 3D field strength. This is attributed to an increased growth rate of the internal kink that drives sawtooth oscillations. Here, 3D fields remove energy from the kink, eliminating the possibility that these fields are an additional energy source that drives growth. Instead, 3D fields catalyse energy transfer from large-to-small scales, where magnetic reconnection is stronger. It is proposed that this energy transfer increases the reconnection rate at small scales, which is consistent with the increased growth rate observed at higher 3D field strengths.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Study of the ferromagnetic quantum phase transition in Ce 3– x Mg x Co 9

The Ce 3-x Mg x Co 9 system evolves from a Pauli paramagnetic ground state for x = 0 to a ferromagnetic ground state for x≈0.80 in single-phase, polycrystalline samples [Lamichhane, V. Taufour, A. Palasyuk, Q. Lin, S.L. Budko, and P.C. Canfield, Ce3-xMgxCo9 : transformation of a Pauli paramagnet into a strong permanent magnet, Phys. Rev. Appl. 9 (2018), p. 024023]. In order to better understand this behaviour, single-crystalline samples of Ce 3-x Mg x Co 9 for x = 0.01, 0.16, 0.24, 0.35, 0.43 and 0.50 were grown using the flux growth technique, and electrical transport and magnetic properties were studied. The T C-x phase diagram we infer shows that the system has a quantum phase transition near x = 0.35, transforming to a ferromagnetic ground state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Deep Reinforcement Learning based Model-free On-line Dynamic Multi-Microgrid Formation to Enhance Resilience

Multi-microgrid formation (MMGF) is a promising solution for enhancing power system resilience. This paper proposes a new deep reinforcement learning (RL) based model-free on-line dynamic MMGF scheme. Additionally, the dynamic MMGF problem is formulated as a Markov decision process, and a complete deep RL framework is specially designed for the topologytransformable micro-grids. In order to reduce the large action space caused by flexible switch operations, a topology transformation method is proposed and an action-decoupling Q-value is applied. Then, a convolutional neural network (CNN) based multi-buffer double deep Q-network (CM-DDQN) is developed to further improve the learning ability of the original DQN method. The proposed deep RL method provides real-time computing to support the on-line dynamic MMGF scheme, and the scheme handles a long-term resilience enhancement problem using an adaptive on-line MMGF to defend changeable conditions. The effectiveness of the proposed method is validated using a 7-bus system and the IEEE 123-bus system. The results show strong learning ability, timely response for varying system conditions and convincing resilience enhancement.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Advanced PGM-free Cathode Engineering for High Power Density and Durability

Polymer electrolyte fuel cells (PEFCs) are among the most promising technologies for future electric vehicles by using clean H2 with much-improved energy conversion efficiency, longer range, and rapid refueling. However, due to a large amount of platinum group metal (PGM) catalyst used in their electrodes, their prohibitively high cost hinders broad commercialization of PEFCs for transportation. Therefore, there is a critical need to develop low-cost, high-performance PGM-free cathode catalysts that have the potential to dramatically transform the economics of PEFC commercialization by reducing catalyst costs by one to two orders of magnitude. However, before PGM-free cathodes become viable, several technical challenges associated with PGM-free cathodes must be addressed, including insufficient activity and stability of the catalysts, as well as severe water flooding and large transport losses in the electrodes. Overcoming those barriers and ultimately meeting the challenging automotive PEFC performance targets was the focus of this comprehensive research and development effort on new PGM-free cathodes. To this end, we assembled a team including leading researchers from universities and industry with different but complementary expertise and capabilities. The project combined three novel and promising approaches: Advanced metal-organic framework (MOF)-derived M-N-C catalysts with a high activity and impressive durability, Novel PGM-free specific cathode architectures and fabrication strategies capable of addressing the substantial flooding and transport resistances in thicker cathodes by introducing engineered hydrophobicity through additives and support layers, and Advanced electrode ionomers with high proton conductivity for low ohmic losses across the electrode and more uniform catalyst utilization. The implementation of these new materials and electrode designs was supported by a suite of advanced experimental and simulation tools that allows us to identify performance and durability bottlenecks, devise solutions, and establish rational material design and synthesis targets. These methods include advanced electrochemical characterization, high-resolution imaging, and multi-scale modeling. In addition, the project team leveraged a broad cross-section of the ElectroCat consortium’s national laboratory facilities and expertise in advancing these materials and design strategies. Finally, the industry partners on the project facilitated the evaluation of scaled-up synthesis and manufacturing in the United States. Over its four-year period, the project made significant year-over-year advances in PGM-free cathode performance and viability. A combination of high activity and highly durable catalysts were developed through novel catalyst synthesis strategies, which met several performance and durability targets. More specifically, a catalyst prepared from MOFs and Fe2O3 nanoparticles with ammonium chloride and chemical vapor deposition treatments yielded a significant advancement in PGM-free cathode durability. Several novel strategies for fabricating cathodes were demonstrated, including those designed to reduce flooding and thickness of the cells for significantly increased volumetric power density. An optimized cathode with high conductivity ionomer and tuned ink processing for hydrophobicity yielded high fuel cell performance with new levels power density and maximum current. The scientific studies and modeling assessment also provided an outlook for future efforts, including a focus on catalysts with an increased density of the highly stable active sites developed in this project.

08 HYDROGEN↗

Advanced control sequences and FDD technology. Just shiny objects, or ready for scale?

Innovations in commercial building control sequences (ASHRAE guideline 36) and fault detection and diagnostics (FDD) technology have the potential to transform existing building operational efficiency by realizing whole-building level savings on the order of 15% and higher. However, several technical and market barriers related to up-front estimation of achievable savings, verifying implementation, and ensuring persistence are slowing down their adoption as a core offering through diverse owner-funded initiatives and rate-payer funded programs. This paper describes a suite of solutions to overcome these barriers to program delivery of advanced HVAC controls integrated with FDD energy management and information system (EMIS) technology. First, the Guideline 36 conformance test offers an automated method to confirm correct sequence implementation by the manufacturer, before field deployment. A successful test of a controller was conducted using a new manufacturer-independent hardware-in-the-loop testbed demonstrating the viability and scalability of this approach. Second, the Guideline 36 energy savings calculator uses modeling paired with high-level user inputs to estimate building-specific savings potential, target cost effective implementation and minimize uncertainty. Initial results indicate the baseline control sequences significantly impact energy savings, however, as much as 50% savings may be possible for the worst-case baseline scenario. Third, a functional specification provides minimum recommended EMIS-FDD capabilities, and best practices to integrate the technology into organizational practice and ensure that advanced control sequences provide persistent savings.

Pritoni, Marco↗

Defect Properties, Anion Ordering, and Photochromic Mechanism in Yttrium Oxyhydride

Yttrium oxyhydride (YHO) undergoes a reversible photochromic transition when exposed to ultraviolet light. However, the mechanism for this transformation is not fully understood, and the structure and precise chemical composition of YHO remain under debate. Here, we use first-principles density functional theory calculations with a hybrid functional to study the structure, chemical stability, and point defect properties of YHO. As experiments have shown, we find that YHO prefers a cubic structure, with H and O anions present in equal concentrations and located on tetrahedral sites. Stoichiometric and ordered YHO is chemically stable, but it has a wide band gap of 5.01 eV, considerably larger than that measured in experiments (2.4–3.8 eV). On the other hand, Y4H10O has a smaller band gap of 2.97 eV and also has a region of chemical stability; thus, the actual material may include some fraction of this H-rich structure. The defect chemistry of YHO is dominated by anionic antisite species (H O and O H ), with hydrogen interstitials (H i ) and vacancies (V H ) also present in reasonably high concentrations. We show that antisite disorder lowers the band gap relative to the perfectly ordered structure, bringing the magnitude of the gap into closer agreement with experiment. Based on our calculations of defect migration and the positions of defect states relative to the band edges, we link the onset of photochromic behavior to the reaction H O – → V O 0 + H i – , which follows photoexcitation of a H O + defect. H i – can subsequently migrate away and be trapped by additional H O + defects, contributing to the persistence of the reaction, while the resultant oxygen vacancy, V O 0 , introduces an occupied defect state that leads to optical absorption at visible wavelengths. Our results can explain reported discrepancies between experimental and computational results for YHO, and they allow us to propose specific atomic-scale processes that can lead to photochromism. In conclusion, understanding these mechanisms is key for unlocking YHO’s application in devices ranging from smart windows and optoelectronics to electrochemical synapses for neural networks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Energy Conversion from Heat to Electricity by Highly Reversible Phase-Transforming Ferroelectrics

The search for performant multiferroic materials has attracted general research interest in energy science as they have been increasingly exploited as the conversion media among thermal, electric, magnetic, and mechanical energies by using their temperature-dependent ferroic properties. Here we report a material development strategy that guides us to discover a reversible phase-transforming ferroelectric material exhibiting enduring energy harvesting from small temperature differences. The material satisfies the crystallographic compatibility condition between polar and nonpolar phases, which shows only 2.5°C thermal hysteresis and a high figure of merit. It stably generates 15μA of electricity in consecutive thermodynamic cycles in the absence of any bias fields. We demonstrate our device to consistently generate 6μA/cm 2 current density near 100°C over 540 complete phase transformation cycles without any electric and functional degradation. The energy-conversion device can light up an LED directly without attaching an external power source. Furthermore, this promising material candidate brings the low-grade waste-heat harvesting closer to a practical realization, e.g., small temperature fluctuations around the water boiling point can be considered as a clean energy source.

30 DIRECT ENERGY CONVERSION↗

A Quasi-Ordered Mn-Rich Cathode with Highly Reversible Oxygen Anion Redox Chemistry

Anionic oxygen redox chemistry in Li-rich Mn-based layer oxide cathodes represents a transformative approach for boosting the energy density of next-generation lithium-ion batteries. However, conventional oxygen redox reactions often induce oxygen dimerization at high voltages, leading to irreversible lattice oxygen loss and a rapid voltage fade. Herein, we achieve highly reversible oxygen redox chemistry through a new quasi-ordered structural design that incorporates both intra- and interlayer cation disorder configurations. This unique structure significantly enhances lattice oxygen stability, effectively stabilizes oxidized oxygen, and inhibits the formation of peroxo- or superoxol-like species, thereby enabling anionic redox reactions to proceed reversibly even at deep delithiation states. The quasi-ordered design mitigates irreversible phase transitions and preserves the structural integrity throughout extended cycling. Consequently, the proposed cathode demonstrates exceptional cyclability with negligible capacity and voltage fade, retaining 99% capacity and 98% average voltage after long-term cycling. Finally this work provides fresh insights into addressing issues related to lattice oxygen instabilities and reforming strategies for developing long-life, high-energy-density anionic redox cathode materials for advanced batteries.

chemical structure↗

Coordinate transformation methodology for simulating quasistatic elastoplastic solids

Molecular dynamics simulations frequently employ periodic boundary conditions where the positions of the periodic images are manipulated in order to apply deformation to the material sample. For example, Lees-Edwards conditions use moving periodic images to apply simple shear. Here, we examine the problem of precisely comparing this type of simulation to continuum solid mechanics. We employ a hypo-elastoplastic mechanical model, and develop a projection method to enforce quasi-static equilibrium. We introduce a simulation framework that uses a fixed Cartesian computational grid on a reference domain, and imposes deformation via a time-dependent coordinate transformation to the physical domain. As a test case for our method, we consider the evolution of shear bands in a bulk metallic glass using the shear transformation zone theory of amorphous plasticity. We examine the growth of shear bands in simple shear and pure shear conditions as a function of the initial preparation of the bulk metallic glass.

74 ATOMIC AND MOLECULAR PHYSICS↗

Phase transformation and growth mechanism of RF sputtered ferroelectric lead scandium tantalate (PbSc 0.5 Ta 0.5 O 3 ) films

Lead scandium tantalate (PbSc 0.5 Ta 0.5 O 3 , PST), an order/disorder ferroelectric, is a potential candidate for electrocaloric cooling and pyroelectric infrared (IR) detector. In this work, we report the phase transformation kinetics from two series of samples containing pure amorphous and mixture of amorphous and pyrochlore to desired perovskite phase using postdeposition rapid thermal processing (RTP) as well as growth mechanism of RF sputtered PST thin films using excess lead target on platinized silicon (Pt/Ti/SiO 2 /Si) substrates. We find that small changes in the temperature ramp have a large effect on the degree of perovskite conversion (ferroelectric phase), orientation (crystallographic texture), and long-range order parameter (< S 111 >). Through isothermal annealing, we obtained optimal perovskite phase at ≥700°C temperature. The phase transformation is characterized by spontaneous formation of center-type in-plane radial rosette-like structures revealed by scanning electron microscopy. The PST perovskite crystallites were found to coexist with pyrochlore in RTP annealed films. The volume fractions for perovskite and pyrochlore phase were obtained from the analysis of “rosettes” and respective X-ray diffraction intensities which helped to determine various parameters associated with phase kinetics (n, k, and activation energy, Ea) and accompanying growth. The effective activation energies of perovskite transition and growth were found to be 332 ± 11 kJ/mol (345 ± 11 kJ/mol) and 114 ± 10 kJ/mol (122 ± 10 kJ/mol), respectively, for pure amorphous only (and mixed amorphous and pyrochlore) phase following nucleation-growth controlled Avrami's equation. A linear growth rate (n~1) for the perovskite phase indicates predominant interface-controlled process and diffusion-limited phenomena thus inhibiting rosette size owing to reactant depletion and soft impingement at the grain boundary. However, the growth behavior is isotropic in two-dimension parallel to the plane of the substrates for both sample series. Furthermore, lead loss was severe for in-situ growth and RTP combined with conventional furnace annealing than those of RTP only films, which were closer to stoichiometric albeit with excess lead and marginal oxygen vacancies (V o ).

36 MATERIALS SCIENCE↗

Phase transformation of hydrous ringwoodite to the lower-mantle phases and the formation of dense hydrous silica

In order to understand the effects of H 2 O on the mineral phases forming under the pressure-temperature conditions of the lower mantle, we have conducted laser-heated diamond-anvil cell experiments on hydrous ringwoodite (Mg 2 SiO 4 with 1.1wt% H 2 O) at pressures between 29 and 59 GPa and temperatures between 1200 and 2400 K. Our experimental results show that hydrous ringwoodite (hRw) converts to crystalline dense hydrous silica, stishovite (Stv) or CaCl 2 -type SiO 2 (mStv), containing 1 wt% H 2 O together with Brd and MgO at the pressure-temperature conditions expected for shallow lower-mantle depths between approximately 660 to 1600 km. Considering lack of sign for melting in our experiments, our preferred interpretation of the observation is that Brd partially breaks down to dense hydrous silica and periclase (Pc), forming Brd + Pc + Stv mineralogy. Our experiments may provide an explanation for the enigmatic coexistence of Stv and Fp inclusions in lower-mantle diamonds

58 GEOSCIENCES↗

Integration of a DER Management System in Riverside. Final report

The tasks in this project covered various aspects, including algorithm development, algorithm integration into a commercial Active Network Management (ANM) platform, hardware-in-the-loop (HIL) testing in an industry-standard testing platform, pilot demonstration in Riverside, California, and also cost and benefit analysis. The DERMS platform in this project can host different algorithms developed on different platforms (e.g., MATLAB and Python) and it can interact with different hardware devices (e.g., different PV inverters, battery inverters, and different sensors). The DER control solution are based on an advanced model-free, layered, and clustered DER control paradigm. At the core of the DER control algorithms was the concept of Extremum Seeking (ES), which is a model-free probing-based control technique. The ES-based control algorithms were tested on major real-world inverters; both individually and in a cluster. It was shown that even legacy equipment (or when paired with a few additional advanced equipment) can support such advanced control. The monitoring algorithms utilize a heterogeneous set of legacy and advanced sensor measurements, such as behind-the-meter DER sensors, distribution-level Phase Measurement Units, distribution-substation Supervisory Control and Data Acquisition (SCADA), and line current sensors, with their limited availability; in order to infer practical network conditions. Sensor data are utilized to achieve resource forecasting, phase identification, and distribution system state estimation. The technology that was developed and demonstrated in this project could be transformational to utilities, including the smaller municipal utilities such as in Riverside, which may not have the resources to deploy advanced distribution system and DERMS solutions in order to support high penetration of solar power integration. This project created a real-world prototype to provide utilities with an assessment of smart grid monitoring and control technologies.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Fundamental Insights from a Single-Crystal Sodium Iridate Battery

Electrochemically driven chemical transformations play the key role in controlling storage of energy in chemical bonds and subsequent conversion to power electric vehicles and consumer electronics. The promise of coupling anionic oxygen redox with cationic redox to achieve a substantial increase in capacities has inspired research in a wide range of electrode materials. A key challenge is that these studies have focused on polycrystalline materials, where it is hard to perform precise structural determinations, especially related to the location of light atoms. Here a different approach is utilized and a highly ordered single crystal, Na 2-x IrO 3 is harnessed, to explore the role of defects and structural transformations in layered transition metal oxide materials on redox-activity, capacity, reversibility, and stability. Within a combined experimental and theoretical framework, it is demonstrated that 1) it is possible to cycle Na 2-x IrO 3 , offering proof of principle for single-crystal based batteries 2) structural phase transitions coincide with Ir 4+ /Ir 5+ redox couple with no evident contribution from anionic redox 3) strong irreversibility and capacity fade observed during cycling correlates with the Na + migration resulting in progressive growth of an electrochemically inert O 3 -type NaIrO 3 phase.

25 ENERGY STORAGE↗

Type IV-like pili facilitate transformation in naturally competent archaea

Naturally competent organisms are capable of DNA uptake directly from the environment through the process of transformation. Despite the importance of transformation to microbial evolution, DNA uptake remains poorly characterized outside the bacterial domain. Here, we identify the pilus as a necessary component of the transformation machinery in archaea. We describe two naturally competent organisms: Methanococcus maripaludis and Methanoculleus thermophilus. In M. maripaludis, replicative vectors were transferred with an average efficiency of 2.4 x 10 3 transformants μg -1 DNA. In M. thermophilus, integrative vectors were transferred with an average efficiency of 2.7 x 10 3 transformants μg -1 DNA. Additionally, natural transformation of M. thermophilus could be used to introduce chromosomal mutations. To our knowledge, this is the first demonstration of a method to introduce targeted mutations in a member of the order Methanomicrobiales. For both organisms, mutants lacking structural components of the type IV-like pilus filament were defective for DNA uptake, demonstrating the importance of pili for natural transformation. Interestingly, competence could be induced in a non-competent strain of M. maripaludis by expressing pilin genes from a replicative vector. Furthermore, these results expand the known natural competence pili to include examples from the archaeal domain and highlight the importance of pili for DNA uptake in diverse microbial organisms.

59 BASIC BIOLOGICAL SCIENCES↗

High Resolution Data Analysis: Plans and Prospects [Book Chapter]

Herein, a report on the progress on the high resolution data analysis of the ADMX experimental results is presented. In this paper, tools are developed and tested on a blind injection mimicking a Maxwellian like signal in the frequency domain. This blind injection will be used as a test bed which can be later implemented on all the high resolution data. The high resolution data is stored in the Fermilab server. In this analysis a PostgreSQL query was made to ensure the blind injection is in the middle of the frequency spectrum and 19 such files were found. The time series data is read using a c++ program. An apodization function is applied on the time series data and zero filled to reduce the frequency spacing in order to achieve a better interpolation. A FFTW header is used to compute the Fourier transform of the time series data. A Savitzky–Golay filter is applied on the unnormalized power which then can be used to remove the spectral shape. Each frequency spectrum has a bandwidth of 50 kHz.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗