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At least 37 records · Page 2

A Method of Moments Wide Band Adaptive Rational Interpolation Method for High-Quality Factor Resonant Cavities

A new adaptive rational interpolation method is proposed to obtain the wideband frequency response of a resonant cavity simulated with the method of moments (MoM). This interpolation method uses both the Loewner matrix to construct a rational expression for the solution vector of MoM’s matrix system and an error estimator generated by the solution vectors and their derivatives. This error estimator is implemented in the adaptive procedure to gain a minimum set of frequencies and solution vectors required in the interpolation. The resulting set of frequencies and solution vectors is applied to interpolate other system variables, such as shielding effectiveness and input impedance. Here numerical results of a slotted cylindrical cavity supporting high-quality factor resonances are presented, showing that the new rational interpolation method is accurate and efficient in interpolating the complicated resonant response of the solution vector functions.

42 ENGINEERING↗

Transactive Energy Rationing in Islanded Electric Power Systems

Extreme weather events, many of which are climate change related, are occurring with increasing frequency and intensity and causing catastrophic outages. One of the major modern-day concerns of utilities is dealing with such extreme outages and consequently, its repercussions on the lives of people in society and social aspects. Traditionally, operators have been using rolling blackouts as a contingency plan to serve critical loads during such events when electricity supply is scarce. However, such blackouts practices are executed on a last-minute mandatory basis, depriving customers having low-capacity high priority loads (i.e. refrigeration, water, telecommunication, etc) that should also be serviced if at all possible. Historically, policymakers have often adopted quota-based regulatory actions or rationing for other commodities (such as gasoline, butter, sugar) to handle scarcity situations. Motivated from such quota based systems, our contribution presented in this work is an alternative transactive rationing mechanism that would provide some minimum level of service to all of the customers and serve the critical loads using market-based control during such scarcity-based contingencies. This is in contrast to the state-of-art TE mechanisms that allocate resources to customers solely based on their willingness-to-pay. The effectiveness of the proposed mechanism is demonstrated through simulation-based evaluation on two real-life use cases having feeder-level and microgrid-level configurations respectively. The simulation results clearly demonstrate the capability of the rationing scheme to serve customers’ high-priority loads through prolonged outages even during extreme scarcity scenarios.

42 ENGINEERING↗

Rational design of stable functional metal–organic frameworks

Functional porous metal–organic frameworks (MOFs) have been explored for a number of potential applications in catalysis, chemical sensing, water capture, gas storage, and separation. MOFs are among the most promising candidates to address challenges facing our society related to energy and environment, but the successful implementation of functional porous MOF materials are contingent on their stability; therefore, the rational design of stable MOFs plays an important role towards the development of functional porous MOFs. In this Focus article, we summarize progress in the rational design and synthesis of stable MOFs with controllable pores and functionalities. The implementation of reticular chemistry allows for the rational top-down design of stable porous MOFs with targeted topological networks and pore structures from the pre-selected building blocks. We highlight the reticular synthesis and applications of stable MOFs: (1) MOFs based on high valent metal ions (e.g., Al 3+ , Cr 3+ , Fe 3+ , Ti 4+ and Zr 4+ ) and carboxylate ligands; (2) MOFs based on low valent metal ions (e.g., Ni 2+ , Cu 2+ , and Zn 2+ ) and azolate linkers. We envision that the synthetic strategies, including modulated synthesis and post-synthetic modification, can potentially be extended to other more complex systems like metal-phosphonate framework materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Rational surfaces, flows and radial structure in the TJ-II stellarator

Abstract In this work, we report on the results obtained by measuring several turbulent quantities well inside the plasma edge by means of a Langmuir probe during dynamical rotational transform scans in the TJ-II stellarator, while applying a radial electric field to the edge plasma using a biasing probe. By calculating the intermittence parameter from floating potential measurements, we are able to identify a major low order rational surface and hence relate the probe measurements to the local value of the rotational transform. Based on the former, we are able to show that the poloidal plasma velocity (and hence radial electric field) has a significant radial structure that is clearly related to the rotational transform profile and in particular the lowest order rational surfaces in the range studied. The poloidal velocity is also affected by the edge biasing. The particle flux Γ was also found to exhibit a radial pattern, as did the flow shear suppression term ω E × B , but the relation of the former to the low-order rational surfaces was less clear. We surmise that this lack of direct correspondence is due to an unknown term in the turbulence evolution equation: the instability growth rate, γ . We make use of a reduced Magnetohydrodynamic turbulence model to interpret the results. Overall, a picture is obtained in which the plasma self-organizes towards a state with a clear radial pattern of the radial electric field, in line with expectations from some numerical studies describing the spontaneous formation of an ‘ E × B staircase’, consisting of alternating layers with fast and slow radial transport. In this state, the radial profiles of various quantities (density, temperature, pressure) will not be smooth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effective rationality for local unitary invariants of mixed states of two qubits

Abstract We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine algebraically independent polynomial invariants. We do so by constructing a relative section, in the sense of invariant theory, whose Weyl group is a finite abelian group. From this construction, we are able to give explicit expressions for the generating invariants in terms of the Bloch matrix representation of mixed states of two qubits. We also prove similar rationality results for the local unitary invariants of symmetrically mixed states of two qubits. We also provide a sketch of how to generalize our results to the case of an arbitrary number of qubits. Our results apply to both complex-valued and real-valued invariants.

Physics↗

p -adic reconstruction of rational functions in multiloop amplitudes

Numerical reconstruction techniques are widely employed in the calculation of multiloop scattering amplitudes. In recent years, it has been observed that the rational functions in multiloop calculations greatly simplify under partial fractioning. In this article, we present a technique to reconstruct rational functions directly in partial-fractioned form, by evaluating the functions at special integer points chosen for their properties under a p -adic metric. As an application, we apply this technique to reconstruct the largest rational function in the integration-by-parts reduction of one of the rank-5 integrals appearing in two-loop five-point full-color massless amplitude calculations in quantum chromodynamics. The number of required numerical probes (per prime field) is found to be around 25 times smaller than in conventional techniques, and the obtained result is 130 times smaller. The reconstructed result displays signs of additional structure that could be used to further reduce its size and the number of required probes. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Performance improvements of the windowed multipole formalism using a rational fraction approximation of the Faddeeva function

The windowed multipole (WMP) formalism was introduced as a way to calculate Doppler broadened cross sections on the fly during Monte Carlo simulations. While more arithmetic is needed compared to point-wise cross section look-ups, performance remained competitive from the large memory reductions and sequential data access. The single most expensive function call in a depleted fuel assembly problem using WMP comes from the evaluation of the Faddeeva function, which previously relied on a highly accurate, highly-branching algorithm. This paper explores the use of rational fraction approximations tailored to the domain interest of reactor physics applications and the development of lower accuracy approximations sufficient for our application. The rational approximations were implemented and tested in OpenMC on an infinite medium problem to stress the cross section calculation routine and a PWR assembly problem. In both cases, the rational approximation nearly eliminated the ∼ 20% penalty previously observed when comparing to point-wise libraries. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Coutsias, Evangelos A.↗

Rational Design of Nanoplasmonic Array Geometries for Biosensing

Background: Molecular diagnostics provide early and accurate diagnosis, which is essential for the prevention and treatment of infectious as well as chronic diseases. These tests are designed to detect disease-specific bioanalytes such as nucleic acid (DNA or RNA) or protein (antigens, antibodies) biomarkers. In the context of infectious disease diagnosis, nucleic acid-based detection methods are known to provide more specific and sensitive results. Here, the presence of a unique sequence belonging to the pathogenic genomic material is targeted to identify species, organism, genera and/or antimicrobial resistant gene markers. The majority of the common nucleic acid based diagnostic techniques require amplification (polymerase chain reaction, isothermal amplification etc.) of the pathogenic genetic material prior to detection impacting diagnostic speed, complexity, and cost thereby limiting ease of use. Thus, the development of simplified nucleic acid-based diagnostics that can be even used in resource-poor settings may hugely benefit patients across the globe. Nanopath is a molecular diagnostics company utilizing a solid-state nanosensor to enable sequence-specific detection of target nucleic acids without the need of amplification. These nanostructures enable ultra-sensitive biomarker detection using geometric, feature-dependent properties highly dependent on the local dielectric environment, allowing them to be sensitive to low concentration binding events. This paper describes an application of this approach to provide highly relevant clinical information within a single doctor’s office visit. Intro: The Nanopath team is in collaboration with NASA (National Aeronautics and Space Administration) and NIST (National Institute of Standards and Technology) to push the bounds of the fundamental physics associated with their biosensing platform. The ability of metals to support electromagnetic surface waves gives rise to surface plasmons when optically illuminated. This property, and its strong sensitivity to changes in the local refractive index, allows for the use of metal nanoparticles as ultra-sensitive transducers. In prior work by members of this team, ensembles of randomly oriented nanoparticles (i.e., colloidal nanorods dispersed on chip) were employed for sequence-specific nucleic acid sensing (1-3). While these particle sensors have the advantage of rapid fabrication, they suffer from low sensitivity and quality factor due to the random particle dispersity. In contrast, in this study we employ ordered array nanoparticle ensembles which can be used to improve sensor sensitivity and figure-of-merit. Study Methods Overview: In this talk, we detail the results of sensing experiments and computational simulations to outline a rational design of the structure of these plasmonic nanoparticle arrays for biomolecular sensing. Through simulation and experiment, we iteratively tailor nanostructure dimension to provide high quality signal and large resonance shifts upon modeled nucleic acid binding. In particular, full-wave electromagnetic simulations were conducted using Lumerical photonic simulation software in which periodic boundary conditions were applied in the x- and y- dimensions for each of the nanoplasmonic sensor geometries. To simulate the resonance response to changes in the bulk solution in contact with the sensor surface, the refractive index of the surrounding media was changed appropriately. Nucleic acid hybridization events were modeled using either using spherical structures approximating the relevant radius of genomic material as estimated by polymer models, or as conformal layers with the known refractive indices for nucleic acids. On the basis of initial simulations, nanosensors were fabricated using traditional electron-beam lithography protocols at NIST. To evaluate consensus between simulations and experiments, bulk sensing experiments were carried out in which the resonance peaks were obtained by submerging the sensors in refractive index standards. Key nanosensor characteristics including resonance peak locations, resonance peak shifts as a function of refractive index, and figure of merit (FOM) of extinction curves were examined between the experimental and simulation results prior to proceeding with simulations on additional geometries and more complex solution conditions, and further device fabrication. This iterative process is repeated toward a rational design of nanoplasmonic array geometries for biosensing optimizing response for targeted disease detection. In summary, this study puts forth a methodology for rational design and characterization of regularly spaced nanoparticle arrays for optics-based biosensing. The results of this study will allow for more informed design of nanostructure geometries towards sequence-specific nucleic acid detection. These improved designs have the potential to improve clinical sensitivity and limit-of-detection across disease indication.

sensor↗

The Effect of Dietary Exposure to Coal Ash Contaminants within Food Ration on Growth and Reproduction in Daphnia magna

Coal ash contains numerous contaminants and is the focus of regulatory actions and risk assessments due to environmental spills. In this work, we exposed Daphnia magna to a gradient of coal ash contamination under high and low food rations to assess the sublethal effects of dietary exposures. Whereas exposure to contaminants resulted in significant reductions in growth and reproduction in daphnids, low, environmentally relevant food rations had a much greater effect on these endpoints.

59 BASIC BIOLOGICAL SCIENCES↗

Spectral Mesh-Free Quadrature for Planar Regions Bounded by Rational Parametric Curves

This article presents spectral, mesh-free, Green’s theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find intermediate quadrature rules for line integrals along the region’s boundary curves corresponding to Green’s theorem. (2) We then use a high-order quadrature rule to compute the numerical antiderivative of the integrand along a coordinate axis, which is used to evaluate the Green’s theorem line integral. We present two methods to compute the intermediate quadrature rule. The first is spectrally accurate (it converges faster than any algebraic order with respect to number of quadrature points) and is relatively easy to implement, but has no guarantee of polynomial exactness. The second guarantees exactness for polynomial integrands up to a pre-specified degree with an a priori-known number of quadrature points and retains the convergence properties of the first, but is slightly more complicated. The quadrature schemes have applications to computation of geometric moments, immersogeometric analysis, conservative field transfer between high-order meshes, and initialization of multi-material simulations with rational geometry. We compare the quadrature schemes produced using our method to other methods in the literature and show that they are much more efficient both in terms of number of quadrature points and computational time. We provide an open-source implementation of the algorithm in MATLAB.

97 MATHEMATICS AND COMPUTING↗

Allocation Mechanisms in Rationed Markets

Economic theory has come to play an important role in power system operations through the design of wholesale markets that are central to their operation. Furthermore, transactive energy places economic theory as a cornerstone in its operational concept as it seeks to integrate the technical needs of the power system with the preferences of its participants. Traditionally the mechanism employed is the continuous double-auction but de-pending on the circumstances the power system find itself in, this mechanism may or may not be the most appropriate, i.e. a one-size fits all market institution cannot be recommended without regard for the features of the underlying trading environment. This paper seeks to explain the economic rationale that guides the choice of a market institution and takes recourse to a theoretical demonstration in the context of a rationed power system scenario where demand exceeds generation (due to any number of events such as outages, microgrid operation, etc) and electrical energy must be rationed to better understand which types of mechanisms are most appropriate.

transactive energy, power system economics, econom↗

Rational Control of Off‐State Heterogeneity in a Photoswitchable Fluorescent Protein Provides Switching Contrast Enhancement**

Abstract Reversibly photoswitchable fluorescent proteins are essential markers for advanced biological imaging, and optimization of their photophysical properties underlies improved performance and novel applications. Here we establish a link between photoswitching contrast, one of the key parameters that dictate the achievable resolution in nanoscopy applications, and chromophore conformation in the non‐fluorescent state of rsEGFP2, a widely employed label in REversible Saturable OpticaL Fluorescence Transitions (RESOLFT) microscopy. Upon illumination, the cis chromophore of rsEGFP2 isomerizes to two distinct off ‐state conformations, trans1 and trans2 , located on either side of the V151 side chain. Reducing or enlarging the side chain at this position (V151A and V151L variants) leads to single off ‐state conformations that exhibit higher and lower switching contrast, respectively, compared to the rsEGFP2 parent. The combination of structural information obtained by serial femtosecond crystallography with high‐level quantum chemical calculations and with spectroscopic and photophysical data determined in vitro suggests that the changes in switching contrast arise from blue‐ and red‐shifts of the absorption bands associated to trans1 and trans2 , respectively. Thus, due to elimination of trans2 , the V151A variants of rsEGFP2 and its superfolding variant rsFolder2 display a more than two‐fold higher switching contrast than their respective parent proteins, both in vitro and in E. coli cells. The application of the rsFolder2‐V151A variant is demonstrated in RESOLFT nanoscopy. Our study rationalizes the connection between structural and photophysical chromophore properties and suggests a means to rationally improve fluorescent proteins for nanoscopy applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Combined DSC/TGA Analysis to Rationalize the As-Sintered Microstructure in Binder Jet Additively Manufactured H13 Tool Steel

In this study, a combined DSC/TGA analysis has been used to rationalize the constant liquid channel width at higher sintering temperatures in H13 tool steel manufactured by binder jet additive manufacturing. Using enthalpy conservation along with coupled DSC + TGA analysis, the phase fractions of liquid and austenite phases during heating and cooling respectively were estimated. The estimates from the DSC/TGA analysis were compared with equilibrium phase fraction predictions from ThermoCalc. The resulting phase evolution was correlated to the as-sintered microstructure to rationalize the unexpected lack of change in liquid channel width at higher sintering temperatures.

Kannan, Rangasayee↗

Rational Design of a Ni 3 N 0.85 Electrocatalyst to Accelerate Polysulfide Conversion in Lithium–Sulfur Batteries

Slow kinetics of polysulfide conversion reactions lead to severe issues for lithium–sulfur (Li–S) batteries, for example, low rate capability, polysulfide migration, and low Coulombic efficiencies. These challenges hinder the practical applications of Li–S batteries. Here, we proposed a rational strategy of tuning the d-band of catalysts to accelerate the conversion of polysulfides. Nitrogen vacancies were engineered in hexagonal Ni 3 N (space group P 6 3 22) to tune its d-band center, leading to the strong interaction between polysulfides and Ni 3 N. Because of the greater electron population in the lowest occupied molecular orbital of Li 2 S 4 , the terminal S–S bonds were weakened for breaking. Temperature-dependent experiments confirm that Ni 3 N 0.85 demonstrates a much low activation energy, thereby accelerating the conversion of polysulfides. A Li–S cell using Ni 3 N 0.85 can deliver a high initial discharge capacity of 1445.9 mAh g –1 (at 0.02 C) and low decay per cycle (0.039%). The Ni 3 N 0.85 cell can also demonstrate an initial capacity of 1200.4 mAh g –1 for up to 100 cycles at a high loading of 5.2 mg cm –2 . The high efficiency of rationally designed Ni 3 N 0.85 demonstrates the effectiveness of the d-band tuning strategy to develop low-activation-energy catalysts and to promote the atomic understanding of polysulfide conversion in Li–S batteries.

25 ENERGY STORAGE↗

Sustainable conversion of biomass to rationally designed lithium-ion battery graphite

The carbon net negative conversion of bio-char, the low value byproduct of pyrolysis bio-oil production from biomass, to high value, very high purity, highly crystalline flake graphite agglomerates with rationally designed shape and size tailored for lithium-ion battery energy storage material is reported. The process is highly efficient, 0.41 g/Wh; the energy content of its co-product of the process, bio-oil, exceeds that needed to power the process. It is shown that the shape of the starting material is retained during the transformation, allowing the ultimate morphology of the graphite agglomerates to be engineered from relatively malleable biomass. In contrast to commercial graphite production, the process can be performed at small scale with low equipment costs, enabling individual research laboratories to produce Li-ion grade graphite with customizable shape, size and porosity for Si/graphite composite and other graphite involved anodes. The mechanism of the graphitization of bio-char, a “non-graphitizable” carbon, is explored, suggesting the molten metal catalyst is absorbed into the pore structure, transported through and transforming the largely immobile biochar. Finally, the transformation of biomass to rationally designed graphite morphologies with Li-ion anode performance that closely mimic commercial shaped graphite is demonstrated.

09 BIOMASS FUELS↗

Robust multiresonant nonlocal metasurfaces by rational design

Abstract Dielectric metasurfaces supporting optical resonances have become a promising platform for quantum and nonlinear optics. However, resonant metasurfaces remain limited in their capacity to independently control the behavior of many distinct resonances despite efforts in computational optimization and inverse design. In this work, we overcome longstanding limitations by introducing a generalized rational design paradigm based on symmetry. Specifically, we use symmetry-broken metasurfaces with periodic “quadromer” lattices comprised of four nanostructures per unit cell to enable extensive control of multiple optical resonances. The rationally designed metasurfaces are readily fabricable, and we experimentally demonstrate metasurfaces that support up to four high Q-factor resonances with deliberately chosen free-space polarizations, spectral separations, and mode profiles. Our design paradigm may unlock new applications for multiresonant metasurfaces in quantum and nonlinear optics, optical sensing, and augmented reality displays.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Rational function representation of flap noise spectra including correction for reflection effects

A rational function is presented for the acoustic spectra generated by deflection of engine exhaust jets for under-the-wing and over-the-wing versions of externally blown flaps. The functional representation is intended to provide a means for compact storage of data and for data analysis. The expressions are based on Fourier transform functions for the Strouhal normalized pressure spectral density, and on a correction for reflection effects based on the N-independent-source model of P. Thomas extended by use of a reflected ray transfer function. Curve fit comparisons are presented for blown flap data taken from turbofan engine tests and from large scale cold-flow model tests. Application of the rational function to scrubbing noise theory is also indicated.

Miles, J. H.↗