An Analytical Generator for Wave Energy Converter Optimization Using Co-Design Methods
Innovation side of Wave-SPARC Project. Looking into an analytical generator to use within a co-design optimization study
Anderson, Megan Lee↗
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Results for “Analytical Methods”
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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Analytic soliton solutions of nonlinear extensions of the Schrödinger equation
A method is presented to construct analytic solitary wave solutions in nonlinear extensions of the Schrödinger equation starting from analytic solutions of the ordinary Schrödinger equation. We provide several examples illustrating the method. We rederive three well-known soliton solutions including the N-dimensional non-relativistic Gausson as well as the one-dimensional 1 / cosh-soliton and a theory with a power-like nonlinearity proportional to |ψ| 2λ with λ > 0. We also find several new solutions in different nonlinear theories in various space dimensions which, to the best of our knowledge, have not yet been discussed in literature. Our method can be used to construct further nonlinear theories and generalized to relativistic soliton theories, and may have many applications.
Analytical soliton solutions↗
Efficient general method for numerically modeling laser pulse propagation, overlap, and lifetime effects in amplifiers
An efficient numerical time-dependent general method is developed to address incoherent pulse overlap and lifetime effects in laser amplifiers. The alternating propagation-population laser energetics method (APPLE) has been validated against a semi-discrete coupled rate equation numerical method (SDRE) and analytic formalisms in bounding cases. APPLE is based on decoupled rates applied to a time-dependent framework where both space-time-dependent populations and pulse energetics are consistently updated in each time step. A significant advantage of APPLE lies in its conceptual simplicity, ease of implementation, and relatively small computational cost. SDRE tracks the populations through coupled rates and uses the method of lines to discretize the hyperbolic partial differential transport equations allowing for use of ordinary differential equation solvers. With reasonably sized mesh, we report both energetic and power pulse shape relative differences on the order of one percent between the models over a large range of initial conditions.
47 OTHER INSTRUMENTATION↗
Physics-Based Machine Learning Methods for U-235 Forensics Signatures
Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collectedunder structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore,their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distanceto the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensembleof trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fittingobserved in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inversephysical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of thesource strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations ofunderlying regression methods.
Rao, Nageswara↗
Physics-Based Machine Learning Methods for U-235 Forensics Signatures
Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collected under structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore, their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distance to the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensemble of trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fitting observed in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inverse physical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of the source strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations of underlying regression methods.
Rao, Nageswara↗
Infrasonic directivity of monopole, dipole and bipole ground-surface reflected sources
Infrasound (acoustic waves below 20 Hz) can be used to detect, locate and quantify activity in the atmosphere such as volcanic eruptions and anthropogenic explosions. Attempts to quantify volcanic eruption parameters such as exit velocity, plume height and mass flow rate using infrasound data depend strongly on assumptions of the acoustic source type. Infrasonic sources may produce omnidirectional or directional wavefields, while propagation effects, such as interaction with topography, can induce further wavefield directivity that is measured by field instrumentation. Limited sampling of these wavefields can hinder our ability to infer the underlying source, and thus our understanding of the eruption characteristics. Equivalent sources are often used to represent acoustic source mechanisms and resultant wavefields. In this study, we review equivalent acoustic sources as they pertain to infrasonic scale and wavelengths commonly encountered in very local (<5 km range) geophysical field deployments. We highlight the equivalent infrasonic bipole source that can be induced by ground-reflection of an elevated monopole; we are not aware of any prior infrasound studies that use the bipole source concept. We use analytical and numerical methods to explore source directivity of monopole, dipole and bipole ground-reflected sources at infrasonic frequencies as well as the additional directivity complications introduced by interactions with topography. We illustrate that for typical volcano-infrasound wavelengths, increasing height above the ground as well as increasing source frequency leads to increased wavefield directivity. Numerical modelling using a simple omnidirectional monopole source embedded in topography further illustrates that both horizontal and vertical infrasound directionality can be induced by topography at the distance scales appropriate for local volcano infrasound monitoring. Information summarized in this analytical and numerical exploration of infrasound directivity may be used to help guide future volcano-infrasound field deployments intended to estimate source parameters or quantify wavefield directivity. Analytic solutions for simple whole-space or half-space atmospheres provide useful formulations for planning or initially analysing geophysical field-scale experimental data; however, especially at very local distances from the source (<5 km), 3-D simulations are necessary to account for complex topography commonly encountered in volcano-infrasound applications.
Infrasound↗
The three-point form factor of Tr ϕ 3 to six loops
We study the three-point form factor of the length-three half-BPS operator (Tr ϕ 3 ) in planar $\mathcal{N}$ = 4 Super-Yang-Mills theory, using analyticity and integrability methods. We find that the functions describing the form factor in perturbation theory live in the same restrictive space of multiple polylogarithms as the one describing the form factor of the stress-tensor operator (Tr ϕ 2 ). Furthermore, we find that the leading-order data in the collinear limit provided by the form factor operator product expansion (FFOPE) is enough to fix the form factor uniquely, at least through six loops. We perform various tests of our results using the subleading FFOPE corrections. We also analyze the form factor in the Regge limit where two Mandelstam invariants are large; we obtain a compact representation for the form factor in this limit which is valid to all orders in the coupling.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Poincaré beams from a free electron laser
Poincaré beams are light beams that have spatially inhomogeneous polarization structure that spans a finite portion of the Poincaré sphere. This feature bestows the beams with intriguing topological properties and has led to a surge in research on their fundamental characteristics, their controlled generation and on emerging applications. Here we present an experimental demonstration of a Poincaré beam generated in the extreme ultraviolet (16.7 nm) at the FERMI free electron laser (FEL). The ‘star’ type Poincaré beam is generated by exploiting the phase and intensity structure intrinsic to FEL radiation without relying on optical elements. Here, we controlled the spatial polarization distribution through a precise overlap and power balance between two FEL pulses, each with different transverse phase distributions and orthogonal circular polarizations. The spatial polarization structure was mapped in detail and shows extensive coverage of the Poincaré sphere, in agreement with analytic predictions. This method of in situ Poincaré beam production in FELs enables straightforward flexibility in the orientation and balance of polarization states, and can readily be extended to other vector beams and to shorter wavelengths enabling novel science applications in modern light sources.
Morgan, Jenny [SLAC National Accelerator Laborator↗
Magnetic anisotropy and GGG substrate stray field in YIG films down to millikelvin temperatures
Abstract Quantum magnonics investigates the quantum-mechanical properties of magnons, such as quantum coherence or entanglement for solid-state quantum information technologies at the nanoscale. The most promising material for quantum magnonics is the ferrimagnetic yttrium iron garnet (YIG), which hosts magnons with the longest lifetimes. YIG films of the highest quality are grown on a paramagnetic gadolinium gallium garnet (GGG) substrate. The literature has reported that ferromagnetic resonance (FMR) frequencies of YIG/GGG decrease at temperatures below 50 K despite the increase in YIG magnetization. We investigated a 97 nm-thick YIG film grown on 500 μm-thick GGG substrate through a series of experiments conducted at temperatures as low as 30 mK, and using both analytical and numerical methods. Our findings suggest that the primary factor contributing to the FMR frequency shift is the stray magnetic field created by the partially magnetized GGG substrate. This stray field is antiparallel to the applied external field and is highly inhomogeneous, reaching up to 40 mT in the center of the sample. At temperatures below 500 mK, the GGG field exhibits a saturation that cannot be described by the standard Brillouin function for a paramagnet. Including the calculated GGG field in the analysis of the FMR frequency versus temperature dependence allowed the determination of the cubic and uniaxial anisotropies. We find that the total crystallographic anisotropy increases more than three times with the decrease in temperature down to 2 K. Our findings enable accurate predictions of the YIG/GGG magnetic systems behavior at low and ultralow millikelvin temperatures, crucial for developing quantum magnonic devices.
Serha, Rostyslav O.↗
Comparison of continuum-continuum and Coulomb-laser-coupling delays from visible to midinfrared wavelengths
We compare the various proposed formulas for CLC and CC delays using analytical and numerical methods across a range of wavelengths spanning visible to midinfrared. We show that one of the CC definitions is nearly equal to the CLC delay over a range of photoelectron energies and wavelengths. We furthermore obtain alternate expressions for the CC delays. These expressions are simpler to use and show close correspondence to the CLC delays. Based on this correspondence, we suggest a correction to the CLC delay for low-energy electrons, where the currently used approximation breaks down. Our work provides guidance for when it is valid to treat CC and CLC delays as being equivalent.
74 ATOMIC AND MOLECULAR PHYSICS↗
Pauli potential formalism at finite temperature
At zero temperature, the Pauli potential—the functional derivative of the Pauli kinetic energy density functional—is the key to the accuracy of the orbital-free density functional theory (OFDFT) as it is supposed to capture all the effects associated with the Pauli exclusion principle. Here, we extend this concept to finite temperature by defining Pauli free energy and the modified Pauli free energy, both representing the natural generalizations of the Pauli term from zero- T to finite- T . We discuss their physical interpretation, the mathematical nuances, and the applicability, arguing that the modified Pauli potential should be used as an extension of the zero- T counterpart within the OF-DFT framework. Through analytical and numerical methods, we then analyze some of the exact properties concerning the modified Pauli free- and kinetic-energy terms and examine the temperature dependence of the modified Pauli potential.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Coulomb corrections for the nonflip and spin-flip electromagnetic 𝑝 ↑ 𝐴 amplitudes
It is demonstrated that, within the eikonal approach, the Coulomb corrections to the elastic electromagnetic nonflip and spin-flip proton-nucleus amplitudes are identical when the two amplitudes share the same exponential form factors. This result allows Coulomb corrections to be computed numerically, and with high precision, for both electromagnetic and hadronic elastic 𝑝 ↑ 𝐴 amplitudes in the massless-photon limit, including the effects of soft magnetic photon exchange. The method relies on analytical expressions and numerical integrations over a finite impact-parameter range with nonsingular integrands, providing a practical and systematically controlled framework for phenomenological applications.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Ion-chain sympathetic cooling and gate dynamics
Sympathetic cooling is a technique often employed to mitigate motional heating in trapped-ion quantum computers. However, choosing system parameters such as number of coolants and cooling duty cycle for optimal gate performance requires evaluating trade-offs between motional errors and other slower errors such as qubit dephasing. The optimal parameters depend on cooling power, heating rate, and ion spacing in a particular system. In this study, we aim to analyze best practices for sympathetic cooling of long chains of trapped ions using analytical and computational methods. We use a case study to show that optimal cooling performance is achieved when coolants are placed at the center of the chain and provide a perturbative upper bound on the cooling limit of a mode given a particular set of cooling parameters. In addition, using computational tools, we analyze the trade-off between the number of coolant ions in a chain and the center-of-mass mode heating rate. We also show that cooling as often as possible when running a circuit is optimal when the qubit coherence time is otherwise long. These results provide a roadmap for how to choose sympathetic cooling parameters to maximize circuit performance in trapped-ion quantum computers using long chains of ions.
Cooling & trapping↗
Superexponential primordial black hole production via delayed vacuum decay
If a cosmological first-order phase transition occurs sufficiently slowly, delayed vacuum decay may lead to the formation of primordial black holes. Here we consider a simple model as a case study of how the abundance of the produced black holes depends on the model’s input parameters. We demonstrate, using both numerical and analytical arguments and methods, that the black hole abundance is controlled by a double, “super”-exponential dependence on the three-dimensional Euclidean action over temperature at its minimal value. We show that a modified expansion rate during the phase transition, such as one driven by an additional energy density component, leads to a weaker dependence on the underlying model parameters, but maintains the same superexponential structure. We argue that our findings generalize to any framework of black hole production via delayed vacuum decay. Published by the American Physical Society 2025
Wu, Yanda (ORCID:000000034487305X)↗
Quantum chaos on edge
Recently, the physics of many-body quantum chaotic systems close to their ground states has come under intensified scrutiny. Such studies are motivated by the emergence of model systems exhibiting chaotic fluctuations throughout the entire spectrum [the Sachdev-Ye-Kitaev (SYK) model being a renowned representative] as well as by the physics of holographic principles, which likewise unfold close to ground states. Interpreting the edge of the spectrum as a quantum critical point, here we combine a wide range of analytical and numerical methods to the identification and comprehensive description of two different universality classes: the near edge physics of “sparse” and the near edge of “dense” chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension, which is exponentially small or algebraically small in the sparse and dense case, respectively. Notable representatives of the two classes are generic chaotic many-body models (sparse) and invariant random matrix ensembles or chaotic gravitational systems (dense). While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different. Considering the SYK model as a representative of the sparse class, we apply a combination of field theory and exact diagonalization to a detailed discussion of its edge spectrum. Conversely, Jackiw-Teitelboim gravity is our reference model for the dense class, where an analysis of the gravitational path integral and random matrix theory reveal universal differences to the sparse class, whose implications for the construction of holographic principles we discuss. Published by the American Physical Society 2024
Altland, Alexander (ORCID:0000000229914805)↗
Monitoring Sulfuric Acid and Temperature Using Raman Spectroscopy and Multivariate Chemometrics
Multivariate regression models were optimized for the quantification of sulfuric acid (H 2 SO 4 ) [0–8 M] and temperature (20 °C–80 °C) in the presence of ammonium sulfate ((NH 4 ) 2 SO 4 [0–0.6 M]) using Raman spectroscopy. Optical vibrational spectroscopy is a useful nondestructive technique for the in situ analysis of complex chemical systems notoriously difficult to monitor in situ and in real-time. Multivariate analysis, a chemometrics method, can be paired with these nondestructive optical methods for determining analyte concentration and speciation in complex solutions, such as dissociated species in polyprotic acids, e.g., H 2 SO 4 . The effect of temperature is often overlooked although it can have a major influence on speciation and the corresponding Raman spectra. Here, in this study, partial least squares regression models were optimized for the quantification of H 2 SO 4 and its two deprotonated forms as a function of temperature. Measuring bisulfate as a function of temperature is particularly challenging owing to changes in the second dissociation constant. A designed training set effectively minimized the sample set size and trained a robust predictive model with percent root mean square error of <3% for H 2 SO 4 . The practical strategy employed here was demonstrated to be effective for building chemometric models that directly account for dynamic temperatures with static samples and is shown to be amenable to flow cell analysis applications with a simple calibration transfer for process monitoring applications.
D-optimal design↗
Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. Focusing on the decohered cluster state – a mixed-state symmetry-protected topological state protected by a combined strong and weak symmetry – we construct a parent Lindbladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical and numerical methods, we find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. However, when perturbations introduce only weak symmetry defects, the steady-state mixed-state symmetry-protected topological order remains stable. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.
Shah, Jeet [University of Maryland, College Park, ↗
Propagation of partially spatially coherent laser beams in instantaneous Kerr media
The propagation of intense, partially spatially coherent laser beams in a medium with instantaneous third-order susceptibility is studied analytically and numerically. For sufficiently high power relative to that required for nonlinear self-focusing, the propagation initially proceeds in two stages. In the first stage, spatial coherence builds up, and in the second stage, the number of speckles reduces. Once the degree of coherence is sufficiently high, whole-beam self-focusing occurs. The beam power is mostly confined within the initial spot radius. Two analytical approaches for describing the evolution of the beam are presented. The method of moments leads to an analytical solution for the rms spot radius that is in excellent agreement with simulations. This method does not require any knowledge of the field statistics beyond the initial conditions and provides no information about the evolution of the individual speckles. The other approach employs a self-similar solution for the second-order coherence function of the field and assumes that the fourth-order coherence function is factorizable and obeys complex circular Gaussian random statistics. The latter method also leads to an analytical expression for the spot radius, but its predictions for the qualitative evolution of the speckles disagree with wave-optics simulations.
lasers↗