A generalized multiple scales approach to a class of linear differential equations
Generalized multiple scales method for solving linear differential equations with variable coefficients applied to Liouville-Green approximation
Ramnath, R. V.↗
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Results for “linear scaling”
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Properties of the Flight Model Gas Electron Multiplier for the GEMS Mission
We present the gain properties of the gas electron multiplier (GEM) foil in pure dimethyl ether (DME) at 190 Torr. The GEM is one of the micro pattern gas detectors and it is adopted as a key part of the X-ray polarimeter for the GEMS mission. The X-ray polarimeter is a time projection chamber operating in pure DME gas at 190 Torr. We describe experimental results of (1) the maximum gain the GEM can achieve without any discharges, (2) the linearity of the energy scale for the GEM operation, and (3) the two-dimensional gain variation of the active area. First, our experiment with 6.4 keV X-ray irradiation of the whole GEM area demonstrates that the maximum effective gain is 2 x 10(exp 4) with the applied voltage of 580 V. Second, the measured energy scale is linear among three energies of 4.5, 6.4, and 8.0 keV. Third, the two-dimensional gain mapping test derives the standard deviation of the gain variability of 7% across the active area.
gas electron multiplier (GEM)↗
Input-output description of linear systems with multiple time-scales
It is pointed out that the study of systems evolving at multiple time-scales is simplified by studying reduced-order models of these systems valid at specific time-scales. The present investigation is concerned with an extension of results on the time-scale decomposition of autonomous systems to that of input-output systems. The results are employed to study conditions under which positive realness of a transfer function is preserved under singular perturbation. Attention is given to the perturbation theory for linear operators, the multiple time-scale structure of autonomous linear systems, the input-output description of two time-scale linear systems, the positive realness of two time-scale systems, and multiple time-scale linear systems.
Madriz, R. S.↗
A comparison of linear acoustic theory with experimental noise data for a small-scale hovering rotor
Linear acoustic calculations based on full aerodynamic data as input are presented and compared with measured cases reported by Boxwell et al. (1978). The full aerodynamic data are obtained using three programs giving radial loading, chordwise loading, and chordwise position of transition. It is shown that in the theoretical results the most significant noise source mechanism is due to blade thickness. Thus the conclusions of Boxwell et al. as to the importance of nonlinearities around the blades are upheld. These conclusions concern the width, shape and the level of the acoustic pressure calculated from linear acoustic theory. Some of the approximations involved in the application of acoustic analogy using quadrupole sources are discussed. It is necessary that the near- and far-field problems of rotating blades be treated together as shown for the case of an oscillating sphere.
Farassat, F.↗
Oceanic turbulence - Big bangs or continuous creation?
A hypothesis concerning the turbulence characteristics of 'microstructure' patches in the ocean is proposed in which a turbulence field is driven at the same time and scale at which it is observed. The driving energy is converted into turbulence kinetic energy in such a way that the observed overturning thickness scale is linearly related to the length scale. This hypothesis is contrasted with that of Gibson (1982), in which the 'patches' are produced by rare, powerful turbulence generators that have 'fossilized' prior to their observation. Careful attention is given to the sampling process and its assumptions.
Caldwell, D. R.↗
Randomized Adiabatic Quantum Linear Solver Algorithm with Optimal Complexity Scaling and Detailed Running Costs
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number 𝜅 of the linear system and the target error 𝜖. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling 𝑂(𝜅log (1/𝜖))—an exponential improvement in 𝜖, and a shaving of a log 𝜅 scaling factor in 𝜅. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is 837𝜅 at 𝜖 = 10 −10 for Hermitian matrices.
97 MATHEMATICS AND COMPUTING↗
Comparison of Multi-Scale Nonlinear and Conventional Linear Methods for Stress Analysis of Nb 3 Sn Superconducting Magnets
Here this is an extension of the work on a multi-scale nonlinear procedure that demonstrated how to conduct nonlinear stress analysis of Nb 3 Sn superconducting accelerator magnets. The nonlinear procedure uses measured stress-strain curves of annealed copper, Nb 3 Sn strands and coil samples as inputs, which reduces the number of assumptions made for material properties—key uncertainties of any engineering analysis. The results from nonlinear analysis, semi-nonlinear analysis, and linear analysis of the same QFFB2 Nb 3 Sn quadrupole magnet under the same temperature and loads, were compared and discussed. The comparison illustrates that nonlinear stress analysis is significantly more accurate than other methods. As the superconducting coil block is a complex, composite material, it would be inadequate to assume the whole coil block to be linear, either isotropic or orthotropic. It is imperative to conduct nonlinear analysis by simulating the superconducting coil to the level of detail of the individual cables and individual strands. The nonlinear stress analysis procedure can be used to simulate not only Nb 3 Sn magnets, but also NbTi and HTS magnets.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Image Gradient Decomposition for Parallel and Memory-Efficient Ptychographic Reconstruction
Ptychography is a popular microscopic imaging modality for many scientific discoveries and sets the record for highest image resolution. Unfortunately, the high image resolution for ptychographic reconstruction requires significant amount of memory and computations, forcing many applications to compromise their image resolution in exchange for a smaller memory footprint and a shorter reconstruction time. In this paper, we propose a novel image gradient decomposition method that significantly reduces the memory footprint for ptychographic reconstruction by tessellating image gradients and diffraction measurements into tiles. In addition, we propose a parallel image gradient decomposition method that enables asynchronous point-to-point communications and parallel pipelining with minimal overhead on a large number of GPUs. Our experiments on a Titanate material dataset (PbTiO3) with 16632 probe locations show that our Gradient Decomposition algorithm reduces memory footprint by 51 times. In addition, it achieves time-to-solution within 2.2 minutes by scaling to 4158 GPUs with a super-linear strong scaling efficiency at 364% compared to runtimes at 6 GPUs. This performance is 2.7 times more memory efficient, 9 times more scalable and 86 times faster than the state-of-the-art algorithm.
Wang, Xiao↗
Aerospace plane guidance using time-scale decomposition and feedback linearization
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Van Buren, Mark A.↗
Fast Magnetic Reconnection with Turbulence in High Lundquist Number Limit
Here, we use extensive 3D resistive MHD simulations to study how large-scale current sheets will undergo fast reconnection in the high Lundquist number S limit (above ~104), when the system is subject to different externally driven turbulence levels and the self-generated turbulence produced by 3D reconnection dynamics. We find that the normalized global reconnection rate ~0.01–0.13 is weakly dependent on S. Global reconnection with the classic inflow/outflow configurations is observed, and 3D flux ropes are hierarchically formed and ejected from reconnection regions. A statistical separation of the reconnected magnetic field lines follows a superdiffusive behavior, from which the rate is measured to be very similar to that obtained from the mixing of tracer populations. We find that the reconnection rate scales roughly linearly with the turbulence level during the peak of reconnection. This scaling is consistent with the turbulence properties produced by both the externally driven and self-generation processes. These results imply that large-scale thin current sheets tend to undergo rigorous reconnection.
79 ASTRONOMY AND ASTROPHYSICS↗
Towards exascale for wind energy simulations
We examine large-eddy-simulation modeling approaches and computational performance of two open-source computational fluid dynamics codes for the simulation of atmospheric boundary layer flows that are of direct relevance to wind energy production. The first code, NekRS, is a high-order, unstructured-grid, spectral element code. The second code, AMR-Wind, is a second-order, block-structured, finite-volume code with adaptive mesh refinement capabilities. The objective of this study is to co-develop these codes in order to improve model fidelity and performance for each. These features will be critical for running ABL-based applications such as wind farm analysis on advanced computing architectures. To this end, we investigate the performance of NekRS and AMR-Wind on the Oak Ridge Leadership Facility supercomputers Summit, using 4 to 800 nodes (24 to 4,800 NVIDIA V100 GPUs), and Crusher, the testbed for the Frontier exascale system, using 18 to 384 Graphics Compute Dies on AMD MI250X GPUs. We compare strong- and weak-scaling capabilities, linear solver performance, and time to solution. We also identify leading inhibitors to parallel scaling.
17 WIND ENERGY↗
Scale-bridging with the extended/generalized finite element method for linear elastodynamics
This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEMgl framework is expanded to enable the numerical solution of multiscale problems through the automated construction of specially-tailored shape functions, thereby enabling high-fidelity finite element modeling on simple, fixed finite element meshes. Furthermore, this introduces time-dependencies in the shape functions in that they are subject to continuous adaptation with time. The temporal aspects of the formulation are investigated by considering the Newmark-β time integration scheme, and the efficacy of mass lumping strategies is explored in an explicit time-stepping scheme. This method is demonstrated on representative wave propagation examples as well as a dynamic fracture problem to assess its accuracy and flexibility.
36 MATERIALS SCIENCE↗
Static Subspace Approximation for Random Phase Approximation Correlation Energies: Implementation and Performance
Developing theoretical understanding of complex reactions and processes at interfaces requires using methods that go beyond semilocal density functional theory to accurately describe the interactions between solvent, reactants and substrates. Methods based on many-body perturbation theory, such as the random phase approximation (RPA), have previously been limited due to their computational complexity. However, this is now a surmountable barrier due to the advances in computational power available, in particular through modern GPU-based supercomputers. In this work, we describe the implementation of RPA calculations within BerkeleyGW and show its favorable computational performance on large complex systems relevant for catalysis and electrochemistry applications. Our implementation builds off of the static subspace approximation which, by employing a compressed representation of the frequency dependent polarizability, enables the evaluation of the RPA correlation energy with significant acceleration and systematically controllable accuracy. We find that the computational cost of calculating the RPA correlation energy scales only linearly with system size for systems containing up to 50 thousand bands, and is expected to scale quadratically thereafter. We also show excellent strong scaling results across several supercomputers, demonstrating the performance and portability of this implementation.
algorithmic development↗
Cooling of solar flares plasmas. 1: Theoretical considerations
Theoretical models of the cooling of flare plasma are reexamined. By assuming that the cooling occurs in two separate phase where conduction and radiation, respectively, dominate, a simple analytic formula for the cooling time of a flare plasma is derived. Unlike earlier order-of-magnitude scalings, this result accounts for the effect of the evolution of the loop plasma parameters on the cooling time. When the conductive cooling leads to an 'evaporation' of chromospheric material, the cooling time scales L(exp 5/6)/p(exp 1/6), where the coronal phase (defined as the time maximum temperature). When the conductive cooling is static, the cooling time scales as L(exp 3/4)n(exp 1/4). In deriving these results, use was made of an important scaling law (T proportional to n(exp 2)) during the radiative cooling phase that was forst noted in one-dimensional hydrodynamic numerical simulations (Serio et al. 1991; Jakimiec et al. 1992). Our own simulations show that this result is restricted to approximately the radiative loss function of Rosner, Tucker, & Vaiana (1978). for different radiative loss functions, other scaling result, with T and n scaling almost linearly when the radiative loss falls off as T(exp -2). It is shown that these scaling laws are part of a class of analytic solutions developed by Antiocos (1980).
Cargill, Peter J.↗
Topology-Dependent Performance of Free-Space Photonic Quantum Networks Under Noise
Photonic quantum communication enables secure and high-fidelity information transfer beyond classical limits, with direct relevance to emerging quantum networks operating in free-space environments. While physical-layer models of depolarizing noise, Gamma–Gamma turbulence statistics, entanglement swapping, and decoy-state QKD security bounds are individually well established, prior work typically treats these components in isolation or under fixed network assumptions. In this work, we develop a unified topology-aware analytical framework that simultaneously integrates free-space optical link budgets, turbulence-induced visibility degradation, depolarizing qubit noise, multi-hop entanglement cascade dynamics, teleportation fidelity thresholds, CHSH nonlocality certification, and asymptotic decoy-state secret key rate bounds across star, mesh, and ring graph structures. Rather than introducing new physical channel models, we demonstrate that identical physical links exhibit fundamentally different end-to-end performance once embedded within different network topologies. Mesh architectures minimize visibility cascade through hop-count reduction but incur quadratic hardware scaling. Star topologies minimize link count but concentrate noise and synchronization overhead at the hub. Ring configurations offer linear hardware scaling with multiplicative fidelity degradation. The results establish topology as a first-order design parameter in near-term free-space quantum networks operating without full quantum repeater infrastructures. While motivated by distributed multi-agent architectures, the framework applies broadly to terrestrial, airborne, and satellite-assisted photonic quantum communication systems.
QKD↗
Decentrally stabilizable linear and bilinear large-scale systems
Two classes of large-scale systems are identified, which can always be stabilized by decentralized feedback control. For the class of systems composed of interconnected linear subsystems, we can choose local controllers for the subsystems to achieve stability of the overall system. The same linear feedback scheme can be used to stabilize a class of linear systems with bilinear interconnections. In this case, however, the scheme is used to establish a finite region of stability for the overall system. The stabilization algorithm is applied to the design of a control system for the Large-Space Telescope.
Siljak, D. D.↗
On the Observed Changes in Upper Stratospheric and Mesospheric Temperatures from UARS HALOE
Temperature versus pressure or T(p) time series from the Halogen Occultation Experiment (HALOE) on the Upper Atmosphere Research Satellite (UARS) have been extended and re-analyzed for the period of 1991-2005 and for the upper stratosphere and mesosphere in 10-degree wide latitude zones from 60S to 60N. Even though sampling from a solar occultation experiment is somewhat limited, it is shown to be quite adequate for developing both the seasonal and longer-term variations in T(p). Multiple linear regression (MLR) techniques were used in the re-analyses for the seasonal and the significant interannual, solar cycle (SC-like or decadal-scale), and linear trend terms. A simple SC-like term of 11-yr period was fitted to the time series residuals after accounting for the seasonal and interannual terms. Highly significant SC-like responses were found for both the upper mesosphere and the upper stratosphere. The phases of these SC-like terms were checked for their continuity with latitude and pressure-altitude, and in almost all cases they are directly in-phase with that of standard proxies for the solar flux variations. The analyzed, max minus min, responses at low latitudes are of order 1 K, while at middle latitudes they are as large as 3 K in the upper mesosphere. Highly significant, linear cooling trends were found at middle latitudes of the middle to upper mesosphere (about -2 K/decade), at tropical latitudes of the middle mesosphere (about -1 K/decade), and at 2 hPa (or order -1 K/decade).
Remsberg, Ellis E.↗
Experimental evaluation of shear modulus scaling of dynamic strength at extreme pressures
Recent progress in the development of dynamic strength experimental platforms is allowing for unprecedented insight into the assumptions used to construct constitutive models operating in extreme conditions. In this work, we make a quantitative assessment of how tantalum strength scales with its shear modulus to pressures of hundreds of gigapascals through a cross-platform examination of three dynamic strength experiments. Specifically, we make use of Split–Hopkinson pressure bar and Richtmyer–Meshkov instability experiments to assess the low-pressure strain and strain rate dependence. Concurrent examination of magnetically driven ramp-release experiments up to pressures of 350GPa allows us to examine the pressure dependence. In this work, using a modern description of the shear modulus, validated against both ab initio theory and experimental measurements, we then assess how the experimentally measured pressure dependence scales with shear modulus. Furthermore, we find that the common assumption of scaling strength linearly with the shear modulus is too soft at high pressures and offer discussion as to how descriptions of slip mediated plasticity could result in an alternative scaling that is consistent with the data.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗