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Results for “finite-size scaling”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2

Precision study of the massive Schwinger model near quantum criticality

We perform a numerical analysis of the massive Schwinger model in the presence of a background electric field. Using the Density Matrix Renormalization Group approach, we efficiently compute the spectrum of the Schwinger model on a staggered lattice with up to 3000 qubits. As a result, we achieve a precise computation of the critical mass of the massive Schwinger model to five digits using four different “criticality criteria,” observing perfect agreement among them Additionally, we discuss the effect of a four-fermion operator deformation of the Schwinger model and compute the critical mass for various values of the deformation parameter.

Critical phenomena↗

Architectural scaling tradeoffs in modular 3D bosonic quantum processors

We propose a modular three-dimensional bosonic quantum processor built from repeatable coupled-cavity modules linked by configurable interconnect networks. Using hardware-motivated graph-theoretic measures, we compare nearest-neighbor, hub-based, and hybrid architectures in terms of interconnect count, communication distance, resource concentration, and implementation complexity. Rather than identifying a universally optimal topology, our analysis shows how these architectures redistribute the costs of scaling, including wiring and port requirements, nonlocal communication distance, exposure to shared resources, routing bottlenecks, and scheduling overhead. Case studies of a \(3\times3\) processor and a larger hierarchical architecture further distinguish finite-size performance from asymptotic scaling. The resulting framework provides a systematic basis for evaluating modular three-dimensional bosonic processors and for identifying the device-level parameters required for quantitative hardware design.

Zhu, Shaojiang [Fermilab] (ORCID:0000000293180092)↗

Himalayan sandpiles

Himalayan avalanches are examined for agreement with power-law behavior between frequency of outfall and rock volume. The data support a scaling state beyond the size ranges in which corresponding sandpile experiments have suffered from finite-size effects. Large-scale data (12 orders of magnitude in rock volume) additionally suggest a possible role for the numerically predicted 'snowball effects' of large rocks triggering more net dislodging events.

Noever, David A.↗

Self-organized criticality in sandpiles - Nature of the critical phenomenon

The scaling behavior of sandpile models is investigated analytically. First, it is shown that sandpile models contain a set of domain walls, referred to as troughs, which bound regions that can experience avalanches. It is further shown that the dynamics of the troughs is governed by a simple set of rules involving birth, death, and coalescence events. A simple trough model is then introduced, and it is proved that the model has a phase transition with the density of the troughs as an order parameter and that, in the thermodynamic limit, the trough density goes to zero at the transition point. Finally, it is shown that the observed scaling behavior is a consequence of finite-size effects.

Carlson, J. M.↗

Complex orders and chirality in the classical Kitaev-Γ model

It is well recognized that the low-energy physics of many Kitaev materials is governed by two dominant energy scales, the Ising-type Kitaev coupling 𝐾 and the symmetric off-diagonal Γ coupling. An understanding of the interplay between these two scales is therefore the natural starting point toward a quantitative description that includes subdominant perturbations that are inevitably present in real materials. This study focuses on the classical 𝐾−Γ model on the honeycomb lattice, with a specific emphasis on the region 𝐾< 0 and Γ > 0 , which is the most relevant for the available materials and which remains enigmatic in both quantum and classical limits, despite much effort. We employ large-scale Monte Carlo simulations on specially designed finite-size clusters and unravel the presence of a complex multisublattice magnetic order in a wide region of the phase diagram, whose structure is characterized in detail. We show that this order can be quantified in terms of a coarse-grained scalar-chirality order, featuring a counterrotating modulation on the two spin sublattices. Here, we also provide a comparison to previous studies and discuss the impact of quantum fluctuations on the phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Electrostatic Kelvin-Helmholtz instability in a radially injected plasma cloud

An elecrostatic finite-sized particle simulation model is used to study the early time-scale phenomena asociated with an impulsively injected plasma, expanding radially, normal to a strong ambient magnetic field. Results of the simulation show the early formation of a radial polarization electric field due to ion-electron charge separation which causes electrons to drift in the azimuthal direction. Velocity shear within this motion gives rise to a Kelvin-Helmholtz (dioxotron) instability, creating a radial fluted pattern as the plasma expands. In the nonlinear stage of instability, azimuthal variations in the electric field are observed which cause electrons to drift across the magnetic field, thereby reducing the space charge created by energetic ion expansion. The results of a linear stability analysis reveal that for a decreasing amount of charge separation in the plasma, the number of unstable azimuthal modes at maximum growth rate increases. Also, as the thickness of the electron ring increases, a fewer number of unstable modes develops for a given amount of charge separation. It is concluded that electrons become unstable at the very early time scale, within an ion gyroperiod, and that unstable electrons lead to modification of the ion dynamics.

Sydora, R. D.↗

Multiscale simulation of spatially correlated microstructure via a latent space representation

When deformation gradients act on the scale of the microstructure of a part due to geometry and loading, spatial correlations and finite-size effects in simulation cells cannot be neglected. We propose a multiscale method that accounts for these effects using a variational autoencoder to encode the structure–property map of the stochastic volume elements making up the statistical description of the part. In this paradigm the autoencoder can be used to directly encode the microstructure or, alternatively, its latent space can be sampled to provide likely realizations. Furthermore, we demonstrate the method on three examples using the common additively manufactured material AlSi10Mg in: (a) a comparison with direct numerical simulation of the part microstructure, (b) a push forward of microstructural uncertainty to performance quantities of interest, and (c) a simulation of functional gradation of a part with stochastic microstructure.

Elastoplasticity↗

Itinerant ferromagnetism in transition metal dichalcogenide moiré superlattices

Moiré materials are artificial crystals formed at van der Waals heterojunctions that have emerged as a highly tunable platform that is able to realize much of the rich quantum physics of electrons in atomic scale solids, and in several cases even new quantum phases of matter. Here we use finite-size exact diagonalization methods to explore the physics of single-band itinerant electron ferromagnetism in semiconductor moiré materials. As a result, we predict where ferromagnetism is likely to occur in triangular-lattice moiré systems, and where it is likely to yield the highest Curie temperatures.

36 MATERIALS SCIENCE↗

Finite-size effects on long-range correlations: implications for analyzing DNA sequences

We analyze the fluctuations in the correlation exponents obtained for noncoding DNA sequences. We find prominent sample-to-sample variations as well as variations within a single sample in the scaling exponent. To determine if these fluctuations may result from finite system size, we generate correlated random sequences of comparable length and study the fluctuations in this control system. We find that the DNA exponent fluctuations are consistent with those obtained from the control sequences having long-range power-law correlations. Finally, we compare our exponents for the DNA sequences with the exponents obtained from power-spectrum analysis and correlation-function techniques, and demonstrate that the original "DNA-walk" method is intrinsically more accurate due to reduced noise.

NASA Discipline Cardiopulmonary↗

Cavity electrodynamics of van der Waals heterostructures

Van der Waals heterostructures host many-body quantum phenomena that are tunable in situ using electrostatic gates. Their constituent two-dimensional materials and gates can naturally form plasmonic self-cavities, confining light in standing waves of current density due to finite-size effects. The plasmonic resonances of typical graphite gates fall in the gigahertz to terahertz range, corresponding to the same microelectronvolt to millielectronvolt energy scale as the phenomena in van der Waals heterostructures that they electrically control. This raises the possibility that the built-in cavity modes of graphite gates are relevant for shaping the low-energy physics of these heterostructures. However, probing these cavity-coupled electrodynamics is challenging as devices are notably smaller than the diffraction limit at the relevant wavelengths. Here we report on the intrinsic cavity conductivity of gate-tunable graphene heterostructures. As the carrier density is tuned, we observe coupling and spectral weight transfer between graphene and graphite plasmonic cavity modes in the ultrastrong coupling regime. We present an analytical model to describe the results and provide general principles for cavity design. Our findings show that intrinsic cavity effects are important for understanding the low-energy electrodynamics of van der Waals heterostructures and open a pathway for useful functionality through cavity control.

Electronic properties and materials↗

Numerical simulation of nonaxisymmetric adiabatic accretion flow

The hydrodynamics of gas flow past a finite-sized gravitating central object is studied in the adiabatic approximation in two spatial dimensions. The flow morphology is shown to depend on the ratio (epsilon) of the axisymmetric accretion radius to the length scale of the density variation. For small to intermediate epsilon values the flows are highly time dependent, and for large epsilon values a quasi-steady state is obtained.

Fryxell, B. A.↗

Scale setting of SU⁡(𝑁) Yang–Mills theory, topology and large-𝑁 volume independence

We set the scale of SU⁡(𝑁) Yang-Mills theories for 𝑁 =3, 5, 8 and in the large-𝑁 limit via gradient flow, as a first step towards the computation of the large-𝑁 Λ-parameter using step scaling. We adopt twisted boundary conditions to achieve large-𝑁 volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼0.025 fm for all the explored values of 𝑁, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-𝑁 twisted volume reduction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Molecular concentration field design using closed-form steady-state solutions

Control over spatial concentration fields represents a fundamental challenge in designing synthetic biological systems and programmable soft materials. While nature creates morphogen gradients that orchestrate complex developmental processes, synthetic approaches have largely relied on empirical optimization and computationally intensive simulations. Here, we present an analytical framework for steady-state concentration fields generated by finite-sized localized sources in diffusion–degradation systems and derive closed-form solutions for one-, two-, and three-dimensional geometries. By expressing these solutions in dimensionless form, we show that gradient steepness and spatial structure are organized by the Thiele modulus, which captures the competition between diffusion and degradation length scales. The analysis reveals distinct design regimes: in degradation-dominated systems, gradient shape is governed by exponential decay and becomes dimension-independent, whereas in diffusion-dominated systems, gradient magnitude and extent follow dimension-dependent power-law scaling. Building on these results, we introduce a quantitative design strategy that uses threshold-based criteria to program concentration ranges by tuning physically accessible parameters, most directly the production rate, while holding transport and degradation properties fixed. Comparisons with numerical solutions and reported experimental systems demonstrate consistency with the predicted scaling behavior. Together, this work provides a generalizable and physically transparent framework for designing steady-state concentration fields in synthetic biological and soft matter systems, enabling predictive control of gradient-mediated organization without reliance on extensive numerical optimization.

Kim, Dong Woo [Johns Hopkins University, Baltimore↗

On nonsteady accretion in stellar wind-fed X-ray sources

The paper reports on the results of hydrodynamical simulations of nonaxisymmetric gas flow past a finite-sized gravitating object. The asymmetry in the flow is assumed to be due to a transverse density gradient. The solutions are found to be highly time-dependent and exhibit phases in which a disk forms. The direction of circulation of the disk alternates between the direct and counter sense on time scales of approximately 1 hr. While the disk is present, the specific angular momentum is high, and the mass accretion rate, low. The angular momentum capture oscillates about a mean which secularly increases. Such temporal behavior may be relevant to those X-ray pulsing systems (e.g., Vela X-1) which exhibit fluctuations in the X-ray luminosity and pulse period on time scales much shorter than the orbital period of the binary system.

Taam, Ronald E.↗

A Dipolar Chiral Spin Liquid on the Breathed Kagome Lattice

Continuous control over lattice geometry, when combined with long-range interactions, offers a powerful yet underexplored tool to generate highly frustrated quantum spin systems. By considering long-range dipolar antiferromagnetic interactions on a breathed Kagome lattice, we demonstrate how these tools can be leveraged to stabilize a chiral spin liquid. We support this prediction with large-scale density-matrix renormalization group calculations and explore the surrounding phase diagram, identifying a route to adiabatic preparation via a locally varying magnetic field. At the same time, we identify the relevant low-energy degrees of freedom in each unit cell, providing a complementary language to study the chiral spin liquid. Finally, we carefully analyze its stability and signatures in finite-sized clusters, proposing direct, experimentally viable measurements of the chiral edge mode in both Rydberg atom and ultracold polar molecule arrays.

Machado↗

Resolving Nonequilibrium Shape Variations among Millions of Gold Nanoparticles

Nanoparticles, exhibiting functionally relevant structural heterogeneity, are at the forefront of cutting-edge research. Now, high-throughput single-particle imaging (SPI) with X-ray free-electron lasers (XFELs) creates opportunities for recovering the shape distributions of millions of particles that exhibit functionally relevant structural heterogeneity. To realize this potential, three challenges have to be overcome: (1) simultaneous parametrization of structural variability in real and reciprocal spaces; (2) efficiently inferring the latent parameters of each SPI measurement; (3) scaling up comparisons between 10 5 structural models and 10 6 XFEL-SPI measurements. Here, we describe how we overcame these three challenges to resolve the nonequilibrium shape distributions within millions of gold nanoparticles imaged at the European XFEL. These shape distributions allowed us to quantify the degree of asymmetry in these particles, discover a relatively stable “shape envelope” among nanoparticles, discern finite-size effects related to shape-controlling surfactants, and extrapolate nanoparticles’ shapes to their idealized thermodynamic limit. Ultimately, these demonstrations show that XFEL SPI can help transform nanoparticle shape characterization from anecdotally interesting to statistically meaningful.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Bridging the time scale in exascale computing of chemical systems (Final Technical Report)

This report summarizes the work carried out with support of the United States Department of Energy under Award DE-SC0019441. The theme of this project was to develop and apply methods that allowed for the acceleration of atomistic calculations, particularly in challenging areas such as multiphase systems, electrified interfaces, uncertainty estimation, and applications requiring chemical accuracy, which tend to be applications where simulation time is severely bottlenecked by the computational time requirements. Much of the focus was on the application of emerging machine-learning methodologies, although a wide range of methodologies were employed. This report has two major sections. The first focuses on the methodological advances themselves. Within this part, we report a number of major advances, a few examples of which are described here. We report the first machine-learning scheme for the acceleration of electronically grand-canonical calculations (that is, those applicable to electrochemistry). We report new methods of performing transfer learning, in which physics-based priors can be used to provide predictions, often with uncertainty estimates, of images well outside of training sets; we also offer ways to fine-tune these transfer-learning models. We provide a new systematic means to generate and apply minimal training data sets to very large (10,000’s of atoms) systems, with only small training sets appropriate for electronic structure. We developed new methodologies to integrate surface vibrations into surface adsorption calculations. We made advances to the applicability of diffusion Monte Carlo methods to allow (learned) force prediction, finite-size error correction, and force-free means of searching for transition states. We integrated machine-learned atomistic predictions into mechanism generation codes. Additionally, we released new software including AmpTorch, a modernized version of our original atomistic machine-learning code Amp. The second part of this report focuses on the scientific applications that accompanied, and were often enabled by, the methodological advances described earlier. A few examples follow, but full details are in the individual chapters of the report. For example, we developed a general theory of phonon-induced friction on molecular adsorbates. We showed fundamentally how solvent influences the adsorption and desorption process and how it differs from the processes typically involved at the solid–gas interface, making aqueous-phase and electrocatalysis different from traditional thermocatalysis. We examined how metal–insulator and magnetic transitions can be probed, and accelerated exciton dynamics via Frenkel Hamiltonian parameters. We showed that the nearsighted force-training approach, developed within this project, can predict both the stability and reactivity of large nanoparticles, and can also lead to insights on catalyst coverage on binding energies and entropies. These applied studies, which generally integrated with our method development, allowed us to push forward the theoretical understanding of several reaction classes.

08 HYDROGEN↗

Finite-size subthermal regime in disordered SU ( N ) -symmetric Heisenberg chains

SU⁡(N) symmetry is incompatible with the many-body localized (MBL) phase, even when strong disorder is present. However, recent studies have shown that finite-size SU⁡(2) systems exhibit nonergodic, subthermal behavior, characterized by the breakdown of the eigenstate thermalization hypothesis, and by the excited eigenstates entanglement entropy that is intermediate between area and volume law. In this paper, we extend previous studies of the SU⁡(2)-symmetric disordered Heisenberg model to larger systems, using the time-dependent density matrix renormalization group (tDMRG) method. We simulate quench dynamics from weakly entangled initial states up to long times, finding robust subthermal behavior at stronger disorder. Although we find an increased tendency towards thermalization at larger system sizes, the subthermal regime persists at intermediate time scales, nevertheless, and therefore should be accessible experimentally. At weaker disorder, we observe signatures of thermalization; however, entanglement entropy exhibits slow sublinear growth, in contrast to conventional thermalizing systems. Furthermore, we study dynamics of the SU⁡(3)-symmetric disordered Heisenberg model. Similarly, strong disorder drives the system into subthermal regime, albeit thermalizing phase is broader compared to the SU⁡(2) case. Finally, our findings demonstrate the robustness of the subthermal regime in spin chains with non-Abelian continuous symmetry, and are consistent with eventual thermalization at large system sizes and long time scales, suggested by previous studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗