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Results for “Scale Invariance”

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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

$R^2$/Higgs inflation and the hierarchy problem

We analyse Starobinsky inflation in the presence of the Brout Englert Higgs (BEH) boson with a non-minimal coupling to the Ricci scalar, $R$. The latter induces a coupling of the massive scaleron associated with the $R^2$ term to the BEH boson and this leads to a radiative correction to the BEH mass that must be fine tuned to keep the scalar light. For the case of $R^2$ driven inflation this requires a high level of fine tuning of order 1 part in $10^{8}$; for the case of Higgs inflation it is very much greater. We consider a scale invariant extension of the $R^2$/Higgs model and find that for $R^2$ driven inflation but not for Higgs inflation the required fine tuning is significantly reduced to one part in $10^{3-4}$. We consider the vacuum stability of the fine tuned model and its reheating and dilaton abundance after inflation. We also discuss possible gravitational wave signals associated with the model and the constraint on the mass of scalar or fermion dark matter candidates if they are produced by the gravitational couplings of the scalaron.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Naturally Self-Tuned Low Mass Composite Scalars

Scalar bosons composed of a pair of chiral fermions in a non-confining potential have an effective Yukawa coupling, $g$, to free external chiral fermions. At large distance a Feynman loop of external fermions generates a scale invariant potential, $V_{loop}\propto -g^2/{\rho^{2}}$, for separation $\rho$, which acts on valence fermions. This generally forces the $s$-wave ground state to deform to a static, zero mass, configuration, and for slowly running, perturbative $g$, a large external "shroud" wave function forms. This is related to old results of Landau and Lifshitz in quantum mechanics. The massless composite scalar boson ground state is then an extended object. Infra-red effects can generate a small mass for the system. This points to a perturbative BEH-boson composed of top and anti-top quarks and a novel dynamical mechanism for spontaneous electroweak symmetry breaking.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Conservation laws and effective hadronization models

Hadronization models based on local string-breaking dynamics are typically Markovian by construction, yet the physical ensemble of final states is shaped by global constraints that couple the entire fragmentation trajectory. Recasting hadronization as a conditioned stochastic diffusion process provides a precise mathematical resolution to this tension. In particular, this language reveals explicitly that constraints stemming from conservation laws induce non-Markovian correlations between otherwise independent fragmentation steps, and that these correlations can be absorbed exactly into a renormalization of the local dynamics through a Doob $h$-transform. We develop this formalism for a $q\bar{q}$ string in the chiral limit, where the longitudinal-transverse factorization of the Lund kernel becomes exact, enabling systematic power counting and clean ultraviolet (UV)/infrared (IR) separation. The dynamics organize naturally into a tower of effective theories distinguished by the remaining string mass, spanning a UV fixed point with scale-invariant transport coefficients, an intermediate regime where transverse phase space induces controlled running, and an IR boundary layer where non-local effects enter at leading order. The tower exhibits genuine Wilsonian structure, including $β$-functions, anomalous dimensions, and systematic matching conditions. The resulting framework achieves a clean factorization of universal microscopic fragmentation dynamics from infrared constraint effects, and opens new directions for both the theoretical analysis and practical simulation of hadronization.

Menzo, Tony [Alabama U.; Fermilab] (ORCID:00000002↗
DOE OSTI2025

Characterizing leaf-scale fluorescence with spectral invariants

Sun-induced chlorophyll fluorescence (SIF) is increasingly recognized as a non-destructive probe for tracking terrestrial photosynthesis. Emerging developments in spectral invariants theory provide an innovative and efficient approach for representing SIF radiative transfer processes at the canopy scale. However, modeling leaf-scale fluorescence based on the spectral invariants properties (SIP) remains underexplored. In this study, the spectral invariants theory is employed for the first time to model the leaf-scale total, backward and forward fluorescence (leaf-SIP SIF). The leaf-SIP SIF model separates the leaf-scale radiative transfer process into two distinct components: the wavelength-dependent one associated with leaf biochemical properties, and the wavelength-independent component linked to leaf structural characteristics. The leaf structure-related effects are characterized by two spectrally invariant parameters: the photon recollision probability (p) and the scattering asymmetry parameter (q), which are parameterized using the directly measurable leaf dry matter. Evaluation against field measurements shows that the proposed leaf-SIP SIF model has a good performance, with coefficient of determination (R 2 ) of 0.89, 0.89, 0.90 and root mean squared errors (RMSE) of 1.28, 0.69, 0.74 Wm -2 µm -1 sr -1 , respectively for the total, backward, and forward fluorescence (660–800 nm). The leaf-SIP SIF model with a more concise formulation demonstrates comparable performance with the widely used Fluspect model. Further, the leaf-SIP SIF model provides a simple and efficient approach for simulating leaf-scale fluorescence, with the potential to be integrated into a unified SIP-based model framework for simulating the radiative transfer processes across the soil-leaf-canopy-atmosphere continuum.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

Emergence of complex and spinor wave functions in scale relativity. II. Lorentz invariance and bi-spinors

Owing to the non-differentiable nature of the theory of Scale Relativity, the emergence of complex wave functions, then of spinors and bi-spinors occurs naturally in its framework. The wave function is here a manifestation of the velocity field of geodesics of a continuous and non-differentiable (therefore fractal) space-time. In a first paper (Paper I), we have presented the general argument which leads to this result using an elaborate and more detailed derivation than previously displayed. We have therefore been able to show how the complex wave function emerges naturally from the doubling of the velocity field and to revisit the derivation of the non-relativistic Schrödinger equation of motion. In the present paper (Paper II), we deal with relativistic motion and detail the natural emergence of the bi-spinors from such first principles of the theory. Moreover, while Lorentz invariance has been up to now inferred from mathematical results obtained in stochastic mechanics, we display here a new and detailed derivation of the way one can obtain a Lorentz invariant expression for the expectation value of the product of two independent fractal fluctuation fields in the sole framework of the theory of Scale Relativity. These new results allow us to enhance the robustness of our derivation of the two main equations of motion of relativistic quantum mechanics (the Klein-Gordon and Dirac equations) which we revisit here at length.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1978

New trends in cosmology

A review of big-bang cosmology is presented, emphasizing the big-bang model, hypotheses on the origin of galaxies, observational tests of the big-bang model that may be possible with the Large Space Telescope, and the scale-covariant theory of gravitation. Detailed attention is given to the equations of general relativity, the redshift-distance relation for extragalactic objects, expansion of the universe, the initial singularity, the discovery of the 3-K blackbody radiation, and measurements of the amount of deuterium in the universe. The curvature of the expanding universe is examined along with the magnitude-redshift relation for quasars and galaxies. Several models for the origin of galaxies are evaluated, and it is suggested that a model of galaxy formation via the formation of black holes is consistent with the model of an expanding universe. Scale covariance is discussed, a scale-covariant theory is developed which contains invariance under scale transformation, and it is shown that Dirac's (1937) large-numbers hypothesis finds a natural role in this theory by relating the atomic and Einstein units.

Canuto, V. M.↗
NASA NTRS1977

Scale-covariant theory of gravitation and astrophysical applications

Generalized Einstein equations invariant under scale transformations are presented, and several astrophysical tests studied. It is assumed that the dynamics of atoms or clocks used as measuring apparatus is given a priori. Connection with gauge fields and broken symmetries is made through the cosmological constant.

Canuto, V.↗
DOE OSTI2024

Extracting the asymptotic behavior of S-matrix elements from their phases

The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving ratios of invariant mass scales, and those which are functions of ratios of rapidities, so called “rapidity logs”. It has been pointed out by Caron-Huot and Wilhlem [1] that RG anomalous dimension can be extracted from the phase of the S-matrix, which can greatly simplify calculations via unitarity methods. In this paper we generalize the results of [1] to show that the phase can be used to reconstruct rapidity anomalous dimensions, by performing a special type of complex boost. The methodology introduced allows one to calculate without the need for a rapidity regulator which can lead to significant simplifications. We demonstrate the use of this method to derive the rapidity anomalous dimensions in the Sudakov form factor and the two parton soft function at two loops order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Synthesis of wafer-scale SWCNT forests with remarkably invariant structural properties in a bulk-diffusion-controlled kinetic regime

Robust synthesis of vertically aligned carbon nanotubes (VACNT) at large scale is required to accelerate deployment of numerous cutting-edge devices to emerging commercial applications. To address this need, this work demonstrates that the structural characteristics of single-walled CNTs (SWCNTs) produced in a growth regime dominated by bulk diffusion of the gaseous carbon precursor are remarkably invariant over a broad range of process conditions (precursor concentration increased up to 30-fold, catalyst substrate area from 1 cm 2 to 180 cm 2 , growth pressure from 20 to 790 mbar, and gas flowrates up to 8-fold). A simple growth kinetics model is derived that accounts for both reactant bulk diffusion and competing byproduct formation in the presence of excess hydrogen, which quantitatively reproduces the experimental data in the entire isothermal parameter space. The model enables critical predictions for process scale-up optimization including a potential 6-fold increase in CNT production rate, a ~90% carbon conversion efficiency in select conditions, and elimination of reaction rate decay observed at high pressures by using a hydrogen-free growth environment. This model-guided opportunity to substantially improve synthesis throughput and efficiency, in conjunction with the remarkably invariant CNT properties, is appealing for reliable VACNT device fabrication at both small and industrial scales.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Low-Cloud Feedbacks from Cloud-Controlling Factors: A Review

Abstract The response to warming of tropical low-level clouds including both marine stratocumulus and trade cumulus is a major source of uncertainty in projections of future climate. Climate model simulations of the response vary widely, reflecting the difficulty the models have in simulating these clouds. These inadequacies have led to alternative approaches to predict low-cloud feedbacks. Here, we review an observational approach that relies on the assumption that observed relationships between low clouds and the “cloud-controlling factors” of the large-scale environment are invariant across time-scales. With this assumption, and given predictions of how the cloud-controlling factors change with climate warming, one can predict low-cloud feedbacks without using any model simulation of low clouds. We discuss both fundamental and implementation issues with this approach and suggest steps that could reduce uncertainty in the predicted low-cloud feedback. Recent studies using this approach predict that the tropical low-cloud feedback is positive mainly due to the observation that reflection of solar radiation by low clouds decreases as temperature increases, holding all other cloud-controlling factors fixed. The positive feedback from temperature is partially offset by a negative feedback from the tendency for the inversion strength to increase in a warming world, with other cloud-controlling factors playing a smaller role. A consensus estimate from these studies for the contribution of tropical low clouds to the global mean cloud feedback is 0.25 ± 0.18 W m −2 K −1 (90% confidence interval), suggesting it is very unlikely that tropical low clouds reduce total global cloud feedback. Because the prediction of positive tropical low-cloud feedback with this approach is consistent with independent evidence from low-cloud feedback studies using high-resolution cloud models, progress is being made in reducing this key climate uncertainty.

58 GEOSCIENCES↗
DOE OSTI2021

Probing atomic-scale symmetry breaking by rotationally invariant machine learning of multidimensional electron scattering

Abstract The 4D scanning transmission electron microscopy (STEM) method maps the structure and functionality of solids on the atomic scale, yielding information-rich data sets describing the interatomic electric and magnetic fields, structural and electronic order parameters, and other symmetry breaking distortions. A critical bottleneck is the dearth of analytical tools that can reduce complex 4D-STEM data to physically relevant descriptors. We propose an approach for the systematic exploration of 4D-STEM data using rotationally invariant variational autoencoders (rrVAE), which disentangle the general rotation of the object from other latent representations. The implementation of purely rotational rrVAE is discussed as are applications to simulated data for graphene and zincblende structures. The rrVAE analysis of experimental 4D-STEM data of defects in graphene is illustrated and compared to the classical center-of-mass analysis. This approach is universal for probing symmetry-breaking phenomena in complex systems and can be implemented for a broad range of diffraction methods.

36 MATERIALS SCIENCE↗
NASA NTRS1980

A scaling theory for linear systems

A theory of scaling for rational (transfer) functions in terms of transformation groups is developed. Two different four-parameter scaling groups which play natural roles in studying linear systems are identified and the effect of scaling on Fisher information and related statistical measures in system identification are studied. The scalings considered include change of time scale, feedback, exponential scaling, magnitude scaling, etc. The scaling action of the groups studied is tied to the geometry of transfer functions in a rather strong way as becomes apparent in the examination of the invariants of scaling. As a result, the scaling process also provides new insight into the parameterization question for rational functions.

Brockett, R. W.↗
DOE OSTI2023

Interactions of particles with “continuous spin” fields

Powerful general arguments allow only a few families of long-range interactions, exemplified by gauge field theories of electromagnetism and gravity. However, all of these arguments presuppose that massless fields have zero spin scale (Casimir invariant) and hence exactly boost invariant helicity. This misses the most general behavior compatible with Lorentz symmetry. We present a Lagrangian formalism describing interactions of matter particles with bosonic “continuous spin” fields with arbitrary spin scale ρ. Remarkably, physical observables are well approximated by familiar theories at frequencies larger than ρ, with calculable deviations at low frequencies and long distances. For example, we predict specific ρ-dependent modifications to the Lorentz force law and the Larmor formula, which lay the foundation for experimental tests of the photon’s spin scale. We also reproduce known soft radiation emission amplitudes for nonzero ρ. The particles’ effective matter currents are not fully localized to their worldlines when ρ ≠ 0, which motivates investigation of manifestly local completions of our theory. Our results also motivate the development of continuous spin analogues of gravity and non-Abelian gauge theories. Given the correspondence with familiar gauge theory in the small ρ limit, we conjecture that continuous spin particles may in fact mediate known long-range forces, with testable consequences.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Mid-circuit correction of correlated phase errors using an array of spectator qubits

Scaling up invariably error-prone quantum processors is a formidable challenge. Although quantum error correction ultimately promises fault-tolerant operation, the required qubit overhead and error thresholds are daunting. In a complementary proposal, colocated, auxiliary “spectator” qubits act as in situ probes of noise and enable real-time, coherent corrections of data qubit errors. We used an array of cesium spectator qubits to correct correlated phase errors on an array of rubidium data qubits. By combining in-sequence readout, data processing, and feedforward operations, these correlated errors were suppressed within the execution of the quantum circuit. The protocol is broadly applicable to quantum information platforms and establishes key tools for scaling neutral-atom quantum processors: mid-circuit readout of atom arrays, real-time processing and feedforward, and coherent mid-circuit reloading of atomic qubits.

Science & Technology - Other Topics↗