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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Comparison of the canonical transformation and energy functional formalisms for ab initio calculations of self-localized polarons

In materials with strong electron-phonon (e-ph) interactions, charge carriers can distort the surrounding lattice and become trapped, forming self-localized (small) polarons. We recently developed an ab initio approach based on canonical transformations to efficiently compute the formation and energetics of small polarons A different approach based on a Landau-Pekar energy functional has been proposed in the recent literature. Here in this work, we analyze and compare these two methods in detail. We show that the small polaron energy is identical in the two formalisms when using the same polaron wave function. We also show that our canonical transformation formalism can predict polaron band structures and can properly treat zero- and finite-temperature lattice vibration effects, although at present using a fixed polaron wave function. Conversely, the energy functional approach can compute the polaron wave function, but as we show here, it neglects lattice vibrations and cannot address polaron self-localization and thermal band narrowing. Taken together, this work relates two different methods developed recently to study polarons from first-principles, highlighting their merits and shortcomings and discussing them both in a unified formalism.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Curvature-slope correlation of nuclear symmetry energy and its imprints on the crust-core transition, radius, and tidal deformability of canonical neutron stars

Background: The nuclear symmetry energy E sym (ρ) encodes information about the energy necessary to make nuclear systems more neutron-rich. While its slope parameter L at the saturation density ρ 0 of nuclear matter has been relatively well constrained by recent astrophysical observations and terrestrial nuclear experiments, its curvature K sym characterizing the E sym (ρ) around 2ρ 0 remains largely unconstrained. Over 520 calculations for E sym (ρ) using various nuclear theories and interactions in the literature have predicted several significantly different K sym –L correlations. Purpose: If a unique K sym –L correlation of E sym (ρ) can be firmly established, it will enable us to progressively better constrain the high-density behavior of E sym (ρ) using the available constraints on its slope parameter L. Here, we investigate if and by how much the different K sym –L correlations may affect neutron star observables. Method: A meta-model of nuclear Equation of States (EOSs) with three representative K sym –L correlation functions is used to generate multiple EOSs for neutron stars. We then examine effects of the K sym –L correlation on the crust-core transition density and pressure as well as the radius and tidal deformation of canonical neutron stars. Results: The K sym –L correlation affects significantly both the crust-core transition density and pressure. It also has strong imprints on the radius and tidal deformability of canonical neutron stars especially at small L values. The available data from LIGO/VIRGO and NICER set some useful limits for the slope L but can not distinguish the three representative K sym –L correlations considered.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Understanding protein-complex assembly through grand canonical maximum entropy modeling

Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are far more protein complexes that are yet to be solved because of their dynamic associations with one another. Nevertheless, it is possible to infer these protein complexes through a physical model. However, it is often not clear to physicists what kind of data from biology is necessary for such a modeling endeavor. Here, we aim to model these clusters of coarse-grained protein assemblies from multiple subunits through the constraints of interactions among the subunits and the chemical potential of each subunit. We obtained the constraints on the interactions among subunits from the known protein structures. We inferred the chemical potential that dictates the particle number distribution of each protein subunit from the knowledge of protein abundance from experimental data. Guided by the maximum entropy principle, we formulated an inverse statistical mechanical method to infer the distribution of particle numbers from the data of protein abundance as chemical potentials for a grand canonical multicomponent mixture. Using grand canonical Monte Carlo simulations, we captured a distribution of high-order clusters in a protein complex of succinate dehydrogenase with four known subunits. The complexity of hierarchical clusters varies with the relative protein abundance of each subunit in distinctive cell types such as lung, heart, and brain. When the crowding content increases, we observed that crowding stabilizes emergent clusters that do not exist in dilute conditions. We, therefore, proposed a testable hypothesis that the hierarchical complexity of protein clusters on a molecular scale is a plausible biomarker of predicting the phenotypes of a cell.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Geodesic-based relaxation for deep canonical correlation analysis

Deep canonical correlation analysis (DCCA) is often applied to paired data samples from diverse sources to extract meaningful common information. However, when the data sources are heterogeneous, some of the useful information may be complementary but not exactly common. In spite of this fact, existing techniques learn maximally correlated representations from multiple views and are formulated so that they aim to yield identical latent subspaces for each view. This approach is sub-optimal in estimating the true signal subspaces for heterogeneous data sources. We propose a residual relaxation for deep canonical correlation analysis (RDCCA) based on a subspace distance metric, which generalizes the existing problem formulation and extracts representations that are better estimates of the actual, non-identical subspaces. We demonstrate that when using such a relaxation, the learned representations are closer to the true ones and that RDCCA outperforms CCA and DCCA in scenarios with heterogeneous data.

Kuschel, Maurice↗
DOE OSTI2021

Deletion of a non-canonical regulatory sequence causes loss of Scn1a expression and epileptic phenotypes in mice

Abstract Background Genes with multiple co-active promoters appear common in brain, yet little is known about functional requirements for these potentially redundant genomic regulatory elements. SCN1A, which encodes the Na V 1.1 sodium channel alpha subunit, is one such gene with two co-active promoters. Mutations in SCN1A are associated with epilepsy, including Dravet syndrome (DS). The majority of DS patients harbor coding mutations causing SCN1A haploinsufficiency; however, putative causal non-coding promoter mutations have been identified. Methods To determine the functional role of one of these potentially redundant Scn1a promoters, we focused on the non-coding Scn1a 1b regulatory region, previously described as a non-canonical alternative transcriptional start site. We generated a transgenic mouse line with deletion of the extended evolutionarily conserved 1b non-coding interval and characterized changes in gene and protein expression, and assessed seizure activity and alterations in behavior. Results Mice harboring a deletion of the 1b non-coding interval exhibited surprisingly severe reductions of Scn1a and Na V 1.1 expression throughout the brain. This was accompanied by electroencephalographic and thermal-evoked seizures, and behavioral deficits. Conclusions This work contributes to functional dissection of the regulatory wiring of a major epilepsy risk gene, SCN1A . We identified the 1b region as a critical disease-relevant regulatory element and provide evidence that non-canonical and seemingly redundant promoters can have essential function.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Canonical Transformation of Potential Model Hamiltonian Mechanics to Geometrical Form I

Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the corresponding motions are along geodesic curves. The advantage of this representation is that it admits the computation of geodesic deviation as a test for local stability, shown in recent previous studies to be a very effective criterion for the stability of the orbits generated by the potential model Hamiltonian. We describe here an algorithm for finding the generating function for the canonical transformation and describe some of the properties of this mapping under local diffeomorphisms. We give a convergence proof for this algorithm for the one-dimensional case, and provide a precise geometric formulation of geodesic deviation which relates the stability of the motion in the geometric form to that of the Hamiltonian standard form. We apply our methods to a simple one-dimensional harmonic oscillator and conclude with a discussion of the relation of bounded domains in the two representations for which Morse theory would be applicable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

An efficient algorithm for calculation of the Luenberger canonical form

An algorithm is suggested to obtain the Luenberger canonical form for multivariable systems. The method computes the canonical form directly without having to compute the transformation matrix. In addition, there is a large reduction in the number of calculations. The reduced computations along with Gaussian techniques lend to greater inherent accuracy and the ability to refine the solution with additional computations.

Jordan, D.↗
NASA NTRS1972

Canonical fluid thermodynamics

The space-time integral of the thermodynamic pressure plays the role of the thermodynamic potential for compressible, adiabatic flow in the sense that the pressure integral for stable flow is less than for all slightly different flows. This stability criterion can be converted into a variational minimum principle by requiring the molar free-enthalpy and the temperature, which are the arguments of the pressure function, to be generalized velocities, that is, the proper-time derivatives of scalar spare-time functions which are generalized coordinates in the canonical formalism. In a fluid context, proper-time differentiation must be expressed in terms of three independent quantities that specify the fluid velocity. This can be done in several ways, all of which lead to different variants (canonical transformations) of the same constraint-free action integral whose Euler-Lagrange equations are just the well-known equations of motion for adiabatic compressible flow.

Schmid, L. A.↗
NASA NTRS1972

Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3

Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.

Sitchin, A.↗
NASA NTRS1973

An algorithm for calculation of the Jordan canonical form of a matrix

Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.

Sridhar, B.↗
NASA NTRS1973

Classification of ERTS-1 MSS data by canonical analysis

The objective of canonical analysis is to obtain the maximum separability among a number of catergories. The application of canonical analysis was investigated using the merged MSS ERTS-1 data for one area viewed on two dates. The effect of threshold values on classification regions and confusion regions was investigated.

Lachowski, H. M.↗
NASA NTRS1973

An efficient algorithm for calculation of the Luenberger canonical form.

A new algorithm is presented to obtain the Luenberger canonical form for multivariable systems. A distinct feature of the method is that the canonical form is obtained directly and, if necessary, the similarity transformation can be computed. There is a substantial reduction in the amount of computation compared to Luenberger's method. The reduced computations along with Gaussian techniques lend greater inherent accuracy and the ability to refine the solution with additional computations. An example is presented to illustrate the technique.

Jordan, D.↗
NASA NTRS1974

On the use and computation of the Jordan canonical form in system theory

This paper investigates various aspects of the application of the Jordan canonical form of a matrix in system theory and develops a computational approach to determining the Jordan form for a given matrix. Applications include pole placement, controllability and observability studies, serving as an intermediate step in yielding other canonical forms, and theorem proving. The computational method developed in this paper is both simple and efficient. The method is based on the definition of a generalized eigenvector and a natural extension of Gauss elimination techniques. Examples are included for demonstration purposes.

Sridhar, B.↗
NASA NTRS1986

Canonical solution of the two critical argument problem

The solution by Sessin and Ferraz-Mello (1984) of the Hori auxiliary system for the motion of two planets with periods nearly commensurate in the ratio 2:1 is considerably simplified by the introduction of canonical variables. An analogous canonical transformation simplifies the elliptic restricted problem.

Wisdom, J.↗
NASA NTRS1989

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II - Quantitative analysis

It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.

Han, D.↗
NASA NTRS1989

Orthogonal canonical forms for second-order systems

The authors prove that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations, while this reduction is always possible for the modal damping commonly assumed for models of flexible structures. The type of canonical form obtainable by means of orthogonal transformations acting on a second-order system is heavily dependent on the type of damping considered. If the damping matrix is merely positive semi-definite symmetric, it is generally not possible to obtain a reduction to Hessenberg-triangular form, while this reduction is trivial for zero or Rayleigh damping. If damping is modal, however, as is commonly assumed in structural models, the reduction exists and is nontrivial. Furthermore, reduction to triangular second-order Schur form is always possible for such damping: this canonical form appears likely to have applications to second-order system theory.

Williams, Trevor↗