SEARCH · Search NASA

Results for “fixed points”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

All sources NASA NTRS DOE OSTI

DOE OSTI2023

The Gross-Neveu-Yukawa archipelago

We perform a bootstrap analysis of a mixed system of four-point functions of bosonic and fermionic operators in parity-preserving 3d CFTs with O(N) global symmetry. Our results provide rigorous bounds on the scaling dimensions of the O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases N = 1, 2, 4, 8, which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1982

Construction of solutions for some nonlinear two-point boundary value problems

Constructive existence and uniqueness results for boundary value problems associated with some simple special cases of the second order equation y'' = f(x,y,y') 0 or = x or = 1, are sought. The approach considered is to convert the differential equation and boundary conditions to an integral equation via Green's functions, and then to apply fixed point and contraction map principles to a sequence of successive approximations. The approach is tested on several applied problems. Difficulties in trying to prove general theorems are discussed.

Pennline, J. A.↗

DOE OSTI2023

The myth of URANS

Since the 1990s, RANS practitioners have observed spontaneous unsteadiness in RANS simulations. Some have suggested deliberately using this as a method of resolving large turbulent structures. However, to date, no one has produced a theoretical justification for this unsteady RANS (URANS) approach. Here, we extend the dynamical system fixed point analysis to create a theoretical model for URANS dynamics. The results are compared to URANS simulations for homogeneous isotropic decaying turbulence. The model shows that URANS can predict incorrect decay rates and that the solution tends towards steady RANS over time. Similar analysis for forced turbulence shows a fixed modelled energy of about 30% of total energy, regardless of the model parameters. The same analysis can be used to show how hybrid type models can begin to address these issues.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Properties of the new $ \mathcal{N} $ = 1 AdS 4 vacuum of maximal supergravity

The recent comprehensive numerical study of critical points of the scalar potential of four-dimensional N = 8, SO(8) gauged supergravity using Machine Learning software in [1] has led to a discovery of a new N = 1 vacuum with a triality-invariant SO(3) symmetry. Guided by the numerical data for that point, we obtain a consistent SO(3) × Z 2 -invariant truncation of the N = 8 theory to an N = 1 supergravity with three chiral multiplets. Critical points of the truncated scalar potential include both the N = 1 point as well as two new non-supersymmetric and perturbatively unstable points not found by previous searches. Studying the structure of the submanifold of SO(3) × Z 2 -invariant supergravity scalars, we find that it has a simple interpretation as a submanifold of the 14-dimensional Z $3\atop{2}$ -invariant scalar manifold (SU(1, 1)/U(1)) 7 , for which we find a rather remarkable superpotential whose structure matches the single bit error correcting (7, 4) Hamming code. This 14-dimensional scalar manifold contains approximately one quarter of the known critical points. We also show that there exists a smooth supersymmetric domain wall which interpolates between the new N = 1 AdS4 solution and the maximally supersymmetric AdS4 vacuum. Using holography, this result indicates the existence of an N = 1 RG flow from the ABJM SCFT to a new strongly interacting conformal fixed point in the IR.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Many-body localization near the critical point

Here, we examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the so-called avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough qualitative level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus, we show that this MBL transition is in a universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent $\textit{ν → ∞}$, but the divergence is weaker than for the KT transition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1958

Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients

In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at two points are identical, whether studied in Lagrange's or in Euler's systems. We then consider new spectra of turbulence, obtained by study of the simultaneous velocities along a straight line of given direction. We determine some relations between these spectra and the correlation coefficients. Examining the relation between the spectrum of the turbulence measured at a fixed point and the longitudinal-correlation curve given by G. I. Taylor, we find that this equation is exact only when the coefficient is very small.

Frenkiel, Francois N.↗

NASA NTRS1981

Parameter estimation for slit-type scanning sensors

The Infrared Astronomical Satellite, scheduled for launch into a 900 km near-polar orbit in August 1982, will perform an infrared point source survey by scanning the sky with slit-type sensors. The description of position information is shown to require the use of a non-Gaussian random variable. Methods are described for deciding whether separate detections stem from a single common source, and a formulism is developed for the scan-to-scan problems of identifying multiple sightings of inertially fixed point sources for combining their individual measurements into a refined estimate. Several cases are given where the general theory yields results which are quite different from the corresponding Gaussian applications, showing that argument by Gaussian analogy would lead to error.

Fowler, J. W.↗

NASA NTRS1994

Missileborne Artificial Vision System (MAVIS)

Several years ago when INTEL and China Lake designed the ETANN chip, analog VLSI appeared to be the only way to do high density neural computing. In the last five years, however, digital parallel processing chips capable of performing neural computation functions have evolved to the point of rough equality with analog chips in system level computational density. The Naval Air Warfare Center, China Lake, has developed a real time, hardware and software system designed to implement and evaluate biologically inspired retinal and cortical models. The hardware is based on the Adaptive Solutions Inc. massively parallel CNAPS system COHO boards. Each COHO board is a standard size 6U VME card featuring 256 fixed point, RISC processors running at 20 MHz in a SIMD configuration. Each COHO board has a companion board built to support a real time VSB interface to an imaging seeker, a NTSC camera, and to other COHO boards. The system is designed to have multiple SIMD machines each performing different corticomorphic functions. The system level software has been developed which allows a high level description of corticomorphic structures to be translated into the native microcode of the CNAPS chips. Corticomorphic structures are those neural structures with a form similar to that of the retina, the lateral geniculate nucleus, or the visual cortex. This real time hardware system is designed to be shrunk into a volume compatible with air launched tactical missiles. Initial versions of the software and hardware have been completed and are in the early stages of integration with a missile seeker.

Andes, David K.↗

DOE OSTI2022

Interaction-induced velocity renormalization in magic-angle twisted multilayer graphene

Abstract Twistronics heterostructures provide a novel route to control the electronic single particle velocity and thereby to engineer strong effective interactions. Here we show that the reverse may also hold, i.e. that these interactions strongly renormalize the band structure. We demonstrate this mechanism for alternating-twist magic-angle three- and four-layer graphene at charge neutrality and in the vicinity of a phase transition which can be described by an Ising Gross-Neveu critical point corresponding, e.g. to the onset of valley Hall or Hall order. While the non-interacting model displays massless Dirac excitations with strongly different velocities, we show that interaction corrections make them equal in the infrared. However, the renormalization group flow of the velocities and of the coupling to the critical bosonic mode is strongly non-monotonic and dominated by the vicinity of a repulsive fixed point. We predict experimental consequences of this theory for tunneling and transport experiments and discuss the expected behavior at other quantum critical points, including those corresponding to intervalley coherent ordering.

Classen, Laura↗

DOE OSTI2020

Quantum Criticality in the 2D Quasiperiodic Potts Model

Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic q-state Potts model in 2+1D. Using a controlled real-space renormalization group approach, we find that the critical behavior is largely independent of q, and is controlled by an infinite-quasiperiodicity fixed point. In conclusion, the correlation length exponent is found to be ν = 1, saturating a modified version of the Harris-Luck criterion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1985

The number of stable points of an infinite-range spin glass memory

A rigorous asymptotic expression for the number of stable points of an infinite-range spin glass with independently identically distributed (i.i.d) zero-mean gaussian exchange interactions is discussed. The result also applies tot he number of stable points of a Hopfield Memory (a kind of associative memory) when the memory connections are i.i.d. zero-mean gaussians. The result is that the number of stable points is asymptotic to a constant slightly larger than 1 times 2 to a power slightly larger thann/4, where n is the number of spins in the glass, or the length of the n-tuples to be remembered by the memory. The answer is easily derived using simple asymptotic techniques from an exact expression for the probability that an arbitrary plus or minus 1 n-tuple of spins is a fixed point. This expression is obtained from the fact that any distribution of joint zero-mean gaussians of given covariances is specified solely by these covariances. This is a far shorter derivation of the result than those existing.

Posner, E. C.↗

NASA NTRS1996

The Role of Linear Acceleration in Visual-Vestibular Interactions and Implications in Aircraft Operations

While considerable attention has been given to visual-vestibular interaction (VVI) during angular motion of the head as might occur during an aircraft spin, much less attention has been given to VVI during linear motion of the head. Such interaction might occur, for example, while viewing a stationary or moving display during vertical take-off and landing operations Research into linear VVI, particularly during prolonged periods of linear acceleration, has been hampered by the unavailability of a programmable translator capable of large excursions We collaborated with Otis Elevator Co. and used their research tower and elevator, whose motion could be digitally programmed, to vertically translate human subjects over a distance of 92.3 meters with a peak linear acceleration of 2 meters/sec(exp 2) During pulsatile or sinusoidal translation, the subjects viewed moving stripes (optokinetic stimulus) or a fixed point source (light emitting diode, led, display), respectively and it was generally found that. The direction of linear acceleration relative to the cardinal head axes and the direction of the slow component of optokinetic nystagmus (OKN) determined the extent of VVI during concomitant stripe motion and linear acceleration. Acceleration along the z head axis (A(sub z)) produced the largest VVI, particularly when the slow component of OKN was in the same direction as eye movements produced by the linear acceleration and Eye movements produced by linear acceleration are suppressed by viewing a fixed target at frequencies below 10 Hz But, above this frequency the suppression produced by VVI is removed. Finally, as demonstrated in non-human primates, vergence of the eyes appears to modulate the vertical eye movement response to linear acceleration in humans.

Correia, Manning J.↗

DOE OSTI2022

Solvable theory of a strange metal at the breakdown of a heavy Fermi liquid

In this work, we introduce an effective theory for quantum critical points (QCPs) in heavy-fermion systems, involving a change in carrier density without symmetry breaking. Our theory captures a strongly coupled metallic QCP, leading to robust marginal Fermi-liquid transport phenomenology, and associated linear in temperature (T) "strange metal" resistivity, all within a controlled large-N limit. In the parameter regime of strong damping of emergent bosonic excitations, the QCP also displays a near-universal "Planckian" transport lifetime τ tr ~ℏ/(k B T). This is contrasted with the conventional so-called "slave boson" theory of the Kondo breakdown, where the large-N limit describes a weak coupling fixed point and nontrivial transport behavior may only be obtained through uncontrolled 1/N corrections. We also compute the weak-field Hall coefficient within the effective model as the system is tuned across the transition. We then find that, between the two plateaus reflecting the different carrier densities in the two Fermi-liquid phases, the Hall coefficient can develop a peak in the critical crossover regime, like in recent experimental findings, in the parameter regime of weak boson damping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1987

Chaotic nature of the spin-glass phase

The microscopic structure of the ordered phase of spin glasses is investigated theoretically in the framework of the T = 0 fixed-point model (McMillan, 1984; Fisher and Huse, 1986; and Bray and Moore, 1986). The sensitivity of the ground state to changes in the interaction strengths at T = 0 is explored, and it is found that for sufficiently large length scales the ground state is unstable against arbitrarily weak perturbations to the bonds. Explicit results are derived for d = 1, and the implications for d = 2 and d = 3 are considered in detail. It is concluded that there is no hidden order pattern for spin glasses at all T less than T(C), the ordered-phase spin correlations being chaotic functions of spin separation at fixed temperature or of temperature (for a given pair of spins) at scale lengths L greater than (T delta T) exp -1/zeta, where zeta = d(s)/2 - y, d(s) is the interfacial fractal dimension, and -y is the thermal eigenvalue at T = 0.

Bray, A. J.↗

NASA NTRS1989

Thin-plate spline quadrature of geodetic integrals

Thin-plate spline functions (known for their flexibility and fidelity in representing experimental data) are especially well-suited for the numerical integration of geodetic integrals in the area where the integration is most sensitive to the data, i.e., in the immediate vicinity of the evaluation point. Spline quadrature rules are derived for the contribution of a circular innermost zone to Stoke's formula, to the formulae of Vening Meinesz, and to the recursively evaluated operator L(n) in the analytical continuation solution of Molodensky's problem. These rules are exact for interpolating thin-plate splines. In cases where the integration data are distributed irregularly, a system of linear equations needs to be solved for the quadrature coefficients. Formulae are given for the terms appearing in these equations. In case the data are regularly distributed, the coefficients may be determined once-and-for-all. Examples are given of some fixed-point rules. With such rules successive evaluation, within a circular disk, of the terms in Molodensky's series becomes relatively easy. The spline quadrature technique presented complements other techniques such as ring integration for intermediate integration zones.

Vangysen, Herman↗

NASA NTRS2001

Investigation of the Polytropic Relationship Between Density and Temperature Within Interplanetary Coronal Mass Ejections Using Numerical Simulations

Single-point spacecraft measurements within coronal mass ejections (CMEs) often exhibit a negative correlation between electron density and temperature. At least two opposing interpretations have been suggested for this relationship. If, on one hand, these single spacecraft observations provide direct measures of the polytropic properties of the plasma, then they imply that the polytropic index for the electrons gamma(sub e) is often < 1. Moreover, since the electrons carry the bulk of the pressure (via their significantly higher temperature), this further implies that the dynamics of CME evolution are dominated by an effective polytropic index gamma(sub e)ff < 1. On the other hand, gamma < 1 implies that as the ejecta propagate away from the Sun and expand, they also heat up; a result clearly at odds with in situ observations. In contrast to these CME intervals, many studies have shown that the quiescent solar wind exhibits a positive correlation between electron density and temperature, suggesting that gamma(sub e) > 1. In this study we simulate the evolution of a variety of CME-like disturbances in the solar wind using a one-dimensional, single-fluid model, to address the interpretation of the relationship between electron density and temperature within CMEs at fixed locations in space. Although we strictly impose a polytropic relationship (with gamma = constant) throughout our simulations, we demonstrate that a variety of correlations can exist between density and temperature at fixed points. Furthermore, we demonstrate that the presence of only local uncorrelated random fluctuations in density and temperature can produce a negative correlation. Consequently, we conclude that these single-point observations of negative correlations between electron density and temperature cannot be used to infer the value of gamma(sub e). Instead, we suggest that entropy variations, together with the plasma's tendency to achieve pressure balance with its surroundings, are responsible for the observed profiles.

Riley, Pete↗

DOE OSTI2025

Celestial Topology, Symmetry Theories, and Evidence for a NonSUSY D3‐Brane CFT

Symmetry Theories (SymThs) provide a flexible framework for analyzing the global categorical symmetries of a D -dimensional QFT D in terms of a (D + 1)-dimensional bulk system SymTh D+1 . In QFTs realized via local string backgrounds, these SymThs naturally arise from dimensional reduction of the linking boundary geometry. To track possible time dependent effects we introduce a celestial generalization of the standard “boundary at infinity” of a SymTh. As an application of these considerations we revisit large N quiver gauge theories realized by spacetime filling D3-branes probing a non-supersymmetric orbifold $\mathbb{R}$ 6 /Γ. Comparing the imprint of symmetry breaking on the celestial geometry at small and large ‘t Hooft coupling we find evidence for an intermediate symmetry preserving conformal fixed point.

conformal field theory↗

DOE OSTI2024

A taxonomy of automatic differentiation pitfalls

Automatic differentiation is a popular technique for computing derivatives of computer programs. While automatic differentiation has been successfully used in countless engineering, science, and machine learning applications, it can sometimes nevertheless produce surprising results. In this paper, we categorize problematic usages of automatic differentiation, and illustrate each category with examples such as chaos, time-averages, discretizations, fixed-point loops, lookup tables, linear solvers, and probabilistic programs, in the hope that readers may more easily avoid or detect such pitfalls. We also review debugging techniques and their effectiveness in these situations.

Autodiff↗