Toroidal and slab ETG instability dominance in the linear spectrum of JET-ILW pedestals

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.

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Superfluid Phonons in Neutron Star Core

Universe ◽

10.3390/universe7010016 ◽

2021 ◽

Vol 7 (1) ◽

pp. 16

Author(s):

Marcello Baldo

Keyword(s):

Neutron Star ◽

Inner Core ◽

Mutual Influence ◽

Collective Excitation ◽

Neutron Matter ◽

Superfluid Phase ◽

S Wave ◽

Spectral Functions ◽

Open Problems ◽

Linear Spectrum

In neutron stars the nuclear asymmetric matter is expected to undergo phase transitions to a superfluid state. According to simple estimates, neutron matter in the inner crust and just below should be in the s-wave superfluid phase, corresponding to the neutron-neutron 1S0 channel. At higher density in the core also the proton component should be superfluid, while in the inner core the neutron matter can be in the 3P2 superfluid phase. Superluidity is believed to be at the basis of the glitches phenomenon and to play a decisive influence on many processes like transport, neutrino emission and cooling, and so on. One of the peculiarity of the superfluid phase is the presence of characteristic collective excitation, the so called ’phonons’, that correspond to smooth modulations of the order parameter and display a linear spectrum at low enough momentum. This paper is a brief review of the different phonons that can appear in Neutron Star superfuid matter and their role in several dynamical processes. Particular emphasis is put on the spectral functions of the different components, that is neutron, protons and electrons, which reveal their mutual influence. The open problems are discussed and indications on the work that remain to be done are given.

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Books for use and books for show

Book Ownership in Stuart England ◽

10.1093/oso/9780198870128.003.0006 ◽

2021 ◽

pp. 111-137

Author(s):

David Pearson

Keyword(s):

Seventeenth Century ◽

Case Studies ◽

History Of Reading ◽

Human History ◽

Self Image ◽

Linear Spectrum ◽

History Of

We may believe that books should be bought to be read and studied, but there is plentiful evidence, through human history, of people being mocked for owning books more for display and self-image. This chapter looks seriously and systematically at motivations for book ownership in the seventeenth century, recognizing that there is a range of attitudes between textual utility and the valuing of books for their aesthetic or luxurious qualities. Bookbindings, bookplates, heraldic markings, wills, and other kinds of evidence are drawn on, through various case studies, to show that for most people a mixture of approaches was probably involved—that we should think more in terms of a matrix than a linear spectrum. Book historians may define the history of reading as the key interface to be explored between books and people, but this is too narrow a focus if we really want to understand why people owned books.

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MULTIFRACTALITY IN THE GENERALIZED AUBRY–ANDRÉ QUASIPERIODIC LOCALIZATION MODEL WITH POWER-LAW HOPPINGS OR POWER-LAW FOURIER COEFFICIENTS

Fractals ◽

10.1142/s0218348x19500075 ◽

2019 ◽

Vol 27 (02) ◽

pp. 1950007 ◽

Cited By ~ 5

Author(s):

CÉCILE MONTHUS

Keyword(s):

Power Law ◽

Fourier Coefficients ◽

Nearest Neighbor ◽

Real Space ◽

Equivalent Model ◽

Translation Invariant ◽

Fourier Basis ◽

Quasiperiodic Potential ◽

Linear Spectrum ◽

Localization Model

The nearest-neighbor Aubry–André quasiperiodic localization model is generalized to include power-law translation-invariant hoppings [Formula: see text] or power-law Fourier coefficients [Formula: see text] in the quasiperiodic potential. The Aubry–André duality between [Formula: see text] and [Formula: see text] manifests when the Hamiltonian is written in the real-space basis and in the Fourier basis on a finite ring. The perturbative analysis in the amplitude [Formula: see text] of the hoppings yields that the eigenstates remain power-law localized in real space for [Formula: see text] and are critical for [Formula: see text] where they follow the strong multifractality linear spectrum, as in the equivalent model with random disorder. The perturbative analysis in the amplitude [Formula: see text] of the quasiperiodic potential yields that the eigenstates remain delocalized in real space (power-law localized in Fourier space) for [Formula: see text] and are critical for [Formula: see text] where they follow the weak multifractality Gaussian spectrum in real space (or strong multifractality linear spectrum in the Fourier basis). This critical case [Formula: see text] for the Fourier coefficients [Formula: see text] corresponds to a periodic function with discontinuities, instead of the cosinus function of the standard self-dual Aubry–André model.

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The Lodge Rubberlike Liquid Behavior for Cheese in Large Amplitude Oscillatory Shear

Applied Rheology ◽

10.1515/arh-2001-0017 ◽

2001 ◽

Vol 11 (6) ◽

pp. 312-319 ◽

Cited By ~ 8

Author(s):

Y.-C. Wang ◽

S. Gunasekaran ◽

A. J. Giacomin

Keyword(s):

Stress Responses ◽

Relaxation Spectrum ◽

Large Strain ◽

Small Strain ◽

Oscillatory Shear ◽

Linear Relaxation ◽

Linear Regime ◽

Linear Spectrum ◽

Liquid Behavior ◽

Scale Down

AbstractThe viscoelasticity of reduced-fat Cheddar and Mozzarella cheeses was characterized in small (parallel disk rheometer, go = 0.01) and large (sliding plate rheometer, 0.2< go <7) amplitude oscillatory shear at 40 and 60˚C. We deduced the linear relaxation spectrum from the small strain measurements. At large strain amplitudes, we found sinusoidal stress responses whose amplitudes are well below those predicted from the linear relaxation spectrum, and yet remarkably linear with strain amplitude. We call this the large strain linear regime. We discovered that the Lodge rubberlike liquid can quantitatively explain the large strain linear regime if we scale down the relaxation moduli in the linear spectrum by a constant. This large strain linear regime persists to much higher strain amplitudes for Cheddar (go £ 4) than for Mozzarella (go £ 1). This is perhaps due to oriented structure of the protein matrix in the Mozzarella cheese.

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Nonlinear two-dimensional terahertz photon echo and rotational spectroscopy in the gas phase

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1609558113 ◽

2016 ◽

Vol 113 (42) ◽

pp. 11800-11805 ◽

Cited By ~ 41

Author(s):

Jian Lu ◽

Yaqing Zhang ◽

Harold Y. Hwang ◽

Benjamin K. Ofori-Okai ◽

Sharly Fleischer ◽

...

Keyword(s):

Gas Phase ◽

Degrees Of Freedom ◽

Terahertz Spectroscopy ◽

Electromagnetic Spectrum ◽

Dynamic Features ◽

Dipole Orientation ◽

Rotational Spectra ◽

Dipole Interactions ◽

Linear Spectrum ◽

Rotational Coupling

Ultrafast 2D spectroscopy uses correlated multiple light−matter interactions for retrieving dynamic features that may otherwise be hidden under the linear spectrum; its extension to the terahertz regime of the electromagnetic spectrum, where a rich variety of material degrees of freedom reside, remains an experimental challenge. We report a demonstration of ultrafast 2D terahertz spectroscopy of gas-phase molecular rotors at room temperature. Using time-delayed terahertz pulse pairs, we observe photon echoes and other nonlinear signals resulting from molecular dipole orientation induced by multiple terahertz field−dipole interactions. The nonlinear time domain orientation signals are mapped into the frequency domain in 2D rotational spectra that reveal J-state-resolved nonlinear rotational dynamics. The approach enables direct observation of correlated rotational transitions and may reveal rotational coupling and relaxation pathways in the ground electronic and vibrational state.

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Energy Content Analysis of Closed Basin Wave Simulation Using Linear and Nonlinear Fourier Analysis

Volume 3: Structures, Safety, and Reliability ◽

10.1115/omae2018-78754 ◽

2018 ◽

Author(s):

Ali Mohtat ◽

Solomon C. Yim ◽

Alfred R. Osborne

Keyword(s):

Fourier Analysis ◽

Energy Content ◽

Wave Train ◽

Stokes Wave ◽

State University ◽

Linear Spectrum ◽

Wave Basin ◽

Significant Difference ◽

Nonlinear Components ◽

Oregon State University

This study focuses on the computation and analysis of the energy content of a wave train and the influence of nonlinear components, such as nonlinear wave profile as in Stokes wave and phased locked breathers, on the content. To this end, an overview of a state-of-the-art nonlinear Fourier analysis tools for the nonlinear Schrödinger equation is presented. Experimental measurements from a set of performance tests of the directional wave basin at Oregon State University were analyzed using this tool and the energy contents, both from the linear spectrum and nonlinear spectrum, were calculated. The deviation of the energy content from linear analysis and its relationship to the level of nonlinearity of the wave train is investigated. The Benjamin-Feir parameter presents the degree of nonlinearity of the wave train. An increasing energy deviation was observed for increasing nonlinearity of the wave field. Spatial evolution of such behavior is also investigated. It was confirmed that the significant difference from the linear energy is due to increase in the nonlinear components and the more distance the wave train could travel (without substantial dissipation) the more erratic and more significant energy deviations were observed.

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