scholarly journals Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics

2021 ◽  
Author(s):  
Yu Deng ◽  
Christian Zillinger
Keyword(s):  
Euler Equations ◽  
High Frequency ◽  
Low Frequency ◽  
Linear Instability ◽  
Instability Mechanism ◽  
Resonance Mechanism ◽  
Gevrey Regularity ◽  
Precise Analysis ◽  
Frequency Regime ◽  
Type Spaces

AbstractIn this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to be a (secondary) linear instability mechanism. Furthermore, we develop a more precise analysis of cancellations in the resonance mechanism, which yields a modified exponent in the high frequency regime. This allows us, in addition, to remove a logarithmic constraint on the perturbations present in prior works by Bedrossian, Deng and Masmoudi, and to construct solutions which are initially in a Gevrey class for which the velocity asymptotically converges in Sobolev regularity but diverges in Gevrey regularity.

scholarly journals Greybody Factors for Schwarzschild Black Holes: Path-Ordered Exponentials and Product Integrals

Universe ◽  
2018 ◽  
Vol 4 (9) ◽  
pp. 93 ◽  
Author(s):  
Finnian Gray ◽  
Matt Visser
Keyword(s):  
Black Holes ◽  
High Frequency ◽  
Low Frequency ◽  
Intermediate Frequency ◽  
General Context ◽  
Matrix Formalism ◽  
Barrier Penetration ◽  
Frequency Regime ◽  
Transfer Matrix Formalism ◽  
Numerical Approaches

In earlier work concerning the sparsity of the Hawking flux, we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focusing specifically on Schwarzschild black holes, we have re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a pedagogically useful semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, being based on a variant of the “transfer matrix” formalism, are closely related to so-called “product integrals”, leading to quite straightforward and direct numerical evaluation, while side-stepping any need for numerically solving the relevant ordinary differential equations. Furthermore, while considerable analytic information is already available regarding both the high-frequency and low-frequency asymptotics of these greybody factors, numerical approaches seem better adapted to finding suitable “global models” for these greybody factors in the intermediate frequency regime, where most of the Hawking flux is actually concentrated. Working in a more general context, these path-ordered-exponential techniques are also likely to be of interest for generic barrier-penetration problems.

scholarly journals Precorrected-FFT Accelerated Singular Boundary Method for High-Frequency Acoustic Radiation and Scattering

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 238
Author(s):  
Weiwei Li ◽  
Fajie Wang
Keyword(s):  
High Frequency ◽  
Acoustic Radiation ◽  
Low Frequency ◽  
Singular Boundary ◽  
Cpu Time ◽  
Interpolation Matrix ◽  
Collocation Points ◽  
Boundary Method ◽  
Frequency Regime ◽  
Singular Boundary Method

This paper presents a precorrected-FFT (pFFT) accelerated singular boundary method (SBM) for acoustic radiation and scattering in the high-frequency regime. The SBM is a boundary-type collocation method, which is truly free of mesh and integration and easy to program. However, due to the expensive CPU time and memory requirement in solving a fully-populated interpolation matrix equation, this method is usually limited to low-frequency acoustic problems. A new pFFT scheme is introduced to overcome this drawback. Since the models with lots of collocation points can be calculated by the new pFFT accelerated SBM (pFFT-SBM), high-frequency acoustic problems can be simulated. The results of numerical examples show that the new pFFT-SBM possesses an obvious advantage for high-frequency acoustic problems.

scholarly journals On the Effectiveness of Low Frequency Perturbations

2019 ◽  
Author(s):  
Yash Sharma ◽  
Gavin Weiguang Ding ◽  
Marcus A. Brubaker
Keyword(s):  
High Frequency ◽  
State Of The Art ◽  
Low Frequency ◽  
Human Perception ◽  
Search Space ◽  
Frequency Space ◽  
Performance Improvements ◽  
Frequency Regime ◽  
Frequency Components ◽  
Norm Constraint

Carefully crafted, often imperceptible, adversarial perturbations have been shown to cause state-of-the-art models to yield extremely inaccurate outputs, rendering them unsuitable for safety-critical application domains. In addition, recent work has shown that constraining the attack space to a low frequency regime is particularly effective. Yet, it remains unclear whether this is due to generally constraining the attack search space or specifically removing high frequency components from consideration. By systematically controlling the frequency components of the perturbation, evaluating against the top-placing defense submissions in the NeurIPS 2017 competition, we empirically show that performance improvements in both the white-box and black-box transfer settings are yielded only when low frequency components are preserved. In fact, the defended models based on adversarial training are roughly as vulnerable to low frequency perturbations as undefended models, suggesting that the purported robustness of state-of-the-art ImageNet defenses is reliant upon adversarial perturbations being high frequency in nature. We do find that under L-inf-norm constraint 16/255, the competition distortion bound, low frequency perturbations are indeed perceptible. This questions the use of the L-inf-norm, in particular, as a distortion metric, and, in turn, suggests that explicitly considering the frequency space is promising for learning robust models which better align with human perception.

scholarly journals Effect of grain-scale gas patches on the seismic properties of double porosity rocks

2016 ◽  
Vol 208 (1) ◽  
pp. 432-436 ◽  
Author(s):  
Stanislav Glubokovskikh ◽  
Boris Gurevich
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Rock Physics ◽  
Time Lapse ◽  
Double Porosity ◽  
Ultrasonic Velocities ◽  
Seismic Properties ◽  
Partially Saturated ◽  
Frequency Regime ◽  
Wave Induced

Time-lapse ultrasonic measurements constitute a tool to establish and calibrate rock physics models for surface seismic monitoring of partially saturated rocks. This workflow requires one to take into account seismic dispersion caused by frequency-dependent wave-induced fluid flow. We develop a theory of squirt flow in rocks saturated with a viscoelastic material containing isolated gas patches between compliant intergranular contacts. This model is valid for the entire frequency range, from seismic to ultrasonic. In the limit of full saturation the derived equations reduce to the Gassmann equations in the low-frequency regime and traditional squirt theory in the high-frequency regime. The model prediction of ultrasonic velocities versus saturation matches with experimental observations.

scholarly journals Modeling the Epidemic Growth of Preprints on COVID-19 and SARS-CoV-2

2021 ◽  
Vol 9 ◽  
Author(s):  
Giovani L. Vasconcelos ◽  
Luan P. Cordeiro ◽  
Gerson C. Duarte-Filho ◽  
Arthur A. Brum
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Growth Dynamics ◽  
Low Rank ◽  
Cumulative Number ◽  
High Frequency Region ◽  
Short Period ◽  
Frequency Regime ◽  
Near Future ◽  
Current Stage

The response of the scientific community to the global health emergency caused by the COVID-19 pandemic has produced an unprecedented number of manuscripts in a short period of time, the vast majority of which have been shared in the form of preprints posted on online preprint repositories before peer review. This surge in preprint publications has in itself attracted considerable attention, although mostly in the bibliometrics literature. In the present study we apply a mathematical growth model, known as the generalized Richards model, to describe the time evolution of the cumulative number of COVID-19 related preprints. This mathematical approach allows us to infer several important aspects concerning the underlying growth dynamics, such as its current stage and its possible evolution in the near future. We also analyze the rank-frequency distribution of preprints servers, ordered by the number of COVID-19 preprints they host, and find that it follows a power law in the low rank (high frequency) region, with the high rank (low frequency) tail being better described by a q-exponential function. The Zipf-like law in the high frequency regime indicates the presence of a cumulative advantage effect, whereby servers that already have more preprints receive more submissions.

Microparticle Trapping in Streaming Flows in Open Rectangular Chambers Undergoing Low Frequency Vertical Vibrations

2014 ◽  
Author(s):  
Prashant Agrawal ◽  
Prasanna S. Gandhi ◽  
Adrian Neild
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Mode Switching ◽  
Small Particles ◽  
Low Frequencies ◽  
Different Types ◽  
Frequency Regime ◽  
Vertical Vibrations ◽  
Rectangular Chamber ◽  
Streaming Flows

Microparticle collection in microfluidic systems via mechanical vibrations has been demonstrated in both low frequency systems (in the range of 100Hz) and in the high frequency regime (in the range of 1MHz). However, in most systems, collection of particles with lower inertia is hindered by second order time-averaged streaming flows. In our approach, we experimentally demonstrate collection of small particles (about 3 μm in diameter) by trapping them in streaming flows in a liquid filled open rectangular chamber undergoing vertical vibrations at low frequencies. The proposed method is then utilized to separate two different types of particles in distinct patterns through mode-switching.

Modeling and Quantification of Acoustic Damping Induced by Vortex Shedding in Non-Compact Thermoacoustic Systems

2019 ◽  
Author(s):  
Thomas Hofmeister ◽  
Tobias Hummel ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Vortex Shedding ◽  
High Frequency ◽  
Low Frequency ◽  
Network Models ◽  
Test Case ◽  
Acoustic Damping ◽  
Linearized Euler Equations ◽  
Damping Rate ◽  
Frequency Regime ◽  
Swirl Stabilized Combustion

Abstract This paper presents a methodology to compute acoustic damping rates of transversal, high-frequency modes induced by vortex-shedding. The acoustic damping rate presents one key quantity for the assessment of the linear thermoacoustic stability of gas turbine combustors. State of the art network models — as employed to calculate damping rates in low-frequency, longitudinal systems — cannot fulfill this task due to the acoustic non-compactness encountered in the high-frequency regime. Furthermore, it is yet unclear, whether direct eigensolutions of the Linearized Euler Equations (LEE), which capture the mechanism of vortex shedding, yield correct damping rate results constituted by the implicit presence of acoustic as well as hydrodynamic contributions in these solutions. The methodology’s applicability to technically relevant systems is demonstrated by a validation test case using a lab-scale, swirl-stabilized combustion system.

Effect of coupling strength on the intermodulation distortion in DFB laser

1996 ◽  
Vol 74 (S1) ◽  
pp. 5-8 ◽  
Author(s):  
Hanan Anis ◽  
J. Goodwin ◽  
T. Makino ◽  
J. M. Xu
Keyword(s):  
Coupling Strength ◽  
High Frequency ◽  
Relaxation Oscillation ◽  
Low Frequency ◽  
Intermodulation Distortion ◽  
Frequency Regime ◽  
Dfb Laser

In this work the effect of increasing the coupling strength on the intermodulation distortion is investigated. It is shown that only if other effects such as the change in the relaxation oscillation are absent, higher coupling strength leads to a higher intermodulation distortion. Otherwise, the dependence of distortion on the coupling strength is not monotonic and exhibits trends in the mid- and high-frequency regimes that are very different from that in the low-frequency regime.

Modeling and Quantification of Acoustic Damping Induced by Vortex Shedding in Noncompact Thermoacoustic Systems

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Thomas Hofmeister ◽  
Tobias Hummel ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Vortex Shedding ◽  
High Frequency ◽  
Low Frequency ◽  
Network Models ◽  
Test Case ◽  
Acoustic Damping ◽  
Linearized Euler Equations ◽  
Damping Rate ◽  
Frequency Regime ◽  
Swirl Stabilized Combustion

Abstract This paper presents a methodology to compute acoustic damping rates of transversal, high-frequency modes induced by vortex-shedding. The acoustic damping rate presents one key quantity for the assessment of the linear thermoacoustic stability of gas turbine combustors. State-of-the-art network models—as employed to calculate damping rates in low-frequency, longitudinal systems—cannot fulfill this task due to the acoustic noncompactness encountered in the high-frequency regime. Furthermore, it is yet unclear, whether direct eigensolutions of the linearized Euler equations (LEE), which capture the mechanism of vortex shedding, yield correct damping rate results constituted by the implicit presence of acoustic as well as hydrodynamic contributions in these solutions. The methodology's applicability to technically relevant systems is demonstrated by a validation test case using a lab-scale, swirl-stabilized combustion system.

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