Kinetic theory of turbulence for parallel propagation revisited: Low-to-intermediate frequency regime

2015 ◽  
Vol 22 (9) ◽  
pp. 092307 ◽  
Author(s):  
Peter H. Yoon
Keyword(s):  
Kinetic Theory ◽  
Intermediate Frequency ◽  
Parallel Propagation ◽  
Frequency Regime

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 Translocation of structured biomolecule through a vibrating nanopore

2018 ◽  
Author(s):  
M. A. Shahzad
Keyword(s):  
Protein Transport ◽  
Protein Translocation ◽  
Intermediate Frequency ◽  
Global Maximum ◽  
Cylindrical Pore ◽  
Transport Dynamics ◽  
Frequency Regime ◽  
Translocation Time ◽  
Static Channel ◽  
Resonant Activation

ABSTRACTWe study the effect of fluctuating environment in protein transport dynamics. In particular, we investigate the translocation of a structured biomolecule (protein) across a temporally modulated nano-pore. We allow the radius of the cylindrical pore to oscillate harmonically with certain frequency and amplitude about an average radius. The protein is imported inside the pore whose dynamics is influences by the fluctuating nature of the pore. We investigate the dynamic and thermodynamical properties of the translocation process by revealing the statistics of translocation time as a function of the pulling inward force acting along the axis of the pore, and the frequency of the time dependent radius of the channel. We also examine the distribution of translocation time in the intermediate frequency regime. We observe that the shaking mechanism of pore leads to accelerate the translocation process as compared to the static channel that has a radius equal to the mean radius of oscillating pore. Moreover, the translocation time shows a global maximum as a function of frequency of the oscillating radius, hence revealing a resonant activation phenomenon in the dynamics of protein translocation.

scholarly journals Transition to turbulence in pulsating pipe flow

2017 ◽  
Vol 831 ◽  
pp. 418-432 ◽  
Author(s):  
Duo Xu ◽  
Sascha Warnecke ◽  
Baofang Song ◽  
Xingyu Ma ◽  
Björn Hof
Keyword(s):  
Pipe Flow ◽  
Oscillation Amplitude ◽  
Intermediate Frequency ◽  
Finite Amplitude ◽  
Decay Rates ◽  
Transition To Turbulence ◽  
Pulsation Frequency ◽  
Onset Of Turbulence ◽  
Frequency Regime ◽  
The Impact

Fluid flows in nature and applications are frequently subject to periodic velocity modulations. Surprisingly, even for the generic case of flow through a straight pipe, there is little consensus regarding the influence of pulsation on the transition threshold to turbulence: while most studies predict a monotonically increasing threshold with pulsation frequency (i.e. Womersley number, $\unicode[STIX]{x1D6FC}$), others observe a decreasing threshold for identical parameters and only observe an increasing threshold at low $\unicode[STIX]{x1D6FC}$. In the present study we apply recent advances in the understanding of transition in steady shear flows to pulsating pipe flow. For moderate pulsation amplitudes we find that the first instability encountered is subcritical (i.e. requiring finite amplitude disturbances) and gives rise to localized patches of turbulence (‘puffs’) analogous to steady pipe flow. By monitoring the impact of pulsation on the lifetime of turbulence we map the onset of turbulence in parameter space. Transition in pulsatile flow can be separated into three regimes. At small Womersley numbers the dynamics is dominated by the decay turbulence suffers during the slower part of the cycle and hence transition is delayed significantly. As shown in this regime thresholds closely agree with estimates based on a quasi-steady flow assumption only taking puff decay rates into account. The transition point predicted in the zero $\unicode[STIX]{x1D6FC}$ limit equals to the critical point for steady pipe flow offset by the oscillation Reynolds number (i.e. the dimensionless oscillation amplitude). In the high frequency limit on the other hand, puff lifetimes are identical to those in steady pipe flow and hence the transition threshold appears to be unaffected by flow pulsation. In the intermediate frequency regime the transition threshold sharply drops (with increasing $\unicode[STIX]{x1D6FC}$) from the decay dominated (quasi-steady) threshold to the steady pipe flow level.

scholarly journals On the dimensionally correct kinetic theory of turbulence for parallel propagation

2015 ◽  
Vol 22 (3) ◽  
pp. 032310 ◽  
Author(s):  
R. Gaelzer ◽  
P. H. Yoon ◽  
Sunjung Kim ◽  
L. F. Ziebell
Keyword(s):  
Kinetic Theory ◽  
Parallel Propagation

scholarly journals A science friction story – Molecular interactions in semiflexible polymer networks

2021 ◽  
Author(s):  
Paul Mollenkopf ◽  
Dusan Prascevic ◽  
Martin Glaser ◽  
David M. Smith ◽  
Jörg Schnauß
Keyword(s):  
Molecular Interactions ◽  
Mechanical Response ◽  
Polymer Networks ◽  
Intermediate Frequency ◽  
Model Systems ◽  
Semiflexible Polymers ◽  
Friction Forces ◽  
Semiflexible Polymer ◽  
Frequency Regime ◽  
Nonlinear Deformations

AbstractEstablished model theories, developed to capture the mechanical behavior of soft complex materials composed of semiflexible polymers assume entropic interactions between filaments to determine the mechanical response. In recent studies, the general accepted tube model has been challenged in terms of its basic assumption about filament-filament interactions, but also because of its predictions regarding the frequency dependence of the elastic modulus in the intermediate frequency regime. A central question is how molecular interactions and friction between network constituents influence the rheological response of isotropic entangled networks of semiflexible polymers. It was shown that friction forces between aligned pairs of actin filaments are not negligible. Here, we systematically investigate the influence of friction forces and attractive interactions on network rheology by means of a targeted surface modification. We show that these forces have a qualitative and quantitative influence on the viscoelastic properties of semiflexible polymer networks and contribute to the response to nonlinear deformations. By comparing two polymer model systems with respect to their surface compositions we give a possible explanation about the origin of acting forces on a molecular level.

Interaction of positive and negative energy waves in a magnetized bi-ion plasma with differential ion streaming

2008 ◽  
Vol 74 (3) ◽  
pp. 345-352
Author(s):  
J. F. MCKENZIE ◽  
Q. HU
Keyword(s):  
Intermediate Frequency ◽  
Negative Energy ◽  
Acoustic Mode ◽  
Positive Energy ◽  
Energy Proton ◽  
Ion Plasma ◽  
Frequency Regime ◽  
Cyclotron Mode ◽  
Wave Normal ◽  
Proton Cyclotron

AbstractIn this paper the concept of negative energy waves facilitates the analysis of instability in a magnetized bi-ion plasma with differential ion streaming. There are three frequency regimes in which instability may arise. For frequencies less than the alpha particle gyrofrequency, a negative energy alpha ion-cyclotron mode can interact with a positive energy proton-cyclotron mode. In the intermediate frequency regime lying between the alpha and proton gyrofrequencies, a negative energy alpha-acoustic mode interacts with a positive energy proton-cyclotron mode. In the high-frequency regime above the proton-cyclotron frequency a negative energy alpha-acoustic mode interacts with a positive energy proton-acoustic mode. The resonance (or coalescence) condition which lends itself to a simple geometrical interpretation as the intersection between the proton and alpha mode wave normal diagrams with differential streaming permits the evaluation of the instability growth rate in each frequency regime, which is calculated for both subsonic and supersonic differential streaming.

Jeans analysis with κ-deformed Kaniadakis distribution in f (R) gravity

2022 ◽  
Author(s):  
Ke-Rong He
Keyword(s):  
Dispersion Relation ◽  
Kinetic Theory ◽  
Growth Rates ◽  
Effective Temperature ◽  
Gravitational Instability ◽  
Low Frequency ◽  
Distribution Index ◽  
Frequency Regime ◽  
Jeans Instability

Abstract The influence of the κ-deformed Kaniadakis distribution on Jeans instability in the background of f(R) gravity is investigated, the dispersion relation considering the κ-deformed Kaniadakis distribution is derived by exploiting the kinetic theory. The cases of high and low frequency perturbations are analyzed, respectively, it is found that the range of the unstable modes and the growth rates decrease with the increased distribution index κ in both of high and low frequency regime. Finally, based on the derivation of effective temperature, the relation between Jeans mass and temperature is studied, it is found that lower Jeans mass means that the system is more likely to collapse due to gravitational instability, the system is unstable for lower distribution index κ.

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