scholarly journals Material barriers to diffusive and stochastic transport

2018 ◽  
Vol 115 (37) ◽  
pp. 9074-9079 ◽  
Author(s):  
George Haller ◽  
Daniel Karrasch ◽  
Florian Kogelbauer
Keyword(s):  
Coherent Structures ◽  
Fluid Transport ◽  
Order Term ◽  
Velocity Fields ◽  
Leading Order ◽  
Transport Barrier ◽  
Material Surfaces ◽  
Stochastic Transport ◽  
Transport Barriers ◽  
Enhancer Detection

We seek transport barriers and transport enhancers as material surfaces across which the transport of diffusive tracers is minimal or maximal in a general, unsteady flow. We find that such surfaces are extremizers of a universal, nondimensional transport functional whose leading-order term in the diffusivity can be computed directly from the flow velocity. The most observable (uniform) transport extremizers are explicitly computable as null surfaces of an objective transport tensor. Even in the limit of vanishing diffusivity, these surfaces differ from all previously identified coherent structures for purely advective fluid transport. Our results extend directly to stochastic velocity fields and hence enable transport barrier and enhancer detection under uncertainties.

Effect of Acoustic Feedback on Lagrangian Coherent Structures in a Backward Facing Step Combustor With a Partially Premixed Flame

2017 ◽  
Author(s):  
Ramgopal Sampath ◽  
S. R. Chakravarthy
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Pressure Oscillation ◽  
Velocity Fields ◽  
Premixed Flame ◽  
Time Resolved ◽  
Acoustic Feedback ◽  
Acoustic Characterization ◽  
Partially Premixed ◽  
Partially Premixed Flame

The thermoacoustic oscillations of a partially premixed flame stabilized in a backward facing step combustor are studied at a constant equivalence ratio in long and short combustor configurations corresponding to with and without acoustic feedback respectively. We perform simultaneous time-resolved particle image velocimetry (TR-PIV) and chemiluminescence for selected flow conditions based on the acoustic characterization in the long combustor. The acoustic characterization shows a transition in the dominant pressure amplitudes from low to high magnitudes with an increase in the inlet flow Reynolds number. This is accompanied by a shift in the dominant frequencies. For the intermittent pressure oscillations in the long combustor, the wavelet analysis indicates a switch between the acoustic and vortex modes with silent zones of relatively low-pressure amplitudes. The short combustor configuration indicates the presence of the vortex shedding frequency and an additional band comprising the Kelvin Helmholtz mode. Next, we apply the method of finite-time Lyapunov exponent (FTLE) to the time-resolved velocity fields to extract features of the Lagrangian coherent structures (LCS) of the flow. In the long combustor post transition with the time instants with dominant acoustic mode, a large-scale modulation of the FTLE boundaries over one cycle of pressure oscillation is evident. Further, the FTLEs and the flame boundaries align each other for all phases of the pressure oscillation. In the short combustor, the FTLEs indicate the presence of small wavelength waviness that overrides the large-scale vortex structure, which corresponds to the vortex shedding mode. This behaviour contrasts with the premixed flame in the short combustor reported earlier in which such large scales were found to be seldom present. The presence of the large-scale structures even in the absence of acoustic feedback in a partially premixed flame signifies its inherent unstable nature leading to large pressure amplitudes during acoustic feedback. Lastly, the FTLE boundaries provide the frequency information of the identified coherent structure and also acts as the surrogate flame boundaries that are estimated from just the velocity fields.

Derivation of the maximum voltage drop in power grids of integrated circuits with an array bonding package

2012 ◽  
Vol 23 (6) ◽  
pp. 797-819
Author(s):  
M. AGUARELES ◽  
J. de HARO
Keyword(s):  
Integrated Circuits ◽  
Iterative Scheme ◽  
Voltage Drop ◽  
Order Term ◽  
Singular Limit ◽  
Power Grids ◽  
Leading Order ◽  
Conformal Maps ◽  
Maximum Value ◽  
Aligned Array

In this work we derive a formula for the maximum value of the voltage drop that takes place in power grids of integrated circuits with an array bonding package. We consider a simplified model for the power grid where the voltage is represented as the solution of the Poisson's equation in an infinite planar domain with a regularly aligned array of small square pads where the voltage is set to be zero. We study the singular limit where these pads' size tends to be zero and we derive an asymptotic formula in terms of a power series in ε, being 2ε the side of the square. We also discuss pads of more general shapes, for which we provide an expression for the leading order term. To deduce all these formulae we use the method of matched asymptotic expansions using an iterative scheme, along with conformal maps to compare this problem with the corresponding one when the pads are circular.

Plasma-turbulence suppression and transport-barrier formation by externally driven radiofrequency waves in spherical tokamaks

2001 ◽  
Vol 65 (3) ◽  
pp. 235-253 ◽  
Author(s):  
K. KOMOSHVILI ◽  
S. CUPERMAN ◽  
C. BRUMA
Keyword(s):  
Electric Fields ◽  
Turbulent Transport ◽  
Plasma Turbulence ◽  
Ion Temperature ◽  
Transport Barrier ◽  
Ion Temperature Gradient ◽  
Turbulence Suppression ◽  
Barrier Formation ◽  
Transport Barriers ◽  
Fast Waves

Turbulent transport of heat and particles is the principle obstacle confronting controlled fusion today. We investigate quantitatively the suppression of turbulence and formation of transport barriers in spherical tokamaks by sheared electric fields generated by externally driven radiofrequency (RF) waves, in the frequency range ωA ∼ ω < ωci (where ωA and ωci are the Alfvén and ion cyclotron frequencies).This investigation consists of the solution of the full-wave equation for a spherical tokamak in the presence of externally driven fast waves and the evaluation of the power dissipation by the mode-converted Alfvén waves. This in turn provides a radial flow shear responsible for the suppression of plasma turbulence. Thus a strongly nonlinear equation for the radial sheared electric field is solved, and the turbulent transport suppression rate is evaluated and compared with the ion temperature gradient (ITG) instability increment.

scholarly journals Pollution Transport Patterns Obtained Through Generalized Lagrangian Coherent Structures

Atmosphere ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 168
Author(s):  
Peter J. Nolan ◽  
Hosein Foroutan ◽  
Shane D. Ross
Keyword(s):  
Velocity Field ◽  
Coherent Structures ◽  
Initial Conditions ◽  
Saddle Points ◽  
Chemical Species ◽  
Lagrangian Coherent Structures ◽  
Time Interval ◽  
Pollution Transport ◽  
Material Transport ◽  
Material Surfaces

Identifying atmospheric transport pathways is important to understand the effects of pollutants on weather, climate, and human health. The atmospheric wind field is variable in space and time and contains complex patterns due to turbulent mixing. In such a highly unsteady flow field, it can be challenging to predict material transport over a finite-time interval. Particle trajectories are often used to study how pollutants evolve in the atmosphere. Nevertheless, individual trajectories are sensitive to their initial conditions. Lagrangian Coherent Structures (LCSs) have been shown to form the template of fluid parcel motion in a fluid flow. LCSs can be characterized by special material surfaces that organize the parcel motion into ordered patterns. These key material surfaces form the core of fluid deformation patterns, such as saddle points, tangles, filaments, barriers, and pathways. Traditionally, the study of LCSs has looked at coherent structures derived from integrating the wind velocity field. It has been assumed that particles in the atmosphere will generally evolve with the wind. Recent work has begun to look at the motion of chemical species, such as water vapor, within atmospheric flows. By calculating the flux associated with each species, a new effective flux-based velocity field can be obtained for each species. This work analyzes generalized species-weighted coherent structures associated with various chemical species to find their patterns and pathways in the atmosphere, providing a new tool and language for the assessment of pollutant transport and patterns.

Transport and Mixing in Kinematic and Dynamically Consistent Flows

2007 ◽  
Vol 64 (10) ◽  
pp. 3640-3651 ◽  
Author(s):  
P. H. Haynes ◽  
D. A. Poet ◽  
E. F. Shuckburgh
Keyword(s):  
Large Range ◽  
Vorticity Field ◽  
Transport Barrier ◽  
Multiple Jets ◽  
Mixing Behavior ◽  
Transport Barriers ◽  
Flow Evolution ◽  
Transport And Mixing ◽  
Dynamical Consistency ◽  
Strong Vorticity

Abstract The interplay between dynamics and transport in two-dimensional flows is examined by comparing the transport and mixing in a kinematic flow in which the velocity field is imposed as a given function of time with that in an analogous dynamically consistent flow in which the advected vorticity field controls the flow evolution. In both cases the variation of the transport and mixing behavior with a parameter ε governing the strength of the time dependence is considered. It is shown that dynamical consistency has the effect of (i) postponing the breaking of a central transport barrier as ε increases and (ii) removing the property of the kinematic flow that, for a large range of ε, a weakly permeable central barrier persists. The first effect is associated with the development of a strong vorticity gradient and the associated jet along the central transport barrier. The second effect is associated with the fact that, in the dynamically consistent flow, the breaking of the central barrier is accompanied by a drastic change in the vorticity field and hence in the structure of the flow. The relation between the vorticity field and transport barriers is further examined using a range of simple kinematic and dynamically consistent models. Implications for formulation of predictive models that represent the interactions between dynamics, transport, and mixing (and might be suggested as a basis for parameterizing eddies in flows that form multiple jets) are discussed.

scholarly journals Extracting Hawking radiation near the horizon of AdS black holes

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Krishan Saraswat ◽  
Niayesh Afshordi
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Evaporation Rate ◽  
Order Term ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Leading Order ◽  
Proper Distance ◽  
Ads Black Holes ◽  
A Cell

Abstract We study how the evaporation rate of spherically symmetric black holes is affected through the extraction of radiation close to the horizon. We adopt a model of extraction that involves a perfectly absorptive screen placed close to the horizon and show that the evaporation rate can be changed depending on how close to the horizon the screen is placed. We apply our results to show that the scrambling time defined by the Hayden-Preskill decoding criterion, which is derived in Pennington’s work (arXiv:1905.08255) through entanglement wedge reconstruction is modified. The modifications appear as logarithmic corrections to Pennington’s time scale which depend on where the absorptive screen is placed. By fixing the proper distance between the horizon and screen we show that for small AdS black holes the leading order term in the scrambling time is consistent with Pennington’s scrambling time. However, for large AdS black holes the leading order Log contains the Bekenstein-Hawking entropy of a cell of characteristic length equal to the AdS radius rather than the entropy of the full horizon. Furthermore, using the correspondence between the radial null energy condition (NEC) and the holographic c-theorem, we argue that the screen cannot be arbitrarily close to the horizon. This leads to a holographic argument that black hole mining using a screen cannot significantly alter the lifetime of a black hole.

A note on fractional Bessel equation and its asymptotics

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Wojciech Okrasiński ◽  
Łukasz Płociniczak
Keyword(s):  
Power Series ◽  
Asymptotic Formula ◽  
Asymptotic Analysis ◽  
Fractional Derivative ◽  
Order Term ◽  
High Accuracy ◽  
Fast Convergence ◽  
Leading Order ◽  
Bessel Equation ◽  
Integer Order

AbstractIn this note we propose a fractional generalization of the classical modified Bessel equation. Instead of the integer-order derivatives we use the Riemann-Liouville version. Next, we solve the fractional modified Bessel equation in terms of the power series and provide an asymptotic analysis of its solution for large arguments. We find a leading-order term of the asymptotic formula for the solution to the considered equation. This behavior is verified numerically and shows high accuracy and fast convergence. Our results reduce to the classical formulas when the order of the fractional derivative goes to integer values.

scholarly journals Kicked Burgers turbulence

2000 ◽  
Vol 416 ◽  
pp. 239-267 ◽  
Author(s):  
J. BEC ◽  
U. FRISCH ◽  
K. KHANIN
Keyword(s):  
Numerical Simulations ◽  
Power Law ◽  
Large Scale ◽  
Order Term ◽  
Inviscid Limit ◽  
Order Structure ◽  
Legendre Transform ◽  
Leading Order ◽  
Space And Time ◽  
Burgers Turbulence

Burgers turbulence subject to a force f(x, t) = [sum ]jfj(x)δ(t − tj), where tj are 'kicking times' and the 'impulses' fj(x) have arbitrary space dependence, combines features of the purely decaying and the continuously forced cases. With large-scale forcing this ‘kicked’ Burgers turbulence presents many of the regimes proposed by E et al. (1997) for the case of random white-noise-in-time forcing. It is also amenable to efficient numerical simulations in the inviscid limit, using a modification of the fast Legendre transform method developed for decaying Burgers turbulence by Noullez & Vergassola (1994). For the kicked case, concepts such as ‘minimizers’ and ‘main shock’, which play crucial roles in recent developments for forced Burgers turbulence, become elementary since everything can be constructed from simple two-dimensional area-preserving Euler–Lagrange maps.The main results are for the case of identical deterministic kicks which are periodic and analytic in space and are applied periodically in time. When the space integrals of the initial velocity and of the impulses vanish, it is proved and illustrated numerically that a space- and time-periodic solution is achieved exponentially fast. In this regime, probabilities can be defined by averaging over space and time periods. The probability densities of large negative velocity gradients and of (not-too-large) negative velocity increments follow the power law with −7/2 exponent proposed by E et al. (1997) in the inviscid limit, whose existence is still controversial in the case of white-in-time forcing. This power law, which is seen very clearly in the numerical simulations, is the signature of nascent shocks (preshocks) and holds only when at least one new shock is born between successive kicks.It is shown that the third-order structure function over a spatial separation Δx is analytic in Δx although the velocity field is generally only piecewise analytic (i.e. between shocks). Structure functions of order p ≠ 3 are non-analytic at Δx = 0. For even p there is a leading-order term proportional to [mid ]Δx[mid ] and for odd p > 3 the leading-order term ∝Δx has a non-analytic correction ∝Δx[mid ]Δx[mid ] stemming from shock mergers.

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