On the closed-form output correlation function of power-law devices

1966 ◽  
Vol 54 (11) ◽  
pp. 1625-1626 ◽  
Author(s):  
M. Fukada ◽  
S. Rauch
Keyword(s):  
Correlation Function ◽  
Closed Form ◽  
Power Law

TESTING POWER-LAW RELAXATION SCENARIOS IN A METASTABLE LIQUID

2012 ◽  
Vol 26 (29) ◽  
pp. 1250146 ◽  
Author(s):  
BHASKAR SEN GUPTA ◽  
SHANKAR P. DAS
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Hard Sphere ◽  
Numerical Solutions ◽  
Packing Fraction ◽  
Equilibrium Density ◽  
Density Correlation ◽  
Density Correlation Function ◽  
Basic Model ◽  
The One

The renormalized dynamics described by the equations of nonlinear fluctuating hydrodynamics (NFH) treated at one loop order gives rise to the basic model of the mode coupling theory (MCT). We investigate here by analyzing the density correlation function, a crucial prediction of ideal MCT, namely the validity of the multi step relaxation scenario. The equilibrium density correlation function is calculated here from the direct solutions of NFH equations for a hard sphere system. We make first detailed investigation for the robustness of the correlation functions obtained from the numerical solutions by varying the size of the grid. For an optimum choice of grid size we analyze the decay of the density correlation function to identify the multi-step relaxation process. Weak signatures of two step power law relaxation is seen with exponents which do not match predictions from the one loop MCT. For the final relaxation stretched exponential (KWW) behavior is seen and the relaxation time grows with increase of density. But apparent power law divergences indicate a critical packing fraction much higher than the corresponding MCT predictions for a hard sphere fluid.

scholarly journals Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light cone

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Nils O. Abeling ◽  
Lorenzo Cevolani ◽  
Stefan Kehrein
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Light Cone ◽  
Relativistic Quantum ◽  
Initial State ◽  
Quantum Theories ◽  
Luttinger Model ◽  
Power Law Decay ◽  
Exactly Solvable ◽  
Exponentially Small

In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the correlation function of two local disjoint observables at different times if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

scholarly journals Comparison of Non-Parabolic Hydrodynamic Models Based On Different Band Structure Models

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 177-180
Author(s):  
Arlynn W. Smith ◽  
Kevin F. Brennan
Keyword(s):  
Dispersion Relation ◽  
Band Structure ◽  
Energy Range ◽  
Closed Form ◽  
Power Law ◽  
Hydrodynamic Model ◽  
Wide Energy Range ◽  
Hydrodynamic Models ◽  
Wide Energy ◽  
Extended Power

This paper presents two non-parabolic hydrodynamic model formulations suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship, (ℏk)2/2m = W(1+αW). The second formulation makes use of a power law, (ℏk)2/2m = xWy, for the dispersion relation. The non-parabolicity and energy range of the hydrodynamic model based on the Kane dispersion relation is limited. The power law formulation produces closed form coefficients similar to those under the parabolic band approximation but the carrier concentration can deviate. An extended power law dispersion relation is proposed to account for band structure effects, (ℏk)2/2m = xW1+yW. This dispersion relation closely matches the calculated band structure over a wide energy range and may lead to closed form coefficients for the hydrodynamic model.

scholarly journals DUGDALE-MAUGIS ADHESIVE NORMAL CONTACT OF AXISYMMETRIC POWER-LAW GRADED ELASTIC BODIES

2018 ◽  
Vol 16 (1) ◽  
pp. 9 ◽  
Author(s):  
Emanuel Willert
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Power Law ◽  
Analytic Solution ◽  
Normal Contact ◽  
Elastic Bodies ◽  
Tabor Parameter

A closed-form general analytic solution is presented for the adhesive normal contact of convex axisymmetric power-law graded elastic bodies using a Dugdale-Maugis model for the adhesive stress. The case of spherical contacting bodies is studied in detail. The known JKR- and DMT-limits can be derived from the general solution, whereas the transition between both can be captured introducing a generalized Tabor parameter depending on the material grading. The influence of the Tabor parameter and the material grading is studied.

scholarly journals Angular clustering of point sources at 150 MHz in the TGSS survey

2019 ◽  
Vol 485 (4) ◽  
pp. 5891-5896 ◽  
Author(s):  
Sandeep Rana ◽  
Jasjeet S Bagla
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Low Frequency ◽  
Point Sources ◽  
Radio Sources ◽  
Redshift Distribution ◽  
Intensity Mapping ◽  
Flux Limit ◽  
Sky Survey ◽  
Angular Correlation Function

Abstract We study the angular clustering of point sources in The GMRT (Giant Metrewave Radio Telescope) Sky Survey (TGSS). The survey at 150 MHz with δ > −53.5° has a sky coverage of 3.6π steradians, i.e. $90{{\ \rm per\ cent}}$ of the whole sky. We created subsamples by applying different total flux thresholds limit (Sflux ≫ 5σ) for good completeness and measured the angular correlation function ω(θ) of point sources at large scales (≥1°). We find that the amplitude of angular clustering is higher for brighter subsamples; this indicates that higher threshold flux samples are hosted by massive haloes and cluster strongly: this conclusion is based on the assumption that the redshift distribution of sources does not change with flux and this is supported by models of radio sources. We compare our results with other low-frequency studies of clustering of point sources and verify that the amplitude of clustering varies with the flux limit. We quantify this variation as a power-law dependence of the amplitude of correlation function with the flux limit. This dependence can be used to estimate foreground contamination due to clustering of point sources for low-frequency H i intensity mapping surveys for studying the epoch of reionization.

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