Finite size effects in classical string solutions of the Schrödinger geometry

Abstract We study finite size corrections to the semiclassical string solutions of the Schrödinger spacetime. We compute the leading order exponential corrections to the infinite size dispersion relation of the single spin giant magnon and of the single spin single spike solutions. The solutions live in a S3 subspace of the five-sphere and extent in the Schrödinger part of the metric. In the limit of zero deformation the finite size dispersion relations flow to the undeformed AdS5 × S5 counterparts and in the infinite size limit the correction term vanishes and the known infinite size dispersion relations are obtained.

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On finite size corrections to the dispersion relations of giant magnon and single spike on γ-deformed T 1,1

The European Physical Journal C ◽

10.1140/epjc/s10052-013-2312-2 ◽

2013 ◽

Vol 73 (3) ◽

Author(s):

M. Michalcik ◽

R. C. Rashkov

Keyword(s):

Finite Size ◽

Dispersion Relations ◽

Single Spike ◽

Finite Size Corrections

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Finite-size effects for single spike

Journal of High Energy Physics ◽

10.1088/1126-6708/2008/07/105 ◽

2008 ◽

Vol 2008 (07) ◽

pp. 105-105 ◽

Cited By ~ 16

Author(s):

Changrim Ahn ◽

P Bozhilov

Keyword(s):

Size Effects ◽

Finite Size ◽

Finite Size Effects ◽

Single Spike

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An experimental study of the onset of parametrically pumped surface waves in viscous fluids

Journal of Fluid Mechanics ◽

10.1017/s0022112095001169 ◽

1995 ◽

Vol 288 ◽

pp. 325-350 ◽

Cited By ~ 90

Author(s):

John Bechhoefer ◽

Valerie Ego ◽

Sebastien Manneville ◽

Brad Johnson

Keyword(s):

Surface Waves ◽

Size Effects ◽

Experimental Studies ◽

Finite Size ◽

Finite Depth ◽

Finite Size Effects ◽

Polar Fluid ◽

Faraday Instability ◽

Theoretical Predictions ◽

Finite Size Corrections

We measure the threshold accelerations necessary to excite surface waves in a vertically vibrated fluid container (the Faraday instability). Under the proper conditions, the thresholds and onset wavelengths agree with recent theoretical predictions for a laterally infinite, finite-depth container filled with a viscous fluid. Experimentally, we show that by using a viscous, non-polar fluid, the finite-size effects of sidewalls and the effects of surface contamination can be made negligible. We also show that finite-size corrections are of order h/L, where h is the fluid depth and L the container size. Based on these measurements, one can more easily interpret certain unexpected observations from previous experimental studies of the Faraday instability.

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Finite size corrections for the Johnson–Mehl–Avrami–Kolmogorov equation

Journal of Materials Research ◽

10.1557/jmr.1997.0020 ◽

1997 ◽

Vol 12 (1) ◽

pp. 124-132 ◽

Cited By ~ 36

Author(s):

L. E. Levine ◽

K. Lakshmi Narayan ◽

K. F. Kelton

Keyword(s):

Size Effects ◽

Finite Size ◽

Nucleation And Growth ◽

Growth Behavior ◽

Kolmogorov Equation ◽

Experimental Measurements ◽

Finite Size Effects ◽

Sample Shape ◽

Wide Range ◽

Finite Size Corrections

The Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation is frequently used to describe phase transformations involving nucleation and growth. The assumptions used in the derivation of this equation, however, are frequently violated when making experimental measurements; use of the JMAK equation for analyzing such data can often produce invalid results. Finite-size effects are among the most serious of these problems. We present modified analytic JMAK equations that correct for the finite-size effects and are roughly independent of both the sample shape and the shape of the growing nuclei. A comparison with computer simulations shows that these modified JMAK equations accurately reproduce the growth behavior over a wide range of conditions.

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