scholarly journals Third-order perturbation expansion of the two-point correlation function of the dissipative quantum φ4 theory

2021 ◽  
Vol 104 (7) ◽  
Author(s):  
Panagiotis V. Alatas ◽  
Vlasis G. Mavrantzas ◽  
Hans Christian Öttinger
Keyword(s):  
Correlation Function ◽  
Perturbation Expansion ◽  
Order Perturbation ◽  
Third Order ◽  
Point Correlation ◽  
Point Correlation Function

scholarly journals Bounds on the Effective Transport and Elastic Properties of a Random Array of Cylindrical Fibers in a Matrix

1988 ◽  
Vol 55 (2) ◽  
pp. 347-354 ◽  
Author(s):  
S. Torquato ◽  
F. Lado
Keyword(s):  
Correlation Function ◽  
Upper And Lower Bounds ◽  
Third Order ◽  
Volume Fractions ◽  
The Third ◽  
Plastic Composite ◽  
Wide Range ◽  
Effective Transport ◽  
Point Correlation ◽  
Point Correlation Function

This paper studies the determination of rigorous upper and lower bounds on the effective transport and elastic moduli of a transversely isotropic fiber-reinforced composite derived by Silnutzer and by Milton. The third-order Silnutzer bounds on the transverse conductivity σe, the transverse bulk modulus ke, and the axial shear modulus μe, depend upon the microstructure through a three-point correlation function of the medium. The fourth-order Milton bounds on σe and μe depend not only upon three-point information but upon the next level of information, i.e., a four-point correlation function. The aforementioned microstructure-sensitive bounds are computed, using methods and results of statistical mechanics, for the model of aligned, infinitely long, equisized, circular cylinders which are randomly distributed throughout a matrix, for fiber volume fractions up to 65 percent. For a wide range of volume fractions and phase property values, the Silnutzer bounds significantly improve upon corresponding second-order bounds due to Hill and to Hashin; the Milton bounds, moreover, are narrower than the third-order Silnutzer bounds. When the cylinders are perfectly conducting or perfectly rigid, it is shown that Milton’s lower bound on σe or μe provides an excellent estimate of these effective parameters for the wide range of volume fractions studied here. This conclusion is supported by computer-simulation results for σe and by experimental data for a graphite-plastic composite.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals A two-point correlation function for Galactic halo stars

2011 ◽  
Vol 417 (3) ◽  
pp. 2206-2215 ◽  
Author(s):  
A. P. Cooper ◽  
S. Cole ◽  
C. S. Frenk ◽  
A. Helmi
Keyword(s):  
Correlation Function ◽  
Galactic Halo ◽  
Halo Stars ◽  
Point Correlation ◽  
Point Correlation Function

scholarly journals TOWARDS THE PROOF OF AGT-W RELATION: TODA 3-POINT FUNCTION AND ${\mathcal W}_{1+\infty}$ ALGEBRA

2013 ◽  
Vol 21 ◽  
pp. 138-139
Author(s):  
SHOTARO SHIBA
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Point Function ◽  
Gauge Groups ◽  
Promising Direction ◽  
Quiver Gauge Theory ◽  
Conformal Theory ◽  
Conformal Field ◽  
Point Correlation ◽  
Point Correlation Function

The AGT-W relation is a conjecture of the nontrivial duality between 4-dim quiver gauge theory and 2-dim conformal field theory. We verify a part of this conjecture for all the cases of quiver gauge groups by studying on the property of 3-point correlation function of conformal theory. We also mention the relation to [Formula: see text] algebra as one of the promising direction towards the proof of the remaining part.

scholarly journals A general treatment of snow microstructure exemplified by an improved relation for the thermal conductivity

2012 ◽  
Vol 6 (6) ◽  
pp. 4673-4693 ◽  
Author(s):  
H. Löwe ◽  
F. Riche ◽  
M. Schneebeli
Keyword(s):  
Thermal Conductivity ◽  
Correlation Function ◽  
Pore Space ◽  
Anisotropy Parameter ◽  
Micro Computed Tomography ◽  
Data Set ◽  
Microstructural Parameters ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Snow Microstructure

Abstract. Finding relevant microstructural parameters beyond the density is a longstanding problem which hinders the formulation of accurate parametrizations of physical properties of snow. Towards a remedy we address the effective thermal conductivity tensor of snow via known anisotropic, second-order bounds. The bound provides an explicit expression for the thermal conductivity and predicts the relevance of a microstructural anisotropy parameter Q which is given by an integral over the two-point correlation function and unambiguously defined for arbitrary snow structures. For validation we compiled a comprehensive data set of 167 snow samples. The set comprises individual samples of various snow types and entire time series of metamorphism experiments under isothermal and temperature gradient conditions. All samples were digitally reconstructed by micro-computed tomography to perform microstructure-based simulations of heat transport. The incorporation of anisotropy via Q considerably reduces the root mean square error over the usual density-based parametrization. The systematic quantification of anisotropy via the two-point correlation function suggests a generalizable route to incorporate microstructure into snowpack models. We indicate the inter-relation of the conductivity to other properties and outline a potential impact of Q on dielectric constant, permeability and adsorption rate of diffusing species in the pore space.

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