INVESTIGATION OF SPONTANEOUS CHIRAL-SYMMETRY BREAKING FROM LATTICE QCD WITH MASSLESS QUARKS

2007 ◽  
Vol 22 (07n10) ◽  
pp. 491-498
Author(s):  
XIANG-QIAN LUO
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Dirac Operator ◽  
Lattice Qcd ◽  
Probability Distribution Function ◽  
Function Method ◽  
Chiral Symmetry Breaking ◽  
Chiral Condensate ◽  
Massless Limit ◽  
Massless Dirac Operator

We apply the probability distribution function method to the study of chiral properties of QCD with quarks in the exact massless limit. A relation among the chiral condensate, zeros of the Bessel function and eigenvalue of Dirac operator is also given. The chiral condensate in this limit can be measured with small number of eigenvalues of the massless Dirac operator and without any ambiguous mass extrapolation. Results for lattice QCD with Kogut-Susskind quarks are shown.

The probability distribution function of structure factors with non-integral indices. III. The joint probability distribution in the P1¯ case

1999 ◽  
Vol 55 (2) ◽  
pp. 322-331 ◽  
Author(s):  
Carmelo Giacovazzo ◽  
Dritan Siliqi ◽  
Angela Altomare ◽  
Giovanni Luca Cascarano ◽  
Rosanna Rizzi ◽  
...  
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Function Method ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Conditional Distributions ◽  
Structure Factors ◽  
Joint Probability Distribution Function ◽  
Atomic Parameters

The joint probability distribution function method has been developed in P1¯ for reflections with rational indices. The positional atomic parameters are considered to be the primitive random variables, uniformly distributed in the interval (0, 1), while the reflection indices are kept fixed. Owing to the rationality of the indices, distributions like P(F p 1 , F p 2 ) are found to be useful for phasing purposes, where p 1 and p 2 are any pair of vectorial indices. A variety of conditional distributions like P(|F p 1 | | |F p 2 |), P(|F p 1 | |F p 2 ), P(\varphi_{{\bf p}_1}|\,|F_{{\bf p}_1}|, F_{{\bf p}_2}) are derived, which are able to estimate the modulus and phase of F p 1 given the modulus and/or phase of F p 2 . The method has been generalized to handle the joint probability distribution of any set of structure factors, i.e. the distributions P(F 1, F 2,…, F n+1), P(|F 1| |F 2,…, F n+1) and P(\varphi1| |F|1, F 2,…, F_{n+1}) have been obtained. Some practical tests prove the efficiency of the method.

Develop Probability Distribution Function to Select Pavement Preventive Maintenance Materials and Methods

2011 ◽  
Vol 255-260 ◽  
pp. 3450-3453
Author(s):  
Mohammad M. Khabiri
Keyword(s):  
Decision Making ◽  
Distribution Function ◽  
Probability Distribution ◽  
Preventive Maintenance ◽  
Probability Distribution Function ◽  
Function Method ◽  
Probability Function ◽  
Useful Life ◽  
Process Cost ◽  
Maintenance Process

Maintenance and protection of road pavements are one of important tasks of highway agencies. Many studies are done about specifying suitable time for pavement preventive maintenance. The probability distribution isn't used in this study, although the significant factor in decision making is relevant to probability function. In present paper, the suitable time between two preventive repairs is determined by Erlangen probability distribution function method. Economical factors are one of important parameters in this method, so, maintenance and repairing process cost, the useful life of maintenance process and the cutting of traffic flow are applied in calculation of suggested method.

scholarly journals An Online Application for ΔR Calculation

Radiocarbon ◽  
2016 ◽  
Vol 59 (5) ◽  
pp. 1623-1627 ◽  
Author(s):  
Ron W Reimer ◽  
Paula J Reimer
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Calibration Curve ◽  
Probability Distribution Function ◽  
Museum Collections ◽  
Online Program ◽  
Online Application ◽  
Radiocarbon Calibration

AbstractA regional offset (ΔR) from the marine radiocarbon calibration curve is widely used in calibration software (e.g. CALIB, OxCal) but often is not calculated correctly. While relatively straightforward for known-age samples, such as mollusks from museum collections or annually banded corals, it is more difficult to calculate ΔR and the uncertainty in ΔR for 14C dates on paired marine and terrestrial samples. Previous researchers have often utilized classical intercept methods that do not account for the full calibrated probability distribution function (pdf). Recently, Soulet (2015) provided R code for calculating reservoir ages using the pdfs, but did not address ΔR and the uncertainty in ΔR. We have developed an online application for performing these calculations for known-age, paired marine and terrestrial 14C dates and U-Th dated corals. This article briefly discusses methods that have been used for calculating ΔR and the uncertainty and describes the online program deltar, which is available free of charge.

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

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