288 research outputs found
Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique
We study QCD at finite density and low temperature by using the complex
Langevin method. We employ the gauge cooling to control the unitarity norm and
introduce a deformation parameter in the Dirac operator to avoid the
singular-drift problem. The reliability of the obtained results are judged by
the probability distribution of the magnitude of the drift term. By making
extrapolations with respect to the deformation parameter using only the
reliable results, we obtain results for the original system. We perform
simulations on a lattice and show that our method works well even
in the region where the reweighting method fails due to the severe sign
problem. As a result we observe a delayed onset of the baryon number density as
compared with the phase-quenched model, which is a clear sign of the Silver
Blaze phenomenon.Comment: 8 pages, 6 figures, presented at the 35th International Symposium on
Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spai
Testing the criterion for correct convergence in the complex Langevin method
Recently the complex Langevin method (CLM) has been attracting attention as a
solution to the sign problem, which occurs in Monte Carlo calculations when the
effective Boltzmann weight is not real positive. An undesirable feature of the
method, however, was that it can happen in some parameter regions that the
method yields wrong results even if the Langevin process reaches equilibrium
without any problem. In our previous work, we proposed a practical criterion
for correct convergence based on the probability distribution of the drift term
that appears in the complex Langevin equation. Here we demonstrate the
usefulness of this criterion in two solvable theories with many dynamical
degrees of freedom, i.e., two-dimensional Yang-Mills theory with a complex
coupling constant and the chiral Random Matrix Theory for finite density QCD,
which were studied by the CLM before. Our criterion can indeed tell the
parameter regions in which the CLM gives correct results.Comment: 16 pages, 2 figures; (v2) reference and comment added; (v3) minor
revision; (v4) final version published in JHE
Studies on the Power Requirement of Mixing Impellers (II) : Method of Measuring Power Consumption
Concentration Gradient in a Continuous Countercurrent Extraction Column with Longitudinal Back-Mixing
The following relations have been derived by the authors for the variation of concentration in a continuous countercurrent extraction column in which there is longitudinal back-mixing of the continuous phase, on the assumption that the diffusivity of the back-mixing and liquid velocity are constant and the solutions are dilute : When 1+β>0 Cc-α/Cc₀-α = (1+√1+β)e²ᵞ√¹⁺ᵝ⁽¹⁻ˣ/ᴸ⁾-(1-√1+β)2√1+βeᵞ⁽¹⁺√¹⁺ᵝ⁾⁽¹⁻ˣ/ᴸ⁾ and when 1+β<0 Cc-α/Cc₀-α = i√1+β cos[γi√1+β(1-x/L)]+sin[γi√1+β(1-x/L)]i√1+βeᵞ⁽¹⁻ˣ/ᴸ⁾ where : α = C*c₀-(mFc/Fd)Cc₀1-(mFc/Fd), β = 2MN/(M+NQ)², γ = M+NQ, M = Luc/2EcHc, N = Kcα′(1- mFc/Fd)(LHc/uc), Q = 1/2 1/(Fd/mFc)-1. The applicability of these equations is discussed, and the performance of an extraction column is analyzed
Criteria for the Scaling Up of Mixing Vessels
There are several concepts for the scaling up of mixing vessels. They are neither consistent nor conclusive. The authors propose an idea that the selection must be made depending upon the mixing objects. The classification of the types of scaling up is as follows : (1) Similarity for power requirement. Power requirement is correlated by Reynolds-, Froude- and Weber-numbers. The latter two are negligible in an ordinary correlation. (2) Similarity for mixing velocity of homogeneous liquid phase. The authors conclude that the similarity in blending speed is obtained by equal impeller speeds. (3) Similarity for heat and mass transfer on the fixed surface. Rushton et al. proposed the method of scaling-up by the following equation. (n₂/n₁)=(D₁/D₂)⁽²ˣ⁻¹⁾/ˣ This criterion should be limited in the case of the heat and mass transfer on a fixed surface. (4) Similarity for suspension of solid particles, dispersion of gas and liquid, and mass transfer on dispersed objects. The authors support the criterion of equal power per unit volume proposed by W.Büche
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