Strong coupling methods in QCD thermodynamics

For a long time, strong coupling expansions have not been applied systematically in lattice QCD thermodynamics, in view of the success of numerical Monte Carlo studies. The persistent sign problem at finite baryo-chemical potential, however, has motivated investigations using these methods, either by themselves or combined with numerical evaluations, as a route to finite density physics. This article reviews the strategies, by which a number of qualitative insights have been attained, notably the emergence of the hadron resonance gas or the identification of the onset transition to baryon matter in specific regions of the QCD parameter space. For the simpler case of Yang–Mills theory, the deconfinement transition can be determined quantitatively even in the scaling region, showing possible prospects for continuum physics.

Gluon shadowing and nuclear entanglement entropy

Relying on previous results, that link entanglement entropy and parton distribution functions in deep inelastic scattering, and focusing on the small Bjorken scaling region we present here indications that gluon shadowing might indeed be explained as due to a depletion of the entanglement entropy, between observed and unobserved degrees of freedom, per nucleon within a nucleus, with respect to the free nucleon. We apply to gluon shadowing the general Page approach to the calculation of the entanglement entropy in bipartite systems, giving physical motivations of the results.

In the Vicinity of the Critical Points

Chapter 15 introduces the notion of the scaling region near the critical points, identified by the deformations of the critical action by means of the relevant operators. The renormalization group flows that originate from these deformations are subjected to important constraints, which can be expressed in terms of sum-rules. This chapter also discusses the nature of the perturbative series based on the conformal theories. Further, it describes how the analysis of the off-critical theories poses a series of interesting questions, and also covers ultraviolet divergences, structure constants, the two-point function of the Yang–Lee model, the RG and β‎-functions and the c-theorem.

Truncated Hilbert Space Approach

Chapter 25 covers the Truncated Hilbert Space Approach provides a very efficient numerical algorithm to study many properties of a perturbed conformal field theory defined on a finite geometry, typically an infinite cylinder of radius R. These include the masses of the various excitations, their number below threshold, the presence of false vacua and resonances, on-shell three-particle coupling, etc. The implementation of this approach does not depend on the integrability of the off-critical model and therefore it is a very useful tool to extend study to the entire scaling region around the critical point. This chapter discusses the basis of such an algorithm and provides some interesting applications thereof.

A NOVEL METHOD TO IDENTIFY THE SCALING REGION OF ROUGH SURFACE PROFILE

Scaling region identification is of great importance in calculating the fractal dimension of a rough surface profile. A new method used to identify the scaling region is presented to improve the calculation accuracy of fractal dimension. In this method, the second derivative of the double logarithmic curve is first calculated and the [Formula: see text]-means algorithm method is adopted to identify the scaling region for the first time. Then the margin of error is reasonably set to get a possible scaling region. Finally, the [Formula: see text]-means method is used again to obtain a more accurate scaling region. The effectiveness of the proposed method is compared with the existing methods. Both the simulation and experimental results show that the proposed method provides more precise results for extracting the scaling regions and leads to a higher calculation precision of fractal dimensions.

Effect of Orifice Geometry on the Development of Slightly Heated Turbulent Jets

Passive scalar (temperature) mixing with different orifice geometries is considered at low Reynolds number. The kinetic energy dissipation rate shows that the three jets achieve a self-similar state quickly compared to a nozzle jet. Scalar dissipation evolves faster to the self-preserving state than kinetic energy dissipation and the asymptotic value of the normalized kinetic and scalar dissipation on the jet centerline can be predicted. Taylor and Corrsin microscales start evolving linearly with x/D as early as x/D = 10. Normalized spectra using these length scales continue to evolve for the circular jet and collapse faster for the six-lobe jet, when Rλ reach a constant value. The scaling factor and range for the velocity and the scalar suggest that the scaling region “similar to the inertial range” reaches equilibrium before small scales reach complete equilibrium. The use of multilobe jets promotes the development toward a complete self-preserving state for the scalar field.