Gluon confinement criterion in QCD

We fix exactly and uniquely the infrared structure of the full gluon propagator in QCD, not solving explicitly the corresponding dynamical equation of motion. By construction, this structure is an infinite sum over all possible severe (i.e., more singular than $1/q^2$) infrared singularities. It reflects the zero momentum modes enhancement effect in the true QCD vacuum, which is due to the self-interaction of massless gluons. It existence automatically exhibits a characteristic mass (the so-called mass gap). It is responsible for the scale of nonperturbative dynamics in the true QCD ground state. The theory of distributions, complemented by the dimensional regularization method, allows one to put the severe infrared singularities under the firm mathematical control. By an infrared renormalization of a mass gap only, the infrared structure of the full gluon propagator is exactly reduced to the simplest severe infrared singularity, the famous $(q^2)^{-2}$. Thus we have exactly established the interaction between quarks (concerning its pure gluon (i.e., nonlinear) contribution) up to its unimportant perturbative part. This also makes it possible for the first time to formulate the gluon confinement criterion and intrinsically nonperturbative phase in QCD in a manifestly gauge-invariant ways.Comment: 10 pages, no figures, no tables. Typos corrected and the clarification is intoduced. Shorten version to appear in Phys. Lett.

Inference for threshold models with variance components from the generalized linear mixed model perspective

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Multi-scale Pore Network Modeling of a Reactive Packed Bed

In this study, we introduce a novel multi-scale Pore Network Model (PNM) designed to couple reactor-scale and particle-scale transport phenomena. To model reactor-scale phenomena, we employ a 3D reactor-scale PNM. This reactor-scale PNM is extracted from a packed column filled with spherical particles. Through analysis of the reactor-scale PNM, we obtain insight into the flow behavior of the reactor, which, in turn, is utilized for modeling species dispersion. For modeling particle-scale transport phenomena, we employ a 3D particle-scale PNM to simulate species diffusion and reaction within a spherical porous catalyst particle. This particle is represented with thousands of micro-spheres to represent the porous catalyst particles. The developed particle-scale PNM allows the treatment of realistic 3D boundary conditions on the catalyst particle’s surface. This paper presents an innovative methodology by combining the reactor-scale PNM with the particle-scale PNM, achieved through the incorporation of surface fragments. Both the reactor-scale and particle-scale PNMs have undergone thorough calibration and validation in our previous research (Fathiganjehlou et al. 2023; 2024). The developed multi-scale PNM offers a fast model capable of generating local partially resolved results for the catalytic packed bed reactor within a matter of minutes. This model lays the foundation for multi-scale pore network modeling of real packed bed reactors

The Effect of a Temperature-Dependent Viscosity on Cooling Droplet-Droplet Collisions

A detailed understanding of the collision dynamics of liquid droplets is relevant to natural phenomena and industrial applications. These droplets could experience temperature changes altering their physical properties, which affect the droplet collisions. As viscosity is one of the relevant physical properties, this study focuses on the effect of temperature on viscosity, with an Arrhenius temperature dependence, of collisions of two equal-sized droplets using the Volume of Fluid Method. The results show that the higher temperature of the droplets leads to an effectively lower viscosity, leading to increased interface oscillations. This leads to the onset of separation at lower Weber numbers as expected. The local cooling droplets will create a local viscosity profiles, which results in the formation of a ridge upon combination of droplets. In addition, the collision outcomes sometimes cannot be explained solely on basis of an effective viscosity, undermining the usefulness of existing collision regime maps