Induced QCD and Hidden Local ZN Symmetry

We show that a lattice model for induced lattice QCD which was recently proposed by Kazakov and Migdal has a $Z_N$ gauge symmetry which, in the strong coupling phase, results in a local confinement where only color singlets are allowed to propagate along links and all Wilson loops for non-singlets average to zero. We argue that, if this model is to give QCD in its continuum limit, it must have a phase transition. We give arguments to support presence of such a phase transition

Near wall hemodynamics: Modelling the glycocalyx and the endothelial surface

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.In this paper a coarse-grained model for blood flow in small arteries is presented. Blood is modelled as a two-component incompressible fluid: the plasma and corpuscular elements dispersed in it. The latter are modelled as deformable liquid droplets having greater density and viscosity. Interfacial surface tension and membrane effects are present to mimic key properties and to avoid droplets’ coalescence. The mesoscopic model also includes the presence of the wavy wall, due to the endothelial cells and incorporates a representation of the glycocalyx, covering the vessel wall. The glycocalyx is modelled as a porous medium, the droplets being subjected to a repulsive elastic force when approaching it, during their transit. Preliminary simulations are intended to show the influence of the undulation on the wall together with that of the glycocalyx

Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann

On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as porous media or microfluidic devices. The possibility to specify the exact position of the boundary, independent of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow to freely specify the direction of the flux, and it should be straight forward to implement in three dimensions. Furthermore, especially for parallelized solvers it is of great advantage if the boundary condition can be applied locally, involving only information available on the current lattice site. We meet this need by describing in detail how to transfer the approach suggested by Zou and He to a D3Q19 lattice. The boundary condition acts locally, is independent of the details of the relaxation process during collision and contains no artificial slip. In particular, the case of an on-site no-slip boundary condition is naturally included. We test the boundary condition in several setups and confirm that it is capable to accurately model the velocity field up to second order and does not contain any numerical slip.Comment: 13 pages, 4 figures, revised versio

Asymptotics of Expansion of the Evolution Operator Kernel in Powers of Time Interval Δt\Delta t

The upper bound for asymptotic behavior of the coefficients of expansion of the evolution operator kernel in powers of the time interval \Dt was obtained. It is found that for the nonpolynomial potentials the coefficients may increase as $n!$. But increasing may be more slow if the contributions with opposite signs cancel each other. Particularly, it is not excluded that for number of the potentials the expansion is convergent. For the polynomial potentials \Dt-expansion is certainly asymptotic one. The coefficients increase in this case as $\Gamma(n \frac{L-2}{L+2})$, where $L$ is the order of the polynom. It means that the point \Dt=0 is singular point of the kernel.Comment: 12 pp., LaTe

On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure

Phase Transitions in SO(3) Lattice Gauge Theory

The phase diagram of SO(3) lattice gauge theory is investigated by Monte Carlo techniques on both symmetric and asymmetric lattices with a view (i) to understanding the relationship between the bulk transition and the deconfinement transition, and (ii) to resolving the current ambiguity about the nature of the high temperature phase. A number of tests, including an introduction of a magnetic field and measurement of different correlation functions in the phases with positive and negative values for the adjoint Polyakov line, lead to the conclusion that the two phases correspond to the same physical state. Studies on lattices of different sizes reveal only one phase transition for this theory on all of them and it appears to have a deconfining nature.Comment: Latex 19 pages, 9 figures. Minor changes in introduction and summary sections. The version that appeared in journa

Dual variables for the SU(2) lattice gauge theory at finite temperature

We study the three-dimensional SU(2) lattice gauge theory at finite temperature using an observable which is dual to the Wilson line. This observable displays a behaviour which is the reverse of that seen for the Wilson line. It is non-zero in the confined phase and becomes zero in the deconfined phase. At large distances, it's correlation function falls off exponentially in the deconfined phase and remains non-zero in the confined phase. The dual variable is non-local and has a string attached to it which creates a Z(2) interface in the system. It's correlation function measures the string tension between oppositely oriented Z(2) domains. The construction of this variable can also be made in the four-dimensional theory where it measures the surface tension between oppositely oriented Z(2) domains.Comment: 13 pages, LaTeX, 4 figures are included in the latex fil

Kirchhoff's Loop Law and the maximum entropy production principle

In contrast to the standard derivation of Kirchhoff's loop law, which invokes electric potential, we show, for the linear planar electric network in a stationary state at the fixed temperature,that loop law can be derived from the maximum entropy production principle. This means that the currents in network branches are distributed in such a way as to achieve the state of maximum entropy production.Comment: revtex4, 5 pages, 2 figure