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We studied the COVID-19 pandemic evolution in selected African countries. For each country considered, we modeled simultaneously the data of the active, recovered and death cases. In this study, we used a year of data since the first cases were reported. We estimated the time-dependent basic reproduction numbers, $R_0$, and the fractions of infected but unaffected populations, to offer insights into containment and vaccine strategies in African countries. We found that $R_0\leq 4$ at the start of the pandemic but has since fallen to $R_0 \sim 1$. The unaffected fractions of the populations studied vary between $1-10$\% of the recovered cases., 27 pages, 9 figures and 1 table

Non-equilibrium dynamics for relativistic fluid or quark gluon plasma (QGP) have already been calculated earlier upto third order using both kinetic and thermodynamic approaches. Calculations presented in this manuscript are based on thermodynamics principles. The expressions for third order dissipative fluxes have been derived from equation for entropy 4-current developed earlier by A. Muronga. The relaxation equations in the present work have been developed in a simple Bjorken (1+1)D scenario and Eckart frame. The relaxation equations are found to have slightly different values for the coupling coefficients as compared to calculations from earlier models. The solutions to the differential equations have been found to be sensitive to values of these coefficients. The shear relaxation equations derived in third order theory are discussed term by term. Effects of third order theory on shear relaxation time has been discussed. Thermodynamic quantities related to hot and dense matter have been calculated as functions of proper time. Moreover, various initial conditions for the relaxation equations have been assumed to study their effects on above mentioned observables. A LHC QGP formation time of $\tau_0$ = 0.4 fm/c and temperature of T$_0$ = 500 MeV have been assumed., Comment: 15 pages, 16 figures (Fig. 6 is with two plots)

Relativistic dissipative hydrodynamic equations are extended by taking into account particle number changing processes in a gluon system, which expands in one dimension boost-invariantly. Chemical equilibration is treated by a rate equation for the particle number density based on Boltzmann equation and Grad's ansatz for the off-equilibrium particle phase space distribution. We find that not only the particle production, but also the temperature and the momentum spectra of the gluon system, obtained from the hydrodynamic calculations, are sensitive to the rates of particle number changing processes. Comparisons of the hydrodynamic calculations with the transport ones employing the parton cascade BAMPS show the inaccuracy of the rate equation at large shear viscosity to entropy density ratio. To improve the rate equation, the Grad's ansatz has to be modified beyond the second moments in momentum., Comment: 20 pages, 11 figures

We investigate the dependence of hadronic ratios on the baryon number using a thermal model incorporating exact baryon number and strangeness conservation.

In order to evaluate qualitatively the space-time evolution of hot and dense nuclear matter the underlying equation of state and transport coefficients must be known. In this study a specific equation of state is studied: the pion gas. The classical or standard transport coefficients, namely the bulk viscosity, shear viscsoity and thermal conductivity are devided by the relaxation times for the corresponding dissipative fluxes and then studied as functions of mass to temperature ratio., 5 pages, Strange Quark Matter 2007, Levoca, Slovakia

We use the generalized entropy four-current of the Muller-Israel-Stewart (MIS) theory of relativistic dissipative fluids to obtain information about fluctuations around equilibrium. This allows one to compute the non-classical coefficients of the entropy 4-flux in terms of the equilibrium distribution functions. The Green-Kubo formulae are used to compute the classical or standard transport coefficients from the fluctuations of entropy due to dissipative fluxes., 8 pages, Zimanyi 75 Memorial Workshop on Hadronic and Quark Matter, Budapest, Hungary, 2007

Relativistic nonideal fluid dynamics is formulated in $3+1$ space-time dimensions. The equations governing dissipative relativistic hydrodynamics are given in terms of the time and three-space quantities which correspond to those familiar from nonrelativistic physics. Dissipation is accounted for by applying the causal theory of relativistic dissipative fluid dynamics. As a special case, we consider a fluid without viscous/heat couplings in the causal system of transport/relaxation equations. For the study of physical systems, we consider pure ($1+1$)-dimensional expansion in planar geometry, ($1+1$)-dimensional spherically symmetric (fireball) expansion, ($1+1$)-dimensional cylindrically symmetric expansion, and a ($2+1$)-dimensional expansion with cylindrical symmetry in the transverse plane (firebarrel expansion). The transport/relaxation equations are given in terms of the spatial components of the dissipative fluxes, since these are not independent. The choice for the independent components is analogous to the nonrelativistic equations.

We study the role of viscosity in the early stages of relativistic heavy ion collisions. We investigate the role of viscosity on the chemical equilibration of a parton gas. In the presence of viscosity the lifetime of the system is increased. The temperature as well as the parton fugacities evolve more slowly compared to the ideal fluid dynamics., Comment: 4 pages, Strange Quark Matter 2004, Cape Town, South Africa

In the causal theory of relativistic dissipative fluid dynamics, there are conditions on the equation of state and other thermodynamic properties such as the second-order coefficients of a fluid that need to be satisfied to guarantee that the fluid perturbations propagate causally and obey hyperbolic equations. The second-order coefficients in the causal theory, which are the relaxation times for the dissipative degrees of freedom and coupling constants between different forms of dissipation (relaxation lengths), are presented for partonic and hadronic systems. These coefficients involves relativistic thermodynamic integrals. The integrals are presented for general case and also for different regimes in the temperature--chemical potential plane. It is shown that for a given equation of state these second-order coefficients are not additional parameters but they are determined by the equation of state. We also present the prescription on the calculation of the freeze-out particle spectra from the dynamics of relativistic non-ideal fluids., 47 pages, 2 figures, added references, added typos

Non-equilibrium fluid dynamics derived from the extended irreversible thermodynamics of the causal M\"uller--Israel--Stewart theory of dissipative processes in relativistic fluids based on Grad's moment method is applied to the study of the dynamics of hot matter produced in ultra--relativistic heavy ion collisions. The temperature, energy density and entropy evolution are investigated in the framework of the Bjorken boost--invariant scaling limit. The results of these second order theories are compared to those of first order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler. In the presence of dissipation perfect fluid dynamics is no longer valid in describing the evolution of the matter. First order theories fail in the early stages of evolution. Second order theories give a better description in good agreement with transport models. It is shown in which region the Navier--Stokes--Fourier laws (first order theories) are a reasonable limiting case of the more general extended thermodynamics (second order theories)., Comment: 45 pages, 28 figures, corrected typos

Non‐ideal fluid dynamics is used to describe the space‐time evolution of matter produced in relativistic nuclear collisions such as those at RHIC in BNL and at LHC in CERN. Dissipation is accounted for by employing causal theory of relativistic dissipative fluid dynamics derived from extended irreversible thermodynamics. The results are compared to those obtained by using Navier‐Stokes theory and the ones obtained by perfect fluid approximation.

The transport coefficient of shear viscosity is studied for a hadron matter through microscopic transport model, the Ultra--relativistic Quantum Molecular Dynamics (UrQMD), using the Green--Kubo formulas. Molecular--dynamical simulations are performed for a system of light mesons in a box with periodic boundary conditions. Starting from an initial state composed of $\pi, \eta ,\omega ,\rho ,\phi$ with a uniform phase--space distribution, the evolution takes place through elastic collisions, production and annihilation. The system approaches a stationary state of mesons and their resonances, which is characterized by common temperature. After equilibration, thermodynamic quantities such as the energy density, particle density, and pressure are calculated. From such an equilibrated state the shear viscosity coefficient is calculated from the fluctuations of stress tensor around equilibrium using Green--Kubo relations. We do our simulations here at zero net baryon density so that the equilibration times depend on the energy density. We do not include hadron strings as degrees of freedom so as to maintain detailed balance. Hence we do not get the saturation of temperature but this leads to longer equilibration times., Comment: 15 pages, 17 figures, corrected typos

In the context of the M\"uller-Israel-Stewart second-order theory for dissipative fluids due to Grad, we analyze the effects of thermal conduction and viscosity in heavy ion collisions. We contrast the results to those of the first-order theory due to Eckart and to Landau and Lifshitz and to those of perfect (ideal) fluid due to Euler. We study the energy density and entropy density evolution of a pion gas produced in the heavy ion collisions. The truncated version of the second-order theory is used to find the dissipative quantities., Comment: 10 pages, 4 figures, Proceedings of the 17th Winter Workshop on Nuclear Dynamics, Park City, Utah, March 10-17, 2001

The M\"uller-Israel-Stewart second order theory of relativistic imperfect fluids based on Grad's moment method is used to study the expansion of hot matter produced in ultra-relativistic heavy ion collisions. The temperature evolution is investigated in the framework of the Bjorken boost-invariant scaling limit. The results of these second-order theories are compared to those of first-order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler., Comment: 5 pages, 4 figures, size of y-axis tick marks for Figs. 3 and 4 fixed

The recent notion of the perfect fluid created at the relativistic heavy ion collider (RHIC) has been embraced by many experimentalists and theorists alike. However, much of the evidence to this notion has been based on the success of describing some experimental observables by non-viscous hydrodynamics or by small shear viscosity to entropy density ratio. Developments on viscous hydrodynamics evolved from (0+1) dimensions (Bjorken scaling solution) over (1+1) dimensions (Bjorken + transverse flow) to (2+1) dimensions (elliptic flow) and currently (3+1) dimensions. There still exist some formal issues concerning the allowed form of the relativistic viscous hydrodynamic equations and what effects the new additional or higher order terms will have on the spacetime evolution and the experimental observables. Starting with a brief introduction of the basics of relativsitic fluid dynamics, I will discuss our current knowledge of relativistic theory of fluid dynamics in the presence of dissipative fluxes.

The ratio of shear viscosity to volume density of entropy has generated much interest even beyond RHIC and LHC physics. In this presentation, we focus on the dissipative fluxes/processes that might be responsible for entropy production. We compare the equilibrium entropy density to the non-equilibrium one.

Diversity, Equity, Inclusion, and Accessibility (DEIA) are not only called for to ensure morality and justice in our society, they also support ongoing and future excellence in particle physics. Over the past decade, the particle physics community has devised programs to support DEIA along multiple axes, and the way we think about measuring and implementing these initiatives has evolved. DEIA in physics is a broad topic, so in this paper we focus on the experiences of marginalized communities and outline ways different stakeholders can build a culture of equitable access for the success of marginalized individuals. Specifically, we identify urgent needs in the following areas: (1) We need to acquire a better understanding of the status quo, both quantitatively and qualitatively, to assess the effectiveness of existing programs and to develop best practices; (2) we need to develop effective and inclusive ways to engage marginalized communities; (3) we need to create infrastructure to better support members of marginalized communities, on an academic, financial and personal level; (4) we need to create an environment conducive to equitable access and success by establishing community expectations, fostering inclusion in social interactions, and holding individuals and institutions accountable; and (5) we need to establish a mechanism to monitor progress in the area of DEIA, including the implementation of the recommendations enumerated in this paper and others during the Snowmass 2021 process., Comment: Contribution to Snowmass 2021