Class of dilute granular Couette flows with uniform heat flux

In a recent paper [F. Vega Reyes et al., Phys. Rev. Lett. 104, 028001 (2010)] we presented a preliminary description of a special class of steady Couette flows in dilute granular gases. In all flows of this class the viscous heating is exactly balanced by inelastic cooling. This yields a uniform heat flux and a linear relationship between the local temperature and flow velocity. The class (referred to as the LTu class) includes the Fourier flow of ordinary gases and the simple shear flow of granular gases as special cases. In the present paper we provide further support for this class of Couette flows by following four different routes, two of them being theoretical (Grad's moment method of the Boltzmann equation and exact solution of a kinetic model) and the other two being computational (molecular dynamics and Monte Carlo simulations of the Boltzmann equation). Comparison between theory and simulations shows a very good agreement for the non-Newtonian rheological properties, even for quite strong inelasticity, and a good agreement for the heat flux coefficients in the case of Grad's method, the agreement being only qualitative in the case of the kinetic model.Comment: 15 pages, 10 figures; v2: change of title plus some other minor change

Fluid/solid transition in a hard-core system

We prove that a system of particles in the plane, interacting only with a certain hard-core constraint, undergoes a fluid/solid phase transition

Entrepreneurship Education: A Global Consideration From Practice to Policy Around the World

As entrepreneurship continues to gain momentum and visibility as an engine of global economic development, it is critical to understand and optimize the role that entrepreneurship education plays. Based on a detailed review of the literature on the entrepreneurship education ecosystems and frameworks in the United States, China, Finland, and Qatar, this report identifies the current state of entrepreneurship education and training around the world, and establishes an inventory of best practices. The discussion of common themes across the four country cases, as well as examples of unique in-country qualities, provides recommendations and implications on which policy makers can act and experiment

EQUATION OF STATE OF CLASSICAL SYSTEMS OF CHARGED PARTICLES

Recent developments in the classical theory of fully ionized gases and strong electrolyte solutions are reviewed, and are used to discuss the equation of state at high temperature and low densities. The pressure is calculated using the ring-integral approximation, and quantitative estimates of higher correction terms are given. The effect of short-range repulsive forces is shown by comparing the results with two kinds of potential functions: hard spheres of diameter a, and "soft" spheres for which the short-range potential cancels the Coulomb potential at the origin, and decreases exponentially with distance. It is found that the use of either type of potential extends the range of validity of the ring integral approximation to considerably higher densities and lower temperatures. Since there is little difference in the results for the hard spheres and the soft spheres in this range, the latter is investigated more extensively since it is more easily handled by analytical methods. The expressions derived for the free energy of a system of charged particles can also be used in ionization equilibrium calculations, and the effect of electrostatic interactions on the equilibrium concentrations of various kinds of ions is indicated

Criticality in strongly correlated fluids

In this brief review I will discuss criticality in strongly correlated fluids. Unlike simple fluids, molecules of which interact through short ranged isotropic potential, particles of strongly correlated fluids usually interact through long ranged forces of Coulomb or dipolar form. While for simple fluids mechanism of phase separation into liquid and gas was elucidated by van der Waals more than a century ago, the universality class of strongly correlated fluids, or in some cases even existence of liquid-gas phase separation remains uncertain.Comment: Proceedings of Scaling Concepts and Complex Systems, Merida, Mexic

The Boltzmann Entropy for Dense Fluids Not in Local Equilibrium

We investigate, via computer simulations, the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables $M$ describing the system are the (empirical) particle density f=\{f(\un{x},\un{v})\} and the total energy $E$. We find that $S(f_t,E)$ is monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of $S(M_t) = S(M_{X_t})$ should hold generally for ``typical'' (the overwhelming majority of) initial microstates (phase-points) $X_0$ belonging to the initial macrostate $M_0$, satisfying $M_{X_0} = M_0$. This is a direct consequence of Liouville's theorem when $M_t$ evolves autonomously.Comment: 8 pages, 5 figures. Submitted to PR

‘Question Moments’: A Rolling Programme of Question Opportunities in Classroom Science

This article has been made available through the Brunel Open Access Publishing Fund.This naturalistic study integrates specific 'question moments' into lesson plans to increase pupils' classroom interactions. A range of teaching tools has explored students' ideas through opportunities to ask and write questions. Their oral and written outcomes provide data on individual and group misunderstandings. Changes to the schedule of lessons were introduced to discuss these questions and solve disparities. Flexible lesson planning over fourteen lessons across a four-week period of highschool chemistry accommodated students' contributions and increased student participation, promoted inquiring and individualised teaching, with each teaching strategy feeding forward into the next

Quasi-classical Molecular Dynamics Simulations of the Electron Gas: Dynamic properties

Results of quasi-classical molecular dynamics simulations of the quantum electron gas are reported. Quantum effects corresponding to the Pauli and the Heisenberg principle are modeled by an effective momentum-dependent Hamiltonian. The velocity autocorrelation functions and the dynamic structure factors have been computed. A comparison with theoretical predictions was performed.Comment: 8 figure

The dynamics of thin vibrated granular layers

We describe a series of experiments and computer simulations on vibrated granular media in a geometry chosen to eliminate gravitationally induced settling. The system consists of a collection of identical spherical particles on a horizontal plate vibrating vertically, with or without a confining lid. Previously reported results are reviewed, including the observation of homogeneous, disordered liquid-like states, an instability to a `collapse' of motionless spheres on a perfect hexagonal lattice, and a fluctuating, hexagonally ordered state. In the presence of a confining lid we see a variety of solid phases at high densities and relatively high vibration amplitudes, several of which are reported for the first time in this article. The phase behavior of the system is closely related to that observed in confined hard-sphere colloidal suspensions in equilibrium, but with modifications due to the effects of the forcing and dissipation. We also review measurements of velocity distributions, which range from Maxwellian to strongly non-Maxwellian depending on the experimental parameter values. We describe measurements of spatial velocity correlations that show a clear dependence on the mechanism of energy injection. We also report new measurements of the velocity autocorrelation function in the granular layer and show that increased inelasticity leads to enhanced particle self-diffusion.Comment: 11 pages, 7 figure

Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments.

Starting from the Kramers equation for the phase-space dynamics of the N-body probability distribution, we derive a dynamical density functional theory (DDFT) for colloidal fluids including the effects of inertia and hydrodynamic interactions (HI). We compare the resulting theory to extensive Langevin dynamics simulations for both hard rod systems and three-dimensional hard sphere systems with radially symmetric external potentials. As well as demonstrating the accuracy of the new DDFT, by comparing with previous DDFTs which neglect inertia, HI, or both, we also scrutinize the significance of including these effects. Close to local equilibrium we derive a continuum equation from the microscopic dynamics which is a generalized Navier–Stokes-like equation with additional non-local terms governing the effects of HI. For the overdamped limit we recover analogues of existing configuration-space DDFTs but with a novel diffusion tensor