Thermodynamic consistency of liquid-gas lattice Boltzmann simulations

Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multi-phase fluid systems. However, the underlying second order analysis of the equation of motion has long been known to be insufficient to consistently derive the fourth order terms that are necessary to represent an extended interface. These same terms are also responsible for thermodynamic consistency, i.e. to obtain a true equilibrium solution with both a constant chemical potential and a constant pressure. In this article we present an equilibrium analysis of non-ideal lattice Boltzmann methods of sufficient order to identify those higher order terms that lead to a lack of thermodynamic consistency. We then introduce a thermodynamically consistent forcing method.Comment: 12 pages, 8 figure

Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath

The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed.Comment: 31 pages, 19 figures accepted: Applied Mathematical Modellin

Kaon production from 1 to 40 A GeV

Kaon production is studied within the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) model. Results are compared with experiment and with other models. The influence of the kaon potential on the kaon azimuthal distributions at SIS energies is considered. We also discuss the role of the many-body collisions at high-density phase of reaction.Comment: 6 pages, 4 figures, Proc. of the Int. Workshop on Hot and Dense Matter in Relativistic Heavy Ion Collisions, 09-12.04.2006, Budapes

Kaon and Pion production in relativistic heavy-ion collisions

The BUU transport model is applied to study strangeness and pion production in nucleus-nucleus collisions. Starting from proton induced reactions, we further investigate Si+Au, Au+Au and Pb+Pb collisions in the energy range between 2 and 40 A$\cdot$GeV and compare with data and with other transport calculations. The $q \bar q$ annihilation, or resonance, channel simulated by the string model in meson-nucleon collisions at $\sqrt{s} > 2$ GeV is introduced. The importance of this channel for a good description of the proton-nucleus data on $K^+$ production is demonstrated. We, furthermore, show that the meson-meson collisions contribute significantly to the $K \bar K$ production in heavy-ion collisions above 5 A GeV and improve an agreement with data on the $K^+/\pi^+$ ratio. Finally, we study the influence of the in-medium modifications of the FRITIOF model on the pion and kaon production.Comment: 20 pages, 25 figures, added statistical errors in figure

Timelike deeply virtual Compton scattering with a linearly polarized real (or quasi-real) photon beam

We calculate timelike virtual Compton scattering amplitudes in the generalized Bjorken scaling regime and focus on a new polarization asymmetry in the scattering process with a linearly polarized photon beam in the medium energy range, which will be studied intensely at JLab12 experiments. We demonstrate that new observables help us to access the polarized quark and gluon generalized parton distributions $\tilde H(x, \xi, t)$ and $\tilde E(x, \xi, t)$.Comment: To appear in the proceedings XXII. International Workshop on Deep Inelastic Scattering and Related Subjects (DIS 2014), 28 April - 2 May 2014, Warsaw, Polan

Spin coating of an evaporating polymer solution

We consider a mathematical model of spin coating of a single polymer blended in a solvent. The model describes the one-dimensional development of the thin layer of the mixture as the layer thins due to flow created by a balance of viscous forces and centrifugal forces and due to evaporation of the solvent. In the model both the diffusivity of the solvent in the polymer and the viscosity of the mixture are very rapidly varying functions of the solvent volume fraction. Guided by numerical solutions an asymptotic analysis reveals a number of different possible behaviours of the thinning layer dependent on the nondimensional parameters describing the system.\ud \ud The main practical interest is in controlling the appearance and development of a ``skin'' on the polymer where the solvent concentration reduces rapidly on the outer surface leaving the bulk of the layer still with high concentrations of solvent. The critical parameters controlling this behaviour are found to be $\epsilon$ the ratio of the diffusion to advection time scales, $\delta$ the ratio of the evaporation to advection time scales and $\exp(\gamma)$, the ratio of the diffusivity of the initial mixture and the pure polymer. In particular, our analysis shows that for very small evaporation with $\delta << \exp(-3/(4\gamma)) \epsilon^{3/4}$ skin formation can be prevented

Kaon production from 1 to 40 A GeV

Kaon production is studied within the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) model. Results are compared with experiment and with other models. The influence of the kaon potential on the kaon azimuthal distributions at SIS energies is considered. We also discuss the role of the many-body collisions at high-density phase of reaction.Comment: 6 pages, 4 figures, Proc. of the Int. Workshop on Hot and Dense Matter in Relativistic Heavy Ion Collisions, 09-12.04.2006, Budapes

Liquid rocket metal tanks and tank components

Significant guidelines are presented for the successful design of aerospace tanks and tank components, such as expulsion devices, standpipes, and baffles. The state of the art is reviewed, and the design criteria are presented along with recommended practices. Design monographs are listed

A perturbation analysis of existing resonant satellites

Perturbation analysis of existing resonant satellite