Development of a central-moment phase-field lattice Boltzmann model for thermocapillary flows: Droplet capture and computational performance

This study develops a computationally efficient phase-field lattice Boltzmann model with the capability to simulate thermocapillary flows. The model was implemented into the open-source simulation framework, waLBerla, and extended to conduct the collision stage using central moments. The multiphase model was coupled with both a passive-scalar thermal LB, and a RK solution to the energy equation in order to resolve temperature-dependent surface tension phenomena. Various lattice stencils (D3Q7, D3Q15, D3Q19, D3Q27) were tested for the passive-scalar LB and both the second- and fourth-order RK methods were investigated. There was no significant difference observed in the accuracy of the LB or RK schemes. The passive scalar D3Q7 LB discretisation tended to provide computational benefits, while the second order RK scheme is superior in memory usage. This paper makes contributions relating to the modelling of thermocapillary flows and to understanding the behaviour of droplet capture with thermal sources analogous to thermal tweezers. Four primary contributions to the literature are identified. First, a new 3D thermocapillary, central-moment phase-field LB model is presented and implemented in the open-source software, waLBerla. Second, the accuracy and computational performance of various techniques to resolve the energy equation for multiphase, incompressible fluids is investigated. Third, the dynamic droplet transport behaviour in the presence of thermal sources is studied and insight is provided on the potential ability to manipulate droplets based on local domain heating. Finally, a concise analysis of the computational performance together with near-perfect scaling results on NVIDIA and AMD GPU-clusters is shown. This research enables the detailed study of droplet manipulation and control in thermocapillary devices

CFT dual of the AdS Dirichlet problem: Fluid/Gravity on cut-off surfaces

We study the gravitational Dirichlet problem in AdS spacetimes with a view to understanding the boundary CFT interpretation. We define the problem as bulk Einstein's equations with Dirichlet boundary conditions on fixed timelike cut-off hypersurface. Using the fluid/gravity correspondence, we argue that one can determine non-linear solutions to this problem in the long wavelength regime. On the boundary we find a conformal fluid with Dirichlet constitutive relations, viz., the fluid propagates on a `dynamical' background metric which depends on the local fluid velocities and temperature. This boundary fluid can be re-expressed as an emergent hypersurface fluid which is non-conformal but has the same value of the shear viscosity as the boundary fluid. The hypersurface dynamics arises as a collective effect, wherein effects of the background are transmuted into the fluid degrees of freedom. Furthermore, we demonstrate that this collective fluid is forced to be non-relativistic below a critical cut-off radius in AdS to avoid acausal sound propagation with respect to the hypersurface metric. We further go on to show how one can use this set-up to embed the recent constructions of flat spacetime duals to non-relativistic fluid dynamics into the AdS/CFT correspondence, arguing that a version of the membrane paradigm arises naturally when the boundary fluid lives on a background Galilean manifold.Comment: 71 pages, 2 figures. v2: Errors in bulk metrics dual to non-relativistic fluids (both on cut-off surface and on the boundary) have been corrected. New appendix with general results added. Fixed typos. 82 pages, 2 figure

IL-9 production of naive CD4+ T cells depends on IL-2, is synergistically enhanced by a combination of TGF-beta and IL-4, and is inhibited by IFN-gamma

Dense CD4+ T cells isolated from naive mice produce only trace amounts of IL-9 when stimulated by immobilized anti-CD3 in combination with anti-CD28 Abs. In this situation, IL-9 production is significantly stimulated by TGF-beta and further enhanced by the addition of IL-4, which, by itself, has only a minimal influence. IFN-gamma was found to inhibit the enhancing effect of IL-4. However, increasing amounts of IL-4 in the presence of a constant concentration of IFN-gamma could overcome the inhibitory activity of IFN-gamma. The application of CD4+ T cells isolated from IL-2 knockout mice unequivocally revealed that IL-2 is essential for the production of IL-9 by T cells. In addition, the use of T cells from IL-4 knockout mice elucidated that the basic (IL-2 + TGF-beta) mediated IL-9 production is independent of IL-4. Therefore, our results demonstrate that optimal IL-9 production of naive dense CD4+ T cells is positively regulated at different levels: 1) by IL-2, which is essential for IL-9 secretion; 2) followed by TGF-beta, which promotes a considerable increase in IL-9 production above the level induced by IL-2; and 3) finally, by IL-4, which requires the presence of IL-2 and TGF-beta to strongly enhance the production of IL-9. IFN-gamma inhibits the production of IL-9 mainly at the level of IL-4 by neutralizing the effect of this cytokine

Multichannel SQUID system with integrated magnetic shielding for magnetocardiography of mice

A multichannel low transition temperature SQUID magnetometer system with integrated superconducting magnetic shielding is described,. which is intended for recording the magnetocardiogram (MCG) of mice in a biolaboratory environment. The Dewar has a horizontal warm bore surrounded by a superconducting niobium shield. The mouse is situated in the center of the warm bore close to the SQUID magnetometers while its MCG is measured. We have characterized the system by determining the shielding behavior of the magnetic shield and by measuring the magnetic noise. We determined the attenuation of an external magnetic dipole field to be better than 10(-6) in the warm bore and better than 10(-7) at the magnetometer positions. The magnetic flux density noise of the system above 10 Hz is 2.7 fT/root Hz, thus about twice as high as the intrinsic noise of the magnetometers. We determined the system performance by detecting the MCG of mice. Important physiological features like P-wave, QRS complex and T-wave could be resolved

Volatility Derivatives

Volatility derivatives are a class of derivative securities where the payoff explicitly depends on some measure of the volatility of an underlying asset. Prominent examples of these derivatives include variance swaps and VIX futures and options. We provide an overview of the current market for these derivatives. We also survey the early literature on the subject. Finally, we provide relatively simple proofs of some fundamental results related to variance swaps and volatility swaps.variance swap, volatility swap, realized variance, realized volatility, implied volatility