Metaphysics and Law

The dichotomy between questions of fact and questions of law serves as a starting point for the following discussion of the nature of legal reasoning. In the course of the dialogue the author notes similarities and dissimilarities between legal reasoning and philosophical and mathematical reasoning. In the end we are left with a clearer insight into the distinctive features of the adjudicative process

Thickness of the rim of an expanding lamella near the splash threshold

The evolution of the ejected liquid sheet, or lamella, created after impact of a liquid drop onto a solid surface is studied using high-speed video in order to observe the detailed time evolution of the thickness of the rim of the lamella. Since it has been suggested that splashing behavior is set at very early times after impact, we study early times up to D-0/U-0, where D-0 and U-0 are the diameter and speed of the impacting drop, respectively, for different liquid viscosities and impact speeds below the splashing threshold. Within the regime of our experiments, our results are not consistent with the idea that the lamella rim grows similar to the boundary layer thickness. Rather, we find that the rim thickness is always much larger than the boundary layer thickness, and that the rim thickness decreases with increasing impact speed. For lower impact speeds, the increase in the rim thickness is consistent with a root t response over the limited time range available, but the dependence is not simply proportional to root nu, where nu is the kinematic viscosity, and there is a strong dependence of the rim thickness on the impact speed U-0. Scaling of the rim height using a balance of inertial and surface tension forces provides some collapse of the data at lower impact speeds. We also observe an unusual plateau behavior in thickness versus time at higher impact speeds as we approach the splash threshold. (C) 2010 American Institute of Physics. [doi:10.1063/1.3313360

Manganese-oxidizing bacteria mediate the degradation of 17α-ethinylestradiol

Manganese (II) and manganese-oxidizing bacteria were used as an efficient biological system for the degradation of the xenoestrogen 17 alpha-ethinylestradiol (EE2) at trace concentrations. Mn(2+)-derived higher oxidation states of Mn (Mn(3+), Mn(4+)) by Mn(2+)-oxidizing bacteria mediate the oxidative cleavage of the polycyclic target compound EE2. The presence of manganese (II) was found to be essential for the degradation of EE2 by Leptothrix discophora, Pseudomonas putida MB1, P. putida MB6 and P. putida MB29. Mn(2+)-dependent degradation of EE2 was found to be a slow process, which requires multi-fold excess of Mn(2+) and occurs in the late stationary phase of growth, implying a chemical process taking place. EE2-derived degradation products were shown to no longer exhibit undesirable estrogenic activity

Magnetothermal and magnetorotational instabilities in hot accretion flows

In a hot, dilute, magnetized accretion flow, the electron mean-free path can be much greater than the Larmor radius, thus thermal conduction is anisotropic and along magnetic field lines. In this case, if the temperature decreases outward, the flow may be subject to a buoyancy instability (the magnetothermal instability, or MTI). The MTI amplifies the magnetic field, and aligns field lines with the radial direction. If the accretion flow is differentially rotating, the magnetorotational instability (MRI) may also be present. Using two-dimensional, time-dependent magnetohydrodynamic simulations, we investigate the interaction between these two instabilities. We use global simulations that span over two orders of magnitude in radius, centered on the region around the Bondi radius where the infall time of gas is longer than the growth time of both the MTI and MRI. Significant amplification of the magnetic field is produced by both instabilities, although we find that the MTI primarily amplifies the radial component, and the MRI primarily the toroidal component, of the field, respectively. Most importantly, we find that if the MTI can amplify the magnetic energy by a factor $F_t$, and the MRI by a factor $F_r$, then when the MTI and MRI are both present, the magnetic energy can be amplified by a factor of $F_t \cdot F_r$. We therefore conclude that amplification of the magnetic energy by the MTI and MRI operates independently. We also find that the MTI contributes to the transport of angular momentum, because radial motions induced by the MTI increase the Maxwell (by amplifying the magnetic field) and Reynolds stresses. Finally, we find that thermal conduction decreases the slope of the radial temperature profile. The increased temperature near the Bondi radius decreases the mass accretion rate.Comment: 8 pages, 9 figures, accepted by MNRA

Instabilities and waves in thin films of living fluids

We formulate the thin-film hydrodynamics of a suspension of polar self-driven particles and show that it is prone to several instabilities through the interplay of activity, polarity and the existence of a free surface. Our approach extends, to self-propelling systems, the work of Ben Amar and Cummings [Phys Fluids 13 (2001) 1160] on thin-film nematics. Based on our estimates the instabilities should be seen in bacterial suspensions and the lamellipodium, and are potentially relevant to the morphology of biofilms. We suggest several experimental tests of our theory.Comment: 4 pages, pdflatex, accepted for publication in Phys Rev Let

Water-based peeling of thin hydrophobic films

Inks of permanent markers and water-proof cosmetics create elastic thin films upon application on a surface. Such adhesive materials are deliberately designed to exhibit water-repellent behavior. Therefore, patterns made up of these inks become resistant to moisture and cannot be cleaned by water after drying. However, we show that sufficiently slow dipping of such elastic films, which are adhered to a substrate, into a bath of pure water allows complete removal of the hydrophobic coatings. Upon dipping, the air-water interface in the bath forms a contact line on the substrate, which exerts a capillary-induced peeling force at the edge of the hydrophobic thin film. We highlight that this capillary peeling process is more effective at lower velocities of the air-liquid interface and lower viscosities. Capillary peeling not only removes such thin films from the substrate but also transfers them flawlessly onto the air-water interface

A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics

We describe a new Godunov algorithm for relativistic magnetohydrodynamics (RMHD) that combines a simple, unsplit second order accurate integrator with the constrained transport (CT) method for enforcing the solenoidal constraint on the magnetic field. A variety of approximate Riemann solvers are implemented to compute the fluxes of the conserved variables. The methods are tested with a comprehensive suite of multidimensional problems. These tests have helped us develop a hierarchy of correction steps that are applied when the integration algorithm predicts unphysical states due to errors in the fluxes, or errors in the inversion between conserved and primitive variables. Although used exceedingly rarely, these corrections dramatically improve the stability of the algorithm. We present preliminary results from the application of these algorithms to two problems in RMHD: the propagation of supersonic magnetized jets, and the amplification of magnetic field by turbulence driven by the relativistic Kelvin-Helmholtz instability (KHI). Both of these applications reveal important differences between the results computed with Riemann solvers that adopt different approximations for the fluxes. For example, we show that use of Riemann solvers which include both contact and rotational discontinuities can increase the strength of the magnetic field within the cocoon by a factor of ten in simulations of RMHD jets, and can increase the spectral resolution of three-dimensional RMHD turbulence driven by the KHI by a factor of 2. This increase in accuracy far outweighs the associated increase in computational cost. Our RMHD scheme is publicly available as part of the Athena code.Comment: 75 pages, 28 figures, accepted for publication in ApJS. Version with high resolution figures available from http://jila.colorado.edu/~krb3u/Athena_SR/rmhd_method_paper.pd