Tipstreaming of a drop in simple shear flow in the presence of surfactant

We have developed a multi-phase SPH method to simulate arbitrary interfaces containing surface active agents (surfactants) that locally change the properties of the interface, such the surface tension coefficient. Our method incorporates the effects of surface diffusion, transport of surfactant from/to the bulk phase to/from the interface and diffusion in the bulk phase. Neglecting transport mechanisms, we use this method to study the impact of insoluble surfactants on drop deformation and breakup in simple shear flow and present the results in a fluid dynamics video.Comment: Two videos are included for the Gallery of Fluid Motion of the APS DFD Meeting 201

Linear Support Vector Machines for Error Correction in Optical Data Transmission

Reduction of bit error rates in optical transmission systems is an important task that is difficult to achieve. As speeds increase, the difficulty in reducing bit error rates also increases. Channels have differing characteristics, which may change over time, and any error correction employed must be capable of operating at extremely high speeds. In this paper, a linear support vector machine is used to classify large-scale data sets of simulated optical transmission data in order to demonstrate their effectiveness at reducing bit error rates and their adaptability to the specifics of each channel. For the classification, LIBLINEAR is used, which is related to the popular LIBSVM classifier. It is found that is possible to reduce the error rate on a very noisy channel to about 3 bits in a thousand. This is done by a linear separator that can be built in hardware and can operate at the high speed required of an operationally useful decode

The Region of Validity of Homogeneous Nucleation Theory

We examine the region of validity of Langer's picture of homogeneous nucleation. Our approach is based on a coarse-grained free energy that incorporates the effect of fluctuations with momenta above a scale k. The nucleation rate I = A_k exp(-S_k) is exponentially suppressed by the action S_k of the saddle-point configuration that dominates tunnelling. The factor A_k includes a fluctuation determinant around this saddle point. Both S_k and A_k depend on the choice of k, but, for 1/k close to the characteristic length scale of the saddle point, this dependence cancels in the expression for the nucleation rate. For very weak first-order phase transitions or in the vicinity of the spinodal decomposition line, the pre-exponential factor A_k compensates the exponential suppression exp(-S_k). In these regions the standard nucleation picture breaks down. We give an approximate expression for A_k in terms of the saddle-point profile, which can be used for quantitative estimates and practical tests of the validity of homogeneous nucleation theory.Comment: 8 pages, 4 figures. v2: Final version with extended discussio

Numerical Study of Boundary Layer Interaction with Shocks: Method Improvement and Test Computation

The objective is the development of a high-order and high-resolution method for the direct numerical simulation of shock turbulent-boundary-layer interaction. Details concerning the spatial discretization of the convective terms can be found in Adams and Shariff (1995). The computer code based on this method as introduced in Adams (1994) was formulated in Cartesian coordinates and thus has been limited to simple rectangular domains. For more general two-dimensional geometries, as a compression corner, an extension to generalized coordinates is necessary. To keep the requirements or limitations for grid generation low, the extended formulation should allow for non-orthogonal grids. Still, for simplicity and cost efficiency, periodicity can be assumed in one cross-flow direction. For easy vectorization, the compact-ENO coupling algorithm as used in Adams (1994) treated whole planes normal to the derivative direction with the ENO scheme whenever at least one point of this plane satisfied the detection criterion. This is apparently too restrictive for more general geometries and more complex shock patterns. Here we introduce a localized compact-ENO coupling algorithm, which is efficient as long as the overall number of grid points treated by the ENO scheme is small compared to the total number of grid points. Validation and test computations with the final code are performed to assess the efficiency and suitability of the computer code for the problems of interest. We define a set of parameters where a direct numerical simulation of a turbulent boundary layer along a compression corner with reasonably fine resolution is affordable

The Loop Group of E8 and Targets for Spacetime

The dimensional reduction of the E8 gauge theory in eleven dimensions leads to a loop bundle in ten dimensional type IA string theory. We show that the restriction to the Neveu-Schwarz sector leads naturally to a sigma model with target space E8 with the ten-dimensional spacetime as the source. The corresponding bundle has a structure group the group of based loops, whose classifying space we study. We explore some consequences of this proposal such as possible Lagrangians and existence of flat connections.Comment: 17 pages, main section improved, change in title, reference and acknowledgement adde

Mystery of Excess Low Energy States in a Disordered Superconductor in a Zeeman Field

Tunneling density of states measurements of disordered superconducting (SC) Al films in high Zeeman fields reveal a significant population of subgap states which cannot be explained by standard BCS theory. We provide a natural explanation of these excess states in terms of a novel disordered Larkin-Ovchinnikov (dLO) phase that occurs near the spin-paramagnetic transition at the Chandrasekhar-Clogston critical field. The dLO superconductor is characterized by a pairing amplitude that changes sign at domain walls. These domain walls carry magnetization and support Andreev bound states, which lead to distinct spectral signatures at low energy.Comment: 5 pages, 4 figures, plus supplementary section describing methods (2 pages