Controlling the partial coalescence of a droplet on a vertically vibrated bath

A new method is proposed to stop the cascade of partial coalescences of a droplet laid on a liquid bath. The strategy consists in vibrating the bath in the vertical direction in order to keep small droplets bouncing. Since large droplets are not able to bounce, they partially coalesce until they reach a critical size. The system behaves as a low pass filter : droplets smaller than the critical size are selected. This size has been investigated as a function of the acceleration and the frequency of the bath vibration. Results suggest that the limit size for bouncing is related to the first mode of the droplet deformation.Comment: 4 pages, 3 figures, accepted in Phys. Rev.

Asymmetry-Driven Structure Formation in Pair Plasmas

The nonlinear propagation of electromagnetic waves in pair plasmas, in which the electrostatic potential plays a very important but subdominant role of a "binding glue" is investigated. Several mechanisms for structure formation are investigated, in particular, the "asymmetry" in the initial temperatures of the constituent species. It is shown that the temperature asymmetry leads to a (localizing) nonlinearity that is new and qualitatively different from the ones originating in ambient mass or density difference. The temperature asymmetry driven focusing-defocusing nonlinearity supports stable localized wave structures in 1-3 dimensions, which, for certain parameters, may have flat-top shapes.Comment: 23 pages, 6 figures, introduction revised, edited typos, accepted for publication in Phys. Rev.

Vortex Bubble Formation in Pair Plasmas

It is shown that delocalized vortex solitons in relativistic pair plasmas with small temperature asymmetries can be unstable for intermediate intensities of the background electromagnetic field. Instability leads to the generation of ever-expanding cavitating bubbles in which the electromagnetic fields are zero. The existence of such electromagnetic bubbles is demonstrated by qualitative arguments based on a hydrodynamic analogy, and by numerical solutions of the appropriate Nonlinear Schr\"odinger equation with a saturating nonlinearity.Comment: 4 pages of two-column text, 2 figure

Influence of Natural Convection During Dendritic Array Growth of Metal Alloys (Gradient Freeze Directional Solidification)

Purpose of this study was to examine the microstructural evolution of primary dendrites during Gradient Freeze Directional Solidification process in cylindrical Pb-5.8% Sb alloy samples to generate the ground- based research data to support a future microgravity experiment on the Space Station in a convection free environment. Pb-5.8Sb was selected for this study because of its ease of processing and availability of physical property data which will be required for predicting the dendrite morphology parameters, such as, primary dendrite spacing and dendrite trunk diameter. This alloy is also susceptible to thermosolutal convection caused by density inversion of the met in the mushy-zone during DS with melt on top and solid below (gravity pointing down). Two furnace cooling rates, 0.5 C/min and 4 C/min were utilized during the gradient freeze DS. Morphology of primary dendrites was observed to change from being branch-less (cellular) in the very beginning of DS, to those showing onset of side-branching, and finally to well-branched tree-like structure having tertiary and higher level side-branches as the solidification progressed from the cold to the hot end of the samples. Extensive macrosegregation was observed along the DS length, initially being solute poor and then becoming more and more solute rich as the solidification progressed. Experimentally observed primary spacings are smaller and the trunk diameter larger than those predicted from theoretical models which assume purely diffusive transport during solidification

Parameterized Study of the Test Cover Problem

We carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the {\sc Test Cover} problem we are given a set $[n]=\{1,...,n\}$ of items together with a collection, $\cal T$, of distinct subsets of these items called tests. We assume that $\cal T$ is a test cover, i.e., for each pair of items there is a test in $\cal T$ containing exactly one of these items. The objective is to find a minimum size subcollection of $\cal T$, which is still a test cover. The generic parameterized version of {\sc Test Cover} is denoted by $p(k,n,|{\cal T}|)$-{\sc Test Cover}. Here, we are given $([n],\cal{T})$ and a positive integer parameter $k$ as input and the objective is to decide whether there is a test cover of size at most $p(k,n,|{\cal T}|)$. We study four parameterizations for {\sc Test Cover} and obtain the following: (a) $k$-{\sc Test Cover}, and $(n-k)$-{\sc Test Cover} are fixed-parameter tractable (FPT). (b) $(|{\cal T}|-k)$-{\sc Test Cover} and $(\log n+k)$-{\sc Test Cover} are W[1]-hard. Thus, it is unlikely that these problems are FPT