13,685 research outputs found
Snapping Graph Drawings to the Grid Optimally
In geographic information systems and in the production of digital maps for
small devices with restricted computational resources one often wants to round
coordinates to a rougher grid. This removes unnecessary detail and reduces
space consumption as well as computation time. This process is called snapping
to the grid and has been investigated thoroughly from a computational-geometry
perspective. In this paper we investigate the same problem for given drawings
of planar graphs under the restriction that their combinatorial embedding must
be kept and edges are drawn straight-line. We show that the problem is NP-hard
for several objectives and provide an integer linear programming formulation.
Given a plane graph G and a positive integer w, our ILP can also be used to
draw G straight-line on a grid of width w and minimum height (if possible).Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Extending the functionalities of shear-driven chromatography nano-channels using high aspect ratio etching
An new injection system is presented for shear-driven chromatography. The device has been fabricated by high aspect ratio etching of silicon. The performance of the injection slit is studied through the aid of computational fluid dynamics, and the first experimental results are presented
Phase transitions during membrane formation of polylactides. I. A morphological study of membranes obtained from the system polylactide-chloroform-methanol
The influence of solid-liquid demixing, liquid-liquid demixing and vitrification on the morphology of polylactide membranes has been investigated. To study the effects of crystallization of polylactides on the membrane and morphology, polylactides of varying stereoregularity were used. The polymers applied were poly--lactide (PLLA) and copolymers with different molar ratios of -lactide and -lactide [poly-L95/D5-lactide (PLA95), poly-L80/D20-lactide (PLA80) and poly-L50/D50-lactide (PDLLA)]. Solutions of polylactides in chloroform cast on a glass plate were immersed in methanol. From solutions containing the slowly crystallizing PLA80 or uncrystallizable PDLLA porous membranes were obtained if the phase separated system was removed from the nonsolvent bath within a few hours after immersion. After longer equilibration times in methanol the structure collapsed. The swelling in the nonsolvent methanol was too high to allow stabilization of the liquid-liquid demixed structure by vitrification. Stable membranes were easily obtained with more rapidly crystallizing polymers like PLLA. Casting solutions with low PLLA concentrations gave membranes with a cellular morphology due to liquid-liquid demixing by nucleation and growth of a polymer poor phase. Crystallization only played a role in the fixation of the liquid-liquid demixed structure. At increasing PLLA concentrations the demixing sequence gradually reversed to crystallization followed by liquid-liquid demixing. In these cases membranes with porous spherulites or spherulites surrounded with a cellular layer were obtained
A morphological study of membranes obtained from the systems polylactide-dioxane-methanol, polylactide-dioxane-water and polylactide-N-methyl pyrrolidone-water
The influence of liquid-liquid demixing, solid-liquid demixing, and vitrification on the membrane morphologies obtained from several polylactide-solvent-nonsolvent systems has been investigated. The polymers investigated were the semicrystalline poly-L-lactide (PLLA) and the amorphous poly-DL-lactide (PDLLA). The solvent-nonsolvent systems used were dioxane-water, N-methyl pyrrolidone-water and dioxane-methanol. For each of these systems it was attempted to relate the membrane morphology to the ternary phase diagram at 25°C. It was demonstrated that for the amorphous poly-DL-lactide the intersection of a glass transition and a liquid-liquid miscibility gap in the phase diagram was a prerequisite for the formation of stable membrane structures. For the semicrystalline PLLA a wide variety of morphologies could be obtained ranging from cellular to spherulitical structures. For membrane-forming combinations that show delayed demixing, trends expected on the basis of phase diagrams were in reasonable agreement with the observed membrane morphologies. Only for the rapidly precipitating system PLLA-N-methyl pyrrolidone-water were structures due to liquid-liquid demixing obtained when structures due to solid-liquid demixing were expected. Probably, rapid precipitation conditions promote solid-liquid demixing over liquid-liquid demixing, because the activation energy necessary for liquid-liquid demixing is lower than that for crystallization
Trajectory Deflection of Spinning Magnetic Microparticles, the Magnus Effect at the Microscale
The deflection due to the Magnus force of magnetic particles with a diameter
of 80 micrometer dropping through fluids and rotating in a magnetic field was
measured. With Reynolds number for this experiment around 1, we found
trajectory deflections of the order of 1 degree, in agreement within
measurement error with theory. This method holds promise for the sorting and
analysis of the distribution in magnetic moment and particle diameter of
suspensions of microparticles, such as applied in catalysis, or objects loaded
with magnetic particles.Comment: 12 pages, 3 figures. Appendix with 6 figure
Parallel single cell analysis on an integrated microfluidic platform for cell trapping, lysis and analysis
We report here a novel and easily scalable microfluidic platform for the parallel analysis of hundreds of individual cells, with controlled single cell trapping, followed by their lysis and subsequent retrieval of the cellular content for on-chip analysis. The device consists of a main channel and an array of shallow side channels connected to the main channel via trapping structures. Cells are individually captured in dam structures by application of a negative pressure from an outlet reservoir, lyzed on site and the cellular content controllably extracted and transported in the individual side channels for on-chip analysis.\u
AdS vacua and RG flows in three dimensional gauged supergravities
We study supersymmetric vacua in N=4 and N=8, three dimensional
gauged supergravities, with scalar manifolds and , non-semisimple Chern-Simons
gaugings and ,
respectively. These are in turn equivalent to SO(4) and
Yang-Mills theories coupled to supergravity. For the N=4 case, we study
renormalization group flows between UV and IR vacua with the same
amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an
analytic solution whereas in another, with (2,0) supersymmetry, we give a
numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e.
they are driven by the expectation value of a relevant operator in the dual
. These provide examples of v.e.v. flows between two vacua
within a gauged supergravity framework.Comment: 35 pages in JHEP form, 3 figures, typos corrected, references adde
Approximating the Maximum Overlap of Polygons under Translation
Let and be two simple polygons in the plane of total complexity ,
each of which can be decomposed into at most convex parts. We present an
-approximation algorithm, for finding the translation of ,
which maximizes its area of overlap with . Our algorithm runs in
time, where is a constant that depends only on and .
This suggest that for polygons that are "close" to being convex, the problem
can be solved (approximately), in near linear time
Statistical mechanics of random two-player games
Using methods from the statistical mechanics of disordered systems we analyze
the properties of bimatrix games with random payoffs in the limit where the
number of pure strategies of each player tends to infinity. We analytically
calculate quantities such as the number of equilibrium points, the expected
payoff, and the fraction of strategies played with non-zero probability as a
function of the correlation between the payoff matrices of both players and
compare the results with numerical simulations.Comment: 16 pages, 6 figures, for further information see
http://itp.nat.uni-magdeburg.de/~jberg/games.htm
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