23,247 research outputs found
The fractional Keller-Segel model
The Keller-Segel model is a system of partial differential equations
modelling chemotactic aggregation in cellular systems. This model has blowing
up solutions for large enough initial conditions in dimensions d >= 2, but all
the solutions are regular in one dimension; a mathematical fact that crucially
affects the patterns that can form in the biological system. One of the
strongest assumptions of the Keller-Segel model is the diffusive character of
the cellular motion, known to be false in many situations. We extend this model
to such situations in which the cellular dispersal is better modelled by a
fractional operator. We analyze this fractional Keller-Segel model and find
that all solutions are again globally bounded in time in one dimension. This
fact shows the robustness of the main biological conclusions obtained from the
Keller-Segel model
Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
We present a new approach to path integral Monte Carlo (PIMC) simulations
based on the worm algorithm, originally developed for lattice models and
extended here to continuous-space many-body systems. The scheme allows for
efficient computation of thermodynamic properties, including winding numbers
and off-diagonal correlations, for systems of much greater size than that
accessible to conventional PIMC. As an illustrative application of the method,
we simulate the superfluid transition of Helium-four in two dimensions.Comment: Fig. 2 differs from that of published version (includes data for
larger system sizes
Fabrication of alignment structures for a fiber resonator by use of deep-ultraviolet lithography
We present a novel method to mount and align an optical-fiber-based resonator
on the flat surface of an atom chip with ultrahigh precision. The structures
for mounting a pair of fibers, which constitute the fiber resonator, are
produced by a spin-coated SU-8 photoresist technique by use of deep-UV
lithography. The design and production of the SU-8 structures are discussed.
From the measured finesses we calculate the coupling loss of the SU-8
structures acting as a kind of fiber splice to be smaller than 0.013 dB.Comment: 4 pages, 3 figure
Effect of sampling rate and record length on the determination of stability and control derivatives
Flight data from five aircraft were used to assess the effects of sampling rate and record length reductions on estimates of stability and control derivatives produced by a maximum likelihood estimation method. Derivatives could be extracted from flight data with the maximum likelihood estimation method even if there were considerable reductions in sampling rate and/or record length. Small amplitude pulse maneuvers showed greater degradation of the derivative maneuvers than large amplitude pulse maneuvers when these reductions were made. Reducing the sampling rate was found to be more desirable than reducing the record length as a method of lessening the total computation time required without greatly degrading the quantity of the estimates
Design and fabrication of a centrifugally driven microfluidic disk for fully integrated metabolic assays on whole blood
For the first time, we present a novel and fully integrated centrifugal microfluidic “ lab-on-a-disk” for rapid metabolic assays in human whole blood. All essential steps comprising blood sampling, metering, plasma extraction and the final optical detection are conducted within t = 150 s in passive structures integrated on one disposable disk. Our technology features a novel plasma extraction structure (V = 500 nL, CV < 5%) without using any hydrophobic microfluidics where the purified plasma (cRBC< 0.11%) is centrifugally separated and subsequently extracted through a capillarily primed extraction channel into the detection chamber. While this capillary extraction requires precisely defined, narrow micro-structures, the reactive mixing and detection is most efficient within larger cavities. The corresponding manufacturing technique of these macro- and micro structures in the range of 30 µ m to 1000 µ m is also presented for the first time: A novel, cost-efficient hybrid prototyping technique of a multiscale epoxy master for subsequent hot embossing of polymer disks
Multispace and Multilevel BDDC
BDDC method is the most advanced method from the Balancing family of
iterative substructuring methods for the solution of large systems of linear
algebraic equations arising from discretization of elliptic boundary value
problems. In the case of many substructures, solving the coarse problem exactly
becomes a bottleneck. Since the coarse problem in BDDC has the same structure
as the original problem, it is straightforward to apply the BDDC method
recursively to solve the coarse problem only approximately. In this paper, we
formulate a new family of abstract Multispace BDDC methods and give condition
number bounds from the abstract additive Schwarz preconditioning theory. The
Multilevel BDDC is then treated as a special case of the Multispace BDDC and
abstract multilevel condition number bounds are given. The abstract bounds
yield polylogarithmic condition number bounds for an arbitrary fixed number of
levels and scalar elliptic problems discretized by finite elements in two and
three spatial dimensions. Numerical experiments confirm the theory.Comment: 26 pages, 3 figures, 2 tables, 20 references. Formal changes onl
The Two Fluid Drop Snap-off Problem: Experiments and Theory
We address the dynamics of a drop with viscosity breaking up
inside another fluid of viscosity . For , a scaling theory
predicts the time evolution of the drop shape near the point of snap-off which
is in excellent agreement with experiment and previous simulations of Lister
and Stone. We also investigate the dependence of the shape and
breaking rate.Comment: 4 pages, 3 figure
Chemotactic Collapse and Mesenchymal Morphogenesis
We study the effect of chemotactic signaling among mesenchymal cells. We show
that the particular physiology of the mesenchymal cells allows one-dimensional
collapse in contrast to the case of bacteria, and that the mesenchymal
morphogenesis represents thus a more complex type of pattern formation than
those found in bacterial colonies. We finally compare our theoretical
predictions with recent in vitro experiments
High resolution Ge/Li/ spectrometer reduces rate-dependent distortions at high counting rates
Modified spectrometer system with a low-noise preamplifier reduces rate-dependent distortions at high counting rates, 25,000 counts per second. Pole-zero cancellation minimizes pulse undershoots due to multiple time constants, baseline restoration improves resolution and prevents spectral shifts
- …