Towards information optimal simulation of partial differential equations

Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an informationally optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier Galerkin methods. We discuss implications of the approximations made

Quantification of Cell Subpopulations, Fractions of Dead Cells and Debris in Cell Suspensions by Laser Diffractometry

Laser diffractometry was employed for size analysis in liver cell and blood cell suspensions to assess its suitability for characterizing cell populations. The method proved sensitive to detect subpopulations in liver cells (bimodal or trimodal distributions) and to quantify their volume fractions. Cell debris and aggregates of cells could also be quantified, dead cell populations recognized by their shift in the mean cell diameter. Laser diffractometry is therefore suitable for determining the quality of cell isolations (e.g. by liver perfusion) or for following alterations in cell populations during culture of cells in suspension. Analysis of human blood allowed differenciations to be made between thrombocytes and other blood cells. No peak separation was obtained for the populations of erythrocytes and granulocytes due to their similarity in size. Monocytes could not be detected due to their extremely low number in the blood indicating the limit of the metho

A geometric protocol for a robust Majorana magic gate

A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this manuscript we present a protocol that achieves the missing, so called, $\pi/8$ 'magic' phase gate. The protocol is based on the manipulation of geometric phases in a universal manner, and does not require fine tuning for distinct physical realizations. The protocol converges exponentially with the number of steps in the geometric path. Furthermore, the magic gate protocol relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to any-phase-gate, where $\pi/8$ is substituted by any $\alpha$.Comment: 14 pages, 8 figures (including appendices), v3: simplified derivation, more explicit connection between topological protection and exponential convergenc

Adjustment of the basin-scale circulation at 26 degrees N to variations in Gulf Stream, deep western boundary current and Ekman transports as observed by the Rapid array

The Rapid instrument array across the Atlantic Ocean along 26 degrees N provides unprecedented monitoring of the basin-scale circulation. A unique feature of the Rapid array is the combination of full-depth moorings with instruments measuring temperature, salinity, pressure time series at many depths with co-located bottom pressure measurements so that dynamic pressure can be measured from surface to bottom. Bottom pressure measurements show a zonally uniform rise (and fall) of bottom pressure of 0.015 dbar on a 5 to 10 day time scale, suggesting that the Atlantic basin is filling and draining on a short time scale. After removing the zonally uniform bottom pressure fluctuations, bottom pressure variations at 4000 m depth against the western boundary compensate instantaneously for baroclinic fluctuations in the strength and structure of the deep western boundary current so there is no basin-scale mass imbalance resulting from variations in the deep western boundary current. After removing the mass compensating bottom pressure, residual bottom pressure fluctuations at the western boundary just east of the Bahamas balance variations in Gulf Stream transport. Again the compensation appears to be especially confined close to the western boundary. Thus, fluctuations in either Gulf Stream or deep western boundary current transports are compensated in a depth independent (barotropic) manner very close to the continental slope off the Bahamas. In contrast, compensation for variations in wind-driven surface Ekman transport appears to involve fluctuations in both western basin and eastern basin bottom pressures, though the bottom pressure difference fluctuations appear to be a factor of 3 too large, perhaps due to an inability to resolve small bottom pressure fluctuations after removal of larger zonal average, baroclinic, and Gulf Stream pressure components. For 4 tall moorings where time series dynamic height (geostrophic pressure) profiles can be estimated from sea surface to ocean bottom and bottom pressure can be added, there is no general correlation between surface dynamic height and bottom pressure. Dynamic height on each mooring is strongly correlated with sea surface height from satellite observations and the variability in both dynamic height and satellite sea surface height decrease sharply as the western boundary is approached

Chiral Bogoliubons in Nonlinear Bosonic Systems

We present a versatile scheme for creating topological Bogoliubov excitations in weakly interacting bosonic systems. Our proposal relies on a background stationary field that consists of a Kagome vortex lattice, which breaks time-reversal symmetry and induces a periodic potential for Bogoliubov excitations. In analogy to the Haldane model, no external magnetic field or net flux is required. We construct a generic model based on the two-dimensional (2D) nonlinear Schr\"odinger equation and demonstrate the emergence of topological gaps crossed by chiral Bogoliubov edge modes. Our scheme can be realized in a wide variety of physical systems ranging from nonlinear optical systems to exciton-polariton condensates.Comment: 6 pages, 3 figures; with Supplemental Material (5 pages; in source

The XENON100 exclusion limit without considering Leff as a nuisance parameter

In 2011, the XENON100 experiment has set unprecedented constraints on dark matter-nucleon interactions, excluding dark matter candidates with masses down to 6 GeV if the corresponding cross section is larger than 10^{-39} cm^2. The dependence of the exclusion limit in terms of the scintillation efficiency (Leff) has been debated at length. To overcome possible criticisms XENON100 performed an analysis in which Leff was considered as a nuisance parameter and its uncertainties were profiled out by using a Gaussian likelihood in which the mean value corresponds to the best fit Leff value smoothly extrapolated to zero below 3 keVnr. Although such a method seems fairly robust, it does not account for more extreme types of extrapolation nor does it enable to anticipate on how much the exclusion limit would vary if new data were to support a flat behaviour for Leff below 3 keVnr, for example. Yet, such a question is crucial for light dark matter models which are close to the published XENON100 limit. To answer this issue, we use a maximum Likelihood ratio analysis, as done by the XENON100 collaboration, but do not consider Leff as a nuisance parameter. Instead, Leff is obtained directly from the fits to the data. This enables us to define frequentist confidence intervals by marginalising over Leff.Comment: 10 pages;, 9 figures; references adde

Characterisation of HTSC ceramics from their resistive transition

The resistivity vs. temperature relation in bulk ceramic HTSC under self-field conditions as well as in weak external magnetic fields is modelled by local Lorentz force induced fluxon motion with temperature dependent pinning. A pinning force density and two viscous drag coefficients in intergrain and intragrain regions, respectively, can be used as characteristic parameters describing the temperature, current, and external field dependences of the sample resistance.Comment: 12 pages, LaTeX2e, 6 figures (epsfig), to be published in Supercond. Sci. and Techno

A novel platform for the production of nonhydroxylated gelatins based on the methylotrophic yeast Hansenula polymorpha

The use of yeast as a host for heterologous expression of proteins that are normally derived from animal tissue is a promising way to ensure defined products that are devoid of potential harmful animal side products. Here we report on the production and secretion of a custom-designed gelatin, Hu3–His8, by the yeast Hansenula polymorpha. We observed that Hu3–His8 was poorly secreted by the heterologous Saccharomyces cerevisiae invertase secretion signal. In contrast, the S. cerevisiae mating factor α prepro sequence efficiently directed secretion into the culture medium. However, at higher copy numbers, intracellular accumulation of Hu3–His8 precursors occurred. Overproduction of Erv29p, a protein required for packaging of the glycosylated pro-α factor into COPII vesicles, did not improve gelatin secretion in the multicopy strain. Previously, H. polymorpha was reported to hydroxylate proline residues in gelatinous sequences. In contrast, we were unable to detect hydroxyprolines in the secreted Hu3–His8. Also, we failed to identify a gene encoding prolyl-4-hydroxylase in the H. polymorpha genome.