A framework for modelling kinematic measurements in gravity field applications

To assess the resolution of the local gravity field from kinematic measurements, a state model for motion in the gravity field of the earth is formulated. The resulting set of equations can accommodate gravity gradients, specific force, acceleration, velocity and position as input data and can take into account approximation errors as well as sensor errors

On finite volume effects in the chiral extrapolation of baryon masses

We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self energies are computed in a finite volume at next-to-next-to-next-to leading order (N$^3$LO), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-$N_c$ sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD. Values for all counter terms relevant at N$^3$LO are predicted. In particular we extract a pion-nucleon sigma term of 39$_{-1}^{+2}$ MeV and a strangeness sigma term of the nucleon of $\sigma_{sN} = 84^{+ 28}_{-\;4}$ MeV. The flavour SU(3) chiral limit of the baryon octet and decuplet masses is determined with $(802 \pm 4)$ MeV and $(1103 \pm 6)$ MeV. Detailed predictions for the baryon masses as currently evaluated by the ETM lattice QCD group are made.Comment: 44 pages, 10 figures and 6 tables - the revised manuscript contains the results of additional fits at the N^2LO level - 4 additional figures show the size of finite volume corrections for each lattice point - more technical details on the evaluation of finite volume effects are give

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

Reconnections of Vortex Loops in the Superfluid Turbulent HeII. Rates of the Breakdown and Fusion processes

Kinetics of merging and breaking down vortex loops is the important part of the whole vortex tangle dynamics. Another part is the motion of individual lines, which obeys the Biot-Savart law in presence of friction force and of applied external velocity fields if any. In the present work we evaluate the coefficients of the reconnection rates $A(l_{1},l_{2},l)$ and $B(l,l_{1},l_{2})$. Quantity $A$ is a number (per unit of time and per unit of volume) of events, when two loops with lengths $l_{1}$and $l_{2}$ collide and form the single loop of length $l=l_{1}+l_{2}$. Quantity $$ describes the rate of events, when the single loop of the length $l$ breaks down into two the daughter loops of lengths $l_{1}$ and $l_{2}$. These quantities ave evaluated as the averaged numbers of zeroes of vector $\mathbf{S}$ connecting two points on the loops of $\xi_{2}$ and $\xi_{1}$ at moment of time $t$. Statistics of the individual loops is taken from the Gaussian model of vortex tangle. PACS-number 67.40Comment: 9 pages, 5 figures, To be submitted to JLT

Mean curvature flow of monotone Lagrangian submanifolds

We use holomorphic disks to describe the formation of singularities in the mean curvature flow of monotone Lagrangian submanifolds in $\mathbb C^{n}$.Comment: 37 pages, 3 figure

Buckling without bending: a new paradigm in morphogenesis

A curious feature of organ and organoid morphogenesis is that in certain cases, spatial oscillations in the thickness of the growing "film" are out-of-phase with the deformation of the slower-growing "substrate," while in other cases, the oscillations are in-phase. The former cannot be explained by elastic bilayer instability, and contradict the notion that there is a universal mechanism by which brains, intestines, teeth, and other organs develop surface wrinkles and folds. Inspired by the microstructure of the embryonic cerebellum, we develop a new model of 2d morphogenesis in which system-spanning elastic fibers endow the organ with a preferred radius, while a separate fiber network resides in the otherwise fluid-like film at the outer edge of the organ and resists thickness gradients thereof. The tendency of the film to uniformly thicken or thin is described via a "growth potential". Several features of cerebellum, +blebbistatin organoid, and retinal fovea morphogenesis, including out-of-phase behavior and a film thickness amplitude that is comparable to the radius amplitude, are readily explained by our simple analytical model, as may be an observed scale-invariance in the number of folds in the cerebellum. We also study a nonlinear variant of the model, propose further biological and bio-inspired applications, and address how our model is and is not unique to the developing nervous system.Comment: version accepted by Physical Review