362 research outputs found
Exponentially small heteroclinic breakdown in the generic Hopf-zero singularity
In this paper we prove the breakdown of an heteroclinic connection in the
analytic versal unfoldings of the generic Hopf-Zero singularity in an open set
of the parameter space. This heteroclinic orbit appears at any order if one
performs the normal form around the origin, therefore it is a phenomenon
"beyond all orders". In this paper we provide a formula for the distance
between the corresponding stable and unstable one dimensional manifolds which
is given by an exponentially small function in the perturbation parameter. Our
result applies both for conservative and dissipative unfoldings
Two state scattering problem to Multi-channel scattering problem: Analytically solvable model
Starting from few simple examples we have proposed a general method for
finding an exact analytical solution for the two state scattering problem in
presence of a delta function coupling. We have also extended our model to deal
with general one dimensional multi-channel scattering problems
Wave Directional Spreading From Point Field Measurements
Ocean waves have multidirectional components. Most wave measurements are taken at a single point, and so fail to capture information about the relative directions of the wave components directly. Conventional means of directional estimation require a minimum of three concurrent time series of measurements at different spatial locations in order to derive information on local directional wave spreading. Here, the relationship between wave nonlinearity and directionality is utilized to estimate local spreading without the need for multiple concurrent measurements, following Adcock & Taylor (Adcock & Taylor 2009 Proc. R. Soc. A 465, 3361-3381. (doi:10.1098/rspa.2009.0031)), with the assumption that directional spreading is frequency independent. The method is applied to measurements recorded at the North Alwyn platform in the northern North Sea, and the results compared against estimates of wave spreading by conventional measurement methods and hindcast data. Records containing freak waves were excluded. It is found that the method provides accurate estimates of wave spreading over a range of conditions experienced at North Alwyn, despite the noisy chaotic signals that characterize such ocean wave data. The results provide further confirmation that Adcock and Taylor's method is applicable to metocean data and has considerable future promise as a technique to recover estimates of wave spreading from single point wave measurement devices
Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale
The detection of sound begins when energy derived from acoustic stimuli
deflects the hair bundles atop hair cells. As hair bundles move, the viscous
friction between stereocilia and the surrounding liquid poses a fundamental
challenge to the ear's high sensitivity and sharp frequency selectivity. Part
of the solution to this problem lies in the active process that uses energy for
frequency-selective sound amplification. Here we demonstrate that a
complementary part involves the fluid-structure interaction between the liquid
within the hair bundle and the stereocilia. Using force measurement on a
dynamically scaled model, finite-element analysis, analytical estimation of
hydrodynamic forces, stochastic simulation and high-resolution interferometric
measurement of hair bundles, we characterize the origin and magnitude of the
forces between individual stereocilia during small hair-bundle deflections. We
find that the close apposition of stereocilia effectively immobilizes the
liquid between them, which reduces the drag and suppresses the relative
squeezing but not the sliding mode of stereociliary motion. The obliquely
oriented tip links couple the mechanotransduction channels to this least
dissipative coherent mode, whereas the elastic horizontal top connectors
stabilize the structure, further reducing the drag. As measured from the
distortion products associated with channel gating at physiological stimulation
amplitudes of tens of nanometres, the balance of forces in a hair bundle
permits a relative mode of motion between adjacent stereocilia that encompasses
only a fraction of a nanometre. A combination of high-resolution experiments
and detailed numerical modelling of fluid-structure interactions reveals the
physical principles behind the basic structural features of hair bundles and
shows quantitatively how these organelles are adapted to the needs of sensitive
mechanotransduction.Comment: 21 pages, including 3 figures. For supplementary information, please
see the online version of the article at http://www.nature.com/natur
Stokes drift
During its periodic motion, a particle floating at the free surface of a water wave experiences a net drift velocity in the direction of wave propagation, known as the Stokes drift (Stokes 1847 Trans. Camb. Philos. Soc.8, 441-455). More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel and the average Eulerian flow velocity of the fluid. This paper reviews progress in fundamental and applied research on the induced mean flow associated with surface gravity waves since the first description of the Stokes drift, now 170 years ago. After briefly reviewing the fundamental physical processes, most of which have been established for decades, the review addresses progress in laboratory and field observations of the Stokes drift. Despite more than a century of experimental studies, laboratory studies of the mean circulation set up by waves in a laboratory flume remain somewhat contentious. In the field, rapid advances are expected due to increasingly small and cheap sensors and transmitters, making widespread use of small surface-following drifters possible. We also discuss remote sensing of the Stokes drift from high-frequency radar. Finally, the paper discusses the three main areas of application of the Stokes drift: in the coastal zone, in Eulerian models of the upper ocean layer and in the modelling of tracer transport, such as oil and plastic pollution. Future climate models will probably involve full coupling of ocean and atmosphere systems, in which the wave model provides consistent forcing on the ocean surface boundary layer. Together with the advent of new space-borne instruments that can measure surface Stokes drift, such models hold the promise of quantifying the impact of wave effects on the global atmosphere-ocean system and hopefully contribute to improved climate projections.This article is part of the theme issue 'Nonlinear water waves'
Curve Crossing Problem with Arbitrary Coupling: Analytically Solvable Model
We give a general method for finding an exact analytical solution for the two
state curve crossing problem. The solution requires the knowledge of the
Green's function for the motion on the uncoupled potential. We use the method
to find the solution of the problem in the case of parabolic potentials coupled
by Gaussian interaction. Our method is applied to this model system to
calculate the effect of curve crossing on electronic absorption spectrum and
resonance Raman excitation profile
Polarimetric Multi-View Inverse Rendering
A polarization camera has great potential for 3D reconstruction since the
angle of polarization (AoP) of reflected light is related to an object's
surface normal. In this paper, we propose a novel 3D reconstruction method
called Polarimetric Multi-View Inverse Rendering (Polarimetric MVIR) that
effectively exploits geometric, photometric, and polarimetric cues extracted
from input multi-view color polarization images. We first estimate camera poses
and an initial 3D model by geometric reconstruction with a standard
structure-from-motion and multi-view stereo pipeline. We then refine the
initial model by optimizing photometric and polarimetric rendering errors using
multi-view RGB and AoP images, where we propose a novel polarimetric rendering
cost function that enables us to effectively constrain each estimated surface
vertex's normal while considering four possible ambiguous azimuth angles
revealed from the AoP measurement. Experimental results using both synthetic
and real data demonstrate that our Polarimetric MVIR can reconstruct a detailed
3D shape without assuming a specific polarized reflection depending on the
material.Comment: Paper accepted in ECCV 202
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Laboratory layered latte
Inducing thermal gradients in fluid systems with initial, well-defined density gradients results in the formation of distinct layered patterns, such as those observed in the ocean due to double-diffusive convection. In contrast, layered composite fluids are sometimes observed in confined systems of rather chaotic initial states, for example, lattes formed by pouring espresso into a glass of warm milk. Here, we report controlled experiments injecting a fluid into a miscible phase and show that, above a critical injection velocity, layering emerges over a time scale of minutes. We identify critical conditions to produce the layering, and relate the results quantitatively to double-diffusive convection. Based on this understanding, we show how to employ this single-step process to produce layered structures in soft materials, where the local elastic properties vary step-wise along the length of the material
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