12,197 research outputs found
On the surface tension of fluctuating quasi-spherical vesicles
We calculate the stress tensor for a quasi-spherical vesicle and we thermally
average it in order to obtain the actual, mechanical, surface tension of
the vesicle. Both closed and poked vesicles are considered. We recover our
results for by differentiating the free-energy with respect to the
proper projected area. We show that may become negative well before the
transition to oblate shapes and that it may reach quite large negative values
in the case of small vesicles. This implies that spherical vesicles may have an
inner pressure lower than the outer one.Comment: To appear in Eur. Phys. J. E, revised versio
Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model
Over the past decades, direct three-dimensional numerical modelling has been successfully used to reproduce the main features of the geodynamo. Here we report on efforts to solve the associated inverse problem, aiming at inferring the underlying properties of the system from the sole knowledge of surface observations and the first principle dynamical equations describing the convective dynamo. To this end we rely on twin experiments. A reference model time sequence is first produced and used to generate synthetic data, restricted here to the large-scale component of the magnetic field and its rate of change at the outer boundary. Starting from a different initial condition, a second sequence is next run and attempts are made to recover the internal magnetic, velocity and buoyancy anomaly fields from the sparse surficial data. In order to reduce the vast underdetermination of this problem, we use stochastic inversion, a linear estimation method determining the most likely internal state compatible with the observations and some prior knowledge, and we also implement a sequential evolution algorithm in order to invert time-dependent surface observations. The prior is the multivariate statistics of the numerical model, which are directly computed from a large number of snapshots stored during a preliminary direct run. The statistics display strong correlation between different harmonic degrees of the surface observations and internal fields, provided they share the same harmonic order, a natural consequence of the linear coupling of the governing dynamical equations and of the leading influence of the Coriolis force. Synthetic experiments performed with a weakly nonlinear model yield an excellent quantitative retrieval of the internal structure. In contrast, the use of a strongly nonlinear (and more realistic) model results in less accurate static estimations, which in turn fail to constrain the unobserved small scales in the time integration of the evolution scheme. Evaluating the quality of forecasts of the system evolution against the reference solution, we show that our scheme can improve predictions based on linear extrapolations on forecast horizons shorter than the system <i>e</i>-folding time. Still, in the perspective of forthcoming data assimilation activities, our study underlines the need of advanced estimation techniques able to cope with the moderate to strong nonlinearities present in the geodynamo
Universal analytic properties of noise. Introducing the J-Matrix formalism
We propose a new method in the spectral analysis of noisy time-series data
for damped oscillators. From the Jacobi three terms recursive relation for the
denominators of the Pad\'e Approximations built on the well-known Z-transform
of an infinite time-series, we build an Hilbert space operator, a J-Operator,
where each bound state (inside the unit circle in the complex plane) is simply
associated to one damped oscillator while the continuous spectrum of the
J-Operator, which lies on the unit circle itself, is shown to represent the
noise. Signal and noise are thus clearly separated in the complex plane. For a
finite time series of length 2N, the J-operator is replaced by a finite order
J-Matrix J_N, having N eigenvalues which are time reversal covariant. Different
classes of input noise, such as blank (white and uniform), Gaussian and pink,
are discussed in detail, the J-Matrix formalism allowing us to efficiently
calculate hundreds of poles of the Z-transform. Evidence of a universal
behaviour in the final statistical distribution of the associated poles and
zeros of the Z-transform is shown. In particular the poles and zeros tend, when
the length of the time series goes to infinity, to a uniform angular
distribution on the unit circle. Therefore at finite order, the roots of unity
in the complex plane appear to be noise attractors. We show that the
Z-transform presents the exceptional feature of allowing lossless undersampling
and how to make use of this property. A few basic examples are given to suggest
the power of the proposed method.Comment: 14 pages, 8 figure
Density Power Spectrum of Compressible Hydrodynamic Turbulent Flows
Turbulent flows are ubiquitous in astrophysical environments, and
understanding density structures and their statistics in turbulent media is of
great importance in astrophysics. In this paper, we study the density power
spectra, , of transonic and supersonic turbulent flows through one
and three-dimensional simulations of driven, isothermal hydrodynamic turbulence
with root-mean-square Mach number in the range of 1 \la M_{\rm rms} \la 10.
From one-dimensional experiments we find that the slope of the density power
spectra becomes gradually shallower as the rms Mach number increases. It is
because the density distribution transforms from the profile with {\it
discontinuities} having for to
the profile with {\it peaks} having for . We also find that the same trend is carried to three-dimension; that is,
the density power spectrum flattens as the Mach number increases. But the
density power spectrum of the flow with has the Kolmogorov
slope. The flattening is the consequence of the dominant density structures of
{\it filaments} and {\it sheets}. Observations have claimed different slopes of
density power spectra for electron density and cold H I gas in the interstellar
medium. We argue that while the Kolmogorov spectrum for electron density
reflects the {\it transonic} turbulence of in the warm
ionized medium, the shallower spectrum of cold H I gas reflects the {\it
supersonic} turbulence of a few in the cold neutral medium.Comment: To appear in ApJ Lett. Pdf file with full resolution figures can be
downloaded from http://canopus.cnu.ac.kr/ryu/kimryu.pd
On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity
We prove an inequality on the Wasserstein distance with quadratic cost
between two solutions of the spatially homogeneous Boltzmann equation without
angular cutoff, from which we deduce some uniqueness results. In particular, we
obtain a local (in time) well-posedness result in the case of (possibly very)
soft potentials. A global well-posedeness result is shown for all regularized
hard and soft potentials without angular cutoff. Our uniqueness result seems to
be the first one applying to a strong angular singularity, except in the
special case of Maxwell molecules.
Our proof relies on the ideas of Tanaka: we give a probabilistic
interpretation of the Boltzmann equation in terms of a stochastic process. Then
we show how to couple two such processes started with two different initial
conditions, in such a way that they almost surely remain close to each other
Geothermal studies - Yellowstone National Park /test site 11/, Wyoming
Summary report of diamond drilling in thermal areas of Yellowstone National Park, and method for determining heat flow in thermal area
Nematic-Wetted Colloids in the Isotropic Phase: Pairwise Interaction, Biaxiality and Defects
We calculate the interaction between two spherical colloidal particles
embedded in the isotropic phase of a nematogenic liquid. The surface of the
particles induces wetting nematic coronas that mediate an elastic interaction.
In the weak wetting regime, we obtain exact results for the interaction energy
and the texture, showing that defects and biaxiality arise, although they are
not topologically required. We evidence rich behaviors, including the
possibility of reversible colloidal aggregation and dispersion. Complex
anisotropic self-assembled phases might be formed in dense suspensions.Comment: 4 pages, 6 figure
Barry Saltzman and the Theory of Climate
Barry Saltzman was a giant in the fields of meteorology and climate science. A leading figure in the study of weather and climate for over 40 yr, he has frequently been referred to as the father of modern climate theory. Ahead of his time in many ways, Saltzman made significant contributions to our understanding of the general circulation and spectral energetics budget of the atmosphere, as well as climate change across a wide spectrum of time scales. In his endeavor to develop a unified theory of how the climate system works, lie played a role in the development of energy balance models, statistical dynamical models, and paleoclimate dynamical models. He was a pioneer in developing meteorologically motivated dynamical systems, including the progenitor of Lorenz\u27s famous chaos model. In applying his own dynamical-systems approach to long-term climate change, he recognized the potential for using atmospheric general circulation models in a complimentary way. In 1998, he was awarded the Carl-Gustaf Rossby medal, the highest honor of the American Meteorological Society for his life-long contributions to the study of the global circulation and the evolution of the earth\u27s climate. In this paper, the authors summarize and place into perspective some of the most significant contributions that Barry Saltzman made during his long and distinguished career. This short review also serves as an introduction to the papers in this special issue of the Journal of Climate dedicated to Barry\u27s memory
Models of Passive and Reactive Tracer Motion: an Application of Ito Calculus
By means of Ito calculus it is possible to find, in a straight-forward way,
the analytical solution to some equations related to the passive tracer
transport problem in a velocity field that obeys the multidimensional Burgers
equation and to a simple model of reactive tracer motion.Comment: revised version 7 pages, Latex, to appear as a letter to J. of
Physics
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