1,801 research outputs found
The Validity of the Super-Particle Approximation during Planetesimal Formation
The formation mechanism of planetesimals in protoplanetary discs is hotly
debated. Currently, the favoured model involves the accumulation of meter-sized
objects within a turbulent disc, followed by a phase of gravitational
instability. At best one can simulate a few million particles numerically as
opposed to the several trillion meter-sized particles expected in a real
protoplanetary disc. Therefore, single particles are often used as
super-particles to represent a distribution of many smaller particles. It is
assumed that small scale phenomena do not play a role and particle collisions
are not modeled. The super-particle approximation can only be valid in a
collisionless or strongly collisional system, however, in many recent numerical
simulations this is not the case.
In this work we present new results from numerical simulations of
planetesimal formation via gravitational instability. A scaled system is
studied that does not require the use of super-particles. We find that the
scaled particles can be used to model the initial phases of clumping if the
properties of the scaled particles are chosen such that all important
timescales in the system are equivalent to what is expected in a real
protoplanetary disc. Constraints are given for the number of particles needed
in order to achieve numerical convergence.
We compare this new method to the standard super-particle approach. We find
that the super-particle approach produces unreliable results that depend on
artifacts such as the gravitational softening in both the requirement for
gravitational collapse and the resulting clump statistics. Our results show
that short range interactions (collisions) have to be modelled properly.Comment: 10 pages, 7 figures, accepted for publication in Astronomy and
Astrophysic
Rescaling the dynamics of evaporating drops
The dynamics of evaporation of wetting droplets has been investigated
experimentally in an extended range of drop sizes, in order to provide trends
relevant for a theoretical analysis. A model is proposed, which generalises
Tanner's law, allowing us to smooth out the singularities both in dissipation
and in evaporative flux at the moving contact line. A qualitative agreement is
obtained, which represents a first step towards the solution of a very old,
complex problem
Turning Optical Complex Media into Universal Reconfigurable Linear Operators by Wavefront Shaping
Performing linear operations using optical devices is a crucial building
block in many fields ranging from telecommunication to optical analogue
computation and machine learning. For many of these applications, key
requirements are robustness to fabrication inaccuracies and reconfigurability.
Current designs of custom-tailored photonic devices or coherent photonic
circuits only partially satisfy these needs. Here, we propose a way to perform
linear operations by using complex optical media such as multimode fibers or
thin scattering layers as a computational platform driven by wavefront shaping.
Given a large random transmission matrix (TM) representing light propagation in
such a medium, we can extract a desired smaller linear operator by finding
suitable input and output projectors. We discuss fundamental upper bounds on
the size of the linear transformations our approach can achieve and provide an
experimental demonstration. For the latter, first we retrieve the complex
medium's TM with a non-interferometric phase retrieval method. Then, we take
advantage of the large number of degrees of freedom to find input wavefronts
using a Spatial Light Modulator (SLM) that cause the system, composed of the
SLM and the complex medium, to act as a desired complex-valued linear operator
on the optical field. We experimentally build several
complex-valued operators, and are able to switch from one to another at will.
Our technique offers the prospect of reconfigurable, robust and
easy-to-fabricate linear optical analogue computation units
Tunable high-index photonic glasses
Materials with extreme photonic properties such as maximum diffuse
reflectance, high albedo, or tunable band gaps are essential in many current
and future photonic devices and coatings. While photonic crystals, periodic
anisotropic structures, are well established, their disordered counterparts,
photonic glasses (PGs), are less understood despite their most interesting
isotropic photonic properties. Here, we introduce a controlled high index model
PG system. It is made of monodisperse spherical TiO colloids to exploit
strongly resonant Mie scattering for optimal turbidity. We report spectrally
resolved combined measurements of turbidity and light energy velocity from
large monolithic crack-free samples. This material class reveals pronounced
resonances enabled by the possibility to tune both the refractive index of the
extremely low polydisperse constituents and their radius. All our results are
rationalized by a model based on the energy coherent potential approximation,
which is free of any fitting parameter. Surprisingly good quantitative
agreement is found even at high index and elevated packing fraction. This class
of PGs may be the key to optimized tunable photonic materials and also central
to understand fundamental questions such as isotropic structural colors, random
lasing or strong light localization in 3D.Comment: Main text: 8 pages, 4 figures; Supporting Information: 5 pages, 5
figure
Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions
2000 Mathematics Subject Classification: 47H04, 65K10.In this paper we investigate the existence of a sequence (xk )
satisfying 0 ∈ f (xk )+ ∇f (xk )(xk+1 − xk )+ 1/2 ∇2 f (xk )(xk+1 − xk )^2 + G(xk+1 ) and converging to a solution x∗ of the generalized equation 0 ∈ f (x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces
The Distribution of High Redshift Galaxy Colors: Line of Sight Variations in Neutral Hydrogen Absorption
We model, via Monte Carlo simulations, the distribution of observed U-B, B-V,
V-I galaxy colors in the range 1.75<z<5 caused by variations in the
line-of-sight opacity due to neutral hydrogen (HI). We also include HI internal
to the source galaxies. Even without internal HI absorption, comparison of the
distribution of simulated colors to the analytic approximations of Madau (1995)
and Madau et al (1996) reveals systematically different mean colors and
scatter. Differences arise in part because we use more realistic distributions
of column densities and Doppler parameters. However, there are also
mathematical problems of applying mean and standard deviation opacities, and
such application yields unphysical results. These problems are corrected using
our Monte Carlo approach. Including HI absorption internal to the galaxies
generaly diminishes the scatter in the observed colors at a given redshift, but
for redshifts of interest this diminution only occurs in the colors using the
bluest band-pass. Internal column densities < 10^17 cm^2 do not effect the
observed colors, while column densities > 10^18 cm^2 yield a limiting
distribution of high redshift galaxy colors. As one application of our
analysis, we consider the sample completeness as a function of redshift for a
single spectral energy distribution (SED) given the multi-color selection
boundaries for the Hubble Deep Field proposed by Madau et al (1996). We argue
that the only correct procedure for estimating the z>3 galaxy luminosity
function from color-selected samples is to measure the (observed) distribution
of redshifts and intrinsic SED types, and then consider the variation in color
for each SED and redshift. A similar argument applies to the estimation of the
luminosity function of color-selected, high redshift QSOs.Comment: accepted for publication in ApJ; 25 pages text, 14 embedded figure
Pre-logarithmic and logarithmic fields in a sandpile model
We consider the unoriented two-dimensional Abelian sandpile model on the
half-plane with open and closed boundary conditions, and relate it to the
boundary logarithmic conformal field theory with central charge c=-2. Building
on previous results, we first perform a complementary lattice analysis of the
operator effecting the change of boundary condition between open and closed,
which confirms that this operator is a weight -1/8 boundary primary field,
whose fusion agrees with lattice calculations. We then consider the operators
corresponding to the unit height variable and to a mass insertion at an
isolated site of the upper half plane and compute their one-point functions in
presence of a boundary containing the two kinds of boundary conditions. We show
that the scaling limit of the mass insertion operator is a weight zero
logarithmic field.Comment: 18 pages, 9 figures. v2: minor corrections + added appendi
High efficiency GaAs-Ge tandem solar cells grown by MOCVD
High conversion efficiency and low weight are obviously desirable for solar cells intended for space applications. One promising structure is GaAs on Ge. The advantages of using Ge wafers as substrates include the following: they offer high efficiency by forming a two-junction tandem cell; low weight combined with superior strength allows usage of thin (3 mil) wafers; and they are a good substrate for GaAs, being lattice matched, thermal expansion matched, and available as large-area wafers
Critical point network for drainage between rough surfaces
In this paper, we present a network method for computing two-phase flows between two rough surfaces with significant contact areas. Low-capillary number drainage is investigated here since one-phase flows have been previously investigated in other contributions. An invasion percolation algorithm is presented for modeling slow displacement of a wetting fluid by a non wetting one between two rough surfaces. Short-correlated Gaussian process is used to model random rough surfaces.The algorithm is based on a network description of the fracture aperture field. The network is constructed from the identification of critical points (saddles and maxima) of the aperture field. The invasion potential is determined from examining drainage process in a flat mini-channel. A direct comparison between numerical prediction and experimental visualizations on an identical geometry has been performed for one realization of an artificial fracture with a moderate fractional contact area of about 0.3. A good agreement is found between predictions and observations
Accuracy of generalized gradient approximation functionals for density functional perturbation theory calculations
We assess the validity of various exchange-correlation functionals for
computing the structural, vibrational, dielectric, and thermodynamical
properties of materials in the framework of density-functional perturbation
theory (DFPT). We consider five generalized-gradient approximation (GGA)
functionals (PBE, PBEsol, WC, AM05, and HTBS) as well as the local density
approximation (LDA) functional. We investigate a wide variety of materials
including a semiconductor (silicon), a metal (copper), and various insulators
(SiO -quartz and stishovite, ZrSiO zircon, and MgO periclase).
For the structural properties, we find that PBEsol and WC are the closest to
the experiments and AM05 performs only slightly worse. All three functionals
actually improve over LDA and PBE in contrast with HTBS, which is shown to fail
dramatically for -quartz. For the vibrational and thermodynamical
properties, LDA performs surprisingly very good. In the majority of the test
cases, it outperforms PBE significantly and also the WC, PBEsol and AM05
functionals though by a smaller margin (and to the detriment of structural
parameters). On the other hand, HTBS performs also poorly for vibrational
quantities. For the dielectric properties, none of the functionals can be put
forward. They all (i) fail to reproduce the electronic dielectric constant due
to the well-known band gap problem and (ii) tend to overestimate the oscillator
strengths (and hence the static dielectric constant)
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