9,693 research outputs found
Online uniformly inserting points on the sphere
Uniformly inserting points on the sphere has been found useful in many scientific and engineering fields. Different from the offline version where the number of points is known in advance, we consider the online version of this problem. The requests for point insertion arrive one by one and the target is to insert points as uniformly as possible. To measure the uniformity we use gap ratio which is defined as the ratio of the maximal gap to the minimal gap of two arbitrary inserted points. We propose a two-phase online insertion strategy with gap ratio of at most 3.69. Moreover, the lower bound of the gap ratio is proved to be at least 1.78
Modelling of Path Arrival Rate for In-Room Radio Channels with Directive Antennas
We analyze the path arrival rate for an inroom radio channel with directive
antennas. The impulse response of this channel exhibits a transition from early
separate components followed by a diffuse reverberation tail. Under the
assumption that the transmitter's (or receiver's) position and orientation are
picked uniformly at random we derive an exact expression of the mean arrival
rate for a rectangular room predicted by the mirror source theory. The rate is
quadratic in delay, inversely proportional to the room volume, and proportional
to the product of beam coverage fractions of the transmitter and receiver
antennas. Making use of the exact formula, we characterize the onset of the
diffuse tail by defining a "mixing time" as the point in time where the arrival
rate exceeds one component per transmit pulse duration. We also give an
approximation for the power-delay spectrum. It turns out that the power-delay
spectrum is unaffected by the antenna directivity. However, Monte Carlo
simulations show that antenna directivity does indeed play an important role
for the distribution of instantaneous mean delay and rms delay spreadComment: Submitted to IEEE Trans. Antennas and Propagatio
Simulation studies of a phenomenological model for elongated virus capsid formation
We study a phenomenological model in which the simulated packing of hard,
attractive spheres on a prolate spheroid surface with convexity constraints
produces structures identical to those of prolate virus capsid structures. Our
simulation approach combines the traditional Monte Carlo method with a modified
method of random sampling on an ellipsoidal surface and a convex hull searching
algorithm. Using this approach we identify the minimum physical requirements
for non-icosahedral, elongated virus capsids, such as two aberrant flock house
virus (FHV) particles and the prolate prohead of bacteriophage , and
discuss the implication of our simulation results in the context of recent
experimental findings. Our predicted structures may also be experimentally
realized by evaporation-driven assembly of colloidal spheres
Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories
Bounded potentials are good models to represent the effective two-body
interaction in some colloidal systems, such as dilute solutions of polymer
chains in good solvents. The simplest bounded potential is that of penetrable
spheres, which takes a positive finite value if the two spheres are overlapped,
being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model
is far from trivial, since interactions are not restricted to nearest neighbors
and so its exact solution is not known. In this paper we first derive the exact
correlation functions of penetrable-rod fluids to second order in density at
any temperature, as well as in the high-temperature and zero-temperature limits
at any density. Next, two simple analytic theories are constructed: a
high-temperature approximation based on the exact asymptotic behavior in the
limit and a low-temperature approximation inspired by the exact
result in the opposite limit . Finally, we perform Monte Carlo
simulations for a wide range of temperatures and densities to assess the
validity of both theories. It is found that they complement each other quite
well, exhibiting a good agreement with the simulation data within their
respective domains of applicability and becoming practically equivalent on the
borderline of those domains. A perspective on the extension of both approaches
to the more realistic three-dimensional case is provided.Comment: 19 pages, 11 figures, 4 tables: v2: minor changes; published final
versio
Statistical approach to Casimir-Polder potentials in heterogeneous media
We explore the statistical properties of the Casimir-Polder potential between
a dielectric sphere and a three-dimensional heterogeneous medium, by means of
extensive numerical simulations based on the scattering theory of Casimir
forces. The simulations allow us to confirm recent predictions for the mean and
standard deviation of the Casimir potential, and give us access to its full
distribution function in the limit of a dilute distribution of heterogeneities.
These predictions are compared with a simple statistical model based on a
pairwise summation of the individual contributions of the constituting elements
of the medium.Comment: 8 pages, 8 figure
Characterization of Maximally Random Jammed Sphere Packings: II. Correlation Functions and Density Fluctuations
In the first paper of this series, we introduced Voronoi correlation
functions to characterize the structure of maximally random jammed (MRJ) sphere
packings across length scales. In the present paper, we determine a variety of
correlation functions that can be rigorously related to effective physical
properties of MRJ sphere packings and compare them to the corresponding
statistical descriptors for overlapping spheres and equilibrium hard-sphere
systems. Such structural descriptors arise in rigorous bounds and formulas for
effective transport properties, diffusion and reactions constants, elastic
moduli, and electromagnetic characteristics. First, we calculate the two-point,
surface-void, and surface-surface correlation functions, for which we derive
explicit analytical formulas for finite hard-sphere packings. We show
analytically how the contacts between spheres in the MRJ packings translate
into distinct functional behaviors of these two-point correlation functions
that do not arise in the other two models examined here. Then, we show how the
spectral density distinguishes the MRJ packings from the other disordered
systems in that the spectral density vanishes in the limit of infinite
wavelengths. These packings are hyperuniform, which means that density
fluctuations on large length scales are anomalously suppressed. Moreover, we
study and compute exclusion probabilities and pore size distributions as well
as local density fluctuations. We conjecture that for general disordered
hard-sphere packings, a central limit theorem holds for the number of points
within an spherical observation window. Our analysis links problems of interest
in material science, chemistry, physics, and mathematics. In the third paper,
we will evaluate bounds and estimates of a host of different physical
properties of the MRJ sphere packings based on the structural characteristics
analyzed in this paper.Comment: 25 pages, 13 Figures; corrected typos, updated reference
Spin relaxation dynamics of quasiclassical electrons in ballistic quantum dots with strong spin-orbit coupling
We performed path integral simulations of spin evolution controlled by the
Rashba spin-orbit interaction in the semiclassical regime for chaotic and
regular quantum dots. The spin polarization dynamics have been found to be
strikingly different from the D'yakonov-Perel' (DP) spin relaxation in bulk
systems. Also an important distinction have been found between long time spin
evolutions in classically chaotic and regular systems. In the former case the
spin polarization relaxes to zero within relaxation time much larger than the
DP relaxation, while in the latter case it evolves to a time independent
residual value. The quantum mechanical analysis of the spin evolution based on
the exact solution of the Schroedinger equation with Rashba SOI has confirmed
the results of the classical simulations for the circular dot, which is
expected to be valid in general regular systems. In contrast, the spin
relaxation down to zero in chaotic dots contradicts to what have to be expected
from quantum mechanics. This signals on importance at long time of the
mesoscopic echo effect missed in the semiclassical simulations.Comment: 14 pages, 9 figure
A practical guide to computer simulations
Here practical aspects of conducting research via computer simulations are
discussed. The following issues are addressed: software engineering,
object-oriented software development, programming style, macros, make files,
scripts, libraries, random numbers, testing, debugging, data plotting, curve
fitting, finite-size scaling, information retrieval, and preparing
presentations.
Because of the limited space, usually only short introductions to the
specific areas are given and references to more extensive literature are cited.
All examples of code are in C/C++.Comment: 69 pages, with permission of Wiley-VCH, see http://www.wiley-vch.de
(some screenshots with poor quality due to arXiv size restrictions) A
comprehensively extended version will appear in spring 2009 as book at
Word-Scientific, see http://www.worldscibooks.com/physics/6988.htm
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