1,268 research outputs found
Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier--Stokes equations
To increase the reliability of simulations by particle methods for
incompressible viscous flow problems, convergence studies and improvements of
accuracy are considered for a fully explicit particle method for incompressible
Navier--Stokes equations. The explicit particle method is based on a penalty
problem, which converges theoretically to the incompressible Navier--Stokes
equations, and is discretized in space by generalized approximate operators
defined as a wider class of approximate operators than those of the smoothed
particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) methods.
By considering an analytical derivation of the explicit particle method and
truncation error estimates of the generalized approximate operators, sufficient
conditions of convergence are conjectured.Under these conditions, the
convergence of the explicit particle method is confirmed by numerically
comparing errors between exact and approximate solutions. Moreover, by focusing
on the truncation errors of the generalized approximate operators, an optimal
weight function is derived by reducing the truncation errors over general
particle distributions. The effectiveness of the generalized approximate
operators with the optimal weight functions is confirmed using numerical
results of truncation errors and driven cavity flow. As an application for flow
problems with free surface effects, the explicit particle method is applied to
a dam break flow.Comment: 27 pages, 13 figure
Structure and Dynamics of Water at the Water-Air Interface Using First-Principles Molecular Dynamics Simulations. II. NonLocal vs Empirical van der Waals Corrections
Anomalous time delays and quantum weak measurements in optical micro-resonators
We study inelastic resonant scattering of a Gaussian wave packet with the
parameters close to a zero of the complex scattering coefficient. We
demonstrate, both theoretically and experimentally, that such near-zero
scattering can result in anomalously-large time delays and frequency shifts of
the scattered wave packet. Furthermore, we reveal a close analogy of these
anomalous shifts with the spatial and angular Goos-H\"anchen optical beam
shifts, which are amplified via quantum weak measurements. However, in contrast
to other beam-shift and weak-measurement systems, we deal with a
one-dimensional scalar wave without any intrinsic degrees of freedom. It is the
non-Hermitian nature of the system that produces its rich and non-trivial
behaviour. Our results are generic for any scattering problem, either quantum
or classical. As an example, we consider the transmission of an optical pulse
through a nano-fiber with a side-coupled toroidal micro-resonator. The zero of
the transmission coefficient corresponds to the critical coupling conditions.
Experimental measurements of the time delays near the critical-coupling
parameters verify our weak-measurement theory and demonstrate amplification of
the time delay from the typical inverse resonator linewidth scale to the pulse
duration scale.Comment: 14 pages, 5 figure
Boosting up quantum key distribution by learning statistics of practical single photon sources
We propose a simple quantum-key-distribution (QKD) scheme for practical
single photon sources (SPSs), which works even with a moderate suppression of
the second-order correlation of the source. The scheme utilizes a
passive preparation of a decoy state by monitoring a fraction of the signal via
an additional beam splitter and a detector at the sender's side to monitor
photon number splitting attacks. We show that the achievable distance increases
with the precision with which the sub-Poissonian tendency is confirmed in
higher photon number distribution of the source, rather than with actual
suppression of the multi-photon emission events. We present an example of the
secure key generation rate in the case of a poor SPS with , in
which no secure key is produced with the conventional QKD scheme, and show that
learning the photon-number distribution up to several numbers is sufficient for
achieving almost the same achievable distance as that of an ideal SPS.Comment: 11 pages, 3 figures; published version in New J. Phy
Avoiding spurious feedback loops in the reconstruction of gene regulatory networks with dynamic bayesian networks
Feedback loops and recurrent structures are essential to the regulation and stable control of complex biological systems. The application of dynamic as opposed to static Bayesian networks is promising in that, in principle, these feedback loops can be learned. However, we show that the widely applied BGe score is susceptible to learning spurious feedback loops, which are a consequence of non-linear regulation and autocorrelation in the data. We propose a non-linear generalisation of the BGe model, based on a mixture model, and demonstrate that this approach successfully represses spurious feedback loops
Accurate molecular orientation at interfaces determined by multimode polarization-dependent heterodyne-detected sum-frequency generation spectroscopy via multidimensional orientational distribution function
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