1,664 research outputs found
An invariant in shock clustering and Burgers turbulence
1-D scalar conservation laws with convex flux and Markov initial data are now
known to yield a completely integrable Hamiltonian system. In this article, we
rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence
from the perspective of integrable systems. Other relevant physical notions
such as energy dissipation and spectrum are also discussed.Comment: 11 pages, no figures; v2: corrections mad
Power analysis on smartcard algorithms using simulation
This paper presents the results from a power analysis of the AES and RSA algorithms by\ud
simulation using the PINPAS tool. The PINPAS tool is capable of simulating the power\ud
consumption of assembler programs implemented in, amongst others, Hitachi H8/300\ud
assembler. The Hitachi H8/300 is a popular CPU for smartcards. Using the PINPAS tool, the\ud
vulnerability for power analysis attacks of straightforward AES and RSA implementations is\ud
examined. In case a vulnerability is found countermeasures are added to the implementation\ud
that attempt to counter power analysis attacks. After these modifications the analysis is\ud
performed again and the new results are compared to the original results
The Newtonian Limit of Hermitian Gravity
We construct the gauge invariant potentials of Hermitian Gravity and derive
the linearized equations of motion they obey. A comparison reveals a striking
similarity to the Bardeen potentials of general relativity. We then consider
the response to a point particle source, and discuss in what sense the
solutions of Hermitian Gravity reduce to the Newtonian potentials. In a rather
intriguing way, the Hermitian Gravity solutions exhibit a generalized
reciprocity symmetry originally proposed by Born in the 1930s. Finally, we
consider the trajectories of massive and massless particles under the influence
of a potential. The theory correctly reproduces the Newtonian limit in three
dimensions and the nonrelativistic acceleration equation. However, it differs
from the light deflection calculated in linearized generalrelativity by 25%.
While the specific complexification of general relativity by extension to
Hermitian spaces performed here does not agree with experiment, it does possess
useful properties for quantization and is well-behaved around singularities.
Another form of complex general relativity may very well agree with
experimental data.Comment: The published version in Gen. Rel. Grav. 24 pages, no figure
An Ensemble Kalman-Particle Predictor-Corrector Filter for Non-Gaussian Data Assimilation
An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change
in the state, followed by a Particle Filer (PF, the corrector) which assigns
importance weights to describe non-Gaussian distribution. The weights are
obtained by nonparametric density estimation. It is demonstrated on several
numerical examples that the new predictor-corrector filter combines the
advantages of the EnKF and the PF and that it is suitable for high dimensional
states which are discretizations of solutions of partial differential
equations.Comment: ICCS 2009, to appear; 9 pages; minor edit
Generation of frequency sidebands on single photons with indistinguishability from quantum dots
Generation and manipulation of the quantum state of a single photon is at the
heart of many quantum information protocols. There has been growing interest in
using phase modulators as quantum optics devices that preserve coherence. In
this Letter, we have used an electro-optic phase modulator to shape the state
vector of single photons emitted by a quantum dot to generate new frequency
components (modes) and explicitly demonstrate that the phase modulation process
agrees with the theoretical prediction at a single photon level. Through
two-photon interference measurements we show that for an output consisting of
three modes (the original mode and two sidebands), the indistinguishability of
the mode engineered photon, measured through the secondorder intensity
correlation (g2(0)) is preserved. This work demonstrates a robust means to
generate a photonic qubit or more complex state (e.g., a qutrit) for quantum
communication applications by encoding information in the sidebands without the
loss of coherence
Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process
As a solvable and broadly applicable model system, the totally asymmetric
exclusion process enjoys iconic status in the theory of non-equilibrium phase
transitions. Here, we focus on the time dependence of the total number of
particles on a 1-dimensional open lattice, and its power spectrum. Using both
Monte Carlo simulations and analytic methods, we explore its behavior in
different characteristic regimes. In the maximal current phase and on the
coexistence line (between high/low density phases), the power spectrum displays
algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the
high/low density phases, we find pronounced \emph{oscillations}, which damp
into power laws. This behavior can be understood in terms of driven biased
diffusion with conserved noise in the bulk.Comment: 4 pages, 4 figure
Temperature-induced crossovers in the static roughness of a one-dimensional interface
At finite temperature and in presence of disorder, a one-dimensional elastic
interface displays different scaling regimes at small and large lengthscales.
Using a replica approach and a Gaussian Variational Method (GVM), we explore
the consequences of a finite interface width on the small-lengthscale
fluctuations. We compute analytically the static roughness of the
interface as a function of the distance between two points on the
interface. We focus on the case of short-range elasticity and random-bond
disorder. We show that for a finite width two temperature regimes exist.
At low temperature, the expected thermal and random-manifold regimes,
respectively for small and large scales, connect via an intermediate `modified'
Larkin regime, that we determine. This regime ends at a temperature-independent
characteristic `Larkin' length. Above a certain `critical' temperature that we
identify, this intermediate regime disappears. The thermal and random-manifold
regimes connect at a single crossover lengthscale, that we compute. This is
also the expected behavior for zero width. Using a directed polymer
description, we also study via a second GVM procedure and generic scaling
arguments, a modified toy model that provides further insights on this
crossover. We discuss the relevance of the two GVM procedures for the roughness
at large lengthscale in those regimes. In particular we analyze the scaling of
the temperature-dependent prefactor in the roughness B(r)\sim T^{2
\text{\thorn}} r^{2 \zeta} and its corresponding exponent \text{\thorn}. We
briefly discuss the consequences of those results for the quasistatic creep law
of a driven interface, in connection with previous experimental and numerical
studies
Shocks in the asymmetric exclusion process with internal degree of freedom
We determine all families of Markovian three-states lattice gases with pair
interaction and a single local conservation law. One such family of models is
an asymmetric exclusion process where particles exist in two different
nonconserved states. We derive conditions on the transition rates between the
two states such that the shock has a particularly simple structure with minimal
intrinsic shock width and random walk dynamics. We calculate the drift velocity
and diffusion coefficient of the shock.Comment: 26 pages, 1 figur
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