14,203 research outputs found
Composing Scalable Nonlinear Algebraic Solvers
Most efficient linear solvers use composable algorithmic components, with the
most common model being the combination of a Krylov accelerator and one or more
preconditioners. A similar set of concepts may be used for nonlinear algebraic
systems, where nonlinear composition of different nonlinear solvers may
significantly improve the time to solution. We describe the basic concepts of
nonlinear composition and preconditioning and present a number of solvers
applicable to nonlinear partial differential equations. We have developed a
software framework in order to easily explore the possible combinations of
solvers. We show that the performance gains from using composed solvers can be
substantial compared with gains from standard Newton-Krylov methods.Comment: 29 pages, 14 figures, 13 table
Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton Hierarchy
Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different
from the original ones. Binary nonlinearization procedure corresponding to the
Bargmann symmetry constraint is carried out for those Lax pairs. The proposed
Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of
commutative, finite dimensional integrable Hamiltonian systems in the Liouville
sense, which also provides us with new examples of finite dimensional
integrable Hamiltonian systems. A sort of involutive solutions to the
Kaup-Newell hierarchy are exhibited through the obtained finite dimensional
integrable systems and the general involutive system engendered by binary
nonlinearization is reduced to a specific involutive system generated by
mono-nonlinearization.Comment: 15 pages, plain+ams tex, to be published in Il Nuovo Cimento
Structure and energetics of the Si-SiO_2 interface
Silicon has long been synonymous with semiconductor technology. This unique
role is due largely to the remarkable properties of the Si-SiO_2 interface,
especially the (001)-oriented interface used in most devices. Although Si is
crystalline and the oxide is amorphous, the interface is essentially perfect,
with an extremely low density of dangling bonds or other electrically active
defects. With the continual decrease of device size, the nanoscale structure of
the silicon/oxide interface becomes more and more important. Yet despite its
essential role, the atomic structure of this interface is still unclear. Using
a novel Monte Carlo approach, we identify low-energy structures for the
interface. The optimal structure found consists of Si-O-Si "bridges" ordered in
a stripe pattern, with very low energy. This structure explains several
puzzling experimental observations.Comment: LaTex file with 4 figures in GIF forma
Front Stability in Mean Field Models of Diffusion Limited Growth
We present calculations of the stability of planar fronts in two mean field
models of diffusion limited growth. The steady state solution for the front can
exist for a continuous family of velocities, we show that the selected velocity
is given by marginal stability theory. We find that naive mean field theory has
no instability to transverse perturbations, while a threshold mean field theory
has such a Mullins-Sekerka instability. These results place on firm theoretical
ground the observed lack of the dendritic morphology in naive mean field theory
and its presence in threshold models. The existence of a Mullins-Sekerka
instability is related to the behavior of the mean field theories in the
zero-undercooling limit.Comment: 26 pp. revtex, 7 uuencoded ps figures. submitted to PR
Probing the Slope of Cluster Mass Profile with Gravitational Einstein Rings: Application to Abell 1689
The strong lensing modelling of gravitational ``rings'' formed around massive
galaxies is sensitive to the amplitude of the external shear and convergence
produced by nearby mass condensations. In current wide field surveys, it is now
possible to find out a large number of rings, typically 10 gravitational rings
per square degree. We propose here, to systematically study gravitational rings
around galaxy clusters to probe the cluster mass profile beyond the cluster
strong lensing regions. For cluster of galaxies with multiple arc systems, we
show that rings found at various distances from the cluster centre can improve
the modelling by constraining the slope of the cluster mass profile. We outline
the principle of the method with simple numerical simulations and we apply it
to 3 rings discovered recently in Abell~1689. In particular, the lens modelling
of the 3 rings confirms that the cluster is bimodal, and favours a slope of the
mass profile steeper than isothermal at a cluster radius \sim 300 \kpc. These
results are compared with previous lens modelling of Abell~1689 including weak
lensing analysis. Because of the difficulty arising from the complex mass
distribution in Abell~1689, we argue that the ring method will be better
implemented on simpler and relaxed clusters.Comment: Accepted for publication in MNRAS. Substantial modification after
referee's repor
Effect of periodic parametric excitation on an ensemble of force-coupled self-oscillators
We report the synchronization behavior in a one-dimensional chain of
identical limit cycle oscillators coupled to a mass-spring load via a force
relation. We consider the effect of periodic parametric modulation on the final
synchronization states of the system. Two types of external parametric
excitations are investigated numerically: periodic modulation of the stiffness
of the inertial oscillator and periodic excitation of the frequency of the
self-oscillatory element. We show that the synchronization scenarios are ruled
not only by the choice of parameters of the excitation force but depend on the
initial collective state in the ensemble. We give detailed analysis of
entrainment behavior for initially homogeneous and inhomogeneous states. Among
other results, we describe a regime of partial synchronization. This regime is
characterized by the frequency of collective oscillation being entrained to the
stimulation frequency but different from the average individual oscillators
frequency.Comment: Comments and suggestions are welcom
Jigsaw Puzzle: Selective Backdoor Attack to Subvert Malware Classifiers
Malware classifiers are subject to training-time exploitation due to the need to regularly retrain using samples collected from the wild. Recent work has demonstrated the feasibility of backdoor attacks against malware classifiers, and yet the stealthiness of such attacks is not well understood. In this paper, we focus on Android malware classifiers and investigate backdoor attacks under the clean-label setting (i.e., attackers do not have complete control over the training process or the labeling of poisoned data). Empirically, we show that existing backdoor attacks against malware classifiers are still detectable by recent defenses such as MNTD. To improve stealthiness, we propose a new attack, Jigsaw Puzzle (JP), based on the key observation that malware authors have little to no incentive to protect any other authors' malware but their own. As such, Jigsaw Puzzle learns a trigger to complement the latent patterns of the malware author's samples, and activates the backdoor only when the trigger and the latent pattern are pieced together in a sample. We further focus on realizable triggers in the problem space (e.g., software code) using bytecode gadgets broadly harvested from benign software. Our evaluation confirms that Jigsaw Puzzle is effective as a backdoor, remains stealthy against state-of-the-art defenses, and is a threat in realistic settings that depart from reasoning about feature-space-only attacks. We conclude by exploring promising approaches to improve backdoor defenses
Finite Size Scaling of Domain Chaos
Numerical studies of the domain chaos state in a model of rotating
Rayleigh-Benard convection suggest that finite size effects may account for the
discrepancy between experimentally measured values of the correlation length
and the predicted divergence near onset
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