27,911 research outputs found
Trajectory Characters of Rogue Waves
We present a simple representation for arbitrary-order rogue wave solution
and study on the trajectories of them explicitly. We find that the global
trajectories on temporal-spatial distribution all look like "X" shape for rogue
waves. Short-time prediction on rogue wave can be done through measuring the
information contained in the initial perturbation twice.Comment: Research paper, 6 pages, 6 figure
Quantitative Relation between Modulational Instability and Several Well-known Nonlinear Excitations
We study on the relations between modulational instability and several
well-known nonlinear excitations in a nonlinear fiber, such as bright soliton,
nonlinear continuous wave, Akhmediev breather, Peregrine rogue wave, and
Kuznetsov-Ma breather. We present a quantitative correspondence between them
based on the dominant frequency and propagation constant of each perturbation
on a continuous wave background. Especially, we find rogue wave comes from
modulational instability under the "resonance" perturbation with continuous
wave background. These results will deepen our understanding on rogue wave
excitation and could be helpful for controllable nonlinear wave excitations in
nonlinear fiber and other nonlinear systems.Comment: 5 pages, 1 figur
Modulational instability and homoclinic orbit solutions in vector nonlinear Schr\"odinger equation
Modulational instability has been used to explain the formation of breather
and rogue waves qualitatively. In this paper, we show modulational instability
can be used to explain the structure of them in a quantitative way. We develop
a method to derive general forms for Akhmediev breather and rogue wave
solutions in a -component nonlinear Schr\"odinger equations. The existence
condition for each pattern is clarified clearly. Moreover, the general
multi-high-order rogue wave solutions and multi-Akhmediev breather solutions
for -component nonlinear Schr\"odinger equations are constructed. The
results further deepen our understanding on the quantitative relations between
modulational instability and homoclinic orbits solutions.Comment: 30 page
RepTFD: Replay Based Transient Fault Detection
The advances in IC process make future chip multiprocessors (CMPs) more and
more vulnerable to transient faults. To detect transient faults, previous
core-level schemes provide redundancy for each core separately. As a result,
they may leave transient faults in the uncore parts, which consume over 50%
area of a modern CMP, escaped from detection. This paper proposes RepTFD, the
first core-level transient fault detection scheme with 100% coverage. Instead
of providing redundancy for each core separately, RepTFD provides redundancy
for a group of cores as a whole. To be specific, it replays the execution of
the checked group of cores on a redundant group of cores. Through comparing the
execution results between the two groups of cores, all malignant transient
faults can be caught. Moreover, RepTFD adopts a novel pending period based
record-replay approach, which can greatly reduce the number of execution orders
that need to be enforced in the replay-run. Hence, RepTFD brings only 4.76%
performance overhead in comparison to the normal execution without
fault-tolerance according to our experiments on the RTL design of an industrial
CMP named Godson-3. In addition, RepTFD only consumes about 0.83% area of
Godson-3, while needing only trivial modifications to existing components of
Godson-3.Comment: 22 pages, 11 figure
Efficient Deterministic Replay Using Complete Race Detection
Data races can significantly affect the executions of multi-threaded
programs. Hence, one has to recur the results of data races to
deterministically replay a multi-threaded program. However, data races are
concealed in enormous number of memory operations in a program. Due to the
difficulty of accurately identifying data races, previous multi-threaded
deterministic record/replay schemes for commodity multi-processor system give
up to record data races directly. Consequently, they either record all shared
memory operations, which brings remarkable slowdown to the production run, or
record the synchronization only, which introduces significant efforts to
replay.
Inspired by the advances in data race detection, we propose an efficient
software-only deterministic replay scheme for commodity multi-processor
systems, which is named RacX. The key insight of RacX is as follows: although
it is NP-hard to accurately identify the existence of data races between a pair
of memory operations, we can find out all potential data races in a
multi-threaded program, in which the false positives can be reduced to a small
amount with our automatic false positive reduction techniques. As a result,
RacX can efficiently monitor all potential data races to deterministically
replay a multi-threaded program.
To evaluate RacX, we have carried out experiments over a number of well-known
multi-threaded programs from SPLASH-2 benchmark suite and large-scale
commercial programs. RacX can precisely recur production runs of these programs
with value determinism. Averagely, RacX causes only about 1.21%, 1.89%, 2.20%,
and 8.41% slowdown to the original run during recording (for 2-, 4-, 8- and
16-thread programs, respectively). The soundness, efficiency, scalability, and
portability of RacX well demonstrate its superiority.Comment: 18 pages, 7 figure
Rational W-shaped Optical Soliton on Continuous Wave in Presence of Kerr Dispersion and Stimulated Raman Scattering
We study localized wave on continuous wave background analytically in a
nonlinear fiber with higher order effects such as higher order dispersion, Kerr
dispersion, and stimulated inelastic scattering. We present an exact rational
W-shaped soliton solutions, whose structural properties depend on the frequency
of the background field. The hump value increase with the decrease of the
background frequency in the certain regime. The highest value of the W-shaped
soliton can be nine times the background's, and the distribution shape is
identical with the one of well-known eyes-shaped rogue wave with its maximum
peak. The numerical stimulations indicate that the W-shaped soliton is stable
with small perturbations.Comment: 5 pages, 4 figure
W-shaped solitons generated from a weak modulation in the Sasa-Satsuma equation
We revisit on rational solution of Sasa-Satsuma equation, which can be used
to describe evolution of optical field in a nonlinear fiber with some
high-order effects. We find a striking dynamical process which involves both
modulational instability and modulational stability regimes, in contrast to the
rogue waves and W-shaped soliton reported before which involves modulational
instability and stability respectively. It is demonstrated that stable W-shaped
solitons can be generated from a weak modulation signal on continuous wave
background. This provides a possible way to obtain stable high-intensity pulse
from low-intensity continuous wave background
High-order Rogue Waves in Vector Nonlinear Schr\"odinger Equations
We study on dynamics of high-order rogue wave in two-component coupled
nonlinear Schr\"{o}dinger equations. We find four fundamental rogue waves can
emerge for second-order vector RW in the coupled system, in contrast to the
high-order ones in single component systems. The distribution shape can be
quadrilateral, triangle, and line structures through varying the proper initial
excitations given by the exact analytical solutions. Moreover, six fundamental
rogue wave can emerge on the distribution for second-order vector rogue wave,
which is similar to the scalar third-order ones. The distribution patten for
vector ones are much abundant than the ones for scalar rogue waves. The results
could be of interest in such diverse fields as Bose-Einstein condensates,
nonlinear fibers, and superfluids.Comment: 5 pages, 4 figure
Darboux transformation and multi-dark soliton for N-component coupled nonlinear Schr\"odinger equations
In this paper, we obtain a uniform Darboux transformation for multi-component
coupled NLS equations, which can be reduced to all previous presented Darboux
transformation. As a direct application, we derive the single dark soliton and
multi-dark soliton solutions for multi-component coupled NLS with defocusing
case and mixed focusing and defocusing case. Some exact single and two-dark
solitons of three-component NLS equation are shown by plotting the picture.Comment: 14 pages, 4 figure
Solving the generalized Higgs model from the generalized CRS model
In this paper, we reveal a direct relation between the generalized
one-dimensional Carinena-Ranada-Santander (CRS) model and the radial part of
two-dimensional generalized Higgs model. By this relation, we construct a
series of quasi-exactly solutions for the two-dimensional Higgs model from a
solved generalized CRS model.Comment: 10 page
- …