429 research outputs found
Frozen water waves over rough topographical bottoms
The propagation of surface water waves over rough topographical bottoms is
investigated by the multiple scattering theory. It is shown that the waves can
be localized spatially through the process of multiple scattering and wave
interference, a peculiar wave phenomenon which has been previously discussed
for frozen light in optical systems (S. John, Nature {\bf 390}, 661, (1997)).
We demonstrate that when frozen, the transmission of the waves falls off
exponentially, and a cooperative behavior appears, fully supporting previous
predictions. A phase diagram method is used to illustrate this distinct phase
states in the wave propagation.Comment: 4 pages and 5 figure
Gravity waves over topographical bottoms: Comparison with the experiment
In this paper, the propagation of water surface waves over one-dimensional
periodic and random bottoms is investigated by the transfer matrix method. For
the periodic bottoms, the band structure is calculated, and the results are
compared to the transmission results. When the bottoms are randomized, the
Anderson localization phenomenon is observed. The theory has been applied to an
existing experiment (Belzons, et al., J. Fluid Mech. {\bf 186}, 530 (1988)). In
general, the results are compared favorably with the experimental observation.Comment: 15 pages, 7 figure
Modeling the interactions of biomatter and biofluid
The internal motions of biomatter immersed in biofluid are investigated. The
interactions between the fragments of biomatter and its surrounding biofluid
are modeled using field theory. In the model, the biomatter is coupled to the
gauge field representing the biofluid. It is shown that at non-relativistic
limit various equation of motions, from the well-known Sine-Gordon equation to
the simultaneous nonlinear equations, can be reproduced within a single
framework.Comment: 10 pages, 3 figure
Cyber Security: China and Russia\u27s Erosion of 21st Century United States\u27 Hegemony
With Russia and China emerging as challengers to U.S. hegemony, the use of cyber warfare could tilt the current balance of power in either of their favors. Using various methods, hackers can acquire sensitive information and destroy online infrastructures. In the development of cyber warfare, China has become a seasoned veteran with computer virus operations dating back to 199714. Russia has emerged as a cyber aggressor, as seen in Russia’s cyber attacks on several countries in the last decade. This paper argues that, with the growth of foreign cyber technology, the probability of cyberspace being used as a military front by state or non-state actors against the United States increases
Bandgaps in the propagation and scattering of surface water waves over cylindrical steps
Here we investigate the propagation and scattering of surface water waves by
arrays of bottom-mounted cylindrical steps. Both periodic and random
arrangements of the steps are considered. The wave transmission through the
arrays is computed using the multiple scattering method based upon a recently
derived formulation. For the periodic case, the results are compared to the
band structure calculation. We demonstrate that complete band gaps can be
obtained in such a system. Furthermore, we show that the randomization of the
location of the steps can significantly reduce the transmission of water waves.
Comparison with other systems is also discussed.Comment: 4 pages, 3 figure
Large time existence for 3D water-waves and asymptotics
We rigorously justify in 3D the main asymptotic models used in coastal
oceanography, including: shallow-water equations, Boussinesq systems,
Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre
approximation and full-dispersion model. We first introduce a ``variable''
nondimensionalized version of the water-waves equations which vary from shallow
to deep water, and which involves four dimensionless parameters. Using a
nonlocal energy adapted to the equations, we can prove a well-posedness
theorem, uniformly with respect to all the parameters. Its validity ranges
therefore from shallow to deep-water, from small to large surface and bottom
variations, and from fully to weakly transverse waves. The physical regimes
corresponding to the aforementioned models can therefore be studied as
particular cases; it turns out that the existence time and the energy bounds
given by the theorem are always those needed to justify the asymptotic models.
We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and
remarks added) To appear in Inventione
- …