5,420 research outputs found
A Trophy of the First World War in the Air: Captain William Wendell Rogers and his Victory over a German Gotha Bomber, 12 December 1917
On 12 December 1917, Captain Wendell Rogers, a Canadian pilot in the Royal Flying Corps, was leading a patrol near Ypres, Belgium when his flight intercepted a group of German bombers. In the ensuing combat Rogers shot down a giant Gotha bomber, the first time such an aircraft had been brought down over continental Europe. A piece of that bomber was recovered and was recently acquired by the Canadian War Museum. The artifact, a fabric Iron Cross salvaged from the wing of the downed Gotha, was donated by Captain Rogers’ son Lloyd. The following article will trace how this object came to reside at the new Canadian War Museum in Ottawa
Two-timing, variational principles and waves
In this paper, it is shown how the author's general theory of slowly varying wave trains may be derived as the first term in a formal perturbation expansion. In its most effective form, the perturbation procedure is applied directly to the governing variational principle and an averaged variational principle is established directly. This novel use of a perturbation method may have value outside the class of wave problems considered here. Various useful manipulations of the average Lagrangian are shown to be similar to the transformations leading to Hamilton's equations in mechanics. The methods developed here for waves may also be used on the older problems of adiabatic invariants in mechanics, and they provide a different treatment; the typical problem of central orbits is included in the examples
Comments on some recent multisoliton solutions
It is shown that some recently proposed multisoliton solutions for the nonlinear Klein-Gordon equations can be reduced to a simple form which can be obtained immediately from the equation
On the excitation of edge waves on beaches
The excitation of standing edge waves of frequency ½ω by a normally incident wave train of frequency ω has been discussed previously (Guza & Davis 1974; Guza & Inman 1975; Guza & Bowen 1976) on the basis of shallow-water theory. Here the problem is formulated in the full water-wave theory without making the shallow-water approximation and solved for beach angles β = π/2N, where N is an integer. The work confirms the shallow-water results in the limit N » 1, shows the effect of larger beach angles and allows a more complete discussion of some aspects of the problem
Sharp bounds on enstrophy growth in the viscous Burgers equation
We use the Cole--Hopf transformation and the Laplace method for the heat
equation to justify the numerical results on enstrophy growth in the viscous
Burgers equation on the unit circle. We show that the maximum enstrophy
achieved in the time evolution is scaled as , where
is the large initial enstrophy, whereas the time needed for
reaching the maximal enstrophy is scaled as . These bounds
are sharp for sufficiently smooth initial conditions.Comment: 12 page
Exact shock solution of a coupled system of delay differential equations: a car-following model
In this paper, we present exact shock solutions of a coupled system of delay
differential equations, which was introduced as a traffic-flow model called
{\it the car-following model}. We use the Hirota method, originally developed
in order to solve soliton equations. %While, with a periodic boundary
condition, this system has % a traveling-wave solution given by elliptic
functions. The relevant delay differential equations have been known to allow
exact solutions expressed by elliptic functions with a periodic boundary
conditions. In the present work, however, shock solutions are obtained with
open boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure
Gradient Catastrophe and Fermi Edge Resonances in Fermi Gas
A smooth spatial disturbance of the Fermi surface in a Fermi gas inevitably
becomes sharp. This phenomenon, called {\it the gradient catastrophe}, causes
the breakdown of a Fermi sea to disconnected parts with multiple Fermi points.
We study how the gradient catastrophe effects probing the Fermi system via a
Fermi edge singularity measurement. We show that the gradient catastrophe
transforms the single-peaked Fermi-edge singularity of the tunneling (or
absorption) spectrum to a set of multiple asymmetric singular resonances. Also
we gave a mathematical formulation of FES as a matrix Riemann-Hilbert problem
Spatial chaos in weakly dispersive and viscous media: a nonperturbative theory of the driven KdV-Burgers equation
The asymptotic travelling wave solution of the KdV-Burgers equation driven by
the long scale periodic driver is constructed. The solution represents a
shock-train in which the quasi-periodic sequence of dispersive shocks or
soliton chains is interspersed by smoothly varying regions. It is shown that
the periodic solution which has the spatial driver period undergoes period
doublings as the governing parameter changes. Two types of chaotic behavior are
considered. The first type is a weak chaos, where only a small chaotic
deviation from the periodic solution occurs. The second type corresponds to the
developed chaos where the solution ``ignores'' the driver period and represents
a random sequence of uncorrelated shocks. In the case of weak chaos the shock
coordinate being repeatedly mapped over the driver period moves on a chaotic
attractor, while in the case of developed chaos it moves on a repellor. Both
solutions depend on a parameter indicating the reference shock position in the
shock-train. The structure of a one dimensional set to which this parameter
belongs is investigated. This set contains measure one intervals around the
fixed points in the case of periodic or weakly chaotic solutions and it becomes
a fractal in the case of strong chaos. The capacity dimension of this set is
calculated.Comment: 32 pages, 12 PostScript figures, useses elsart.sty and boxedeps.tex,
fig.11 is not included and can be requested from <[email protected]
Strongly nonlinear waves in capillary electrophoresis
In capillary electrophoresis, sample ions migrate along a micro-capillary
filled with a background electrolyte under the influence of an applied electric
field. If the sample concentration is sufficiently high, the electrical
conductivity in the sample zone could differ significantly from the
background.Under such conditions, the local migration velocity of sample ions
becomes concentration dependent resulting in a nonlinear wave that exhibits
shock like features. If the nonlinearity is weak, the sample concentration
profile, under certain simplifying assumptions, can be shown to obey Burgers'
equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which
has an exact analytical solution for arbitrary initial condition.In this paper,
we use a numerical method to study the problem in the more general case where
the sample concentration is not small in comparison to the concentration of
background ions. In the case of low concentrations, the numerical results agree
with the weakly nonlinear theory presented earlier, but at high concentrations,
the wave evolves in a way that is qualitatively different.Comment: 7 pages, 5 figures, 1 Appendix, 2 videos (supplementary material
- …