493 research outputs found
The de Broglie Wave as a Localized Excitation of the Action Function
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited.
The equation is shown to permit solutions in the form of breathers
(nondispersive oscillating/spinning solitons), displaying simultaneous
particle-like and wave-like behavior adaptable to the properties of the de
Broglie clock. Within this formalism the de Broglie wave acquires the meaning
of a localized excitation of the classical action function. The problem of
quantization in terms of the breathing action function is discussed.Comment: 11 page
Hydrothermal Surface-Wave Instability and the Kuramoto-Sivashinsky Equation
We consider a system formed by an infinite viscous liquid layer with a
constant horizontal temperature gradient, and a basic nonlinear bulk velocity
profile. In the limit of long-wavelength and large nondimensional surface
tension, we show that hydrothermal surface-wave instabilities may give rise to
disturbances governed by the Kuramoto-Sivashinsky equation. A possible
connection to hot-wire experiments is also discussed.Comment: 11 pages, RevTex, no figure
Stability of Rossby waves in the beta-plane approximation
Floquet theory is used to describe the unstable spectrum at large scales of
the beta-plane equation linearized about Rossby waves. Base flows consisting of
one to three Rossby wave are considered analytically using continued fractions
and the method of multiple scales, while base flow with more than three Rossby
waves are studied numerically. It is demonstrated that the mechanism for
instability changes from inflectional to triad resonance at an O(1) transition
Rhines number Rh, independent of the Reynolds number. For a single Rossby wave
base flow, the critical Reynolds number Re^c for instability is found in
various limits. In the limits Rh --> infinity and k --> 0, the classical value
Re^c = sqrt(2) is recovered. For Rh --> 0 and all orientations of the Rossby
wave except zonal and meridional, the base flow is unstable for all Reynolds
numbers; a zonal Rossby wave is stable, while a meridional Rossby wave has
critical Reynolds number Re^c = sqrt(2). For more isotropic base flows
consisting of many Rossby waves (up to forty), the most unstable mode is purely
zonal for 2 <= Rh < infinity and is nearly zonal for Rh = 1/2, where the
transition Rhines number is again O(1), independent of the Reynolds number and
consistent with a change in the mechanism for instability from inflectional to
triad resonance.Comment: 56 pages, 31 figures, submitted to Physica
Defect-Mediated Stability: An Effective Hydrodynamic Theory of Spatio-Temporal Chaos
Spatiotemporal chaos (STC) exhibited by the Kuramoto-Sivashinsky (KS)
equation is investigated analytically and numerically. An effective stochastic
equation belonging to the KPZ universality class is constructed by
incorporating the chaotic dynamics of the small KS system in a coarse-graining
procedure. The bare parameters of the effective theory are computed
approximately. Stability of the system is shown to be mediated by space-time
defects that are accompanied by stochasticity. The method of analysis and the
mechanism of stability may be relevant to a class of STC problems.Comment: 34 pages + 9 figure
Fingering Instability in Combustion
A thin solid (e.g., paper), burning against an oxidizing wind, develops a
fingering instability with two decoupled length scales. The spacing between
fingers is determined by the P\'eclet number (ratio between advection and
diffusion). The finger width is determined by the degree two dimensionality.
Dense fingers develop by recurrent tip splitting. The effect is observed when
vertical mass transport (due to gravity) is suppressed. The experimental
results quantitatively verify a model based on diffusion limited transport
On disintegration of lean hydrogen flames in narrow gaps
The disintegration of near limit flames propagating through the gap of
Hele-Shaw cells has recently become a subject of active research. In this
paper, the flamelets resulting from the disintegration of the continuous front
are interpreted in terms of the Zeldovich flame-balls stabilized by volumetric
heat losses. A complicated free-boundary problem for 2D self-drifting near
circular flamelets is reduced to a 1D model. The 1D formulation is then
utilized to obtain the locus of the flamelet velocity, size, heat losses and
Lewis numbers at which the self-drifting flamelets may exist.Comment: 10 pages, 12 figures. arXiv admin note: text overlap with
arXiv:2308.0853
Modeling of 2D self-drifting flame-balls in Hele-Shaw cells
The disintegration of near limit flames propagating through the gap of
Hele-Shaw cells has recently become a subject of active research. In this
paper, the flamelets resulting from the disintegration of the continuous front
a reinterpreted in terms of the Zeldovich flame-balls stabilized by volumetric
heat losses. A complicated free-boundary problem for 2D self-drifting near
circular flamelets is reduced to a 1D model. The 1D formulation is then
utilized to obtain the locus of the flamelet velocity, radius, heat losses and
Lewis numbers at which the self-drifting flamelet exists.Comment: 19 pages, 22 figure
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