1,195 research outputs found
Linear superposition in nonlinear wave dynamics
We study nonlinear dispersive wave systems described by hyperbolic PDE's in
R^{d} and difference equations on the lattice Z^{d}. The systems involve two
small parameters: one is the ratio of the slow and the fast time scales, and
another one is the ratio of the small and the large space scales. We show that
a wide class of such systems, including nonlinear Schrodinger and Maxwell
equations, Fermi-Pasta-Ulam model and many other not completely integrable
systems, satisfy a superposition principle. The principle essentially states
that if a nonlinear evolution of a wave starts initially as a sum of generic
wavepackets (defined as almost monochromatic waves), then this wave with a high
accuracy remains a sum of separate wavepacket waves undergoing independent
nonlinear evolution. The time intervals for which the evolution is considered
are long enough to observe fully developed nonlinear phenomena for involved
wavepackets. In particular, our approach provides a simple justification for
numerically observed effect of almost non-interaction of solitons passing
through each other without any recourse to the complete integrability. Our
analysis does not rely on any ansatz or common asymptotic expansions with
respect to the two small parameters but it uses rather explicit and
constructive representation for solutions as functions of the initial data in
the form of functional analytic series.Comment: New introduction written, style changed, references added and typos
correcte
Electrodynamics of balanced charges
In this work we modify the wave-corpuscle mechanics for elementary charges
introduced by us recently. This modification is designed to better describe
electromagnetic (EM) phenomena at atomic scales. It includes a modification of
the concept of the classical EM field and a new model for the elementary charge
which we call a balanced charge (b-charge). A b-charge does not interact with
itself electromagnetically, and every b-charge possesses its own elementary EM
field. The EM energy is naturally partitioned as the interaction energy between
pairs of different b-charges. We construct EM theory of b-charges (BEM) based
on a relativistic Lagrangian with the following properties: (i) b-charges
interact only through their elementary EM potentials and fields; (ii) the field
equations for the elementary EM fields are exactly the Maxwell equations with
proper currents; (iii) a free charge moves uniformly preserving up to the
Lorentz contraction its shape; (iv) the Newton equations with the Lorentz
forces hold approximately when charges are well separated and move with
non-relativistic velocities. The BEM theory can be characterized as
neoclassical one which covers the macroscopic as well as the atomic spatial
scales, it describes EM phenomena at atomic scale differently than the
classical EM theory. It yields in macroscopic regimes the Newton equations with
Lorentz forces for centers of well separated charges moving with
nonrelativistic velocities. Applied to atomic scales it yields a hydrogen atom
model with a frequency spectrum matching the same for the Schrodinger model
with any desired accuracy.Comment: Manuscript was edited to improve the exposition and to remove noticed
typo
Vortical and Wave Modes in 3D Rotating Stratified Flows: Random Large Scale Forcing
Utilizing an eigenfunction decomposition, we study the growth and spectra of
energy in the vortical and wave modes of a 3D rotating stratified fluid as a
function of . Working in regimes characterized by moderate
Burger numbers, i.e. or , our results
indicate profound change in the character of vortical and wave mode
interactions with respect to . As with the reference state of
, for the wave mode energy saturates quite quickly
and the ensuing forward cascade continues to act as an efficient means of
dissipating ageostrophic energy. Further, these saturated spectra steepen as
decreases: we see a shift from to scaling for
(where and are the forcing and dissipation scales,
respectively). On the other hand, when the wave mode energy
never saturates and comes to dominate the total energy in the system. In fact,
in a sense the wave modes behave in an asymmetric manner about .
With regard to the vortical modes, for , the signatures of 3D
quasigeostrophy are clearly evident. Specifically, we see a scaling
for and, in accord with an inverse transfer of energy, the
vortical mode energy never saturates but rather increases for all . In
contrast, for and increasing, the vortical modes contain a
progressively smaller fraction of the total energy indicating that the 3D
quasigeostrophic subsystem plays an energetically smaller role in the overall
dynamics.Comment: 18 pages, 6 figs. (abbreviated abstract
Editorial to the Thematic Topic Towards a more sustainable agriculture through managing soil microbiomes
The decay of turbulence in rotating flows
We present a parametric space study of the decay of turbulence in rotating
flows combining direct numerical simulations, large eddy simulations, and
phenomenological theory. Several cases are considered: (1) the effect of
varying the characteristic scale of the initial conditions when compared with
the size of the box, to mimic "bounded" and "unbounded" flows; (2) the effect
of helicity (correlation between the velocity and vorticity); (3) the effect of
Rossby and Reynolds numbers; and (4) the effect of anisotropy in the initial
conditions. Initial conditions include the Taylor-Green vortex, the
Arn'old-Beltrami-Childress flow, and random flows with large-scale energy
spectrum proportional to . The decay laws obtained in the simulations for
the energy, helicity, and enstrophy in each case can be explained with
phenomenological arguments that separate the decay of two-dimensional from
three-dimensional modes, and that take into account the role of helicity and
rotation in slowing down the energy decay. The time evolution of the energy
spectrum and development of anisotropies in the simulations are also discussed.
Finally, the effect of rotation and helicity in the skewness and kurtosis of
the flow is considered.Comment: Sections reordered to address comments by referee
Neoclassical Theory of Elementary Charges with Spin of 1/2
We advance here our neoclassical theory of elementary charges by integrating
into it the concept of spin of 1/2. The developed spinorial version of our
theory has many important features identical to those of the Dirac theory such
as the gyromagnetic ratio, expressions for currents including the spin current,
and antimatter states. In our theory the concepts of charge and anticharge
relate naturally to their "spin" in its rest frame in two opposite directions.
An important difference with the Dirac theory is that both the charge and
anticharge energies are positive whereas their frequencies have opposite signs
Ice island thinning : rates and model calibration with in situ observations from Baffin Bay, Nunavut
Funding: Instrument development and fieldwork were supported by the Northern Transportation Adaptation Initiative of Transport Canada, the Polar Knowledge Canada Safe Passage project (no. 1516-065), and Polar Knowledge Canada's Northern Scientific Training Program. Anna J. Crawford received personal funding from the Garfield Weston Foundation, the Natural Sciences and Engineering Research Council (Canada), and Environment and Climate Change Canada.A 130 km2 tabular iceberg calved from Petermann Glacier innorthwestern Greenland on 5 August 2012. Subsequent fracturing generated manyindividual large “ice islands”, including Petermann ice island (PII)-A-1-f, which drifted between Nares Strait and the North Atlantic.Thinning caused by basal and surface ablation increases the likelihood thatthese ice islands will fracture and disperse further, thereby increasing therisk to marine transport and infrastructure as well as affecting thedistribution of freshwater from the polar ice sheets. We use a uniquestationary and mobile ice-penetrating radar dataset collected over fourcampaigns to PII-A-1-f to quantify and contextualize ice island surface andbasal ablation rates and calibrate a forced convection basal ablation model.The ice island thinned by 4.7 m over 11 months. The majority of thinning (73 %) resulted from basal ablation, but the volume loss associated withbasal ablation was ∼12 times less than that caused by arealreduction (e.g. wave erosion, calving, and fracture). However, localizedthinning may have influenced a large fracture event that occurred along asection of ice that was ∼40 m thinner than the remainder ofthe ice island. The calibration of the basal ablation model, the first knownto be conducted with field data, supports assigning thetheoretically derived value of 1.2×10−5 m2∕5 s−1/5 ∘C−1 to the model's bulk heat transfercoefficient with the use of an empirically estimated ice–ocean interfacetemperature. Overall, this work highlights the value of systematicallycollecting ice island field data for analyzing deterioration processes,assessing their connections to ice island morphology, and adequatelydeveloping models for operational and research purposes.Publisher PDFPeer reviewe
Assessment by accelerometer of sedentarity and of adherence to physical activity recommendations after cardiac rehabilitation program
Thermodynamic Limit Of The Ginzburg-Landau Equations
We investigate the existence of a global semiflow for the complex
Ginzburg-Landau equation on the space of bounded functions in unbounded domain.
This semiflow is proven to exist in dimension 1 and 2 for any parameter values
of the standard cubic Ginzburg-Landau equation. In dimension 3 we need some
restrictions on the parameters but cover nevertheless some part of the
Benjamin-Feijer unstable domain.Comment: uuencoded dvi file (email: [email protected]
Multi-scale analysis of compressible viscous and rotating fluids
We study a singular limit for the compressible Navier-Stokes system when the
Mach and Rossby numbers are proportional to certain powers of a small parameter
\ep. If the Rossby number dominates the Mach number, the limit problem is
represented by the 2-D incompressible Navier-Stokes system describing the
horizontal motion of vertical averages of the velocity field. If they are of
the same order then the limit problem turns out to be a linear, 2-D equation
with a unique radially symmetric solution. The effect of the centrifugal force
is taken into account
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