118,822 research outputs found
Nonlinear Electron Oscillations in a Viscous and Resistive Plasma
New non-linear, spatially periodic, long wavelength electrostatic modes of an
electron fluid oscillating against a motionless ion fluid (Langmuir waves) are
given, with viscous and resistive effects included. The cold plasma
approximation is adopted, which requires the wavelength to be sufficiently
large. The pertinent requirement valid for large amplitude waves is determined.
The general non-linear solution of the continuity and momentum transfer
equations for the electron fluid along with Poisson's equation is obtained in
simple parametric form. It is shown that in all typical hydrogen plasmas, the
influence of plasma resistivity on the modes in question is negligible. Within
the limitations of the solution found, the non-linear time evolution of any
(periodic) initial electron number density profile n_e(x, t=0) can be
determined (examples). For the modes in question, an idealized model of a
strictly cold and collisionless plasma is shown to be applicable to any real
plasma, provided that the wavelength lambda >> lambda_{min}(n_0,T_e), where n_0
= const and T_e are the equilibrium values of the electron number density and
electron temperature. Within this idealized model, the minimum of the initial
electron density n_e(x_{min}, t=0) must be larger than half its equilibrium
value, n_0/2. Otherwise, the corresponding maximum n_e(x_{max},t=tau_p/2),
obtained after half a period of the plasma oscillation blows up. Relaxation of
this restriction on n_e(x, t=0) as one decreases lambda, due to the increase of
the electron viscosity effects, is examined in detail. Strong plasma viscosity
is shown to change considerably the density profile during the time evolution,
e.g., by splitting the largest maximum in two.Comment: 16 one column pages, 11 figures, Abstract and Sec. I, extended, Sec.
VIII modified, Phys. Rev. E in pres
Periodic solutions with nonconstant sign in Abel equations of the second kind
The study of periodic solutions with constant sign in the Abel equation of
the second kind can be made through the equation of the first kind. This is
because the situation is equivalent under the transformation ,
and there are many results available in the literature for the first kind
equation. However, the equivalence breaks down when one seeks for solutions
with nonconstant sign. This note is devoted to periodic solutions with
nonconstant sign in Abel equations of the second kind. Specifically, we obtain
sufficient conditions to ensure the existence of a periodic solution that
shares the zeros of the leading coefficient of the Abel equation. Uniqueness
and stability features of such solutions are also studied.Comment: 10 page
Non-trivial, non-negative periodic solutions of a system of singular-degenerate parabolic equations with nonlocal terms
We study the existence of non-trivial, non-negative periodic solutions for
systems of singular-degenerate parabolic equations with nonlocal terms and
satisfying Dirichlet boundary conditions. The method employed in this paper is
based on the Leray-Schauder topological degree theory. However, verifying the
conditions under which such a theory applies is more involved due to the
presence of the singularity. The system can be regarded as a possible model of
the interactions of two biological species sharing the same isolated territory,
and our results give conditions that ensure the coexistence of the two species.Comment: 39 page
Positive periodic solutions of singular systems
The existence and multiplicity of positive periodic solutions for second
order non-autonomous singular dynamical systems are established with
superlinearity or sublinearity assumptions at infinity for an appropriately
chosen parameter. Our results provide a unified treatment for the problem and
significantly improve several results in the literature. The proof of our
results is based on the Krasnoselskii fixed point theorem in a cone.Comment: Journal of Differential Equations, 201
An analysis of the field theoretic approach to the quasi-continuum method
Using the orbital-free density functional theory as a model theory, we
present an analysis of the field theoretic approach to quasi-continuum method.
In particular, by perturbation method and multiple scale analysis, we provide a
formal justification for the validity of the coarse-graining of various fields,
which is central to the quasi-continuum reduction of field theories. Further,
we derive the homogenized equations that govern the behavior of electronic
fields in regions of smooth deformations. Using Fourier analysis, we determine
the far-field solutions for these fields in the presence of local defects, and
subsequently estimate cell-size effects in computed defect energies.Comment: 26 pages, 1 figur
Some Homogenization Results for Non-Coercive Hamilton-Jacobi Equations
Recently, C. Imbert & R. Monneau study the homogenization of coercive
Hamilton-Jacobi Equations with a -dependence : this unusual dependence
leads to a non-standard cell problem and, in order to solve it, they introduce
new ideas to obtain the estimates on the oscillations of the solutions. In this
article, we use their ideas to provide new homogenization results for
``standard'' Hamilton-Jacobi Equations (i.e. without a -dependence) but in
the case of {\it non-coercive Hamiltonians}. As a by-product, we obtain a
simpler and more natural proof of the results of C. Imbert & R. Monneau, but
under slightly more restrictive assumptions on the Hamiltonians
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