37,073 research outputs found
Inertial and dimensional effects on the instability of a thin film
We consider here the effects of inertia on the instability of a flat liquid
film under the effects of capillary and intermolecular forces (van der Waals
interaction). Firstly, we perform the linear stability analysis within the long
wave approximation, which shows that the inclusion of inertia does not produce
new regions of instability other than the one previously known from the usual
lubrication case. The wavelength, , corresponding to he maximum
growth, , and the critical (marginal) wavelength do not change at
all. The most affected feature of the instability under an increase of the
Laplace number is the noticeable decrease of the growth rates of the unstable
modes. In order to put in evidence the effects of the bidimensional aspects of
the flow (neglected in the long wave approximation), we also calculate the
dispersion relation of the instability from the linearized version of the
complete Navier-Stokes (N-S) equation. Unlike the long wave approximation, the
bidimensional model shows that can vary significantly with inertia
when the aspect ratio of the film is not sufficiently small. We also perform
numerical simulations of the nonlinear N-S equations and analyze to which
extent the linear predictions can be applied depending on both the amount of
inertia involved and the aspect ratio of the film
On algebraic classification of quasi-exactly solvable matrix models
We suggest a generalization of the Lie algebraic approach for constructing
quasi-exactly solvable one-dimensional Schroedinger equations which is due to
Shifman and Turbiner in order to include into consideration matrix models. This
generalization is based on representations of Lie algebras by first-order
matrix differential operators. We have classified inequivalent representations
of the Lie algebras of the dimension up to three by first-order matrix
differential operators in one variable. Next we describe invariant
finite-dimensional subspaces of the representation spaces of the one-,
two-dimensional Lie algebras and of the algebra sl(2,R). These results enable
constructing multi-parameter families of first- and second-order quasi-exactly
solvable models. In particular, we have obtained two classes of quasi-exactly
solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge
Pressure-induced structural, electronic, and magnetic effects in BiFeO3
We present a first-principles study of multiferroic BiFeO3 at high pressures.
Our work reveals the main structural (change in Bi's coordination and loss of
ferroelectricity), electronic (spin crossover and metallization), and magnetic
(loss of order) effects favored by compression and how they are connected. Our
results are consistent with the striking manifold transition observed
experimentally by Gavriliuk et al. [Phys. Rev. B 77, 155112 (2008)] and provide
an explanation for it.Comment: 4 pages with 4 figures embedded. More information at
http://www.icmab.es/dmmis/leem/jorg
Thin film instability with thermal noise
We study the effects of stochastic thermal fluctuations on the instability of
the free surface of a flat liquid film upon a solid substrate. These
fluctuations are represented as a standard Brownian motion that can be added to
the deterministic equation for the film thickness within the lubrication
approximation. Here, we consider that while the noise term is white in time, it
is coloured in space. This allows for the introduction of a finite correlation
length in the description of the randomized intermolecular interaction.
Together with the expected spatial periodicity of the flow, we find a
dimensionless parameter, , that accounts for the relative importance of
the spatial correlation. We perform here the linear stability analysis (LSA) of
the film under the influence of both terms, and find the corresponding power
spectra for the amplitudes of the normal modes of the instability. We compare
this theoretical result with the numerical simulations of the complete
non-linear problem, and find a good agreement for early times. For late times,
we find that the stochastic LSA predictions on the dominant wavelength remains
basically valid. We also use the theoretical spectra to fit experimental data
from a nanometric melted copper film, and find the corresponding times of the
evolution as well as the values of the parameter,
Quasi-exactly Solvable Lie Superalgebras of Differential Operators
In this paper, we study Lie superalgebras of matrix-valued
first-order differential operators on the complex line. We first completely
classify all such superalgebras of finite dimension. Among the
finite-dimensional superalgebras whose odd subspace is nontrivial, we find
those admitting a finite-dimensional invariant module of smooth vector-valued
functions, and classify all the resulting finite-dimensional modules. The
latter Lie superalgebras and their modules are the building blocks in the
construction of QES quantum mechanical models for spin 1/2 particles in one
dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page
Soliton tunneling with sub-barrier kinetic energies
We investigate (theoretically and numerically) the dynamics of a soliton
moving in an asymmetrical potential well with a finite barrier. For large
values of the width of the well, the width of the barrier and/or the height of
the barrier, the soliton behaves classically. On the other hand, we obtain the
conditions for the existence of soliton tunneling with sub-barrier kinetic
energies. We apply these results to the study of soliton propagation in
disordered systems.Comment: 6 eps figures. To appear in Physical Review E (Rapid Communications
A Novel Multi-parameter Family of Quantum Systems with Partially Broken N-fold Supersymmetry
We develop a systematic algorithm for constructing an N-fold supersymmetric
system from a given vector space invariant under one of the supercharges.
Applying this algorithm to spaces of monomials, we construct a new
multi-parameter family of N-fold supersymmetric models, which shall be referred
to as "type C". We investigate various aspects of these type C models in
detail. It turns out that in certain cases these systems exhibit a novel
phenomenon, namely, partial breaking of N-fold supersymmetry.Comment: RevTeX 4, 28 pages, no figure
Quasi-Exactly Solvable Spin 1/2 Schr\"odinger Operators
The algebraic structures underlying quasi-exact solvability for spin 1/2
Hamiltonians in one dimension are studied in detail. Necessary and sufficient
conditions for a matrix second-order differential operator preserving a space
of wave functions with polynomial components to be equivalent to a \sch\
operator are found. Systematic simplifications of these conditions are
analyzed, and are then applied to the construction of several new examples of
multi-parameter QES spin 1/2 Hamiltonians in one dimension.Comment: 32 pages, LaTeX2e using AMS-LaTeX packag
Making Sustainable Agriculture Real in CAP 2020: The Role of Conservation Agriculture
Europe is about to redefine its Common Agriculture Policy (CAP) for the near future. The question is whether this redefinition is more a fine-tuning of the existing CAP or whether thorough changes can be expected. Looking back to the last revision of CAP the most notable change is, undoubtedly, the concern about EU and global food security. The revival of the interest in agricultural production already became evident during the Health Check as a consequence of climbing commodity prices in 2007/08. It is therefore no surprise that “rising concerns regarding both EU and global food security” is the first topic to appear in the list of justifications for the need for a CAP reform. Other challenges mentioned in this list such as sustainable management of natural resources, climate change and its mitigation, improvement of competitiveness to withstand globalization and rising price volatility, etc., while not new are considered worthwhile enough to be maintained and reappraised
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