711 research outputs found
Hydrodynamic fingering instability of driven wetting films: hindrance by diffusion
Recent experimental and theoretical efforts have revealed the existence of a fingering instability at the moving front of thin liquid films forced to spread under gravitational, rotational or surface shear stresses, as for example by using the Marangoni effect. The authors describe how the presence of a precursor film in front of the spreading macroscopic film, whether it is by prewetting the substrate or by surface diffusion or multilayer absorption, can prevent the development of the instability
Simulations of Solid-on-Solid Models of Spreading of Viscous Droplets
We have studied the dynamics of spreading of viscous non-volatile fluids on
surfaces by MC simulations of SOS models. We have concentrated on the complete
wetting regime, with surface diffusion barriers neglected for simplicity.
First, we have performed simulations for the standard SOS model. Formation of a
single precursor layer, and a density profile with a spherical cap shaped
center surrounded by Gaussian tails can be reproduced with this model.
Dynamical layering (DL), however, only occurs with a very strongly attractive
van der Waals type of substrate potential. To more realistically describe the
spreading of viscous liquid droplets, we introduce a modified SOS model. In the
new model, tendency for DL and the effect of the surface potential are in part
embedded into the dynamics of the model. This allows a relatively simple
description of the spreading under different conditions, with a temperature
like parameter which strongly influences the droplet morphologies. Both rounded
droplet shapes and DL can easily be reproduced with the model. Furthermore, the
precursor width increases proportional to the square root of time, in
accordance with experimental observations. PACS: 68.10.Gw, 05.70.Ln, 61.20.Ja.Comment: to appear in Physica A (1994), standard LaTex, 20 page
Quantum Superposition Principle and Geometry
If one takes seriously the postulate of quantum mechanics in which physical
states are rays in the standard Hilbert space of the theory, one is naturally
lead to a geometric formulation of the theory. Within this formulation of
quantum mechanics, the resulting description is very elegant from the
geometrical viewpoint, since it allows to cast the main postulates of the
theory in terms of two geometric structures, namely a symplectic structure and
a Riemannian metric. However, the usual superposition principle of quantum
mechanics is not naturally incorporated, since the quantum state space is
non-linear. In this note we offer some steps to incorporate the superposition
principle within the geometric description. In this respect, we argue that it
is necessary to make the distinction between a 'projective superposition
principle' and a 'decomposition principle' that extend the standard
superposition principle. We illustrate our proposal with two very well known
examples, namely the spin 1/2 system and the two slit experiment, where the
distinction is clear from the physical perspective. We show that the two
principles have also a different mathematical origin within the geometrical
formulation of the theory.Comment: 10 pages, no figures. References added. V3 discussion expanded and
new results added, 14 pages. Dedicated to Michael P. Ryan on the occasion of
his sixtieth bithda
Exponential families, Kahler geometry and quantum mechanics
Exponential families are a particular class of statistical manifolds which
are particularly important in statistical inference, and which appear very
frequently in statistics. For example, the set of normal distributions, with
mean {\mu} and deviation {\sigma}, form a 2-dimensional exponential family.
In this paper, we show that the tangent bundle of an exponential family is
naturally a Kahler manifold. This simple but crucial observation leads to the
formalism of quantum mechanics in its geometrical form, i.e. based on the
Kahler structure of the complex projective space, but generalizes also to more
general Kahler manifolds, providing a natural geometric framework for the
description of quantum systems. Many questions related to this "statistical
Kahler geometry" are discussed, and a close connection with representation
theory is observed. Examples of physical relevance are treated in details. For
example, it is shown that the spin of a particle can be entirely understood by
means of the usual binomial distribution. This paper centers on the
mathematical foundations of quantum mechanics, and on the question of its
potential generalization through its geometrical formulation
Dynamics of Spreading of Chainlike Molecules with Asymmetric Surface Interactions
In this work we study the spreading dynamics of tiny liquid droplets on solid
surfaces in the case where the ends of the molecules feel different
interactions with respect to the surface. We consider a simple model of dimers
and short chainlike molecules that cannot form chemical bonds with the surface.
We use constant temperature Molecular Dynamics techniques to examine in detail
the microscopic structure of the time dependent precursor film. We find that in
some cases it can exhibit a high degree of local order that can persist even
for flexible chains. Our model also reproduces the experimentally observed
early and late-time spreading regimes where the radius of the film grows
proportional to the square root of time. The ratios of the associated transport
coefficients are in good overall agreement with experiments. Our density
profiles are also in good agreement with measurements on the spreading of
molecules on hydrophobic surfaces.Comment: 12 pages, LaTeX with APS macros, 21 figures available by contacting
[email protected], to appear in Phys. Rev.
Convergence to equilibrium for many particle systems
The goal of this paper is to give a short review of recent results of the
authors concerning classical Hamiltonian many particle systems. We hope that
these results support the new possible formulation of Boltzmann's ergodicity
hypothesis which sounds as follows. For almost all potentials, the minimal
contact with external world, through only one particle of , is sufficient
for ergodicity. But only if this contact has no memory. Also new results for
quantum case are presented
Dewetting, partial wetting and spreading of a two-dimensional monolayer on solid surface
We study the behavior of a semi-infinite monolayer, which is placed initially
on a half of an infinite in both directions, ideal crystalline surface, and
then evolves in time due to random motion of the monolayer particles. Particles
dynamics is modeled as the Kawasaki particle-vacancy exchange process in the
presence of long-range attractive particle-particle interactions. In terms of
an analytically solvable mean-field-type approximation we calculate the mean
displacement X(t) of the monolayer edge and discuss the conditions under which
such a monolayer spreads (X(t) > 0), partially wets (X(t) = 0) or dewets from
the solid surface (X(t) < 0).Comment: 4 pages, 2 figures, to appear in PRE (RC
Dynamical fluctuations in classical adiabatic processes: General description and their implications
Dynamical fluctuations in classical adiabatic processes are not considered by
the conventional classical adiabatic theorem. In this work a general result is
derived to describe the intrinsic dynamical fluctuations in classical adiabatic
processes. Interesting implications of our general result are discussed via two
subtopics, namely, an intriguing adiabatic geometric phase in a dynamical model
with an adiabatically moving fixed-point solution, and the possible "pollution"
to Hannay's angle or to other adiabatic phase objects for adiabatic processes
involving non-fixed-point solutions.Comment: 19 pages, no figures, discussion significantly expanded, published
versio
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