409 research outputs found
Probability of local bifurcation type from a fixed point: A random matrix perspective
Results regarding probable bifurcations from fixed points are presented in
the context of general dynamical systems (real, random matrices), time-delay
dynamical systems (companion matrices), and a set of mappings known for their
properties as universal approximators (neural networks). The eigenvalue spectra
is considered both numerically and analytically using previous work of Edelman
et. al. Based upon the numerical evidence, various conjectures are presented.
The conclusion is that in many circumstances, most bifurcations from fixed
points of large dynamical systems will be due to complex eigenvalues.
Nevertheless, surprising situations are presented for which the aforementioned
conclusion is not general, e.g. real random matrices with Gaussian elements
with a large positive mean and finite variance.Comment: 21 pages, 19 figure
Adsorption hysteresis and capillary condensation in disordered porous solids: a density functional study
We present a theoretical study of capillary condensation of fluids adsorbed
in mesoporous disordered media. Combining mean-field density functional theory
with a coarse-grained description in terms of a lattice-gas model allows us to
investigate both the out-of-equilibrium (hysteresis) and the equilibrium
behavior. We show that the main features of capillary condensation in
disordered solids result from the appearance of a complex free-energy landscape
with a large number of metastable states. We detail the numerical procedures
for finding these states, and the presence or absence of transitions in the
thermodynamic limit is determined by careful finite-size studies.Comment: 30 pages, 18 figures. To appear in J. Phys.: Condens. Matte
Numerical study of multilayer adsorption on fractal surfaces
We report a numerical study of van der Waals adsoprtion and capillary
condensation effects on self-similar fractal surfaces. An assembly of uncoupled
spherical pores with a power-law distributin of radii is used to model fractal
surfaces with adjustable dimensions. We find that the commonly used fractal
Frankel-Halsey-Hill equation systematically fails to give the correct dimension
due to crossover effects, consistent with the findings of recent experiments.
The effects of pore coupling and curvature dependent surface tension were also
studied.Comment: 11 pages, 3 figure
Discrete Nonholonomic LL Systems on Lie Groups
This paper applies the recently developed theory of discrete nonholonomic
mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie
groups. The theory is illustrated with the discrete versions of two classical
nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation
of the reduced energy by the discrete flow is observed and the discrete
momentum conservation is discussed.Comment: 32 pages, 13 figure
Density functional formalism in the canonical ensemble
Density functional theory, when applied to systems with , is based
on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to
Mermin (HKSM theorem). While a straightforward canonical ensemble
generalization fails, work in nanopore systems could certainly benefit from
such extension. We show that, if the asymptotic behaviour of the canonical
distribution functions is taken into account, the HKSM theorem can be extended
to the canonical ensemble. We generate -modified correlation and
distribution functions hierarchies and prove that, if they are employed, either
a modified external field or the density profiles can be indistinctly used as
independent variables. We also write down the % -modified free energy
functional and prove that its minimum is reached when the equilibrium values of
the new hierarchy are used. This completes the extension of the HKSM theorem.Comment: revtex, to be submitted to Phys. Rev. Let
Shapes, contact angles, and line tensions of droplets on cylinders
Using an interface displacement model we calculate the shapes of
nanometer-size liquid droplets on homogeneous cylindrical surfaces. We
determine effective contact angles and line tensions, the latter defined as
excess free energies per unit length associated with the two contact lines at
the ends of the droplet. The dependences of these quantities on the cylinder
radius and on the volume of the droplets are analyzed.Comment: 26 pages, RevTeX, 10 Figure
Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
This paper studies the construction of geometric integrators for nonholonomic
systems. We derive the nonholonomic discrete Euler-Lagrange equations in a
setting which permits to deduce geometric integrators for continuous
nonholonomic systems (reduced or not). The formalism is given in terms of Lie
groupoids, specifying a discrete Lagrangian and a constraint submanifold on it.
Additionally, it is necessary to fix a vector subbundle of the Lie algebroid
associated to the Lie groupoid. We also discuss the existence of nonholonomic
evolution operators in terms of the discrete nonholonomic Legendre
transformations and in terms of adequate decompositions of the prolongation of
the Lie groupoid. The characterization of the reversibility of the evolution
operator and the discrete nonholonomic momentum equation are also considered.
Finally, we illustrate with several classical examples the wide range of
application of the theory (the discrete nonholonomic constrained particle, the
Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a
rotating table and the two wheeled planar mobile robot).Comment: 45 page
Surgical Treatment of Decompensated Cicatricial Stricture of the Esophagus, Grade III-IV Dysphagia, and Compression Syndrome Caused by Nontoxic Multinodular Goiter: A Case Report
Objective: Long-standing gastroesophageal reflux disease is the most common cause of a cicatricial stricture of the esophagus. The treatment of this pathology involves a wide range of methods including conservative and surgical options. Surgeons can encounter technical difficulties in case of concomitant neck and chest pathology.Clinical case: We report a case of a decompensated cicatricial stricture of the esophagus with concomitant paraesophageal hiatal hernia, refractory gastroesophageal reflux disease, and nontoxic multinodular goiter (166.9 cm3). Selecting the optimal management for such patients is often a challenge. Staged treatment significantly improves postoperative quality of life, but the increased length of hospital stay can negatively impact patient compliance
From least action in electrodynamics to magnetomechanical energy -- a review
The equations of motion for electromechanical systems are traced back to the
fundamental Lagrangian of particles and electromagnetic fields, via the Darwin
Lagrangian. When dissipative forces can be neglected the systems are
conservative and one can study them in a Hamiltonian formalism. The central
concepts of generalized capacitance and inductance coefficients are introduced
and explained. The problem of gauge independence of self-inductance is
considered. Our main interest is in magnetomechanics, i.e. the study of systems
where there is exchange between mechanical and magnetic energy. This throws
light on the concept of magnetic energy, which according to the literature has
confusing and peculiar properties. We apply the theory to a few simple
examples: the extension of a circular current loop, the force between parallel
wires, interacting circular current loops, and the rail gun. These show that
the Hamiltonian, phase space, form of magnetic energy has the usual property
that an equilibrium configuration corresponds to an energy minimum.Comment: 29 pages, 9 figures, 65 reference
Modeling adsorption in metal-organic frameworks with open metal sites : propane/propylene separations
We present a new approach for modeling adsorption in metal-organic frameworks (MOFs) with unsaturated metal centers and apply it to the challenging propane/propylene separation in copper(II) benzene-1,3,5-tricarboxylate (CuBTC). We obtain information about the specific interactions between olefins and the open metal sites of the MOP using quantum mechanical density functional theory. A proper consideration of all the relevant contributions to the adsorption energy enables us to extract the component that is due to specific attractive interactions between the pi-orbitals of the alkene and the coordinatively unsaturated metal. This component is fitted using a combination of a Morse potential and a power law function and is then included into classical grand canonical Monte Carlo simulations of adsorption. Using this modified potential model, together with a standard Lennard-Jones model, we are able to predict the adsorption of not only propane (where no specific interactions are present), but also of propylene (where specific interactions are dominant). Binary adsorption isotherms for this mixture are in reasonable agreement with ideal adsorbed solution theory predictions. We compare our approach with previous attempts to predict adsorption in MOFs with open metal sites and suggest possible future routes for improving our model
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