457 research outputs found
A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
This paper presents a geometric description of Lagrangian and Hamiltonian
systems on Lie affgebroids subject to affine nonholonomic constraints. We
define the notion of nonholonomically constrained system, and characterize
regularity conditions that guarantee that the dynamics of the system can be
obtained as a suitable projection of the unconstrained dynamics. It is shown
that one can define an almost aff-Poisson bracket on the constraint AV-bundle,
which plays a prominent role in the description of nonholonomic dynamics.
Moreover, these developments give a general description of nonholonomic systems
and the unified treatment permits to study nonholonomic systems after or before
reduction in the same framework. Also, it is not necessary to distinguish
between linear or affine constraints and the methods are valid for explicitly
time-dependent systems.Comment: 50 page
Rotating saddle trap as Foucault's pendulum
One of the many surprising results found in the mechanics of rotating systems
is the stabilization of a particle in a rapidly rotating planar saddle
potential. Besides the counterintuitive stabilization, an unexpected
precessional motion is observed. In this note we show that this precession is
due to a Coriolis-like force caused by the rotation of the potential. To our
knowledge this is the first example where such force arises in an inertial
reference frame. We also propose an idea of a simple mechanical demonstration
of this effect.Comment: 13 pages, 9 figure
Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior
We study the interplay between hysteresis and equilibrium behavior in
capillary condensation of fluids in mesoporous disordered materials via a
mean-field density functional theory of a disordered lattice-gas model. The
approach reproduces all major features observed experimentally. We show that
the simple van der Waals picture of metastability fails due to the appearance
of a complex free-energy landscape with a large number of metastable states. In
particular, hysteresis can occur both with and without an underlying
equilibrium transition, thermodynamic consistency is not satisfied along the
hysteresis loop, and out-of-equilibrium phase transitions are possible.Comment: 4 pages, 4 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
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
Prediction of remission of type 2 diabetes mellitus after bariatric surgery
Type 2 diabetes prevalence is increasing dramatically worldwide. Conservative therapy doesn’t bring stable effect and is often insufficient, not to mention the lack of prospects to cure the disease. Fortunately, accumulating evidence points towards the notion that a complete remission of type 2 diabetes is feasible following a choice of surgical interventions. The efficacy of bariatric surgery in particular for achieving glycemic control has highlighted surgery as a candidate curative intervention for type 2 diabetes. When compared to intensive medical therapy and lifestyle intervention, metabolic surgery has shown superiority in achieving reducing number of medications and metabolic factors improvement, which translates in long-term benefits on diabetes progression and complications. Understanding factors that predict diabetes remission can help to select patients who will benefit most from bariatric surgery and to choose the most effective type of operation. This literature review analyzes studies of the most significant clinical and biochemical predictors of remission of type 2 diabetes mellitus after bariatric interventions, as well as highlights well-known mathematical prediction models
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
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
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