4,268 research outputs found
Dissipation-preserving discretization of the Cahn--Hilliard equation with dynamic boundary conditions
This paper deals with time stepping schemes for the Cahn--Hilliard equation
with three different types of dynamic boundary conditions. The proposed schemes
of first and second order are mass-conservative and energy-dissipative and --
as they are based on a formulation as a coupled system of partial differential
equations -- allow different spatial discretizations in the bulk and on the
boundary. The latter enables refinements on the boundary without an adaptation
of the mesh in the interior of the domain. The resulting computational gain is
illustrated in numerical experiments
A second-order bulk--surface splitting for parabolic problems with dynamic boundary conditions
This paper introduces a novel approach for the construction of bulk--surface
splitting schemes for semi-linear parabolic partial differential equations with
dynamic boundary conditions. The proposed construction is based on a
reformulation of the system as a partial differential--algebraic equation and
the inclusion of certain delay terms for the decoupling. To obtain a fully
discrete scheme, the splitting approach is combined with finite elements in
space and a BDF discretization in time. Within this paper, we focus on the
second-order case, resulting in a -step scheme. We prove second-order
convergence under the assumption of a weak CFL-type condition and confirm the
theoretical findings by numerical experiments. Moreover, we illustrate the
potential for higher-order splitting schemes numerically
Characterizing Weak Chaos using Time Series of Lyapunov Exponents
We investigate chaos in mixed-phase-space Hamiltonian systems using time
series of the finite- time Lyapunov exponents. The methodology we propose uses
the number of Lyapunov exponents close to zero to define regimes of ordered
(stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The
dynamics is then investigated looking at the consecutive time spent in each
regime, the transition between different regimes, and the regions in the
phase-space associated to them. Applying our methodology to a chain of coupled
standard maps we obtain: (i) that it allows for an improved numerical
characterization of stickiness in high-dimensional Hamiltonian systems, when
compared to the previous analyses based on the distribution of recurrence
times; (ii) that the transition probabilities between different regimes are
determined by the phase-space volume associated to the corresponding regions;
(iii) the dependence of the Lyapunov exponents with the coupling strength.Comment: 8 pages, 6 figure
Density Functional Theory for the Photoionization Dynamics of Uracil
Photoionization dynamics of the RNA base Uracil is studied in the framework
of Density Functional Theory (DFT). The photoionization calculations take
advantage of a newly developed parallel version of a multicentric approach to
the calculation of the electronic continuum spectrum which uses a set of
B-spline radial basis functions and a Kohn-Sham density functional hamiltonian.
Both valence and core ionizations are considered. Scattering resonances in
selected single-particle ionization channels are classified by the symmetry of
the resonant state and the peak energy position in the photoelectron kinetic
energy scale; the present results highlight once more the site specificity of
core ionization processes. We further suggest that the resonant structures
previously characterized in low-energy electron collision experiments are
partly shifted below threshold by the photoionization processes. A critical
evaluation of the theoretical results providing a guide for future experimental
work on similar biosystems
Allelomimesis as universal clustering mechanism for complex adaptive systems
Animal and human clusters are complex adaptive systems and many are organized
in cluster sizes that obey the frequency-distribution . Exponent describes the relative abundance of the cluster
sizes in a given system. Data analyses have revealed that real-world clusters
exhibit a broad spectrum of -values, . We show that allelomimesis is a
fundamental mechanism for adaptation that accurately explains why a broad
spectrum of -values is observed in animate, human and inanimate cluster
systems. Previous mathematical models could not account for the phenomenon.
They are hampered by details and apply only to specific systems such as cities,
business firms or gene family sizes. Allelomimesis is the tendency of an
individual to imitate the actions of its neighbors and two cluster systems
yield different values if their component agents display different
allelomimetic tendencies. We demonstrate that allelomimetic adaptation are of
three general types: blind copying, information-use copying, and non-copying.
Allelomimetic adaptation also points to the existence of a stable cluster size
consisting of three interacting individuals.Comment: 8 pages, 5 figures, 2 table
New Langevin and Gradient Thermostats for Rigid Body Dynamics
We introduce two new thermostats, one of Langevin type and one of gradient
(Brownian) type, for rigid body dynamics. We formulate rotation using the
quaternion representation of angular coordinates; both thermostats preserve the
unit length of quaternions. The Langevin thermostat also ensures that the
conjugate angular momenta stay within the tangent space of the quaternion
coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have
constructed three geometric numerical integrators for the Langevin thermostat
and one for the gradient thermostat. The numerical integrators reflect key
properties of the thermostats themselves. Namely, they all preserve the unit
length of quaternions, automatically, without the need of a projection onto the
unit sphere. The Langevin integrators also ensure that the angular momenta
remain within the tangent space of the quaternion coordinates. The Langevin
integrators are quasi-symplectic and of weak order two. The numerical method
for the gradient thermostat is of weak order one. Its construction exploits
ideas of Lie-group type integrators for differential equations on manifolds. We
numerically compare the discretization errors of the Langevin integrators, as
well as the efficiency of the gradient integrator compared to the Langevin ones
when used in the simulation of rigid TIP4P water model with smoothly truncated
electrostatic interactions. We observe that the gradient integrator is
computationally less efficient than the Langevin integrators. We also compare
the relative accuracy of the Langevin integrators in evaluating various static
quantities and give recommendations as to the choice of an appropriate
integrator.Comment: 16 pages, 4 figure
Irreducible Representations of Diperiodic Groups
The irreducible representations of all of the 80 diperiodic groups, being the
symmetries of the systems translationally periodical in two directions, are
calculated. To this end, each of these groups is factorized as the product of a
generalized translational group and an axial point group. The results are
presented in the form of the tables, containing the matrices of the irreducible
representations of the generators of the groups. General properties and some
physical applications (degeneracy and topology of the energy bands, selection
rules, etc.) are discussed.Comment: 30 pages, 5 figures, 28 tables, 18 refs, LaTex2.0
Bifurcations of periodic and chaotic attractors in pinball billiards with focusing boundaries
We study the dynamics of billiard models with a modified collision rule: the
outgoing angle from a collision is a uniform contraction, by a factor lambda,
of the incident angle. These pinball billiards interpolate between a
one-dimensional map when lambda=0 and the classical Hamiltonian case of elastic
collisions when lambda=1. For all lambda<1, the dynamics is dissipative, and
thus gives rise to attractors, which may be periodic or chaotic. Motivated by
recent rigorous results of Markarian, Pujals and Sambarino, we numerically
investigate and characterise the bifurcations of the resulting attractors as
the contraction parameter is varied. Some billiards exhibit only periodic
attractors, some only chaotic attractors, and others have coexistence of the
two types.Comment: 30 pages, 17 figures. v2: Minor changes after referee comments.
Version with some higher-quality figures available at
http://sistemas.fciencias.unam.mx/~dsanders/publications.htm
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