1,435,613 research outputs found
New criteria for cluster identification in continuum systems
Two new criteria, that involve the microscopic dynamics of the system, are
proposed for the identification of clusters in continuum systems. The first one
considers a residence time in the definition of the bond between pairs of
particles, whereas the second one uses a life time in the definition of an
aggregate. Because of the qualitative features of the clusters yielded by the
criteria we call them chemical and physical clusters, respectively. Molecular
dynamics results for a Lennard-Jones system and general connectivity theories
are presented.Comment: 31 pages, 11 figures, The following article has been accepted by The
Journal of Chemical Physics. After it is published, it will be found at
http://ojps.aip.org/jcpo
Poincar\'e invariance and asymptotic flatness in Shape Dynamics
Shape Dynamics is a theory of gravity that waives refoliation invariance in
favor of spatial Weyl invariance. It is a canonical theory, constructed from a
Hamiltonian, 3+1 perspective. One of the main deficits of Shape Dynamics is
that its Hamiltonian is only implicitly constructed as a functional of the
phase space variables. In this paper, I write down the equations of motion for
Shape Dynamics to show that over a curve in phase space representing a
Minkowski spacetime, Shape Dynamics possesses Poincar\'e symmetry for
appropriate boundary conditions. The proper treatment of such boundary
conditions leads us to completely formulate Shape Dynamics for open manifolds
in the asymptotically flat case. We study the charges arising in this case and
find a new definition of total energy, which is completely invariant under
spatial Weyl transformations close to the boundary. We then use the equations
of motion once again to find a non-trivial solution of Shape Dynamics,
consisting of a flat static Universe with a point-like mass at the center. We
calculate its energy through the new formula and rederive the usual
Schwarzschild mass.Comment: 22 pages, matches accepted versio
Probabilistic Guarded P Systems, A New Formal Modelling Framework
Multienvironment P systems constitute a general, formal
framework for modelling the dynamics of population biology, which consists
of two main approaches: stochastic and probabilistic. The framework
has been successfully used to model biologic systems at both micro (e.g.
bacteria colony) and macro (e.g. real ecosystems) levels, respectively.
In this paper, we extend the general framework in order to include
a new case study related to P. Oleracea species. The extension is made
by a new variant within the probabilistic approach, called Probabilistic
Guarded P systems (in short, PGP systems). We provide a formal definition,
a simulation algorithm to capture the dynamics, and a survey of
the associated software.Ministerio de Economía y Competitividad TIN2012- 37434Junta de Andalucía P08-TIC-0420
Weak index pairs and the Conley index for discrete multivalued dynamical systems
Motivated by the problem of reconstructing dynamics from samples we revisit
the Conley index theory for discrete multivalued dynamical systems. We
introduce a new, less restrictive definition of the isolating neighbourhood. It
turns out that then the main tool for the construction of the index, i.e. the
index pair, is no longer useful. In order to overcome this obstacle we use the
concept of weak index pairs
Sampling equilibrium through descriptive simulations
A definition of sampling equilibrium was introduced in (Osborne and
Rubinstein 1998). A dynamic version of the model was introduced in
(Sethi 2000). However, a descriptive simulation based on the above idea
of procedural rationality (i.e. using the same algorithm of behavior) gave
different results, than those achieved in (Osborne and Rubinstein 1998)
and (Sethi 2000). The simulation was a starting point for new definitions
of both sampling dynamics and sampling equilibrium
Discrete-time port-Hamiltonian systems: A definition based on symplectic integration
We introduce a new definition of discrete-time port-Hamiltonian systems
(PHS), which results from structure-preserving discretization of explicit PHS
in time. We discretize the underlying continuous-time Dirac structure with the
collocation method and add discrete-time dynamics by the use of symplectic
numerical integration schemes. The conservation of a discrete-time energy
balance - expressed in terms of the discrete-time Dirac structure - extends the
notion of symplecticity of geometric integration schemes to open systems. We
discuss the energy approximation errors in the context of the presented
definition and show that their order is consistent with the order of the
numerical integration scheme. Implicit Gauss-Legendre methods and Lobatto
IIIA/IIIB pairs for partitioned systems are examples for integration schemes
that are covered by our definition. The statements on the numerical energy
errors are illustrated by elementary numerical experiments.Comment: 12 pages. Preprint submitted to Systems & Control Letter
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