40,928 research outputs found
Spatio-temporal conjecture for diffusion
We present here a conjecture about the equivalence between the noise density
of states of a system governed by a generalized Langevin equation and the
fluctuation in the energy density of states in a Hamiltonian system. We present
evidence of this for a disordered Heisenberg system.Comment: 6 pages, 1 figure. Submitted to Physica
Fractal escapes in Newtonian and relativistic multipole gravitational fields
We study the planar motion of test particles in gravitational fields produced
by an external material halo, of the type found in many astrophysical systems,
such as elliptical galaxies and globular clusters. Both the Newtonian and the
general-relativistic dynamics are examined, and in the relativistic case the
dynamics of both massive and massless particles are investigated. The halo
field is given in general by a multipole expansion; we restrict ourselves to
multipole fields of pure order, whose Newtonian potentials are homogeneous
polynomials in cartesian coordinates. A pure (n)-pole field has (n) different
escapes, one of which is chosen by the particle according to its initial
conditions. We find that the escape has a fractal dependency on the initial
conditions for (n>2) both in the Newtonian and the relativistic cases for
massive test particles, but with important differences between them. The
relativistic motion of massless particles, however, was found to be regular for
all the fields we could study. The box-counting dimension was used in each case
to quantify the sensitivity to initial conditions which arises from the
fractality of the escape route.Comment: 17 pages, 7 figures, uses REVTE
Superdiffusive Conduction: AC Conductivity with Correlated Noise
We present evidence of the existence of a superdiffusive regime in systems
with correlated disorder for which localization is suppressed. An expression
for anomalous electrical conductivity at low frequencies is found by using a
generalized Langevin equation whose memory function accounts for the
interactions between the carriers. New mechanisms inducing a superdiffusive
conductivity are discussed and experimental possibilities for observing that
phenomenon in nanotubes and superlattices are presented.Comment: 7 pages, no figure
Bias driven coherent carrier dynamics in a two-dimensional aperiodic potential
We study the dynamics of an electron wave-packet in a two-dimensional square
lattice with an aperiodic site potential in the presence of an external uniform
electric field. The aperiodicity is described by at lattice sites
, with being a rational number, and and
tunable parameters, controlling the aperiodicity. Using an exact
diagonalization procedure and a finite-size scaling analysis, we show that in
the weakly aperiodic regime (), a phase of extended states
emerges in the center of the band at zero field giving support to a macroscopic
conductivity in the thermodynamic limit. Turning on the field gives rise to
Bloch oscillations of the electron wave-packet. The spectral density of these
oscillations may display a double peak structure signaling the spatial
anisotropy of the potential landscape. The frequency of the oscillations can be
understood using a semi-classical approach.Comment: 16 pages, to appear in Phys. Lett.
Spanning trees with generalized degree constraints arising in the design of wireless networks
In this paper we describe a minimum spanning tree problem with generalized degree constraints which arises in the design of wireless networks. The signal strength on the receiver side of a wireless link decreases with the distance between transmitter and receiver. In order to work properly, the interference on the receiving part of the link must be under a given threshold. In order to guarantee this constraint, for each node we impose a degree constraint that depends on the ”length” of the links adjacent to the corresponding node, more precisely, nodes adjacent to long links must have a smaller degree and vice-versa. The problem is complicated by considering different signal strengths for each link. Increasing the strength in a link increases the cost of the link. However, it also reduces the maximum allowed degree on its end nodes. We create two models using adequate sets of variables, one may be considered an extended version of the other, and relate, from a theoretical perspective, the corresponding linear programming relaxations.FCT - POCTI-ISFL-1-152FCT - PTDC/EIA/64772/200
Parameterized Verification of Algorithms for Oblivious Robots on a Ring
We study verification problems for autonomous swarms of mobile robots that
self-organize and cooperate to solve global objectives. In particular, we focus
in this paper on the model proposed by Suzuki and Yamashita of anonymous robots
evolving in a discrete space with a finite number of locations (here, a ring).
A large number of algorithms have been proposed working for rings whose size is
not a priori fixed and can be hence considered as a parameter. Handmade
correctness proofs of these algorithms have been shown to be error-prone, and
recent attention had been given to the application of formal methods to
automatically prove those. Our work is the first to study the verification
problem of such algorithms in the parameter-ized case. We show that safety and
reachability problems are undecidable for robots evolving asynchronously. On
the positive side, we show that safety properties are decidable in the
synchronous case, as well as in the asynchronous case for a particular class of
algorithms. Several properties on the protocol can be decided as well. Decision
procedures rely on an encoding in Presburger arithmetics formulae that can be
verified by an SMT-solver. Feasibility of our approach is demonstrated by the
encoding of several case studies
Simulation of Bonded Joints Failure using Progressive Mixed-Mode Damage Models
In the most recent years, structural applications of bonded joints haveincreased remarkably owing to their several advantages relative to otherjoining methods. As a consequence, the development of improved modelsto provide design effi ciency and, at the same time, increase the confi denceof designers acquires special relevancy. Recent developments consideringcohesive and continuum mixed-mode damage models have demonstratedthat these methods are able to deal with several details inherent tomechanical behaviour of bonded joints. Both methods allow simulationof damage initiation and propagation by combining classical strength ofmaterials approaches with fracture mechanics concepts.In this work, several different mixed-mode cohesive laws adapted todifferent types of adhesives mechanical behaviour are presented and discussed.Effectively, while mechanical behaviour of brittle or moderately ductileadhesives is well simulated by means of the simple bilinear cohesivelaw, adhesives with pronounced ductile behaviour require more sophisticatedcohesive laws. The aspects regarding determination of some cohesiveparameters are also given special attention in the present paper. A continuummixed-mode damage model is also presented using the bilinear softeningcohesive law. This model is advantageous since properties degradation takesplace inside solid elements used to simulate the adhesive, which allows theevaluation of specifi c issues like the infl uence of asymmetric propagationon joint mechanical behaviour in a more realistic manner. Important conclusionsabout advantages and drawbacks of both methodologies are drawn
Electronic states and transport properties in the Kronig-Penney model with correlated compositional and structural disorder
We study the structure of the electronic states and the transport properties
of a Kronig-Penney model with weak compositional and structural disorder. Using
a perturbative approach we obtain an analytical expression for the localisation
length which is valid for disorder with arbitrary correlations. We show how to
generate disorder with self- and cross-correlations and we analyse both the
known delocalisation effects of the long-range self-correlations and new
effects produced by cross-correlations. We finally discuss how both kinds of
correlations alter the transport properties in Kronig-Penney models of finite
size.Comment: 23 pages, 5 figure
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