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 $\epsilon_{\bf m} = V\cos{(\pi\alpha m_x^{\nu_x})}\cos{(\pi\alpha m_y^{\nu_y})}$ at lattice sites $(m_x, m_y)$, with $\pi \alpha$ being a rational number, and $\nu_x$ and $\nu_y$ tunable parameters, controlling the aperiodicity. Using an exact diagonalization procedure and a finite-size scaling analysis, we show that in the weakly aperiodic regime ($\nu_x,\nu_y < 1$), 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