Modelling Interdependent Cascading Failures in Real World Complex Networks using a Functional Dependency Model

Infrastructure systems are becoming increasingly complex and interdependent. As a result our ability to predict the likelihood of large-scale failure of these systems has significantly diminished and the consequence of this is that we now have a greatly increased risk of devastating impacts to society. Traditionally these systems have been analysed using physically-based models. However, this approach can only provide information for a specific network and is limited by the number of scenarios that can be tested. In an attempt to overcome this shortcoming, many studies have used network graph theory to provide an alternative analysis approach. This approach has tended to consider infrastructure systems in isolation, but has recently considered the analysis of interdependent networks through combination with percolation theory. However, these studies have focused on the analysis of synthetic networks and tend to only consider the topology of the system. In this paper we develop a new analysis approach, based upon network theory, but accounting for the hierarchical structure and functional dependency observed in real world infrastructure networks. We apply this method to two real world networks, to show that it can be used to quantify the impact that failures within an electricity network have upon a dependent water network

A study of radiation environment in space and its biological effects

Biological effects on man in space resulting from galactic and solar cosmic radiation are discussed. Importance of secondary ions which contribute to galactic cosmic radiation hazards is analyzed. Mathematical model to show rate of production of secondary ions of given atomic number at various points in absorber is presented

Galactic cosmic ray heavy primary secondary doses

Results of a calculation which estimates the heavy primary secondary doses from cosmic ray interaction data are reported. The incident galactic cosmic ray heavy primary spectrum is represented as the sum of helium, nitrogen, magnesium, and iron components. The incident iron nuclei are allowed to fragment into lesser Z secondaries, which are assumed to travel in the same direction and start with the same energy per nucleon as the interacting primary. The total emergent particle energy spectra and dose are then presented for the galactic heavy primary spectrum incident on aluminum and tissue slabs. The importance of the fragmentation parameters assumed is also evaluated. The total dose from the heavy primaries and their secondaries is found to be reduced by only a factor of two in 20 g/sq cm of shielding

The conductance of a multi-mode ballistic ring: beyond Landauer and Kubo

The Landauer conductance of a two terminal device equals to the number of open modes in the weak scattering limit. What is the corresponding result if we close the system into a ring? Is it still bounded by the number of open modes? Or is it unbounded as in the semi-classical (Drude) analysis? It turns out that the calculation of the mesoscopic conductance is similar to solving a percolation problem. The "percolation" is in energy space rather than in real space. The non-universal structures and the sparsity of the perturbation matrix cannot be ignored.Comment: 7 pages, 8 figures, with the correct version of Figs.6-

Study of radiation hazards to man on extended missions

Radiation hazards on extended manned space flight

Energy absorption by "sparse" systems: beyond linear response theory

The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between energy levels is essential. The Kubo formula is modified, replacing the "algebraic" average over the squared matrix elements by a "resistor network" average. Consequently the response becomes semi-linear rather than linear. Some novel results have been obtained in the context of two prototype problems: the heating rate of particles in Billiards with vibrating walls; and the Ohmic Joule conductance of mesoscopic rings driven by electromotive force. Respectively, the obtained results are contrasted with the "Wall formula" and the "Drude formula".Comment: 8 pages, 7 figures, short pedagogical review. Proceedings of FQMT conference (Prague, 2011). Ref correcte

The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems

The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the leading order correction to the adiabatic approximation. The time integral of the autocorrelation function is proportional to the rate of dissipation. The fast quantum system is assumed to be chaotic in the classical limit for each configuration of the slow system. An analytic formula is obtained for the finite time integral of the correlation function, in the framework of random matrix theory (RMT), for a specific dependence on the adiabatically varying parameter. Extension to a wider class of RMT models is discussed. For the Gaussian unitary and symplectic ensembles for long times the time integral of the correlation function vanishes or falls off as a Gaussian with a characteristic time that is proportional to the Heisenberg time, depending on the details of the model. The fall off is inversely proportional to time for the Gaussian orthogonal ensemble. The correlation function is found to be dominated by the nearest neighbor level spacings. It was calculated for a variety of nearest neighbor level spacing distributions, including ones that do not originate from RMT ensembles. The various approximate formulas obtained are tested numerically in RMT. The results shed light on the quantum to classical crossover for chaotic systems. The implications on the possibility to experimentally observe deterministic friction are discussed.Comment: 26 pages, including 6 figure

Rate of energy absorption by a closed ballistic ring

We make a distinction between the spectroscopic and the mesoscopic conductance of closed systems. We show that the latter is not simply related to the Landauer conductance of the corresponding open system. A new ingredient in the theory is related to the non-universal structure of the perturbation matrix which is generic for quantum chaotic systems. These structures may created bottlenecks that suppress the diffusion in energy space, and hence the rate of energy absorption. The resulting effect is not merely quantitative: For a ring-dot system we find that a smaller Landauer conductance implies a smaller spectroscopic conductance, while the mesoscopic conductance increases. Our considerations open the way towards a realistic theory of dissipation in closed mesoscopic ballistic devices.Comment: 18 pages, 5 figures, published version with updated ref

Study of radiation hazards to man on extended near earth missions

Radiation hazards to man on extended near earth mission

Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle

Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal H}(Q,P;x(t))$ where $x(t)=Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy-spreading is studied. The associated irreversible growth of the average energy has the meaning of dissipation. It is found that a dimensionless velocity $v_{PR}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence (QCC). A perturbative regime and a non-perturbative semiclassical regime are distinguished.Comment: 4 pages, clear presentation of the main poin