Understanding the complexity of the L\'evy-walk nature of human mobility with a multi-scale cost/benefit model

Probability distributions of human displacements has been fit with exponentially truncated L\'evy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the city of residence), but with a non-vanishing frequency they visit nearby or far locations too. Herein, we show that an important empirical distribution of human displacements (range: from 1 to 1000 km) can be well fit by three consecutive Pareto distributions with simple integer exponents equal to 1, 2 and ($\gtrapprox$) 3. These three exponents correspond to three displacement range zones of about 1 km $\lesssim \Delta r \lesssim$ 10 km, 10 km $\lesssim \Delta r \lesssim$ 300 km and 300 km $\lesssim \Delta r \lesssim$ 1000 km, respectively. These three zones can be geographically and physically well determined as displacements within a city, visits to nearby cities that may occur within just one-day trips, and visit to far locations that may require multi-days trips. The incremental integer values of the three exponents can be easily explained with a three-scale mobility cost/benefit model for human displacements based on simple geometrical constrains. Essentially, people would divide the space into three major regions (close, medium and far distances) and would assume that the travel benefits are randomly/uniformly distributed mostly only within specific urban-like areas

Towards a General Theory of Extremes for Observables of Chaotic Dynamical Systems

In this paper we provide a connection between the geometrical properties of a chaotic dynamical system and the distribution of extreme values. We show that the extremes of so-called physical observables are distributed according to the classical generalised Pareto distribution and derive explicit expressions for the scaling and the shape parameter. In particular, we derive that the shape parameter does not depend on the chosen observables, but only on the partial dimensions of the invariant measure on the stable, unstable, and neutral manifolds. The shape parameter is negative and is close to zero when high-dimensional systems are considered. This result agrees with what was derived recently using the generalized extreme value approach. Combining the results obtained using such physical observables and the properties of the extremes of distance observables, it is possible to derive estimates of the partial dimensions of the attractor along the stable and the unstable directions of the flow. Moreover, by writing the shape parameter in terms of moments of the extremes of the considered observable and by using linear response theory, we relate the sensitivity to perturbations of the shape parameter to the sensitivity of the moments, of the partial dimensions, and of the Kaplan-Yorke dimension of the attractor. Preliminary numerical investigations provide encouraging results on the applicability of the theory presented here. The results presented here do not apply for all combinations of Axiom A systems and observables, but the breakdown seems to be related to very special geometrical configurations.Comment: 16 pages, 3 Figure

Phase transitions in Pareto optimal complex networks

The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem finding phase transitions of different kinds. Distinct phases are associated to different arrangements of the connections; but the need of drastic topological changes does not determine the presence, nor the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.Comment: 14 pages, 7 figure

Comparison of Direct Multiobjective Optimization Methods for the Design of Electric Vehicles

"System design oriented methodologies" are discussed in this paper through the comparison of multiobjective optimization methods applied to heterogeneous devices in electrical engineering. Avoiding criteria function derivatives, direct optimization algorithms are used. In particular, deterministic geometric methods such as the Hooke & Jeeves heuristic approach are compared with stochastic evolutionary algorithms (Pareto genetic algorithms). Different issues relative to convergence rapidity and robustness on mixed (continuous/discrete), constrained and multiobjective problems are discussed. A typical electrical engineering heterogeneous and multidisciplinary system is considered as a case study: the motor drive of an electric vehicle. Some results emphasize the capacity of each approach to facilitate system analysis and particularly to display couplings between optimization parameters, constraints, objectives and the driving mission

Design and optimization of a micro heat sink for concentrating photovoltaic/thermal (CPVT) systems

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.An optimization methodology for a microchannel heat sink suitable for the cooling of a parabolic trough CPVT system is presented in this study. Two different microchannel configurations are considered, Fixed (FWμ) and stepwise Variable-Width (VWμ) microchannels respectively. The performance evaluation criteria comprise the thermal resistance of the heat sink and the cooling medium pressure drop through the heat sink. Initially, the effect of the geometric parameters on the heat sink thermal and hydrodynamic performance is investigated using a thermal resistance model in order to save computational time. The results of the 1-D model enable the construction of surrogate functions for the thermal resistance and the pressure drop of the heat sink, which are considered as the objective functions for the multiobjective optimization process that leads to the optimal geometric parameters. In a second step, a 3-D numerical model of fluid flow and conjugate heat transfer in the optimized FWμ heat sink is developed in order to investigate in detail the flow and thermal phenomena. The overall analysis demonstrates that microchannel heat sinks achieve very low values of thermal resistance and that the use of variable-width channels can significantly reduce the pressure drop of the cooling fluid. Furthermore, it is proven that the 1-D model is capable of providing a good estimate of the behavior of the heat sink

Optimized multi-objective design of herringbone micromixers

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.A design method which systematically integrates Computational Fluids Dynamics (CFD) with an optimization scheme based on the use of the techniques Design of Experiments (DOE), Function Approximation technique (FA) and Multi-Objective Genetic Algorithm (MOGA), has been applied to the shape optimization of the staggered herringbone micromixer (SHM) at different Reynolds numbers. To quantify the mixing intensity in the mixer a Mixing index is defined on the basis of the intensity of segregation of the mass concentration on the outlet section. Four geometric parameters, i.e., aspect ratio of the mixing channel, ratio of groove depth to channel height, ratio of groove width to groove pitch and the asymmetry factor (offset) of groove, are the design variables selected for optimization. The mixing index at the outlet section and the pressure drop in the mixing channel are the performance criteria used as objective functions. The Pareto front with the optimum trade-offs, maximum mixing index with minimum pressure drop, is obtained. Experiments for qualitative and quantitative validation have been implemented.This study is supported by the Dorothy Hodgkin Postgraduate Award (DHPA) of the Engineering and Physical Sciences Research Council (EPSRC) of United Kingdom and Ebara Research Co. Ltd. of Japan