1,720,982 research outputs found
Extension of Von Karman ansatz to magnetohydrodynamics
No full textThe steady-state axisymmetric motion of an incompressible viscous conducting fluid is studied in the framework of the magnetohydrodynamical model. An ansatz is introduced on the radial dependences of the velocity and magnetic fields, which extends the one used by Von Kármán in the purely hydrodynamical case. It is shown how the extended ansatz can be characterized much in the same way as in hydrodynamics and how it reduces the magnetohydrodynamical system of partial differential equations to a system of ordinary differential equations. The solutions of these equations can be found in exact form in some simplified situations, while, in the general case, numerical approximation methods seem to be the only successful solution procedures
Complex Systems and Networks: from Graph Theory to the World Trade Web
No full textThe modern science of networks has brought significant advances to our understanding of complex systems. The World Trade Web (WTW) is the complex network representation of the international trade system that
allows an analysis at the large scale from an interdisciplinary
approach. Countries are represented as nodes and commercial relations between them as links. The network representation offers a new level of description that goes beyond the country-specific analyses used in
more traditional economic studies of trade.
In this line of research, several tools and methodologies - recently developed in the framework of network science - can be exploited to extract information from the WTW, and to discriminate which properties signal a nontrivial structural organization and which are likely originated by chance or structural constraints. Recent network-inspired models that succeed in explaining the observed complexity of the WTW at a topological level will be discussed, together with some open questions for future research
Introduction to Complex Networks: Theory and Applications
No full textThe modern science of networks has brought significant advances to our understanding of complex systems. Real-world entities are often interconnected with each other through explicit or implicit relationships to form a complex network. Examples of complex networks are found in many fields of science such as biological, technological, economic as well as social systems.
In this seminar the speaker will present an introduction to the science of complex networks, starting from the theoretical foundations of graph theory and giving emphasis to representation, analysis and modeling.
Also several applications of complex networks to real-world problems and data will be proposed.
In particular, the World Trade Web (WTW), as the complex network representation of the international trade system, will be discussed.
In this case, several tools and methodologies - recently developed in the framework of network science - can be exploited to extract information from the trading system in order to point out a nontrivial structural organization. As a result a new level of description, that goes beyond the country-specific analyses used in more traditional economic studies of trade, can be obtained, allowing an analysis at the large scale from an interdisciplinary approach.
Finally the application of recurrence networks to the analysis of nonlinear dynamical systems will be proposed, together with some open questions for future research
Eulerian variational principle for ideal hydrodynamics and two-fluid representation
No full textThe hydrodynamical equations for an ideal fluid with vorticity are derived, in the Eulerian picture, from a constrained variationalprinciple, which, exploiting a two-fluid representation for the density field, both yields a consistent representation for the velocity field and allows one to develop a Hamiltonian formalism
Unbiased information extraction from complex networks by means of the maximum likelihood approach
No full textEffects of network topology on wealth distributions
No full textWe focus on the problem of how the wealth is distributed among the units of a networked economic system. We first review the empirical results documenting that in many economies the wealth distribution is described by a combination of the log-normal and power-law behaviours. We then focus on the Bouchaud–Mézard model of wealth exchange, describing an economy of interacting agents connected through an exchange network. We report analytical and numerical results showing that the system self-organizes towards a stationary state whose associated wealth distribution depends crucially on the underlying interaction network. In particular, we show that if the network displays a homogeneous density of links, the wealth distribution displays either the log-normal or the power-law form. This means that the first-order topological properties alone (such as the scale-free property) are not enough to explain the emergence of the empirically observed mixed form of the wealth distribution. In order to reproduce this nontrivial pattern, the network has to be heterogeneously divided into regions with a variable density of links. We show new results detailing how this effect is related to the higher-order correlation properties of the underlying network. In particular, we analyse assortativity by degree and the pairwise wealth correlations, and discuss the effects that these properties have on each other
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