Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Fluctuations in Saffman-Taylor fingers with quenched disorder

We make an experimental characterization of the effect that static disorder has on the shape of a normal Saffman-Taylor finger. We find that static noise induces a small amplitude and long wavelength instability on the sides of the finger. Fluctuations on the finger sides have a dominant wavelength, indicating that the system acts as a selective amplifier of static noise. The dominant wavelength does not seem to be very sensitive to the intensity of static noise present in the system. On the other hand, at a given flow rate, rms fluctuations of the finger width, decrease with decreasing intensity of static noise. This might explain why the sides of the fingers are flat for typical Saffman-Taylor experiments. Comparison with previous numerical studies of the effect that temporal noise has on the Saffman-Taylor finger, leads to conclude that the effect of temporal noise and static noise are similar. The behavior of fluctuations of the finger width found in our experiments, is qualitatively similar to one recently reported, in the sense that, the magnitude of the width fluctuations decays as a power law of the capillary number, at low flow rates, and increases with capillary number for larger flow rates.

The determinants of industrial location in Spain, 1856-1929

Durant el segle XIX, l'economia espanyola va transitar per les primeres etapes de la industrialització. Aquest procés es va donar en paral·lel a la integració del mercat domèstic de béns i factors, en un moment en què les reformes liberals i la construcció de la xarxa ferroviària, entre d'altres, van generar una important caiguda en els costos detransport. Al mateix temps que es donava aquesta progressiva integració del mercat domèstic espanyol, es van produir canvis significatius en la pauta de localització industrial. D'una banda, hi hagué un augment considerable de la concentració espacial de la indústria des de mitjans de segle XIX i fins a la Guerra Civil, i d¿altra, un increment de l'especialització regional. Ara bé, quines van ser les forces que van generar aquests canvis? Des d¿un punt de vista teòric, el model de Heckscher-Ohlin suggereix que la distribució a l'espai de l¿activitat econòmica ve determinada per l'avantatge comparativa dels territoris en funció de la dotació relativa de factors. Al seu torn, els models de Nova Geografia Econòmica (NEG) mostren l'existència d'una relació en forma de campana entre el procés d'integració econòmica i el grau de concentració geogràfica de l'activitat industrial. Aquest article examina empíricament els determinants de la localització industrial a Espanya entre 1856 i 1929, mitjançant l'estimació d¿un model que combina els elements de tipus Heckscher-Ohlin i els factors apuntats des de la NEG, amb l'objectiu de contrastar la força relativa dels arguments vinculats a aquestes dues interpretacions a l'hora de modular la localització de la indústria a Espanya. L'anàlisi dels resultats obtinguts mostra que tant la dotació de factors com els mecanismes de tipus NEG van ser elements determinants que expliquen la distribució geogràfica de la indústria des del segle XIX, tot i que la seva força relativa va anar variant amb el temps.

The geographical concentration of industry across Spanish Regions, 1856-1995

New economic geography models show that there may be a strong relationship between economic integration and the geographical concentration of industries. Nevertheless, this relationship is neither unique nor stable, and may follow a ?-shaped pattern in the long term. The aim of the present paper is to analyze the evolution of the geographical concentration of manufacturing across Spanish regions during the period 1856-1995. We construct several geographical concentration indices for different points in time over these 140 years. The analysis is carried out at two levels of aggregation, in regions corresponding to the NUTS-II and NUTS-III classifications. We confirm that the process of economic integration stimulated the geographical concentration of industrial activity. Nevertheless, the localization coefficients only started to fall after the beginning of the integration of the Spanish Economy into the international markets in the mid-70s, and this new path was not interrupted by Spain¿s entry in the European Union some years later

The geographical concentration of industry across Spanish Regions, 1856-1995

New economic geography models show that there may be a strong relationship between economic integration and the geographical concentration of industries. Nevertheless, this relationship is neither unique nor stable, and may follow a ?-shaped pattern in the long term. The aim of the present paper is to analyze the evolution of the geographical concentration of manufacturing across Spanish regions during the period 1856-1995. We construct several geographical concentration indices for different points in time over these 140 years. The analysis is carried out at two levels of aggregation, in regions corresponding to the NUTS-II and NUTS-III classifications. We confirm that the process of economic integration stimulated the geographical concentration of industrial activity. Nevertheless, the localization coefficients only started to fall after the beginning of the integration of the Spanish Economy into the international markets in the mid-70s, and this new path was not interrupted by Spain¿s entry in the European Union some years later

Pork Barrel politics in semi-democracies: the Spanish 'Parlamentary roads', 1874-1915

This paper analyzes the effects of parliamentary representation on road infrastructure expenditure during the Spanish Restoration. Using a panel dataset of Spanish provinces in 1880-1914 we find that the allocation of administrative resources among provinces depended both on the delegation characteristics (such as the share of MPs with party leadership positions, and their degree of electoral independence), and the regime"s global search for stability. These results point to the importance of electoral dynamics within semi-democratic political systems, and offer an example of the influence of government tactics on infrastructure allocation.

Pork Barrel politics in semi-democracies: the Spanish 'Parlamentary roads', 1874-1915

This paper analyzes the effects of parliamentary representation on road infrastructure expenditure during the Spanish Restoration. Using a panel dataset of Spanish provinces in 1880-1914 we find that the allocation of administrative resources among provinces depended both on the delegation characteristics (such as the share of MPs with party leadership positions, and their degree of electoral independence), and the regime"s global search for stability. These results point to the importance of electoral dynamics within semi-democratic political systems, and offer an example of the influence of government tactics on infrastructure allocation.