Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation

We formulate and study dynamics from a complex Ginzburg-Landau system with saturable nonlinearity, including asymmetric cross-phase modulation (XPM) parameters. Such equations can model phenomena described by complex Ginzburg-Landau systems under the added assumption of saturable media. When the saturation parameter is set to zero, we recover a general complex cubic Ginzburg-Landau system with XPM. We first derive conditions for the existence of bounded dynamics, approximating the absorbing set for solutions. We use this to then determine conditions for amplitude death of a single wavefunction. We also construct exact plane wave solutions, and determine conditions for their modulational instability. In a degenerate limit where dispersion and nonlinearity balance, we reduce our system to a saturable nonlinear Schr\"odinger system with XPM parameters, and we demonstrate the existence and behavior of spatially heterogeneous stationary solutions in this limit. Using numerical simulations we verify the aforementioned analytical results, while also demonstrating other interesting emergent features of the dynamics, such as spatiotemporal chaos in the presence of modulational instability. In other regimes, coherent patterns including uniform states or banded structures arise, corresponding to certain stable stationary states. For sufficiently large yet equal XPM parameters, we observe a segregation of wavefunctions into different regions of the spatial domain, while when XPM parameters are large and take different values, one wavefunction may decay to zero in finite time over the spatial domain (in agreement with the amplitude death predicted analytically). While saturation will often regularize the dynamics, such transient dynamics can still be observed - and in some cases even prolonged - as the saturability of the media is increased, as the saturation may act to slow the timescale.Comment: 36 page

Essays on Public Economics and Public Policy Evaluation – Methods and Applications

[eng] Economic policies and institutional design and decision-making vary greatly accross countries. Germany, the US and Canada, are federal states, where decision-making and economic policies are highly decentralized, while France and Greece are highly unitary countries. Belgium has had the two largest government formation deadlocks in Europe in the last 20 years, while other countries such as Portugal or Ireland have experienced none. During the COVID-19 crisis, some countries, like New Zealand, applied lockdowns with an incidence rate of 20 cases per milion inhabitants, while others like Spain, delayer their response until the incidence rate was higher than 130 cases per million Do differences in institutional design lead to differences in economic policies? Can these differences be explained? Is the agility of government decision-making influenced by common patterns across countries? The aim of my thesis is to contribute to the existing literature on public policy evaluation, with a particular focus on the role of institutions, providing new methodological, theoretical, and empirical results, to provide answers to questions such as the ones stated before. Five studies are presented in the thesis. In the first study, I analyze one of the most seminals questions that could be asked about governments and economic outcomes: Do government formation deadlocks affect the economy in the short term? From the methodological point of view, I develop a proposal to improve current methodologies to evaluate causal effects on quasi-experimental designs; concretely, the Synthetic Control Method. I illustrate the main advantages of the proposal evaluating the causal economic effects of the ten-month-long government formation impasse in Spain, after the December 2015 elections, as well as reproducing two previous studies: the impact of German reunification (analyzed in Abadie et al. 2015) and the effect of tobacco control programs in California (Abadie et al. 2010). In line with the results obtained by Albalate and Bel (2020) for the 18-month government formation deadlock in Belgium, my estimates indicate that the growth rate in Spain was not affected by the government deadlock, ruling out any damage to the economy attributable to the institutional impasse. The second and third studies focus on how governments decide in a context of high uncertainty and different degrees of information. Concretely, I build a theoretical model to assess the agility of government response to the COVID pandemic and evaluate the model empirically using data from OCDE and European countries. I find solid evidence that during the first outbreak, in a context of incomplete information, the agility of policy response was highly conditioned by a cost-benefit analysis where the perceived healthcare capacity to deal with the outbreak, and the associated economic costs of lockdown measures, significantly delayed the response. Institution design also played a role: federal states reacted faster than unitary ones. Higher competition in multilevel systems with collaborative governance between different levels of government and non-state institutions - (Scavo, Kearne, and Kilroy, 2008; Schwartz and Yen, 2017; Downey and Myers, 2020; Huang, 2020) provided incentives for more agile and effective responses. However, federal states could be dysfunctional in terms of internal coordination and suffer from high inequality in terms of agility within themselves. For the concrete case of the US, I find that Republican-controlled states reacted later and implemented softer contingency measures, which were associated with higher growth in the number of COVID-19 cases (Hallas et al., 2020; Shvetsova et al., 2022). The highly polarized context of the US provided incentives for Republican governors to align with President Trump’s preferred policy, which was to avoid lockdowns. These incentives vanished during the vaccination process, when information about the severity of COVID-19 was complete, and governors, no matter whether Republicans or Democrats, implemented the roll-out of the vaccination program with a similar level of agility. In the fourth paper, I suggest a new approach to assess the effect of institutional and policy developments (i.e. capital city) on economic growth that distort the natural equilibrium of the geographical distribution of the labor market. I propose a theoretical model of the way in which features of geography and nature can account for population density and distribution within a country. The model is empirically examined using data from comparable European regions. This allows us to detect deviations produced by the forces of human action, led mainly by institutions, and to evaluate the consequences in terms of relative economic performance. The results suggest that deviating from nature’s outcomes has a significant negative effect on economic growth and regional convergence. Hence, societies that choose to exploit the opportunities of the best locations, according to the natural endowment, rather than promoting a different distribution of the population across regions by means of institutional intervention, achieve better economic performance. In the last study, we focus on the most relevant government expenditure until the twentieth century: military expenditure. We examine the effects of military and trade alliances in military expenditure. We develop a theoretical model to understand why these alliances could influence military expenditure. In short, when countries build military and trade alliances with military leaders such as the US, they make themselves more valuable to the leader, and hence increase the likelihood of the leader providing military aid in case of an agression. This increases the military costs of a potential agresor, reduces the probability of war and let the non-leader country reduce its military expenditure. To empirically test the hypothesis derived from the model we employ data of 138 countries for the period 1996-2020. Our results show that trade relation with a military leader is a highly significant driver of military expenditure. For each percentage point in US GDP in trade between a certain country and the US, the military expenditure of the country reduces 0.5 percentage points. Moreover, when the trade balance is particularly beneficial for the US, the effect is even larger

Consum d'oxigen estimat i despesa energètica en competicions d'esgrima

Es realitza una estimació del consum d'oxigen i una anàlisi de les demandes energètiques de l'esgrima en competició. En assalts de competició, el consum d'oxigen estimat en dones ( x = 39,6 mL·kg-'·min-1) és inferior al dels homes (X = 53,9 mL·kg-'·min-1). La intensitat individual mitjana es troba entre el 56 % i el 74 % del Vo2max, amb màxims entre el 75 % i el 99 % del Vo2max, el que confirma la rellevància dels requeriments aeròbics en l'esgrima. Les demandes energètiques en la competició internacional són superiors a les registrades en una competició autonòmica i al de diferents situacions d'entrenament. La potència energètica mitjana es-timada al llarg de competicions de nivell internacional i autonòmic és, respectivament, de 15,4 kcal-min-1 (64,5 I<J·min-1) i 12,3 kcal·min-1 (51,6 kj·min-1). Entre tiradors del mateix gènere no s'aprecien diferències significatives en funció de l'arma. De l'anàlisi en competició destaca la variabilitat de la resposta funcional dels esgrimidors atesa la influència de factors com l'adaptació cardiocirculatòria individual, importància de la competició, eliminatòria registrada, nivell del rival, dinàmica competitiva, arma i gènere

Numerical analysis of nonlinear large-strain consolidation and filling

Finite strain consolidation and filling of soft sediments at high water level is a challenging problem because of its highly non-linear physical and mathematical aspects. Several numerical schemes designed for this problem are presented as well as simple numerical improvements for a better handling of the extremely high variations of the material properties with depth. The numerical algorithms developed are robust and verify convergence of the iterative schemes instead of the more classical approaches based on choosing time increments ‘sufficiently’ small and assuming convergence at every step. A set of computer programs has been developed to predict magnitude and rate of large-strain self-weight one-dimensional and pseudo bi-dimensional (i.e. one-dimensional deformation, bi-dimensional flux) consolidation during and after deposition, that is, coupling filling and consolidation phenomena. The actual life of the deposit can be numerically simulated combining filling periods and quiescent periods where surcharges (or capping) can exist. Consequently, they are a basic technique for the design of disposal ponds