Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Driven fragmentation of granular gases

The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the longvelocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f (c)~exp (−cⁿ), with n ≈1.2, regarding less the fragmentation mechanisms

Application of Information Statistical Theory to the Description of the Effect of Heat Conduction on the Chemical Reaction Rate in Gases

The effect of the heat flux on the rate of chemical reaction in dilute gases is shown to be important for reactions characterized by high activation energies and in the presence of very large temperature gradients. This effect, obtained from the second-order terms in the distribution function (similar to those obtained in the Burnett approximation to the solution of the Boltzmann equation), is derived on the basis of information theory. It is shown that the analytical results describing the effect are simpler if the kinetic definition for the nonequilibrium temperature is introduced than if the thermodynamic definition is introduced. The numerical results are nearly the same for both definitions

The Barcelonnettes: an example of network-entrepreneurs in XIX century Mexico. An explanation based on a theory of bounded rational choice with social embeddedness

A theory of network-entrepreneurs or "spin-off system" is presented in this paper for the creation of firms based on the community’s social governance. It is argued that firm’s capacity for accumulation depends on the presence of employees belonging to the same social/ethnic group with expectations of "inheriting" the firm and becoming entrepreneurs once they have been selected for their merits and loyalty towards their patrons. Such accumulation is possible because of the credibility of the patrons’ promises of supporting newcomers due to high social cohesion and specific social norms prevailing in the community. This theory is exemplified through the case of the Barcelonnettes, a group of immigrants from the Alps in the South of France (Provence) who came to Mexico in the XIX Century.

In Search of a theory of debt management

A growing literature integrates theories of debt management into models of optimal fiscal policy. One promising theory argues that the composition of government debt should be chosen so that fluctuations in the market value of debt offset changes in expected future deficits. This complete market approach to debt management is valid even when the government only issues non-contingent bonds. A number of authors conclude from this approach that governments should issue long term debt and invest in short term assets. We argue that the conclusions of this approach are too fragile to serve as a basis for policy recommendations. This is because bonds at different maturities have highly correlated returns, causing the determination of the optimal portfolio to be ill-conditioned. To make this point concrete we examine the implications of this approach to debt management in various models, both analytically and using numerical methods calibrated to the US economy. We find the complete market approach recommends asset positions which are huge multiples of GDP. Introducing persistent shocks or capital accumulation only worsens this problem. Increasing the volatility of interest rates through habits partly reduces the size of these simulations we find no presumption that governments should issue long term debt ? policy recommendations can be easily reversed through small perturbations in the specification of shocks or small variations in the maturity of bonds issued. We further extend the literature by removing the assumption that governments every period costlessly repurchase all outstanding debt. This exacerbates the size of the required positions, worsens their volatility and in some cases produces instability in debt holdings. We conclude that it is very difficult to insulate fiscal policy from shocks by using the complete markets approach to debt management. Given the limited variability of the yield curve using maturities is a poor way to substitute for state contingent debt. The result is the positions recommended by this approach conflict with a number of features that we believe are important in making bond markets incomplete e.g allowing for transaction costs, liquidity effects, etc.. Until these features are all fully incorporated we remain in search of a theory of debt management capable of providing robust policy insights.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Rational first integrals in the Darboux theory of integrability in Cn

"Vegeu el resum a l'inici del document del fitxer adjunt."

On the homotopy theory of spectral categories

"Vegeu el resum a l'inici del document del fitxer adjunt."

Luck and the control theory of knowledge

The dissertation accomplishes two aims: 1) to diagnose what prevents true beliefs from being knowledge; 2) to give an positive account of knowledge. Concerning the first aim, it offers an account of the notion of luck. It defends the view that luck is a form of risk and distinguishes two types of luck. Then, it applies the account to the problem of epistemic luck and distinguishes, accordingly, two types of epistemic luck. It is argued that these two types of epistemic luck explain the whole range of cases of not-known true belief. Concerning the second aim, the dissertation advances an account of knowledge in terms of the notion of cognitive control that deals with the two forms of epistemic luck distinguished.

Tenseness of Riemannian flows

We show that any transversally complete Riemannian foliation &em&F&/em& of dimension one on any possibly non-compact manifold M is tense; namely, (M,&em&F&/em&) admits a Riemannian metric such that the mean curvature form of &em&F&/em& is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize some well known results including Masa's characterization of tautness.

Time-Delayed Theory of the Neolithic Transition in Europe

The classical wave-of-advance model of the neolithic transition (i.e., the shift from hunter-gatherer to agricultural economies) is based on Fisher's reaction-diffusion equation. Here we present an extension of Einstein's approach to Fickian diffusion, incorporating reaction terms. On this basis we show that second-order terms in the reaction-diffusion equation, which have been neglected up to now, are not in fact negligible but can lead to important corrections. The resulting time-delayed model agrees quite well with observations

Salience theory of choice under risk

We present a theory of choice among lotteries in which the decision maker's attention is drawn to (precisely defined) salient payoffs. This leads the decision maker to a context-dependent representation of lotteries in which true probabilities are replaced by decision weights distorted in favor of salient payoffs. By endogenizing decision weights as a function of payoffs, our model provides a novel and unified account of many empirical phenomena, including frequent risk-seeking behavior, invariance failures such as the Allais paradox, and preference reversals. It also yields new predictions, including some that distinguish it from Prospect Theory, which we test.