Transport phenomena in time-dependent media

The main subject of the thesis is the study of Fermi acceleration, regarded nowadays as a fundamental acceleration mechanism, consisting in the increase of the mean energy of particles due to collisions with moving scatterers. Prior to the study of extended systems, the prototype one-dimensional dynamical system exhibiting Fermi acceleration was considered; the stochastic Fermi-Ulam model. The analysis of the dynamics in this system revealed the pitfalls of the standard, widely used, quasi-static approximation, which neglects the impact of the location of the collision events in the configuration space. In order to take this into account, a novel approximation scheme was introduced allowing both the analytical treatment of the acceleration process as well as fast numerical simulations. Furthermore, the limitations and possible inconsistencies stemming from the treatment of Fermi acceleration via the Fokker-Planck equation were brought to light. A new self-consistent methodology on the basis of the Chapman-Kolmogorov equation was put forward, capable of giving an accurate description of Fermi acceleration for all times. The understanding gained through the investigation of the Fermi-Ulam model, was then utilized for the study of Fermi acceleration in spatially extended systems, using as a prototype the two-dimensional randomized Lorentz gas. The newly introduced approximation was generalized for application to higher dimensional systems. The study revealed that the increase of the efficiency of Fermi acceleration depends only on the symmetries of the driving time-law and is insensitive to the geometrical properties of the moving scatterers and the dimensionality of the time-dependent system. Finally, the study of the driven Lorentz gas, in a channel geometry, revealed a completely new aspect of Fermi acceleration, linking it, for the first time, to the phenomenon of self-organized criticality. Particularly it was shown that Fermi acceleration permits the spontaneous synchronization of the motion of the particles with that of the moving scatterers, such that particles can travel collision-free for long times. This, in turn, gives rise to strongly intermittent dynamics, which, as it was shown, is a sufficient condition for the emergence of scale-free cross-correlations between non-interacting particles

Heterogeneity and clustering of defaults

This paper studies how the degree of heterogeneity among hedge funds' demand orders for a risky asset affects the possibility of their defaults being clustered. We find that fire-sales caused by margin calls is a necessary, yet not a sufficient condition for defaults to be clustered. We show that when the degree of heterogeneity is sufficiently high, poorly performing HFs are able to obtain a higher than usual market share, which leads to an improvement of their performance. Consequently, their survival time is prolonged, increasing the probability of them remaining in operation until the downturn of the next leverage cycle. This leads to an increase in the probability of poorly and high-performing hedge funds to default in sync at a later time, and thus also in the probability of collective defaults. Our analytical results establish a connection between the nontrivial aggregate statistics and the presence of infinite memory in the process governing the hedge funds' defaults

Hedging against risk in a heterogeneous leveraged market

This paper provides a theoretical model which highlights the role of heterogeneity of information in the emergence of temporal aggregation (clustering) of defaults in a leveraged economy. We show that the degree of heterogeneity plays a critical role in the persistence of the correlation between defaults in time. Specifically, a high degree of heterogeneity leads to an autocorrelation of the time sequence of defaults characterised by a hyperbolic decay rate, such that the autocorrelation function is not summable (infinite memory) and defaults are clustered. Conversely, if the degree of heterogeneity is reduced the autocorrelation function decays exponentially fast, and thus, correlation between defaults is only transient (short memory). Our model is also able to reproduce stylized facts, such as clustered volatility and non-Normal returns. Our findings suggest that future regulations might be directed at improving publicly available information, reducing the relative heterogeneity

Heterogeneity and clustering of defaults

This paper provides a theoretical model which highlights the role of heterogeneity of information in the emergence of temporal aggregation (clustering) of defaults in a leveraged economy. We show that the degree of heterogeneity plays a critical role in the persistence of the correlation between defaults in time. Specifically, a high degree of heterogeneity leads to an autocorrelation of the time sequence of defaults characterised by a hyperbolic decay rate, such that the autocorrelation function is not summable (infinite memory) and defaults are clustered. Conversely, if the degree of heterogeneity is reduced the autocorrelation function decays exponentially fast, and thus, correlation between defaults is only transient (short memory). Our model is also able to reproduce stylized facts, such as clustered volatility and non-Normal returns. Our findings suggest that future regulations might be directed at improving publicly available information, reducing the relative heterogeneity

“The many faces of sorrow”: An empirical exploration of the psychological plurality of sadness

Sadness has typically been associated with failure, defeat and loss, but it has also been suggested that sadness facilitates positive and restructuring emotional changes. This suggests that sadness is a multi-faceted emotion. This supports the idea that there might in fact be different facets of sadness that can be distinguished psychologically and physiologically. In the current set of studies, we explored this hypothesis. In a first stage, participants were asked to select sad emotional faces and scene stimuli either characterized or not by a key suggested sadness-related characteristic: loneliness or melancholy or misery or bereavement or despair. In a second stage, another set of participants was presented with the selected emotional faces and scene stimuli. They were assessed for differences in emotional, physiological and facial-expressive responses. The results showed that sad faces involving melancholy, misery, bereavement and despair were experienced as conferring dissociable physiological characteristics. Critical findings, in a final exploratory design, in a third stage, showed that a new set of participants could match emotional scenes to emotional faces with the same sadness-related characteristic with close to perfect precision performance. These findings suggest that melancholy, misery, bereavement and despair can be distinguishable emotional states associated with sadness

Heterogeneity and Clustering of Defaults

This paper studies an economy where privately informed hedge funds (HFs) trade a risky asset in order to exploit potential mispricings. HFs are allowed to have access to credit, by using their risky assets as collateral. We analyse the role of the degree of heterogeneity among HFs’ demand for the risky asset in the emergence of clustering of defaults. We find that fire-sales caused by margin calls is a necessary, yet not a sufficient condition for defaults to be clustered. We show that when the degree of heterogeneity is sufficiently high, poorly performing HFs are able to obtain a higher than usual market share at the end of the leverage cycle, which leads to an improvement of their performance. Consequently, their survival time is prolonged, increasing the probability of them remaining in operation until the downturn of the next leverage cycle. This leads to the increase of the probability of poorly and high-performing hedge funds to default in sync at a later time, and thus the probability of collective defaults

Hedging against Risk in a Heterogeneous Leveraged Market

This paper focuses on the use of interest rates as a tool for hedging against the default risk of heterogeneous hedge funds (HFs) in a leveraged market. We assume that the banks study the HFs survival statistics in order to compute default risk and hence the correct interest rate. The emergent non-trivial (heavy-tailed) statistics observed on the aggregate level, prevents the accurate estimation of risk in a leveraged market with heterogeneous agents. Moreover, we show that heterogeneity leads to the clustering of default events and constitutes thus a source of systemic risk