Projects
Purely decaying systems: the transient charm of decaying chaos
The long-term behavior of damped, unforced systems is very simple: due to energy dissipation, all motion eventually ceases. Consequently, if the motion is chaotic, it can only remain chaotic for a finite time. This behavior has previously been identified with the phenomenon of conventional transient chaos; however, a defining feature of typical transient chaos is that an infinite number of perpetually moving trajectories form a fractal set, among which typical trajectories wander. In damped, unforced systems no perpetually moving trajectories exist, and therefore a different type of description is required. Our goal is to provide a detailed theoretical characterization of this behavior, based on tracking the continuously decreasing energy of the system.
Stellar dynamics in time-dependent galactic potential
Although stellar motion is traditionally considered to be regular and predictable, they can become unpredictable and chaotic as stars move through a galaxy. Stellar dynamics is particularly sensitive to initial conditions in time-dependent galactic potential fields, which may arise, for example, from interactions with other galaxies or from episodes of star formation. Modeling stellar orbits and comparing these models with astronomical observations allows us to gain insight into the structure of the Universe and the evolution of galaxies.
Runaway electrons in ITER and other fusion plasma devices
The control of runaway electrons is a critical issue in the design of tokamak fusion devices. These particles, which travel at velocities close to the speed of light, are often generated during disruption events and can cause severe damage to diagnostic and other in-vessel components. Within the framework of this project, we investigate the behavior of runaway electrons by exploiting the analogy between tokamak magnetic field lines and the regular islands and chaotic regions that arise in chaotic dynamical systems. We develop a transport equation that will ultimately enable the modeling and safe design of fusion devices.
Dynamics and earthquake resistance of rocking structures
Studies of freestanding engineering structures have shown that, during earthquakes, they typically undergo only small deformations, and therefore the mechanical stresses that develop within them remain low. However, their rocking motion and the possibility of overturning must be taken into account. Even for relatively simple structures, such as cylindrical bodies, the dynamics can be highly complex under small imperfections. Building on previously studied models, we investigate how impacts, intermittent contacts, and the associated continuous energy dissipation during rocking affect the stability of geometrically imperfect structures. We also examine the influence of time-dependent, earthquake-like loading on structural stability.
Stability of simplified nuclear reactor models
The safe operation of a nuclear reactor requires the interplay of a large number of parameters and variables; accordingly, the models commonly used for this purpose are highly complex. For a global description of reactor behavior, simpler models also exist that are capable of capturing the essential features of the system using only a limited number of variables. Using such simplified models, we seek to address the question of whether operational transients, accident scenarios, or random perturbations can drive the system away from stable operation.
Transients in time-dependent abrasion processes
In unidirectional abrasion processes, such as the erosion of a riverbed by sediment transport, nearly all initial shapes evolve toward the same final form. For an initially elliptical shape, the abrasion process ultimately produces a geometry that preserves its form under further wear. However, it remains an open question through which intermediate shapes this final form is reached and on what timescale. The process is analogous to purely damped dynamical systems, because the key factor is the energy dissipated through collisions during abrasion.