| dc.description.abstract | A typical character of complex systems is the difficulty in modeling due to the complicated relations arising from the degrees of freedom of the system or the interplay between the environment and the system. In this emph{thesis}, we discuss two different types of one-dimensional dynamics in complex systems.
The first topic is the one-dimensional trajectories of a single cell resulting from the interplay between the distributions of mechanosensitive adhesion complexes, myosin motors, and actin network.
All the equations in our active gel model are deterministic, that is, there is no randomness in the equations.
It is found that when the mechanosensitivity of adhesion complexes is weak, the cell moves at a constant velocity as the myosin contractility is sufficiently large.
Furthermore, a cell with highly mechanosensitive adhesion complexes exhibits periodic back-and-forth motion as the myosin contractility increases.
Based on the active gel model, a simplified model is presented to show the mechanisms behind the transitions between these motility behaviors.
The second topic is the statistics of the stick-slip dynamics in solid friction.
In the experiment, a stick-slip event can be characterized by three physical quantities, and their statistics exhibit certain universal behaviors.
This {it thesis} reports a new model based on the experimental data.
In this case, the contact surface between the two solid is random, therefore the equation of motion of the system is not deterministic.
A force landscape is constructed to represent the effect of surface randomness.
The correlation function of the force landscape is Brownian correlated when the distance between two positions is less than a characteristic length $l_d$, and it saturates when the distance is beyond $l_d$.
Our model reproduces the statistics of the key physical quantities including the exponential distribution of the effective elastic constants of the surface, the generalized extreme value distribution for the critical force beyond which slips are initiated, and the power-law distribution of the force drop (slip length) during the slip events.
The force landscape we constructed helps us understand the origin of the universal and non-universal characteristics of stick-slip dynamics. | en_US |