Yen-Liang Chou

Kinetic theory for systems of self-propelled particles with metric-free interactions.

A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75, 1226 (1995)] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, N particles of constant speed v(0) try to align their travel directions with the average direction of a fixed number of closest neighbors. At strong alignment a global flocking state forms. The alignment is defined by a stochastic rule, not by a Hamiltonian. The corresponding interactions are of genuine multibody nature. The theory is based on a Master equation in 3N-dimensional phase space, which is made tractable by means of the molecular chaos approximation. The phase diagram for the transition to collective motion is calculated and compared to direct numerical simulations. A linear stability analysis of a homogeneous ordered state is performed using the kinetic but not the hydrodynamic equations in order to achieve high accuracy. In contrast to the regular metric Vicsek-model no instabilities occur. This confirms previous direct simulations that, for Vicsek-like models with metric-free interactions, there is no formation of density bands and that the flocking transition is continuous.

Ising metamagnets in thin film geometry: Equilibrium properties

Artificial antiferromagnets and synthetic metamagnets have attracted much attention recently due to their potential for many different applications. Under some simplifying assumptions these systems can be modeled by thin Ising metamagnetic films. In this paper we study, using both the Wang/Landau scheme and importance sampling Monte Carlo simulations, the equilibrium properties of these films. On the one hand we discuss the microcanonical density of states and its prominent features. On the other we analyze canonically various global and layer quantities. We obtain the phase diagram of thin Ising metamagnets as a function of temperature and external magnetic field. Whereas the phase diagram of the bulk system only exhibits one phase transition between the antiferromagnetic and paramagnetic phases, the phase diagram of thin Ising metamagnets includes an additional intermediate phase where one of the surface layers has aligned itself with the direction of the applied magnetic field. This additional phase transition is discontinuous and ends in a critical end point. Consequently, it is possible to gradually go from the antiferromagnetic phase to the intermediate phase without passing through a phase transition.

Characterization of non-equilibrium growth through global two-time quantities

In order to characterize non-equilibrium growth processes, we study the behaviour of global quantities that depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response functions and show that the scaling behaviour of the global response can depend on how the system is perturbed. On the one hand we derive exact expressions for systems characterized by linear Langevin equations (as for example the Edwards-Wilkinson and the noisy Mullins-Herring equations), on the other hand we discuss the influence of nonlinearities on the scaling behaviour of global quantities by integrating numerically the Kardar-Parisi- Zhang equation. We also discuss global fluctuation-dissipation ratios and how to use them for the characterization of non-equilibrium growth processes.

Changing growth conditions during surface growth

Motivated by a series of experiments that revealed a temperature dependence of the dynamic scaling regime of growing surfaces, we investigate theoretically how a nonequilibrium growth process reacts to a sudden change of system parameters. We discuss quenches between correlated regimes through exact expressions derived from the stochastic Edwards-Wilkinson equation with a variable diffusion constant. Our study reveals that a sudden change of the diffusion constant leads to remarkable changes in the surface roughness. Different dynamic regimes, characterized by a power-law or by an exponential relaxation, are identified, and a dynamic phase diagram is constructed. We conclude that growth processes provide one of the rare instances where quenches between correlated regimes yield a power-law relaxation.

Parameter-free scaling relation for nonequilibrium growth processes.

We discuss a parameter-free scaling relation that yields a complete data collapse for large classes of nonequilibrium growth processes. We illustrate the power of this scaling relation through various growth models, such as the competitive growth model with random deposition and random deposition with surface diffusion or the restricted solid-on-solid model with different nearest-neighbor height differences, as well as through a deposition model with temperature-dependent diffusion. The scaling relation is compared to the familiar Family-Vicsek relation, and the limitations of the latter are highlighted.

Kinetic roughening, global quantities, and fluctuation–dissipation relations

Growth processes and interface fluctuations can be studied through the properties of global quantities. We here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width, but that is also directly conjugate to an experimentally accessible parameter, thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions. Exploiting the full analyticity of the linear Edwards–Wilkinson and Mullins–Herring equations, we study in detail various two-time functions related to that quantity. This quantity fulfills the fluctuation–dissipation theorem when considering steady-state equilibrium fluctuations.