Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. The motor exhibits distinct states of motility: active motion along filaments, and effectively stationa
ry phase in which it detaches from the filaments and performs passive diffusion in the vicinity of the detachment point due to cytoplasmic crowding. The transition rates between motion and pause phases are asymmetric in general, and considerably affected by changes in environmental conditions which influences the efficiency of cargo delivery to specific targets. By considering the motion of molecular motor on a single filament as well as a dynamic filamentous network, we present an analytical model for the dynamics of self-propelled particles which undergo frequent pause phases. The interplay between motor processivity, structural properties of filamentous network, and transition rates between the two states of motility drastically changes the dynamics: multiple transitions between different types of anomalous diffusive dynamics occur and the crossover time to the asymptotic diffusive or ballistic motion varies by several orders of magnitude. We map out the phase diagrams in the space of transition rates, and address the role of initial conditions of motion on the resulting dynamics.
Ultracold bosonic atoms in optical lattices self-organize into a variety of structural and quantum phases when placed into a single-mode cavity and pumped by a laser. Cavity optomechanical effects induce an atom density modulation at the cavity-mode
wave length that competes with the optical lattice arrangement. Simultaneously short-range interactions via particle hopping promote superfluid order, such that a variety of structural and quantum coherent phases can occur. We analyze the emerging phase diagram in two dimensions by means of an extended Bose-Hubbard model using a local mean field approach combined with a superfluid cluster analysis. For commensurate ratios of the cavity and external lattice wave lengths the Mott insulator-superfluid transition is modified by the appearance of charge density wave and supersolid phases, at which the atomic density supports the buildup of a cavity field. For incommensurate ratios, the optomechanical forces induce the formation of Bose-glass and superglass phases, namely non-superfluid and superfluid phases, respectively, displaying quasi-periodic density modulations, which in addition can exhibit structural and superfluid stripe formation. The onset of such structures is constrained by the onsite interaction and is favourable at fractional densities. Experimental observables are identified and discussed.
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walks displacement. It i
s shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.
We present results from extensive Monte Carlo (MC) simulations of domain growth in ferromagnets and binary mixtures with quenched disorder. These are modeled by the random-bond Ising model and the dilute Ising model with either nonconserved (Glauber)
spin-flip kinetics or conserved (Kawasaki) spin-exchange kinetics. In all cases, our MC results are consistent with power-law growth with an exponent $theta (T,epsilon)$ which depends on the quench temperature $T$ and the disorder amplitude $epsilon$. Such exponents arise naturally when the coarsening domains are trapped by energy barriers which grow logarithmically with the domain size. Our MC results show excellent agreement with the predicted dependence of $theta (T,epsilon)$.
The non-equilibrium dynamics of condensation phenomena in nano-pores is studied via Monte Carlo simulation of a lattice gas model. Hysteretic behavior of the particle density as a function of the density of a reservoir is obtained for various pore ge
ometries in two and three dimensions. The shape of the hysteresis loops depend on the characteristics of the pore geometry. The evaporation of particles from a pore can be fitted to a stretched exponential decay of the particle density $rho_f(t) sim exp [ -(t/tau)^beta]$. Phase separation dynamics inside the pore is effectively described by a random walk of the non-wetting phases. Domain evolution is significantly slowed down in presence of random wall-particle potential and gives rise to a temperature dependent growth exponent. On the other hand roughness of the pore wall only delays the onset of a pure domain growth.
We study the kinetics of domain growth in ferromagnets with random exchange interactions. We present detailed Monte Carlo results for the nonconserved random-bond Ising model, which are consistent with power-law growth with a variable exponent. These
results are interpreted in the context of disorder barriers with a logarithmic dependence on the domain size. Further, we clarify the implications of logarithmic barriers for both nonconserved and conserved domain growth.
The dielectric permittivity of the orientational glass methanol(x=0.73)-$beta$-hydroquinone-clathrate has been studied as function of temperature and waiting time using different temperature-time-protocols. We study aging, rejuvenation and memory eff
ects in the glassy phase and discuss similarities and differences to aging in spin-glasses. We argue that the diluted methanol-clathrate, although conceptually close to its magnetic pendants, takes an intermediate character between a true spin-glass and a pure random field system.
The random field q-States Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found that the domain structure and the Zeeman energy of the domains resembles for general q the random field Is
ing case (q=2), which is also the expectation based on a random-walk picture of the groundstate. The domain size distribution is exponential, and the scaling of the average domain size with the disorder strength is similar for q arbitrary. The zero-temperature properties are compared to the equilibrium spin states at small temperatures, to investigate the effect of local random field fluctuations that imply locally degenerate regions. The response to field pertubabtions (chaos) and the susceptibility are investigated. In particular for the chaos exponent it is found to be 1 for q = 2,...,5. Finally for q=2 (Ising case) the domain length distribution is studied for correlated random fields.
