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The orientational dynamics of weakly inertial axisymmetric particles in a steady flow is investigated. We derive an asymptotic equation of motion for the unit axial vector along the particle symmetry axis, valid for small Stokes number St,…
Successful assembly of suspended nanoscale rod-like particles depends on fundamental phenomena controlling rotational and translational diffusion. Despite the significant developments in fluidic fabrication of nanostructured materials, the…
In the present work, we investigated the correlation-induced localization-delocalization transition in the one-dimensional tight-binding model with fractal disorder. We obtained a phase transition diagram from localized to extended states…
The transport of bio-particles in viscous flows exhibits a rich variety of dynamical behaviour, such as morphological transitions, complex orientation dynamics or deformations. Characterising such complex behaviour under well controlled…
In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
We study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with $n$ vertices and of bounded degree. We show that the relaxation time (defined as…
We study the activated motion of adsorbed polymers which are driven over a structured substrate by a localized point force.Our theory applies to experiments with single polymers using, for example, tips of scanning force microscopes to drag…
The competition between the connectivity and the local or global order in model fully-flexible chain molecules is investigated by molecular-dynamics simulations. States with both missing (melts) and high (crystal) global order are…
We show local and cocycle rigidity for $\R^k \times \Z^l$ partially hyperbolic translation actions on homogeneous spaces $\mc G/ \Lambda$. We consider a large class of actions whose geometric properties are more complicated than previously…
We study the driven translocation of a flexible polymer through an interacting conical pore using Langevin dynamics simulations. We find that, for a fixed value of externally applied force and pore polymer interaction strength, the mean…
We study the Lagrangian dynamics of semi-flexible macromolecules in laminar as well as in homogeneous and isotropic turbulent flows by means of analytically solvable stochastic models and direct numerical simulations. The statistics of the…
Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation…
We revisit a model of semiflexible Gaussian chains proposed by Winkler \textit{et al}, solve the dynamics of the discrete description of the model and derive exact algebraic expressions for some of the most relevant dynamical observables,…
Many active materials and biological systems are driven far from equilibrium by embedded agents that spontaneously generate forces and distort the surrounding material. Probing and characterizing these athermal fluctuations is essential for…
Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a…
The conformations of semiflexible (bio)polymers are studied in flow through geometrically structured microchannels. Using mesoscale hydrodynamics simulations, we show that the polymer undergoes a rod-to-helix transition as it moves from the…
We study of the dynamics of ring polymers confined to diffuse in a background gel at low concentrations. We do this in order to probe the inter-play between topology and dynamics in ring polymers. We develop an algorithm that takes into…
Large deviation principles for hyperbolic systems are well studied and provide exponential rates for the deviations of Birkhoff averages from their limit. This short article presents a local large deviation principle for Smale spaces, in…
Obtaining reliable estimates of the statistical properties of complex macromolecules by computer simulation is a task that requires high computational effort as well as the development of highly efficient simulation algorithms. We present…