Non-Markovian closure kinetics of flexible polymers with hydrodynamic interactions.

This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of the mobility tensor (Zimm dynamics), is shown to reproduce very accurately the results of numerical simulations of the complete nonlinear dynamics. It is found that Markovian treatments based on a Wilemski-Fixman approximation significantly overestimate cyclization times (up to a factor 2), showing the importance of memory effects in the dynamics.

Contact Kinetics in Fractal Macromolecules.

We consider the kinetics of first contact between two monomers of the same macromolecule. Relying on a fractal description of the macromolecule, we develop an analytical method to compute the mean first contact time for various molecular sizes. In our theoretical description, the non-Markovian feature of monomer motion, arising from the interactions with the other monomers, is captured by accounting for the nonequilibrium conformations of the macromolecule at the very instant of first contact.

Cyclization kinetics of Gaussian semiflexible polymer chains.

We consider the dynamics and the cyclization kinetics of Gaussian semiflexible chains, in which the interaction potential tends to align successive bonds. We provide asymptotic expressions for the cyclization time, for the eigenvalues and eigenfunctions, and for the mean square displacement at all time and length scales, with explicit dependence on the capture radius, on the positions of the reactive monomers in the chain, and on the finite number of beads. For the cyclization kinetics, we take into account non-Markovian effects by calculating the distribution of reactive conformations of the polymer, which are not taken into account in the classical Wilemski-Fixman theory.

Slow encounters of particle pairs in branched structures.

On infinite homogeneous structures, two random walkers meet with certainty if and only if the structure is recurrent; i.e., a single random walker returns to its starting point with probability 1.

Transport properties of continuous-time quantum walks on Sierpinski fractals.

We model quantum transport, described by continuous-time quantum walks (CTQWs), on deterministic Sierpinski fractals, differentiating between Sierpinski gaskets and Sierpinski carpets, along with their dual structures. The transport efficiencies are defined in terms of the exact and the average return probabilities, as well as by the mean survival probability when absorbing traps are present. In the case of gaskets, localization can be identified already for small networks (generations).

Gaussian semiflexible rings under angular and dihedral restrictions.

Semiflexible polymer rings whose bonds obey both angular and dihedral restrictions [M. Dolgushev and A. Blumen, J.

NMR relaxation of the orientation of single segments in semiflexible dendrimers.

We study the orientational properties of labeled segments in semiflexible dendrimers making use of the viscoelastic approach of Dolgushev and Blumen [J. Chem. Phys.

Continuous-time random-walk approach to supercooled liquids. II. Mean-square displacements in polymer melts.

The continuous-time random walk (CTRW) describes the single-particle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al.

Continuous-time random-walk approach to supercooled liquids. I. Different definitions of particle jumps and their consequences.

Single-particle trajectories in supercooled liquids display long periods of localization interrupted by "fast moves." This observation suggests a modeling by a continuous-time random walk (CTRW). We perform molecular dynamics simulations of equilibrated short-chain polymer melts near the critical temperature of mode-coupling theory Tc and extract "moves" from the monomer trajectories.

Geometrical aspects of quantum walks on random two-dimensional structures.

We study the transport properties of continuous-time quantum walks (CTQWs) over finite two-dimensional structures with a given number of randomly placed bonds and with different aspect ratios (ARs). Here, we focus on the transport from, say, the left side to the right side of the structure where absorbing sites are placed. We do so by analyzing the long-time average of the survival probability of CTQWs.

Dynamics of discrete semiflexible chains under dihedral constraints: analytic results.

Here we consider the dynamics of semiflexible polymers subject both to angular and to dihedral constraints. We succeed in obtaining analytically the dynamical matrix of such systems by extending the formalism developed by Dolgushev and Blumen [J. Chem.

Dynamics of semiflexible regular hyperbranched polymers.

We study the dynamics of semiflexible Vicsek fractals (SVF) following the framework established by Dolgushev and Blumen [J. Chem. Phys.

Analytical model for the dynamics of semiflexible dendritic polymers.

We study the dynamics of semiflexible dendritic polymers following the method of Dolgushev and Blumen [J. Chem. Phys.

Maximum entropy principle applied to semiflexible ring polymers.

Based on the success of the maximum entropy principle (MEP) in the study of semiflexible treelike polymers [M. Dolgushev and A. Blumen, J.

Random walks on Sierpinski gaskets of different dimensions.

We study random walks (RWs) on classical and dual Sierpinski gaskets (SG and DSG), naturally embedded in d-dimensional Euclidian spaces (ESs). For large d the spectral dimension d(s) approaches 2, the marginal RW dimension. In contrast to RW over two-dimensional ES, RWs over SG and DSG show a very rich behavior.

Cospectral polymers: Differentiation via semiflexibility.

We consider polymer structures which are known in the mathematical literature as "cospectral." Their graphs have (in spite of the different architectures) exactly the same Laplacian spectra. Now, these spectra determine in Gaussian (Rouse-type) approaches many static as well as dynamical polymer characteristics.

Dissipative dynamics with trapping in dimers.

The trapping of excitations in systems coupled to an environment allows one to study the quantum to classical crossover by different means. We show how to combine the phenomenological description by a non-Hermitian Liouville-von Neumann equation (LvNE) approach with the numerically exact path integral Monte Carlo (PIMC) method, and exemplify our results for a system of two coupled two-level systems. By varying the strength of the coupling to the environment we are able to estimate the parameter range in which the LvNE approach yields satisfactory results.

Dynamics of chains and dendrimers with heterogeneous semiflexibility.

Based on our recent model for the dynamics of semiflexlible treelike networks [M. Dolgushev and A. Blumen, J.

Dynamics of semiflexible treelike polymeric networks.

We study the dynamics of general treelike networks, which are semiflexible due to restrictions on the orientations of their bonds. For this we extend the generalized Gaussian structure model, in which the dynamics obeys Langevin equations coupled through a dynamical matrix. We succeed in formulating analytically this matrix for arbitrary treelike networks and stiffness coefficients.

Simulating dynamic crossover behavior of semiflexible linear polymers in solution and in the melt.

We present a molecular dynamics study of the dynamic scaling behavior of linear polymers in solution and in the melt when their character changes from fully flexible to semiflexible. The stiffness of the chains is determined by a bending potential. It is shown that the relaxation times tau(p) characterizing the internal dynamics of the polymer chains as well as the mean square mode amplitudes exhibit a clear crossover from Rouse to bending modes with increasing mode number p.

Protein displacements under external forces: An atomistic Langevin dynamics approach.

We present a fully atomistic Langevin dynamics approach as a method to simulate biopolymers under external forces. In the harmonic regime, this approach permits the computation of the long-term dynamics using only the eigenvalues and eigenvectors of the Hessian matrix of second derivatives. We apply this scheme to identify polymorphs of model proteins by their mechanical response fingerprint, and we relate the averaged dynamics of proteins to their biological functionality, with the ion channel gramicidin A, a phosphorylase, and neuropeptide Y as examples.

Slow excitation trapping in quantum transport with long-range interactions.

Long-range interactions (LRIs) slow down the excitation trapping in quantum transport on a one-dimensional chain with traps at both ends when compared to the case with only nearest-neighbor interactions. This is in contrast to the corresponding classical case, in which LRIs lead to faster excitation trapping. The reason for the slowing down is to be found in subtle changes--due to LRIs--in the spectrum of the Hamiltonian.

Universal behavior of quantum walks with long-range steps.

Continuous-time quantum walks with long-range steps R(-gamma) (R being the distance between sites) on a discrete line behave in similar ways for all gamma > or =2 . This is in contrast to classical random walks, which for gamma>3 belong to a different universality class than for gamma < or =3 . We show that the average probabilities to be at the initial site after time t as well as the mean square displacements are of the same functional form for quantum walks with gamma =2, 4, and with nearest neighbor steps.

Quantum transport on small-world networks: a continuous-time quantum walk approach.

We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWNs). The SWNs are built from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is modeled by continuous-time quantum walks, and we evaluate numerically the ensemble-averaged transition probability to reach any node of the network from the initially excited one.

Survival probabilities in coherent exciton transfer with trapping.

In the quest for signatures of coherent transport we consider exciton trapping in the continuous-time quantum walk framework. The survival probability displays different decay domains, related to distinct regions of the spectrum of the Hamiltonian. For linear systems and at intermediate times the decay obeys a power law, in contrast with the corresponding exponential decay found in incoherent continuous-time random walk situations.