Polymer dynamics in chaotic flows with a strong shear component

We consider the dynamics of a polymer molecule injected into a chaotic flow with a strong mean shear component. The polymer experiences aperiodic tumbling in such flows. We consider a simplified model of the chaotic velocity field given by the superposition of a steady shear flow and a large-scale isotropic short-correlated random component. In the framework of this model, we present a detailed study of the statistical properties of single-polymer dynamics. We obtain the stationary probability distribution function of the polymer orientation, find the distribution of time periods between consequent events of tumbling, and find the tails of the polymer size distribution. The text was submitted by the author in English.     

Mixed acoustic phonons and phase modes in an aperiodic composite crystal

Aperiodic crystals which are long range ordered materials present original dynamics features due to the lack of translational symmetry formally implying the nonvalidity of the Brillouin zone concept. This Letter reports the observation by neutron scattering of an overdamped acousticlike mode at a Bragg peak position in a n-alkane-urea inclusion crystal. This result implies the existence of a gap in the dispersion branch. The gap and anomalous damping of these collective modes are discussed in terms of specific dynamics and interaction in aperiodic materials.     

Collective escape processes in many-particle systems

We study collective escape phenomena in nonlinear chain models. First we investigate the fragmentation of an overdamped polymer chain due to thermal fluctuations in the absence of an external force. We calculate the activation times of individual bonds in the coupled chain system and compare them with times obtained from Brownian dynamics simulations. We also consider a grafted chain exposed to an external force which monotonically grows as time goes on. In underdamped situations we show that collective localized excitations in a nonlinear force field with absorbing states can cause polymer fragmentation. In a similar fashion, localized modes assist a thermally activated escape of interacting particles in a metastable potential landscape which is additionally subjected to a periodic driving. The latter is necessary to obtain overcritical elongations which create localized modes even in case of stronger damping.     

Optical parametric oscillator on dipolaritons

The dynamics of dipolariton states in a planar microcavity under pumping into the middle dipolariton branch is investigated. It is shown that, in the case of exact resonance, the system exhibits an aperiodic behavior whereby pump dipolaritons are converted into dipolaritons of the idler and signal modes.     

Dynamics of an exciton-polariton parametric oscillator

The dynamics of an exciton-polariton parametric oscillator has been investigated. A system of nonlinear differential equations has been obtained for describing the time evolution of the densities of pump polaritons and polaritons of the signal mode. It has been demonstrated that, depending on the system parameters, the time evolution of the density of polaritons can occur in the periodic and aperiodic regimes, as well as at rest. The possibility of exercising phase control of the time evolution of the system has been proved.     

Dynamics of quasicrystals

The (lattice) dynamics of quasicrystals differs in many aspects from that of lattice periodic systems. This they have in common with other aperiodic crystals. The dynamics of quasicrystals is discussed here in the context of these general aperiodic crystals, but the special features of quasicrystals are stressed. The lattice dynamics is now fairly well understood. Especially for aperiodic crystals, there are excitations related to the possibility to describe the systems in superspace. These ‘phasons’ are discussed in particular.     

Coupled multiwave interactions in aperiodically poled nonlinear optical crystals

A new type of coupled nonlinear optical interactions that can be implemented in crystals with an aperiodic modulation of the nonlinear susceptibility is studied. The quasi-phase matching condition is satisfied simultaneously for several conventional three-frequency processes involved in the interaction due to the aperiodic variation of the nonlinearity in space. A simple method for designing aperiodically poled nonlinear optical crystals is proposed and analyzed. The method is based on the superposition of nonlinearity modulations produced by several periodic functions simultaneously so that each of these functions individually corresponds to its own quasi-phase-matched nonlinear process. The dynamics of energy exchange during interaction of five waves with different frequencies that involves three coupled three-frequency parametric interaction processes is investigated thoroughly. The ratio between the effective nonlinear wave coupling coefficients and the amplitudes of pump waves is determined for the case in which the initial stage of the interaction is characterized by the parametric instability. It is demonstrated that the secondary simplification of the coupled differential equations with spatially modulated nonlinear coefficients, which leads to the system of equations with constant nonlinear coefficients, correctly describes the dynamics of interaction of the waves at distances of the order of 50 characteristic nonlinear lengths.     

Carrier-envelope phase measurement by all-optical poling with a polar side-chain polymer

Dependence of all-optical poling efficiency on carrier-envelope phase (CEP) could be measured using photoisomerization of dye molecules which are covalently bound to a polymer main chain and have large difference in static dipole moment between the ground state and excited state. Increased chromophore density leads to an order of magnitude reduction in signal-detection time from a dye doped polymer. Analysis of all-optical poling experiments with CEP changes clearly showed the presence of polarization restoring force to zero polarization. This enables resetting of SH activity in the all-optical poling process to be used for fast response loop of CEP stabilization. Phenomenological model could explain well the difference in the growth-and-decay dynamics of poling between sample of dye doped in polymer studied previously and that grafted to a polymer main chain used in the present paper.     

The compression of polymer brushes under shear: the friction coefficient as a function of compression,shear rate and the properties of the solvent

We present a study of the compression of polymer-grafted surfaces using the dissipative particle dynamics (DPD) method at constant chemical potential. We demonstrate the importance of performing simulations of compression at fixed chemical potential of the solvent by comparing the simulated force-compression curves at constant chemical potential and density with the experimental profile determined for poly(ethylene-propylene) chains grafted onto mica surfaces in a cyclohexane solvent. The simulated force-distance and friction profiles are presented as a function of the polymer grafting density, the shear rate and the nature of the solvent. We also study the influence of the steepness of conservative potential between polymer segments and the size of the solvent elements (particles) on the form of the force-compression and friction-compression profiles.     

Symbolic dynamics and relaxation oscillations

This paper describes the application of qualitative methods of dynamical systems theory to a specific problem. It examines the forced Van der Pol equation as an example of a relaxation oscillation with aperiodic solutions. The technique of symbolic dynamics, particularly for one-dimensional mappings, is used to give a complete topological characterization of the set of these aperiodic solutions for parameter values for which the equation appears structurally stable. These results are a mathematical interpretation of numerical computations and are not the result of rigorous analysis.     

Acoustic characteristics inside cylindrical structure with end plates excited at different frequencies

In order to study coupling between vibration of a structure and a sound field in contact with the structure, a cavity surrounded by a rigid cylinder having thin elastic plates at both ends is adopted as an analytical model. When excitation forces of different frequencies are applied to the respective plates, the plate vibrations and the sound field inside the cavity become aperiodic, because of the coupling between the systems. In the present investigation, distribution of the sound pressure level inside the cavity is studied in detail in order to clarify the coupling behavior. The results show that when the respective plates vibrate at the same circumferential order, the vibration modes of the plates, which effect the coupling of the plate vibrations and the sound field, cause the aperiodic nature of each system to develop. In this case, since the dominant mode exists in formation of the sound field, it significantly influences the aperiodic nature of the coupling systems. In the case of vibration modes where the plates vibrate at different circumferential orders, the behaviors of the three systems, whose coupling has been restrained, approximate a steady state. Consequently, the dominant mode does not appear in the sound field.     

Effective temperature scaled dynamics of a flexible polymer in an active bath

Langevin dynamics simulations are employed to study the dynamical properties of a flexible polymer in an active bath. The diffusion of the centre of mass and end-to-end distance fluctuation are particularly analysed. We modulate both active force and active particle size to probe the activity-induced facilitation of polymer dynamics. Results indicate diffusivity and chain relaxation time can be well scaled by the effective temperature of the active bath. In addition, diffusion dynamics demonstrates an anomalous superdiffusive behaviour in short time scales, which becomes more prominent with increasing active particle size. Lastly, we extract the effective viscosity experienced by the probed chain, showing a sharp decrease with increment of effective temperature. The attenuation of effective viscosity due to activity might be responsible for the facilitated polymer dynamics.     

Static and dynamic properties of grafted ring polymer: Molecular dynamics simulation

The static and dynamic properties of a system of end-grafted flexible ring polymer chains grafted to a flat substrate and exposed to a good solvent are studied by using a molecular dynamics method. The monomers are described by a coarse-grained bead-spring model. Varying the grafting density ρ and the degree of polymerization or chain length N, we obtain the density profiles of monomers, study the structural properties of the chain (radius of gyration, bond orientational parameters, etc.), and also present the dynamic characteristics such as chain energy and bond force. Compared with a linear polymer brush, the ring polymer brush exhibits different static and dynamic properties for moderate or short chain length, while it behaves like linear polymer brush in the regime of long chain length.     

Microrheology and dynamics of an associative polymer

We study the microscopic viscoelastic properties and relaxation dynamics of solutions of a side-chain associative polymer, hydrophobically modified hydroxyethyl cellulose (hmHEC). Dynamic light scattering from small tracer particles suspended in the polymer solutions is used to determine their viscous and elastic moduli on the scale of the particles. Bulk-scale viscoelastic properties are measured by shear rheometry. The motion of the tracer particles in hmHEC is diffusive at short times and subdiffusive at intermediate and long times. The long-time subdiffusive motion was not observed in parallel experiments on unmodified HEC solutions, and is explained in terms of hindered reptation of the hydrophobically modified polymer chains in the associative network. Dynamic light scattering from the polymer molecules themselves shows that chain relaxation in hmHEC is dominated by slow concentration-dependent processes due to the large-scale associative network structure, while that in HEC is dominated by fast concentration-independent Rouse-like dynamics.     

Morphology selection of nanoparticle dispersions by polymer media

Designable media can control properties of nanocomposite materials by spatially organizing nanoparticles. Here we theoretically study particle organization by ultrathin polymer films of grafted chains ("brushes"). Polymer-soluble nanoparticles smaller than a brush-determined threshold disperse in the film to a depth scaling inversely with particle volume. In the polymer-insoluble case, aggregation is directed: provided particles are nonwetting at the film surface, the brush stabilizes the dispersion and selects its final morphology of giant elongated aggregates with a brush-selected width.     

Grazing bifurcations in an elastic structure excited by harmonic impactor motions

In this article, non-smooth dynamics of an elastic structure excited by a harmonic impactor motion is studied through a combination of experimental, numerical, and analytical efforts. The test apparatus consists of a stainless steel cantilever structure with a tip mass that is impacted by a shaker. Soft impact between the impactor and the structure is considered, and bifurcations with respect to quasi-static variation of the shaker excitation frequency are examined. In the experiments, qualitative changes that can be associated with grazing and corner-collision bifurcations are observed. Aperiodic motions are also observed in the vicinity of the non-smooth bifurcation points. Assuming the system response to be dominated by the structure’s fundamental mode, a non-autonomous, single degree-of-freedom model is developed and used for local analysis and numerical simulations. The predicted grazing and corner-collision bifurcations are in agreement with the experimental results. To study the local bifurcation behavior at the corner-collision point and explore the mechanism responsible for the aperiodic motions, a derivation is carried out to construct local Poincaré maps of periodic orbits at a corner-collision point such as the one observed in the soft-impact oscillator.