A static and a dynamical model are introduced to study the physical properties of an elastic polymer adsorbed on a rigid membrane. We analyze the detailed microscopic model for the adhesion problem and show that in the force ensemble a critical force is expected. Forces smaller than the critical value are not able to peel off the filament, while larger forces will cause the filament to completely desorb from the membrane. To demonstrate the nonequilibrium properties of the moving states for forces larger than the critical value, we present the linear response of the system in the form of a force-velocity relation. In addition, we use a very simple short-range static model and obtain the equilibrium phases of the system in different cases where either a fixed force or a fixed height can be applied at the end. For the fixed force the equilibrium phases arising from the static model are in agreement with dynamical model. Forces smaller than the critical value are not able to peel off the filament while the larger forces will cause the filament to completely desorb as in the dynamical model.

We study the impact of excluded volume interactions on the orientation statistics of chain segments in polymer gels, and show that nuclear magnetic resonance (NMR) experiments provide a direct and unique measure of excluded-volume effects on the chain statistics. In particular we consider the tensor order parameter, which can be expressed as the second Legendre polynomial of the segment orientation with respect to a fixed end-to-end distance vector and which is directly related to the residual coupling constant obtained in NMR experiments. We provide analytical results for the case of single chains in a good solvent and for semidilute solutions. Computer simulations using the bond fluctuation model are applied to compare with the analytical predictions. Considering polymer gels at the equilibrium state of swelling we predict a unique relation between the tensor order parameter and the correlation length (blob size) of the gel. Experiments applying multiple-quantum NMR methods to both end-linked and randomly cross-linked polymer networks are in excellent agreement with this prediction. The initial decay of the tensor order parameter as observed in experiments at low and intermediate degrees of swelling can be explained as a solvent effect without making additional assumptions about constraint release processes during swelling.

Motivated by recent DNA-pulling experiments, we revisit the Poland-Scheraga model of melting a double-stranded polymer. We include distinct bending rigidities for both the double-stranded segments and the single-stranded segments forming a bubble. There is also bending stiffness at the branch points between the two segment types. The transfer matrix technique for single persistent chains is generalized to describe the branching bubbles. Properties of spherical harmonics are then exploited in truncating and numerically solving the resulting transfer matrix. This allows efficient computation of phase diagrams and force-extension curves (isotherms). While the main focus is on exposition of the transfer matrix technique, we provide general arguments for a reentrant melting transition in stiff double strands. Our theoretical approach can also be extended to study polymers with bubbles of any number of strands, with potential applications to molecules such as collagen.

We use spatial models of simple predator-prey interactions to predict that predator and prey numbers oscillate in time and space. These oscillations are not seen in the deterministic versions of the models, but are due to stochastic fluctuations about the time-independent solutions of the deterministic equations which are amplified due to the existence of a resonance. We calculate the power spectra of the fluctuations analytically and show that they agree well with results obtained from stochastic simulations. This work extends the analysis of these quasicycles from that previously developed for well-mixed systems to spatial systems, and shows that the ideas and methods used for nonspatial models naturally generalize to the spatial case.

We consider finite-size particles colliding elastically, advected by a chaotic flow. The collisionless dynamics has a quasiperiodic attractor and particles are advected towards this attractor. We show in this work that the collisions have dramatic effects in the system’s dynamics, giving rise to collective phenomena not found in the one-particle dynamics. In particular, the collisions induce a kind of instability, in which particles abruptly spread out from the vicinity of the attractor, reaching the neighborhood of a coexisting chaotic saddle, in an autoexcitable regime. This saddle, not present in the dynamics of a single particle, emerges due to the collective particle interaction. We argue that this phenomenon is general for advected, interacting particles in chaotic flows.

We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any periodic orbits in the corresponding dynamics. As a simple example we consider the scattering of a beam of noninteracting particles off a circular hard scatterer. The performed analysis is focused on experimentally accessible quantities, characterizing the system, like the differential cross sections in the outgoing angle and velocity. Despite the absence of periodic orbits and their manifolds in the dynamics, we show that the cross sections acquire rich and multiple structure when the velocity of the particles in the beam becomes of the same order of magnitude as the maximum velocity of the oscillating target. The underlying dynamical pattern is uniquely determined by the phase of the first collision between the beam particles and the scatterer and possesses a universal profile, dictated by the manifolds of the parabolic orbits, which can be understood both qualitatively as well as quantitatively in terms of scattering off a hard wall. We discuss also the inverse problem concerning the possibility to extract properties of the oscillating target from the differential cross sections.

Departing from a reliable computational method to approximate solutions of dissipative, nonlinear wave equations, we study the bistability of a $(2+1)$-dimensional sine-Gordon system, spatially defined on a bounded square of the first quadrant of the Cartesian plane, and subject to Dirichlet boundary data in the form of harmonic driving on the coordinate axes, oscillating at a frequency in the forbidden band gap of the medium. It is shown numerically that, as its spatially discrete counterpart, the continuous $(2+1)$-dimensional sine-Gordon equation presents the process of nonlinear supratransmission, and that this phenomenon is independent of the discretization procedure. Moreover, our simulations show that a bistable region, where a conducting state and an insulating state may coexist, is present in this system, even in the presence of external damping. As an application, it is shown that the bistable regime may be properly employed in order to transmit certain monochromatic waves through these media.

Experiments on a chain of coupled pendula driven periodically at one end demonstrate the existence of a regime which produces an output frequency at an odd fraction of the driving frequency. The stationary state is then obtained with numerical simulations and modeled with an analytical solution of the continuous sine-Gordon equation that resembles a kinklike motion back and forth in the restricted geometry of the chain. This solution differs from the expressions used to understand nonlinear bistability where the synchronization constraint was the basic assumption. As a result the short pendula chain is shown to possess tristable stationary states and to act as a frequency divider.

We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered $\alpha$-stable processes. The tempering results in the existence of all moments of operational time. The subordination by the inverse tempered $\alpha$-stable process provides diffusion (relaxation) that occupies an intermediate place between subdiffusion (Cole-Cole law) and normal diffusion (exponential law). Here we obtain explicitly the Fokker-Planck equation and the Cole-Davidson relaxation function. This model includes subdiffusion as a particular case.

A formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) [T. Koide, Phys. Rev. E 75, 060103(R) (2007)]. This is an extension of the Green-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as to apply to more general situations.

We determine the distribution of cluster sizes that emerges from an initial phase of homogeneous aggregation with conserved total particle density. The physical ingredients behind the predictions are essentially classical: Supercritical nuclei are created at the Zeldovich rate, and before the depletion of monomers is significant, the characteristic cluster size is so large that the clusters undergo diffusion-limited growth. Mathematically, the distribution of cluster sizes satisfies an advection partial differential equation (PDE) in “size space.” During this creation phase, clusters are nucleated and then grow much larger than the critical size, so nucleation of supercritical clusters at the Zeldovich rate is represented by an effective boundary condition at zero size. The advection PDE subject to the effective boundary condition constitutes a “creation signaling problem” for the evolving distribution of cluster sizes during the creation era. Dominant balance arguments applied to the advection signaling problem show that the characteristic time and cluster size of the creation era are exponentially large in the initial free-energy barrier against nucleation, $G_{*}$. Specifically, the characteristic time is proportional to $e^{(2∕5)G_{*}∕k_{B}T}$ and the characteristic number of monomers in a cluster is proportional to $e^{(3∕5)G_{*}∕k_{B}T}$. The exponentially large characteristic time and cluster size give a posteriori validation of the mathematical signaling problem. In a short note, Marchenko [JETP Lett. 64, 66 (1996)] obtained these exponentials and the numerical prefactors $2∕5$ and $3∕5$. Our work adds the actual solution of the kinetic model implied by these scalings, and the basis for connection to subsequent stages of the aggregation process after the creation era.

The role of thermal fluctuations in the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo transformation to a polygonal shape. The transition occurs in the cases of hardening and softening charge-bending interaction. In the former case the charge and curvature are smoothly distributed along the chain, while in the latter spontaneous kink formation is initiated. The transition to a noncircular conformation is analogous to a phase transition of the second kind.

Neurons are subject to various kinds of noise. In addition to synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal-processing properties of the neuron. We study the response of a stochastic Hodgkin-Huxley neuron to transient input subthreshold pulses. It is found that the average response time decreases but variance increases as the amplitude of channel noise increases. In the case of single-pulse detection, we show that channel noise enables one neuron to detect the subthreshold signals and an optimal membrane area (or channel noise intensity) exists for a single neuron to achieve optimal performance. However, the detection ability of a single neuron is limited by large errors. Here, we test a simple neuronal network that can enhance the pulse-detecting abilities of neurons and find that dozens of neurons can perfectly detect subthreshold pulses. The phenomenon of intrinsic stochastic resonance is also found at both the level of single neurons and the level of networks. At the network level, the detection ability of networks can be optimized for the number of neurons comprising the network.

We study the dynamical response of a circularly driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and quantitative analysis. A scale-free expression defining the separation between possible spinning regimes is obtained.

The phenomenon of Fermi acceleration is addressed for the problem of a classical and dissipative bouncer model, using a scaling description. The dynamics of the model, in both the complete and simplified versions, is obtained by use of a two-dimensional nonlinear mapping. The dissipation is introduced using a restitution coefficient on the periodically moving wall. Using scaling arguments, we describe the behavior of the average chaotic velocities on the model both as a function of the number of collisions with the moving wall and as a function of the time. We consider variations of the two control parameters; therefore critical exponents are obtained. We show that the formalism can be used to describe the occurrence of a transition from limited to unlimited energy growth as the restitution coefficient approaches unity. The formalism can be used to characterize the same transition in two-dimensional time-varying billiard problems.

The interface between two immiscible fluids both is influenced (advected) by the imposed flow and influences (perturbs) it. The perturbation then changes the advection. This phenomenon is taken into account in an extended Doi-Ohta model of rheological behavior of immiscible blends. The agreement of the rheological predictions with experimental data is improved.

Linear and nonlinear convection in a rotating annular cylinder, under experimental boundary conditions, heated from below and rotating about a vertical axis are investigated. In addition to the usual physical parameters such as the Rayleigh and Taylor number, an important geometric parameter, the ratio of the inner to outer radius, enters into the problem. For intermediate ratios, linear stability analysis reveals that there exist two countertraveling convective waves which are nonlinearly significant: a retrograde wave located near the outer sidewall and a prograde wave adjacent to the inner sidewall. Several interesting phenomena of nonlinear convection are found: (i) tempospatially modulated countertraveling waves caused by an instability of the Eckhaus-Benjamin-Feir type, (ii) destructive countertraveling waves in which the existence or disappearance of the prograde wave is determined by its relative phase to the retrograde wave, and (iii) a saddle-node-type bifurcation in which the prograde wave takes an infinite amount of time to pass over the retrograde wave.

A computer simulation model is introduced to study the characteristics of isolated conductors in electrostatic equilibrium. Drawing an analogy between electrons and how they move to the surface of isolated conductors, we randomly initialize a large number of particles inside a small region at the center of simulated conductors and advance them according to their forces of repulsion. By use of optimized numerical techniques of the finite-size particle method associated with Poisson’s equation, the particles are quickly advanced using a fast Fourier transform and their charge is efficiently shared using the clouds-in-cells method. The particle populations in the simulations range from $50\times {10}^3$ to $1\times {10}^6$ that move in various computation domains equal to $128\times 128$, $256\times 256$, and $512\times 512$ grids. When the particles come to an electrostatic equilibrium, they lie on the boundaries of the simulated conductors, from which the equilibrium properties are obtained. Consistent with the theory of electrostatics and charged conductors, we found that the particles move in response to the conductor geometry in such a way that the electrostatic energy is minimized. Good approximation results for the equilibrium properties were obtained using the proposed computer simulation model.

We show that the experimental global coupling (GC) of spatially extended electrochemical oscillators is weak close to a supercritical Hopf bifurcation. A center manifold reduction allows then the normal form which comprises the GC and the naturally existing nonlocal (migration) coupling (NLC) to be derived. We show that the interaction between NLC and GC widens the spectrum of coherent structures found in globally coupled oscillatory media and allows for wavelength selection of standing waves, stabilization of phase clusters without breaking phase invariance, and creation of heteroclinic networks connecting families of oscillatory states characterized by different spatial symmetries.