The dynamic structure and the formation of clusters in nanoparticle colloidal solutions (nanofluids) confined between two parallel walls and submitted to the action of an external force field is studied by extensive Brownian-dynamics simulations. The self-correlation of individual particles and the time correlation between distinct particles are analyzed by calculating the density-density time correlation (van Hove) function. It is shown that the self-diffusion is reduced by the external force field while the lifetime of collective modes of nanoparticles (i.e., natural phonons) is significantly enhanced by this force. We demonstrate that this result is related to disorder-order transitions in the nanoparticle spatial distribution under perturbation. Interestingly, we highlight that the interaction forces mediated by the walls act like repulsive interparticle forces. They tend to increase the structural disorder and to lower the lifetime of collective modes. Our results suggest that the heat transport properties of nanofluids could be actively controlled in nanometer-size systems.

We present a statistical mechanical model of aggregation in colloidal systems with DNA-mediated interactions. We obtain a general result for the two-particle binding energy in terms of the hybridization free energy $\mathrm{\Delta }G$ of DNA and two model-dependent properties: the average number of available DNA bridges $⟨N⟩$ and the effective DNA concentration $c_{\mathrm{eff}}$. We calculate these parameters for a particular DNA bridging scheme. The fraction of all the $n$-mers, including the infinite aggregate, are shown to be universal functions of a single parameter directly related to the two-particle binding energy. We explicitly take into account the partial ergodicity of the problem resulting from the slow DNA binding-unbinding dynamics, and introduce the concept of angular localization of DNA linkers. In this way, we obtain a direct link between DNA thermodynamics and the global aggregation and melting properties in DNA-colloidal systems. The results of the theory are shown to be in quantitative agreement with two recent experiments with particles of micron and nanometer size.

The question regarding a possible correlation of the time scales of primary and secondary relaxations in supercooled liquids is formulated quantitatively. It is shown how this question can be answered using spin-lattice relaxation weighted stimulated-echo experiments, which are presented in an accompanying paper [A. Nowaczyk, B. Geil, G. Hinze, and R. Böhmer, Phys. Rev. E 74, 041505 (2006)]. General theoretical expressions relevant for the description of such experiments in the presence of correlation effects are derived. These expressions are analyzed by Monte Carlo integration for various correlation scenarios also including exchange processes, which are the hallmark of dynamical heterogeneity. The results of these numerical simulations provide clear signatures that allow one to distinguish uncorrelated from differently correlated cases. Since modified spin-lattice relaxation effects occur in the presence of nonexponential magnetization recovery, it is shown how to correct for them to a good approximation.

Using spin-lattice relaxation weighted stimulated-echo spectroscopy, we report evidence for a correlation of the primary and secondary relaxation times. The experiments are performed using deuteron nuclear magnetic resonance somewhat above the calorimetric glass-transition of ortho-terphenyl, D-sorbitol, and cresolphthalein-dimethylether. The data analysis is based on the procedure outlined in the accompanying theoretical paper [B. Geil, G. Diezemann, and R. Böhmer, Phys. Rev. E 74, 041504 (2006)]. Direct experimental evidence for a modified spin-lattice relaxation is obtained from measurements on a methyl deuterated acetyl salicylic acid glass. The limitations of the present experimental method are discussed.

A loosely cross-linked liquid crystal elastomer (LCE) having a disordered director alignment (polydomain texture) slowly recovers to their original shape from the deformed state in the order of ${10}^3\mathrm{s}$ after the imposed field is removed. The mesogen alignment at the cross-linking stage greatly affects the shape recovery dynamics of polydomain LCEs, whereas it has no appreciable influence on the equilibrium characteristics such as the nematic-isotropic transition temperature, degree of swelling, and field-induced strain. The shape recovery of a LCE formed in the polydomain nematic state is considerably faster than that originally prepared in the isotropic state because of the memory effect of the initial director distribution at the cross-linking stage. The relaxation time rapidly increases as the temperature approaches the transition temperatures; this is independent of the initial mesogen alignment during cross linking.

Belief propagation is a candidate for the accelerated evaluation of statistical averages if compared to Monte Carlo approaches. We show that superparamagnetic clustering can be accelerated substantially by means of belief propagation. However, critical slowing down of the method is observed. Origin and strategies of avoidance of the critical slowing down are explained from models of periodic Ising grids. We show that belief-propagation-mediated superparamagnetic clustering provides identical clusters with Monte Carlo-mediated clustering only at the coarse-grained level. Concurring results between the Monte Carlo and the belief-propagation methods can be obtained by means of the sequential superparamagnetic-clustering approach.

The temporal evolution of the fluid circulation generated by a buoyancy force when two-dimensional (2D) arrays of 2D thermals are released into a quiescent incompressible fluid is studied through the results of numerous lattice Boltzmann simulations. It is observed that the circulation magnitude grows to a maximum value in a finite time. When both the maximum circulation and the time at which it occurs are nondimensionalised by appropriately defined characteristic scales, it is shown that two simple Prandtl number (Pr) dependent scaling relations can be devised that fit these data very well over nine decades of Pr spanning the viscous and diffusive regimes and six decades of Rayleigh number (Ra) in the low Ra regime. Also, obtained analytically is the exact result that circulation magnitude continues to grow in time for a 2D laminar or turbulent single buoyant (3D) vortex ring in an infinite unbounded fluid.

We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the complex networks with various sizes of $N$. We find that the lifetime $⟨T⟩$ of a lamb scales as $⟨T⟩\sim N$ and the survival probability $S(N\to \infty ,t)$ becomes finite on scale-free networks with degree exponent $\gamma >3$. However, $S(N,t)$ for $\gamma <3$ has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. This suggests that the second moment of degree distribution $⟨k^2⟩$ is the relevant factor for the dynamical properties in the diffusive capture process. We numerically find that the normalized number of capture events at a node with degree $k$, $n\left(k\right)$, decreases as $n\left(k\right)\sim k^{-\sigma }$. When $\gamma <3$, $n\left(k\right)$ still increases anomalously for $k\approx k_{\max }$, where $k_{\max }$ is the maximum value of $k$ of given networks with size $N$. We analytically show that $n\left(k\right)$ satisfies the relation $n\left(k\right)\sim k^{2}P\left(k\right)$ for any degree distribution $P\left(k\right)$ and the total number of capture events $N_{\mathrm{tot}}$ is proportional to $⟨k^2⟩$, which causes the $\gamma$-dependent behavior of $S(N,t)$ and $⟨T⟩$.

Coupled map lattices of nonhyperbolic local maps arise naturally in many physical situations described by discretized reaction diffusion equations or discretized scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of $N\text{th}$ order which exhibit strongest possible chaotic behavior for small coupling constants $a$. We prove that the expectations of arbitrary observables scale with $\sqrt{a}$ in the low-coupling limit, contrasting the hyperbolic case which is known to scale with $a$. Moreover we prove that there are log-periodic oscillations of period $\ln N^2$ modulating the $\sqrt{a}$ dependence of a given expectation value. We develop a general 1st order perturbation theory to analytically calculate the invariant one-point density, show that the density exhibits log-periodic oscillations in phase space, and obtain excellent agreement with numerical results.

Empirical mode decomposition is investigated as a tool to determine the phase and frequency and to study phase synchronization between complex chaotic oscillators. Within this approach, the oscillator is characterized by a spectrum of frequencies corresponding to the empirical modes. First, the phase and frequency of the oscillators resulting from two well-known methods, based on modified variables and the Poincaré surface of section, are compared with those obtained using empirical mode decomposition. Next, for both parametrically and essentially different chaotic oscillators coupled as a drive-response system, transition to phase synchronization between corresponding empirical modes is investigated, defined as an adjustment of the mode frequencies of the response oscillator to those of the drive oscillator as the coupling is increased. In particular, anomalous and imperfect phase synchronization between modes is observed.

We propose an archetypal system to investigate transitions from smooth to discontinuous dynamics. In the smooth regime, the system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. At the discontinuous limit, however, there is a substantial departure in the dynamics from the standard one. In particular, the velocity flow suffers a jump in crossing from one well to another, caused by the loss of local hyperbolicity due to the collapse of the stable and unstable manifolds of the stationary state. In the presence of damping and external excitation, the system has coexisting attractors and also a chaotic saddle which becomes a chaotic attractor when a smoothness parameter drops to zero. This attractor can bifurcate to a high-period periodic attractor or a chaotic sea with islands of quasiperiodic attractors depending on the strength of damping.

A hybrid simulation method is introduced and used to study two-dimensional single-asperity and multi-asperity contacts both quasistatically and dynamically. The method combines an atomistic treatment of the interfacial region with a finite-element method description of subsurface deformations. The dynamics in the two regions are coupled through displacement boundary conditions applied at the outer edges of an overlap region. The two solutions are followed concurrently but with different time resolution. The method is benchmarked against full atomistic simulations. Accurate results are obtained for contact areas, pressures, and static and dynamic friction forces. The time saving depends on the fraction of the system treated atomistically and is already more than a factor of 20 for the relatively small systems considered here.

We present numerical studies of anomalous diffusion in periodic potentials by simulating a generalized Langevin equation. It is proved that the particle driven by a thermal colored noise with the spectral density vanishing at zero frequency allows superdiffusive motion. It is found that the system subjected to sub- or superohmic damping exhibits two motion modes in a corrugated plane: running oscillated state and mixed running and oscillating states, respectively. Induced, the anomalous power can be enhanced up twice for the latter case and thus a wide range of diffusive regimes is observed with changing titled force.

We study spontaneous imbibition using a phase field model in a two-dimensional system with a dichotomic quenched noise. By imposing a constant pressure ${\mu }_a<0$ at the origin, we study the case when the interface advances at low velocities, obtaining the scaling exponents $z=3.0\pm 0.1$, $\alpha =1.50\pm 0.02$, and ${\alpha }_{\mathit{loc}}=0.95\pm 0.03$ within the intrinsic anomalous scaling scenario. These results are in quite good agreement with experimental data recently published. Likewise, when we increase the interface velocity, the resulting scaling exponents are $z=4.0\pm 0.1$, $\alpha =1.25\pm 0.02$, and ${\alpha }_{\mathit{loc}}=0.95\pm 0.03$. Moreover, we observe that the local properties of the interface change from a superrough to an intrinsic anomalous description when the contrast between the two values of the dichotomic noise is increased. From a linearized interface equation we can compute analytically the global scaling exponents which are comparable to the numerical results, introducing some properties of the quenched noise.

We present lattice Boltzmann simulations of the dynamical equations of motion of a drop of isotropic fluid in a nematic liquid crystal solvent, both in the absence and in the presence of an electric field. The coupled equations we solve are the Beris-Edward equations for the dynamics of the tensor order parameter describing the nematic solvent, the Cahn-Hilliard equation for the concentration evolution, and the Navier-Stokes equations for the determination of the instantaneous velocity field. We implement the lattice Boltzmann algorithm to ensure that spurious velocities are close to zero in equilibrium. We first study the effects of the liquid crystal elastic constant, $K$, anchoring strength, $W$, and surface tension, $\sigma$, on the shape of the droplet and on the director field texture in equilibrium. We then consider how the drop behaves as the director field is switched by an applied electric field. We also show that the algorithm allows us to follow the motion of a drop of isotropic fluid placed in a liquid crystal cell with a tilted director field at the boundaries.

We model the way in which polymers bind to DNA and neutralize its charged backbone by analyzing the dynamics of the distribution of gaps along the DNA. We generalize existing theory for irreversible binding to construct deterministic models which include polymer removal, movement along the DNA, and allow for binding with overlaps. We show that reversible binding alters the capacity of the DNA for polymers by allowing the rearrangement of polymer positions over a longer time scale than when binding is irreversible. When the polymers do not overlap, allowing reversible binding increases the number of polymers adhered and hence the charge that the DNA can accommodate; in contrast, when overlaps occur, reversible binding reduces the amount of charge neutralized by the polymers.

Charge detection biosensors have recently become the focal point of biosensor research, especially field-effect-transistors (FETs) that combine compactness, low cost, high input, and low output impedances, to realize simple and stable in vivo diagnostic systems. However, critical evaluation of the possibility and limitations of charge detection of label-free DNA hybridization using silicon-based ion-sensitive FETs (ISFETs) has been introduced recently. The channel surface of these devices must be covered by relatively thick insulating layers ($\mathrm{Si}{\mathrm{O}}_2$, ${\mathrm{Si}}_3{\mathrm{N}}_4$, ${\mathrm{Al}}_2{\mathrm{O}}_3$, or ${\mathrm{Ta}}_2{\mathrm{O}}_5$) to protect against the invasion of ions from solution. These thick insulating layers are not suitable for charge detection of DNA and miniaturization, as the small capacitance of thick insulating layers restricts translation of the negative DNA charge from the electrolyte to the channel surface. To overcome these difficulties, thin-gate-insulator FET sensors should be developed. Here, we report diamond solution-gate FETs (SGFETs), where the DNA-immobilized channels are exposed directly to the electrolyte solution without gate insulator. These SGFETs operate stably within the large potential window of diamond $(>3.0\mathrm{V})$. Thus, the channel surface does not need to be covered by thick insulating layers, and DNA is immobilized directly through amine sites, which is a factor of 30 more sensitive than existing Si-ISFET DNA sensors. Diamond SGFETs can rapidly detect complementary, 3-mer mismatched $\left(10\mathrm{pM}\right)$ and has a potential for the detection of single-base mismatched oligonucleotide DNA, without biological degradation by cyclically repeated hybridization and denature.

A theoretical model of dynamic instability of a system of linear one-dimensional microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of tubulin. The model differs from earlier models in that the evolution of MTs is based on the rates of single-mesoscopic-unit (e.g., a heterodimer per protofilament) transformations, in contrast to postulating effective rates and frequencies of larger-scale macroscopic changes, extracted, e.g., from the length history plots of MTs. Spontaneous GTP hydrolysis with finite rate after polymerization is assumed, and theoretical estimates of an effective catastrophe frequency as well as other parameters characterizing MT length distributions and cap size are derived. We implement a simple cap model which does not include vectorial hydrolysis. We demonstrate that our theoretical predictions, such as steady-state concentration of free tubulin and parameters of MT length distributions, are in agreement with the numerical simulations. The present model establishes a quantitative link between mesoscopic parameters governing the dynamics of MTs and macroscopic characteristics of MTs in a closed system. Last, we provide an explanation for nonexponential MT length distributions observed in experiments. In particular, we show that the appearance of such nonexponential distributions in the experiments can occur because a true steady state has not been reached and/or due to the presence of a cell edge.

In this paper we study the solutions of a generalized reaction-diffusion system with a bistable reaction term, and considering directional anomalous diffusion. We use the well-known properties of fractional derivatives to model asymmetric anomalous diffusion, and obtain traveling wave solutions that propagate in a direction that depends on the metastability of the front, the fractional exponent and the asymmetry of the diffusion.