The aging behavior of polymer glass, poly(methyl methacrylate), has been investigated through the measurement of the ac-dielectric susceptibility at a fixed frequency after a temperature shift $\Delta T$ $(⩽20\mathrm{K})$ between two temperatures $T_1$ and $T_2$. A crossover from cumulative aging to noncumulative aging could be observed with increasing $\Delta T$ using a twin-temperature $(T‐)$ shift measurement. Based on the growth law of a dynamical coherent length given by activated dynamics, we obtain a unique coherent length for positive and negative $T$ shifts. The possibility of the existence of temperature chaos in polymer glasses is discussed.

We study the statistical mechanics of counterion Wigner crystals associated with hexagonal bundles of chiral biopolymers. We show that, due to spontaneous chiral symmetry breaking induced by frustration, these Wigner crystals would be chiral even if the biopolymers themselves were not chiral. Using a duality transformation of the model onto a “spin-charge” Hamiltonian, we show that melting of the Wigner crystal is due to the unbinding of screw dislocations and that the melting temperature has a singular dependence on the intrinsic chirality of the biopolymers. Finally, we report that, if electrostatic interactions are strongly screened, the counterions can condense in the form of an intermediate achiral Wigner solid phase that melts by the unbinding of fractional topological charges.

The phase diagram of the Ising model in the presence of nearest- and next-nearest-neighbor interactions on a simple cubic lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by employing an effective-field theory with finite clusters consisting of a pair of spins. A functional form is also proposed for the free energy, similar to the Landau expansion, in order to obtain the phase diagram of the model. The transition from the ferromagnetic (or antiferromagnetic) phase to the disordered paramagnetic phase is of second order. On the other hand, a first-order transition is obtained from the lamellar phase to the paramagnetic phase, as well as from the lamellar phase to the ferromagnetic (or antiferromagnetic) phase, with the presence of a critical end point. An expected singular behavior of the first-order line at the critical end point is also obtained.

The well-known Fermi-Pasta-Ulam (FPU) phenomenon (lack of attainment of equipartition of the mode energies at low energies for some exceptional initial data) suggests that the FPU model does not have the mixing property at low energies. We give numerical indications that this is actually the case. This we show by computing orbits for sets of initial data of full measure, sampled out from the microcanonical ensemble by standard Monte Carlo techniques. Mixing is tested by looking at the decay of the autocorrelations of the mode energies, and it is found that the high-frequency modes have autocorrelations that tend instead to positive values. Indications are given that such a nonmixing property survives in the thermodynamic limit. It is left as an open problem whether mixing actually occurs, i.e., whether the autocorrelations vanish as time tends to infinity.

It is well established that rapidly propagating cracks in brittle material are unstable such that they generate side branches. It is also known that cracks are attracted by free surfaces, which means that they attract each other. This information is used here to formulate a generic model of fragmentation in which the small-size part of the fragment-size distribution results from merged crack branches in the damage zones along the paths of the propagating cracks. This model is solved under rather general assumptions for the fragment-size distribution. The model leads to a generic distribution $S^{-\gamma }\exp (-S∕S_0)$ for fragment sizes $S$, where $\gamma =\frac{2d-1}{d}$ with $d$ the Euclidean dimension, and $S_0$ is a material dependent parameter.

Dynamo action in a fully helical Arn’old-Beltrami-Childress flow is studied using both direct numerical simulations and subgrid modeling. Sufficient scale separation is given in order to allow for large-scale magnetic energy buildup. Growth of magnetic energy obtains down to a magnetic Prandtl number $P_M=R_M∕R_V$ close to 0.005, where $R_V$ and $R_M$ are the kinetic and magnetic Reynolds numbers. The critical magnetic Reynolds number for dynamo action $R_M^c$ seems to saturate at values close to 20. Detailed studies of the dependence of the amplitude of the saturated magnetic energy with $P_M$ are presented. When $P_M$ is decreased, numerical experiments are conducted with either $R_V$ or $R_M$ kept constant. In the former case, the ratio of magnetic to kinetic energy saturates to a value slightly below unity as $P_M$ decreases. Examination of energy spectra and structures in real space reveals that quenching of the velocity by a large-scale magnetic field takes place, with an inverse cascade of magnetic helicity and a force-free field at large scale in the saturated regime.

Long, cylindrical metal nanowires have recently been observed to form and be stable for seconds at a time at room temperature. Their stability and structural dynamics is well described by a continuum model, the nanoscale free-electron model, which predicts cylinders in certain intervals of radius to be linearly unstable. In this paper, I study how a small, localized perturbation of such an unstable wire grows exponentially and propagates along the wire with a well-defined front. The front is found to be pulled and forms a coherent pattern behind it. It is well described by a linear marginal stability analysis of front propagation into an unstable state. In some cases, nonlinearities of the wire dynamics are found to trigger an invasive mode that pushes the front. Experimental procedures that could lead to the observation of this phenomenon are suggested.

In this work we compare and characterize the behavior of Langevin and dissipative particle dynamics (DPD) thermostats in a broad range of nonequilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain constant temperature and to reproduce the underlying physical phenomena in nonequilibrium situations. The common practice of switching off the Langevin thermostat in the flow direction is also critically revisited. The efficiency of different weight functions for the DPD thermostat is quantitatively analyzed as a function of the solvent quality and the nonequilibrium situation.

We propose a mechanism for the quantized cycling time based on the interplay of cell-to-cell communication and stochasticity, by investigating a model of coupled genetic oscillators with known topology. In addition, we discuss how inhomogeneity can be used to enhance such quantizing effects, while the degree of variability obtained can be controlled using the noise intensity or adequate system parameters.

Exploiting the density functional theory, we calculate the free energy landscape (FEL) of the hard sphere glass in three dimensions. From the FEL, we estimate the number of the particles in the cooperatively rearranging region (CRR). We find that the density dependence of the number of the particles in the CRR is expressed as a power law function of the density. Analyzing the relaxation process in the CRR, we also find that the string motion is the elementary process for the structural relaxation, which leads to the natural definition of the simultaneously rearranging region as the particles displaced in the string motion.

We study the effect of increasing the range of interactions on phonon relaxation in a chain of atoms with quartic anharmonicity. The study is motivated by recent numerical studies, showing that the value of the exponent $\alpha$ characterizing the divergence of conductivity with system size apparently depends on the presence of second neighbor couplings. We perform a quantum calculation of the wave-vector $\left(q\right)$ dependent relaxation rate $\Gamma \left(q\right)$ in the second order perturbation theory. The nonanalytic dependence of $\Gamma \left(q\right)$ arises due to small-$q$ singularity of the collision integral. We find that $\Gamma \left(q\right)\propto A{q}^{5∕3}+B{q}^2$. This gives rise to an asymptotic value $\alpha =0.4$, but the $q^2$ terms lead to a higher apparent value of $\alpha$ at small sizes of the chain.

Many systems contain an internal time delay, which significantly influences their dynamical properties. Methods to estimate this delay from times series in the presence of dynamical noise are not systematically studied. Addressing this problem, we demonstrate that it is sufficient to analyze the system’s response to short-correlated external disturbances or internal noise. Following this idea, it is shown for linear and nonlinear systems, as well as for periodic dynamics, that the delay can be estimated by analyzing the correlation function. This method covers the case of strong noise and multiple delays.

Rarefied gas flow modeling presents significant challenges in the characterization of nanoscale devices and their applications. An important feature of such flows is the Knudsen layer, which is known to exhibit non-Newtonian viscosity behavior. Significantly, recent research has suggested that the effective viscosity at the surface is about half the standard dynamic viscosity. We examine these claims using numerical solutions of the linearized Boltzmann equation and direct simulation Monte Carlo calculations and discover that (i) the flow exhibits a striking power-law dependence on distance from the solid surface and (ii) the velocity gradient is singular at this surface. This finding contradicts these recent claims and has direct implications for gas flow modeling and the design of nanoscale devices.

We present a general theory of effective media to set up the relationship between the particle responses and the macroscopic system behaviors for artificial metamaterials composed of periodic resonant structures. By treating the unit cell of the periodic structure as a particle, we define the average permittivity and permeability for different unit structures and derive a general form of discrete Maxwell’s equations on the macroscale, from which we obtain different wave modes in metamaterials including the propagation mode, pure plasma mode, and resonant crystal band-gap mode. We explain unfamiliar behaviors of metamaterials from the numerical $S$ parameter retrieval approach. The excellent agreement between theoretical predictions and retrieval results indicates that the defined model and method of analysis fit the physical structures very well. Thereafter, we propose a more advanced form of the fitting formulas for the effective electromagnetic parameters of metamaterials.

We propose an efficient procedure for determining phase diagrams of systems that are described by spin models. It consists of combining cluster algorithms with the method proposed by Sauerwein and de Oliveira where the grand-canonical potential is obtained directly from the Monte Carlo simulation, without the necessity of performing numerical integrations. The cluster algorithm presented in this paper eliminates metastability in first-order phase transitions allowing us to locate precisely the first-order transition lines. We also produce a different technique for calculating the thermodynamic limit of quantities such as the magnetization whose infinite volume limit is not straightforward in first-order phase transitions. As an application, we study the Andelman model for Langmuir monolayers made of chiral molecules that is equivalent to the Blume-Emery-Griffiths spin-1 model. We have obtained the phase diagrams in the case where the intermolecular forces favor interactions between enantiomers of the same type (homochiral interactions). In particular, we have determined diagrams in the surface pressure versus concentration plane, which are more relevant from the experimental point of view and less usual in numerical studies.

We consider two seemingly very different self-assembly processes: formation of viral capsids and crystallization of sticky disks. At low temperatures, assembly is ineffective, since there are many metastable disordered states, which are a source of kinetic frustration. We use fluctuation-dissipation ratios to extract information about the degree of this frustration. We show that our analysis is a useful indicator of the long-term fate of the system, based on the early stages of assembly.

High-resolution quasielastic neutron scattering spectroscopy was used to measure ${\mathrm{H}}_2\mathrm{O}$ hydrated double-wall carbon nanotubes (DWNT). The measurements were made at a series of temperatures from $250\mathrm{K}$ down to $150\mathrm{K}$. The relaxing-cage model was used to analyze the quasielastic spectra. We observed clear evidence of a fragile-to-strong dynamic crossover (FSC) at $T_L=190\mathrm{K}$ in the confined water. We further show that the mean-square atomic displacement of the hydrogen atoms in water exhibits a sharp change in slope at approximately the same temperature $190\mathrm{K}$. Comparing the result with that obtained from the confined water in hydrophilic porous silica material MCM-41, we demonstrate experimentally that water confined in a hydrophobic substrate exhibits a lower dynamic crossover temperature by $\Delta T_L\approx 35\mathrm{K}$.

The growth of nematic liquid crystal nuclei from an isotropic melt follows a power law behavior with exponent $n$ found experimentally to vary between $\frac{1}{2}$ for low quench depths, up to 1 for high quench depths. This behavior has been attributed to the competition between curvature and free energy. We show that curvature cannot account for the low quench depth behavior of the nucleus growth, and attribute this behavior to the diffusion of latent heat. We use a multiscale approach to solve the Landau-Ginzburg order parameter evolution equation coupled to a diffusive heat equation, and discuss this behavior for material parameters experimentally measured for the liquid crystal 8CB.

The elasticity of double-helical DNA on a nm length scale is captured in detail by the rigid base-pair model, whose conformation variables are the relative positions and orientations of adjacent base pairs. Corresponding sequence-dependent elastic potentials have been obtained from all-atom MD simulation and from high-resolution structural data. On the scale of $100\mathrm{nm}$, DNA is successfully described by a continuous wormlike chain model with homogeneous elastic properties, characterized by a set of four elastic constants which have been measured in single-molecule experiments. We present here a theory that links these experiments on different scales, by systematically coarse-graining the rigid base-pair model to an effective wormlike chain description. The average helical geometry of the molecule is accounted for exactly, and repetitive as well as random sequences are considered. Structural disorder is shown to produce a small, additive and short-range correction to thermal conformation fluctuations as well as to entropic elasticity. We also discuss the limits of applicability of the homogeneous wormlike chain on short scales, quantifying the anisotropy of bending stiffness, the non-Gaussian bend angle distribution and the variability of stiffness, all of which are noticeable below a helical turn. The coarse-grained elastic parameters show remarkable overall agreement with experimental wormlike chain stiffness. For the best-matching potential, bending persistence lengths of dinucleotide repeats span a range of $37–53\mathrm{nm}$, with a random DNA value of $43\mathrm{nm}$. While twist stiffness is somewhat underestimated and stretch stiffness is overestimated, the counterintuitive negative sign and the magnitude of the twist-stretch coupling agree with recent experimental findings.

Wavelet representation can provide an effective time-frequency analysis for nonstationary signals, such as the electrocardiogram (EKG) signals, which contain both steady and transient parts. In recent years, wavelet representation has been emerging as a powerful time-frequency tool for the analysis and measurement of EKG signals. The EKG signals contain recurring, near-periodic patterns of $P$, $\mathit{QRS}$, $T$, and $U$ waveforms, each of which can have multiple manifestations. Identification and extraction of a compact set of features from these patterns is critical for effective detection and diagnosis of various disorders. This paper presents an approach to extract a fiducial pattern of EKG based on the consideration of the underlying nonlinear dynamics. The pattern, in a nutshell, is a combination of eigenfunctions of the ensembles created from a Poincare section of EKG dynamics. The adaptation of wavelet functions to the fiducial pattern thus extracted yields two orders of magnitude (some 95%) more compact representation (measured in terms of Shannon signal entropy). Such a compact representation can facilitate in the extraction of features that are less sensitive to extraneous noise and other variations. The adaptive wavelet can also lead to more efficient algorithms for beat detection and QRS cancellation as well as for the extraction of multiple classical EKG signal events, such as widths of $\mathit{QRS}$ complexes and $\mathit{QT}$ intervals.