We have investigated the motion of a single optically trapped colloidal particle close to a limiting wall at time scales where the inertia of the surrounding fluid plays a significant role. The velocity autocorrelation function exhibits a complex interplay due to the momentum relaxation of the particle, the vortex diffusion in the fluid, the obstruction of flow close to the interface, and the harmonic restoring forces due to the optical trap. We show that already a weak trapping force has a significant impact on the velocity autocorrelation function $C\left(t\right)=⟨v\left(t\right)v\left(0\right)⟩$ at times where the hydrodynamic memory leads to an algebraic decay. The long-time behavior for the motion parallel and perpendicular to the wall is derived analytically and compared to numerical results. Then, we discuss the power spectral densities of the displacement and provide simple interpolation formulas. The theoretical predictions are finally compared to recent experimental observations.

An antitrapping current scheme for quantitative phase-field model [A. Karma, Phys. Rev. Lett. 87, 115701 (2001)] is extended to solidification process in a dilute binary alloy system involving diffusion in the solid. It is demonstrated in an asymptotic analysis that in the case of an arbitrary value of the solid diffusivity, five types of constraints exist between interpolating functions used in the phase-field model, which need to be satisfied simultaneously to eliminate all anomalous interface effects. Then, the authors present an appropriate form of the antitrapping current term for the two-sided case to remove all the spurious effects. The convergence test of the output with respect to the interface thickness was carried out for the isothermal dendrite growth process, which demonstrates an excellent performance of the present model.

A theoretical model of spectral transfer for anisotropic magnetohydrodynamic (MHD) turbulence is introduced, approximating energy transport in wave vector $\left(\mathit{k}\right)$ space as a nonlinear diffusion process, extending previous isotropic $k$-space diffusion theories for hydrodynamics and MHD. This formal closure at the spectral equation level may be useful in space and astrophysical applications.

The Debye series expansion expresses the Mie scattering coefficients into a series of Fresnel coefficients and gives physical interpretation of different scattering modes, but when an infinite multilayered cylinder is obliquely illuminated by electromagnetic plane waves, the scattering process becomes very complicated because of cross polarization. Based on the relation of boundary conditions between global scattering process and local scattering processes, the generalized Debye series expansion of plane wave scattering by an infinite multilayered cylinder at oblique incidence is derived in this paper. The formula and the code are verified by the comparison of the results with that of Lorenz-Mie theory in special cases and those presented in the literatures.

The origin of protein folding thermodynamics is examined in terms of the energy landscape, employing an off-lattice protein model with scaled non-native attractions, which is continuously tunable between a Go-like model and a highly frustrated system. Extensive statistical temperature molecular dynamics simulations, combined with inherent structure analysis, reveal the intimate connection between the global geometric properties of the energy landscape and the statistical temperature. The basin depth of the energy landscape is shown to play a key role in the first-order-like characteristics of the statistical temperature, which are easily identified by the squared modulus of the potential energy gradient in the microcanonical ensemble.

We study the quantum fidelity approach to characterize thermal phase transitions. Specifically, we focus on the mixed-state fidelity induced by a perturbation in temperature. We consider the behavior of fidelity in two types of second-order thermal phase transitions (based on the type of nonanaliticity of free energy), and we find that usual fidelity criteria for identifying critical points is more applicable to the case of $\lambda$ transitions (divergent second derivatives of free energy). Our study also reveals that for fixed perturbations, the sensitivity of fidelity at high temperatures (where thermal fluctuations wash out information about the transition) is reduced. From the connection to thermodynamical quantities we propose slight variations to the usual fidelity approach that allow us to overcome these limitations. In all cases we find that fidelity remains a good precriterion for testing thermal phase transitions, and we use it to analyze the nonzero temperature phase diagram of the Lipkin-Meshkov-Glick model.

A solution to a 3-satisfiability (3-SAT) formula can be expanded into a cluster, all other solutions of which are reachable from this one through a sequence of single-spin flips. Some variables in the solution cluster are frozen to the same spin values by one of two different mechanisms: frozen-core formation and long-range frustrations. While frozen cores are identified by a local whitening algorithm, long-range frustrations are very difficult to trace, and they make an entropic belief-propagation (BP) algorithm fail to converge. For the BP algorithm to reach a fixed point, the spin values of a tiny fraction of variables (chosen according to the whitening algorithm) are externally fixed during the iteration. From the calculated entropy values, we infer that, for a large random 3-SAT formula with constraint density close to the satisfiability threshold, the solutions obtained by the survey-propagation or WALKSAT algorithms belong neither to the most dominating clusters of the formula nor to the most abundant clusters. This work indicates that a single-solution cluster of a random 3-SAT formula may have further community structures.

The short-time motion of Brownian particles in an incompressible Newtonian fluid under shear, in which the fluid inertia becomes important, was investigated by direct numerical simulation of particulate flows. Three-dimensional simulations were performed, wherein external forces were introduced to approximately form Couette flows throughout the entire system with periodic boundary conditions. In order to examine the validity of the method, the mean-square displacement of a single spherical particle in a simple shear flow was calculated, and these results were compared with a hydrodynamic analytical solution that includes the effects of the fluid inertia. Finally, the dynamical behavior of a monodisperse dispersion composed of repulsive spherical particles was examined on short-time scales, and the shear-induced diffusion coefficients were measured for several volume fractions up to 0.50.

We studied dissipative structures in the pattern formation of self-organized flow inside a droplet and spontaneous motion of the droplet when two driving forces, mass transfer of a solute from the droplet to surrounding media and continuous supply of solution to the droplet, were applied. When solute concentration increases beyond a critical value, a jetlike flow erupts out of the droplet (eruption). A similar flow simultaneously enters the droplet (irruption), producing internal flow. The resulting internal flow develops into two vortices along the droplet surface. Each vortex moves in a circular orbit along the droplet surface by local flow due to the other vortex, while continuous solute eruptions occur out of the vortex pair. The entire droplet rotates slowly at the same velocity as the rotation of the vortex pair. The vortex pair then oscillates with rotation, inducing droplet wiggle with slow rotation. The vortex motion resembles precession accompanied by nutation of a spinning top about a fixed point. Temporal evolution of droplet motion describes a pattern of short waves superimposed on a long wave. Short waves are induced by “nutation” of the vortex pair, and the long wave by “precession.” The amplitude of the short wave varies with time because of the interaction between vortices. The vortex pair acts as coupled oscillators. Resonance interaction can occur between the long wave and the envelope of short waves when the phase velocity of the long wave becomes equal to the group velocity of short waves, markedly changing droplet motion; vigorous and regular fast rotation of the droplet suddenly occurs.

The phase behavior of a system of hard-cut spheres has been studied using a high-order virial theory and by Monte Carlo simulation. The cut-sphere particles are disks of thickness $L$ formed by symmetrically truncating the end caps of a sphere of diameter $D$. The virial theory predicts a stable nematic phase for aspect ratio $L∕D=0.1$ and a stable cubatic phase for $L∕D=0.15–0.3$. The virial series converges rapidly on the equation of state of the isotropic and nematic phases, while for the cubatic phase the convergence is slower, but still gives good agreement with the simulation at high order. It is found that a high-order expansion (up to $B_8$) is required to predict a stable cubatic phase for $L∕D⩾0.15$, indicating the importance of many-body interactions in stabilizing this phase. Previous simulation work on this system has focused on aspect ratios $L∕D=0.1$, 0.2, and 0.3. We expand this to include also $L∕D=0.15$ and 0.25, and we introduce a fourth-rank tensor to measure cubatic ordering. We have applied a multiparticle move which dramatically speeds the attainment of equilibrium in the nematic phase and therefore is of great benefit in the study of the isotropic-nematic phase transition. In agreement with the theory, our simulations confirm the stability of the nematic phase for $L∕D=0.1$ and the stability of the cubatic phase over the nematic for $L∕D=0.15–0.3$. There is, however, some doubt about the stability of the cubatic phase with respect to the columnar. We have shown that the cubatic phase found on compression at $L∕D=0.1$ is definitely metastable, but the results for $L∕D=0.2$ were less conclusive.

Multiple interlinked positive feedback loops shape the stimulus responses of various biochemical systems, such as the cell cycle or intracellular ${\mathrm{Ca}}^{2+}$ release. Recent studies with simplified models have identified two advantages of coupling fast and slow feedback loops. This dual-time structure enables a fast response while enhancing resistances of responses and bistability to stimulus noise. We now find that (1) the dual-time structure similarly confers resistance to internal noise due to molecule number fluctuations, and (2) model variants with altered coupling, which better represent some specific biochemical systems, share all the above advantages. We also develop a similar bistable model with coupling of a fast autoactivation loop to a slow loop. This model’s topology was suggested by positive feedback proposed to play a role in long-term synaptic potentiation (LTP). The advantages of fast response and noise resistance are also present in this autoactivation model. Empirically, LTP develops resistance to reversal over $\sim 1\mathrm{h}$. The model suggests this resistance may result from increased amounts of synaptic kinases involved in positive feedback.

Spontaneous spiral formation occurs when an excitation wave is input to a heterogeneous network of low- and high-light-intensity cells projected onto a light-sensitive Belousov-Zhabotinsky reaction. The range of network conditions where spirals form is increased if two waves are input at critical time intervals. Spirals degenerate to form multiple spirals and spirals trapped within excitable cells. Spiral formation and degeneration is dependent on network excitability, cell size, and network size. Results exhibit parallels with spiral formation in excitable biological systems such as the heart.

The smallest maximum-kissing-number Voronoi polyhedron of three-dimensional (3D) Euclidean spheres is the icosahedron, and the tetrahedron is the smallest volume that can show up in Delaunay tessellation. No periodic lattice is consistent with either, and hence these dense packings are geometrically frustrated. Because icosahedra can be assembled from almost perfect tetrahedra, the terms “icosahedral” and “polytetrahedral” packing are often used interchangeably, which leaves the true origin of geometric frustration unclear. Here we report a computational study of freezing of 4D Euclidean hard spheres, where the densest Voronoi cluster is compatible with the symmetry of the densest crystal, while polytetrahedral order is not. We observe that, under otherwise comparable conditions, crystal nucleation in four dimensions is less facile than in three dimensions, which is consistent with earlier observations [M. Skoge et al., Phys. Rev. E 74, 041127 (2006)]. We conclude that it is the geometrical frustration of polytetrahedral structures that inhibits crystallization.

We discuss multiscale simulations of long biopolymer translocation through wide nanopores that can accommodate multiple polymer strands. The simulations provide clear evidence of folding quantization, namely the translocation proceeds through multifolded configurations characterized by a well-defined integer number of folds. As a consequence, the translocation time acquires a dependence on the average folding number, which results in a deviation from the single-exponent power law characterizing single-file translocation through narrow pores. The mechanism of folding quantization allows polymers above a threshold length (approximately 1000 persistence lengths for double-stranded DNA) to exhibit cooperative behavior, and as a result to translocate noticeably faster.

The dynamics of sharp interfaces separating two nonhydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the interface. The solids are allowed to exchange mass by transforming one solid into the other, thermodynamic relations for the transformation of a mass element are derived and a linear stability analysis of the interface is carried out. The stability is shown to depend on the order of the phase transition occurring at the interface. Numerical simulations are performed in the nonlinear regime to investigate the evolution and roughening of the interface. It is shown that even small contrasts in the referential densities of the solids may lead to the formation of fingerlike structures aligned with the principal direction of the far field stress.

We study the dynamics of pattern formation of two-dimensional smectic systems constrained to lie on a substrate with sinusoidal topography. We observe a coupling between defects and geometry that induces the preferential location of positive (negative) defects onto regions with positive (negative) Gaussian curvature. For the curvatures studied here we observe unbinding and self-organization of disclination pairs. The local orientation of the pattern and the location of topological defects can be accurately controlled with the curvature of the underlying substrate. Thus, long-range interactions arising from the geometry of the substrate lead to ordered patterns with potential applications to nanotechnology.

The effective renormalized charge of nanoparticles in an aqueous electrolyte is essential to determine their solubility. By using a molecular model for the supporting aqueous electrolyte, we find that the effective renormalized charge of the nanoparticles is strongly dependent on the sign of the bare charge. Negatively charged nanoparticles have a lower effective renormalized charge than positively charged nanoparticles. The degree of asymmetry is a nonmonotonic function of the bare charge of the nanoparticle. We show that the effect is due to the asymmetric charge distribution of the water molecules, which we model using a simple three-site molecular structure of point charges.

Identifying chaos in experimental data—noisy data—remains a challenging problem for which conclusive arguments are still very difficult to provide. In order to avoid problems usually encountered with techniques based on geometrical invariants (dimensions, Lyapunov exponent, etc.), Poon and Barahona introduced a numerical titration procedure which compares one-step-ahead predictions of linear and nonlinear models [Proc. Natl. Acad. Sci. U.S.A. 98, 7107 (2001)]. We investigate the aformentioned technique in the context of colored noise or other types of nonchaotic behaviors. The main conclusion is that in several examples noise titration fails to distinguish such nonchaotic signals from low-dimensional deterministic chaos.