The deterministic conserved threshold transfer process, which is a variant of the conserved threshold transfer process modified in a way as that hopping of a particle is to be deterministic, is proposed. The critical behavior of the model is investigated in one, two, and four dimensions. It is found that the order parameter yields a discontinuous transition; i.e., the transition appears to be first ordered in all dimensions considered. The origin of such a discontinuous transition is investigated, considering clustering of active sites and accumulation of critical sites just before the steady state is reached.

We show that two commonly used definitions for the heat current give different results—through the Kubo formula—for the heat conductivity of oscillator chains. The difference exists for finite chains, and is expected to be important more generally for small structures. For a chain of $N$ particles that are tethered at the ends, the ratio of the heat conductivities calculated with the two currents differs from unity by $O\left(1/N\right)$. For a chain held at constant pressure, the difference from unity decays more slowly, and is consistent with $O\left(1/N^{\eta }\right)$ with $1>\eta >0.5$.

We consider three microscopic model molecular systems, each containing an equimolar mixture of a chiral molecule and its nonsuperimposable mirror image. The molecules in each model are assumed to lie on a thin film in such a way that they occupy the sites of a honeycomb lattice. Although neither enantiomorph is externally favored at low temperatures, we prove that for one range of interactions, chiral segregation into ordered phases containing a single enantiomorph occurs for two of the models and, in a second range of interactions, ordered racemic phases (containing equal numbers of each enantiomorph) occur for the two models. For a third range of interactions, each of the two models has an infinite number of ground-state configurations and, moreover, an associated residual entropy. In all three ranges of interactions considered, the third model has an infinite number of ground-state configurations and a residual entropy.

Ferrofluid-based magnetorheological (MR) fluid is prepared by dispersing micron-size magnetic spheres in a ferrofluid. We report here the mechanism of chain formation in ferrofluid based MR fluid, which is quite different from conventional MR fluid. Some of the nanomagnetic particles of ferrofluid filled inside the microcavities are formed due to association of large particles, and some of them are attached at the end of large particles. Under rotating magnetic field, fragmentation of a single chain into three parts is observed. Two of them are chains of micron-size magnetic particles which are suspended in a ferrofluid, and the third one is the chain of nanomagnetic particles of ferrofluid, which may be the connecting bridge between the two chains of larger magnetic particles. The rupture of a single chain provides evidence for the presence of nanomagnetic particles within the magnetic field-induced chainlike structure in this bidispersed MR fluid.

We present the results of the fast electro-optic response of multiwalled carbon nanotubes (MWCNTs)-doped deformed helix ferroelectric liquid crystal (DHFLC). The fastening of the response in MWCNTs-doped DHFLC has been attributed to the decrease in rotational viscosity and increase in anchoring energy. The decrease in the former is due to the experience of the torque both by MWCNTs and DHFLC and perturbation of order parameter of the DHFLC while the increase in the latter is due to the $\pi \text{−}\pi$ electrons stacking between the MWCNTs, DHFLC molecules, and alignment layers. The increase in conductance in doped cells has also been observed.

For a Bose-Einstein condensate loaded into a weak traveling optical superlattice, it is demonstrated that under a stochastic initial set and in a given parameter region, the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically and different chaotic regions associated with different chaos probabilities are found. The results suggest a method for weakening or strengthening chaos by modulating the moving superlattice.

We analyze the connections between the dynamical generation of continuous variable entanglement and the underlying classical trajectories in pairs of coupled oscillators. In the quantization of a periodic cycle, we find periodic entanglement which has twice the frequency of the corresponding classical motion. Such frequency doubling continues to hold true in the entanglement dynamics for a second model that exhibits a two-frequency orbit in the classical domain. In addition, the periodicity and the quasiperiodicity of the entanglement are found to be independent of the local classical dynamical behavior. Finally, in our third model, the entanglement production rate is found to be (i) higher in the chaotic regime and (ii) insensitive toward the choice of regular or chaotic initial condition in the mixed regime. In summary, we have illustrated through our sample models that the generation of dynamical pattern of entanglement can depend completely on the global classical dynamical regime without being influenced by the local classical behavior.

Self-organized critical behavior in a catalytic reaction network system induced by smallness in the molecule number is reported. The system under a flow of chemicals is shown to undergo a transition from a stationary to an intermittent reaction phase when the flow rate is decreased. In the intermittent reaction phase, two temporal regimes with active and halted reactions alternate. The number frequency of reaction events at each active regime and its duration time are shown to obey a universal power law with the exponents 4/3 and 3/2, respectively, independently of the parameters and network structure. These power laws are explained by a one-dimensional random-walk representation of the number of catalytically active chemicals. Possible relevance of the result to reaction dynamics in artificial and biological cells is briefly discussed.

The statistical mechanical approach to Casimir problems for dielectrics separated by a vacuum gap turns out to be compact and effective. A central ingredient of this method is the effect of interacting fluctuating dipole moments of the polarizable particles. At arbitrary temperature the path-integral formulation of quantized particles, developed by Høye-Stell and others, is needed. At high temperature—the limit considered in the present paper—the classical theory is, however, sufficient. Our present theory is related to an idea put forward earlier by Jancovici and Šamaj (2004), namely, to evaluate the Casimir force between parallel plates invoking an electronic plasma model and the Debye-Hückel theory for electrolytes. Their result was recently recovered by Høye (2008), using a related statistical mechanical method. In the present paper we generalize this by including a constant permittivity in the description. The present paper generalizes our earlier theory for parallel plates (1998), as well as for spherical dielectrics (2001). We also consider the Casimir force between a polarizable particle and a conductor with a small density of charges, finding agreement with the result recently derived by Pitaevskii (2008).

Avalanche dynamics and related power-law statistics are ubiquitous in nature, arising in phenomena such as earthquakes, forest fires, and solar flares. Very interestingly, an analogous behavior is associated with many condensed-matter systems, such as ferromagnets and martensites. Bearing it in mind, we study the prototypical random-field Ising model at $T=0$. We find a finite correlation between waiting intervals and the previous avalanche size. This correlation is not found in other models for avalanches but it is experimentally found in earthquakes and in forest fires. Our study suggests that this effect occurs in critical points that are at the end of a first-order discontinuity separating two regimes: one with high activity from another with low activity.

Friction plays a key role in controlling the rheology of dense granular flows. Counting the number of constraints vs the number of variables indicates that critical coordination numbers $Z_c=3$ (in $D=2$) and $Z_c=4$ (in $D=3$) are special, in that states in which all contacts roll without frictional sliding are naively possible at and below these average coordination numbers. We construct an explicit example of such a state in $D=2$ based on a honeycomb lattice. This state has surprisingly large values for the typical angular velocities of the particles. Solving for the forces in such a state, we conclude that organized shear can exist in this state only on scales $\ell <d/I$, where $d$ is the grain diameter and $I=d\dot{\gamma }/\sqrt{P/{\rho }_g}$ is the dimensionless “inertia number.” Above this scale the coherent shear is destabilized by the disappearance of normal forces between a significant fraction of the grains. Moving to disordered lattices, we observe that rolling regions in such lattices are characterized by an antiferromagnetic short-range ordering of the particle rotations; the frustration of this ordering links the shearing states of the grain packing to low-energy spin-glass states on the same lattice. Random lattice states are also expected to exhibit large values for the typical angular velocities and to also have regions of coherent shear limited to be smaller than $\ell$.

The nonlinear dynamic behavior of superparamagnetic beads exposed to a periodic array of micromagnets and an external rotating field is simulated as a function of the relative size of the bead with respect to the micromagnet size and the strength of the external field relative to the pole density of the substrate. For large bead sizes, it is confirmed that the motion of the beads corresponds to the dynamics of an overdamped nonlinear harmonic oscillator. For lower bead sizes, additional subharmonic locking effects are observed along with the emergence of bounded orbits. These results qualitatively support previous experimental investigations of traveling-wave magnetophoresis and provide guidelines for achieving nearly infinite separation resolution between differently sized beads.

A discrete lattice model is developed to describe diffusion-mediated polymerization occurring within mesopores, where reaction is enhanced at catalytic sites distributed within the interior of the pores. Diffusive transport of monomers and polymers is one-dimensional, diffusion coefficients for the latter decreasing with polymer length. Kinetic Monte Carlo simulation is utilized to analyze model behavior focusing on a “clogging” regime, where the amount of polymer within the pores grows. We characterize the evolution of the overall and mean length of polymers, the mean number of polymers, as well as the polymer spatial and length distributions.

Boundary-element methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the protein-solvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, the accuracy of simulations can depend strongly on seemingly minor details of how the entries of the BEM matrix are calculated. We demonstrate that when the dielectric interface is discretized into flat tiles, the qualocation method of Tausch et al. [IEEE Trans Comput.-Comput.-Aided Des. 20, 1398 (2001)] to compute the BEM matrix elements is always more accurate than the traditional centroid-collocation method. Qualocation is not more expensive to implement than collocation and can save significant computational time by reducing the number of boundary elements needed to discretize the dielectric interfaces.

Using microscopic particle image velocimetry, we examine the flow field around an oil droplet as it is formed by hydrodynamic focusing in an aqueous solution using a pressure-driven cross-channel microfluidic device. By detecting the temporal dependence of the instantaneous flow fields of the continuous phase in the dripping regime, we show that shear is not the primary mechanism that initiates droplet formation in our low flow rate and moderate capillary number experimental conditions. Instead, the advancing finger of oil partially and temporarily plugs the outlet channel, creating a pressure difference that builds up and is released when water from the side channels pushes the tip of the finger into the outlet channel, thereby facilitating the birth of the droplet by interfacial pinch-off that is primarily initiated by an extensional flow.

Preferential concentration of inertial particles in turbulence is studied numerically by evaluating the Lagrangian compressibility of the particle velocity field using the “full Lagrangian method.” This is compared with the “mesoscopic Eulerian particle velocity field” both in a direct numerical simulation of turbulence and in a synthetic flow field. We demonstrate that the Lagrangian method, in contrast to the Eulerian, accurately predicts the compressibility of the particle velocity field even when the latter is characterized by singularities. In particular we use the method to evaluate the growth rates of spatial moments of the particle number density which reflect the fractal structure of segregation and the occurrence of singularities.

A periodically forced two-dimensional cellular automata model is used to reproduce and analyze the complex spatiotemporal patterns observed in the transmission of vector infectious diseases. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector-transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult, and immature vector populations. The dynamics includes external seasonality forcing, human and mosquito mobility, and vector control effects. The model parameters, even if bounded to well-defined intervals obtained from reported data, can be selected to reproduce specific epidemic outbursts. In the current study, explicit results are obtained by comparison with actual data retrieved from the time series of dengue epidemics in two cities in Brazil. The results show fluctuations that are not captured by mean-field models. It also reveals the qualitative behavior of the spatiotemporal patterns of the epidemics. In the extreme situation of the absence of external periodic drive, the model predicts a completely distinct long-time evolution. The model is robust in the sense that it is able to reproduce the time series of dengue epidemics of different cities, provided that the forcing term takes into account the local rainfall modulation. Finally, an analysis is provided of the effect of the dependence between epidemics threshold and vector control actions, both in the presence and absence of human mobility factor.

We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously and we explore them using experiments and simulations with the chaotic Colpitts oscillator as an example system. We explore the impact of model imperfection on the ability to extract valid information from an experimental system. We compare two optimization methods: an initial value method and a constrained method. Each of these involves coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold. We explore both time-dependent and time-independent coupling and discuss the use of periodic impulse coupling. We also examine both optimized and fixed (or manually adjusted) coupling. For the case of an optimized time-dependent coupling function $u\left(t\right)$ we find a robust structure which includes sharp peaks and intervals where it is zero. This structure shows a strong correlation with the location in phase space and appears to depend on noise, imperfections of the model, and the Lyapunov direction vectors. For time-independent coupling we find the counterintuitive result that often the optimal rms error in fitting the model to the data initially increases with coupling strength. Comparison of this result with that obtained using simulated data may provide one measure of model imperfection. The constrained method with time-dependent coupling appears to have benefits in synchronizing long data sets with minimal impact, while the initial value method with time-independent coupling tends to be substantially faster, more flexible, and easier to use. We also describe a method of coupling which is useful for sparse experimental data sets. Our use of the Colpitts oscillator allows us to explore in detail the case of a system with one positive Lyapunov exponent. The methods we explored are easily extended to driven systems such as neurons with time-dependent injected current. They are expected to be of value in nonchaotic systems as well. Software is available on request.