We present an experimental study of the tunable anisotropic wetting behavior of chemically patterned anisotropic surfaces. Asymmetric glycerol droplet shapes, arising from patterns of alternating hydrophilic (pristine ${\text{SiO}}_2$) and hydrophobic (fluoroalkylsilane self-assembled monolayers) stripes with dimensions in the low-micrometer range, are investigated in relation to stripe widths. Owing to the well-defined small droplet volume, the equilibrium shape as well as the observed contact angles exhibit unique scaling behavior. Only the relative width of hydrophilic and hydrophobic stripes proves to be a relevant parameter. Our results on morphologically flat, chemically patterned surfaces show similarities with those of experiments on topographically corrugated substrates. They are discussed in terms of the energetics at the liquid-solid interface.

We develop an application of linear cable theory to protein receptor trafficking in the surface membrane of a neuron’s dendritic tree. We assume that receptors diffuse freely in the dendritic membrane but exhibit periods of confined motion through interactions with small mushroomlike protrusions known as dendritic spines. We use cable theory to determine how receptor trafficking depends on the geometry of the dendritic tree and various important biophysical parameters such as membrane diffusivity, the density of spines, the strength of diffusive coupling between dendrites and spines, and the rates of constitutive recycling of receptors between the surface of spines and intracellular pools. We also use homogenization theory to determine corrections to cable theory arising from the discrete nature of spines.

The earthquake size-frequency distribution of individual seismic faults commonly differs from the Gutenberg-Richter law of regional seismicity by the presence of an excess of large earthquakes. Here we present a cellular automaton of the forest-fire model type that is able to reproduce several size-frequency distributions depending on the number and location of asperities on the fault plane. The model describes a fault plane as a two-dimensional array of cells where each cell can be either a normal site or a trigger site. Earthquakes start on trigger sites. Asperities appear as the dual entities of the trigger sites. We study the effect that the number and distribution of asperities (the dual of the set of trigger sites), the earthquake rate, and the aspect ratio of the fault have on the size-frequency distribution. Size-frequency distributions have been grouped into subcritical, critical, and supercritical, and the relationship between the model parameters and these three kinds of distributions is presented in the form of phase maps for each of the five asperity types tested. We also study the connection between the model parameters and the aperiodicity of the large earthquakes. For this purpose the concept of aperiodicity spectrum is introduced. The aperiodicity in the recurrence of the large earthquakes in a fault shows an interesting variability that can be potentially useful for prediction purposes.

We present a control method based on two steps: prediction and prevention. For prediction we use the anticipated synchronization scheme, considering unidirectional coupling between excitable systems in a master-slave configuration. The master is the perturbed system to be controlled, meanwhile the slave is an auxiliary system which is used to predict the master’s behavior. The prevention is obtained by sending a control signal to the master system, which temporarily lowers its excitability threshold and prevents its future reaction to the external perturbation. We demonstrate theoretically and experimentally that an efficient control may be achieved.

Like ion channels, nanochannels are known to exhibit curious non-Ohmic current-voltage $\left(I\text{−}V\right)$ characteristics with an approximate piece-wise constant differential resistance. Using a nanoslot model and a nonequilibrium ion transport theory, we attribute the nonlinear resistance to overlapping double layers inside and an extended polarized layer of space charge outside the nanochannel. The overlimiting current beyond a critical voltage is shown to develop when the polarized layer is destabilized by a microvortex instability at one entrance. By extending earlier nanochannel and polarized layer models to include this instability, nonideal ion permselectivity and field-focusing effect, quantitative predictions—together with explicit differential resistance expressions—are offered for the nonlinear $I\text{−}V$ features of a nanochannel surrounded by microreservoirs from a simple pseudo-one-dimensional model.

We explicitly calculate the orientation-dependent second virial coefficient of short charged rods in an electrolytic solvent, assuming the rod-rod interactions to be a pairwise sum of hard-core and segmental screened-Coulomb repulsions. From the parallel and isotropically averaged second virial coefficient, we calculate the effective length and diameter of the rods, for charges and screening lengths that vary over several orders of magnitude. Using these effective dimensions, we determine the phase diagram, where we distinguish a low-charge and strong-screening regime with a liquid crystalline nematic and smectic phase, and a high-charge and weak-screening regime with a plastic crystal phase in the phase diagram.

We investigate possible effects of high-order nonlinearities on the shapes of infection refugia of the reservoir of an infectious disease. We replace Fisher-type equations that have been recently used to describe, among others, the Hantavirus spread in mouse populations by generalizations capable of describing Allee effects that are a consequence of the high-order nonlinearities. After analyzing the equations to calculate steady-state solutions, we study the stability of those solutions and compare to the earlier Fisher-type case. Finally, we consider the spatial modulation of the environment and find that unexpected results appear, including a bifurcation that has not been studied before.

The effect of signal integration through cis-regulatory modules (CRMs) on synchronization and clustering of populations of two-component genetic oscillators coupled with quorum sensing is investigated in detail. We find that the CRMs play an important role in achieving synchronization and clustering. For this, we investigate six possible cis-regulatory input functions with AND, OR, ANDN, ORN, XOR, and EQU types of responses in two possible kinds of cell-to-cell communications: activator-regulated communication (i.e., the autoinducer regulates the activator) and repressor-regulated communication (i.e., the autoinducer regulates the repressor). Both theoretical analysis and numerical simulation show that different CRMs drive fundamentally different cellular patterns, such as complete synchronization, various cluster-balanced states and several cluster-nonbalanced states.

When a certain “seed” disturbance begins to spread on a large network, the number of nodes infected is a function of time. Regarding the set of infected nodes as constituting a dynamic network that evolves continuously in time, we ask: how does the order in the collective dynamics of the network vary with time? Utilizing synchronizability as a measure of the order, we find that there exists a time at which a maximum amount of disorder corresponding to a minimum degree of synchronizability can arise before the system settles into a more ordered steady state. This phenomenon of transient disorder occurs for networks of both regular and complex topologies. We present physical analyses and numerical support to establish the generality of the phenomenon.

We report experimental evidence of the route to spatiotemporal chaos in a large one-dimensional array of hotspots in a thermoconvective system. As the driving force is increased, a stationary cellular pattern becomes unstable toward a mixed pattern of irregular clusters which consist of time-dependent localized patterns of variable spatiotemporal coherence. These irregular clusters coexist with the basic cellular pattern. The Fourier spectra corresponding to this synchronization transition reveal the weak coupling of a resonant triad. This pattern saturates with the formation of a unique domain of high spatiotemporal coherence. As we further increase the driving force, a supercritical bifurcation to a spatiotemporal beating regime takes place. The new pattern is characterized by the presence of two stationary clusters with a characteristic zig-zag geometry. The Fourier analysis reveals a stronger coupling than the previous mixed pattern and enables us to find out that this beating phenomenon is produced by the splitting of the fundamental spatiotemporal frequencies in a narrow band. Both secondary instabilities are phaselike synchronization transitions with global and absolute character. Far beyond this threshold, a new instability takes place when the system is not able to sustain the spatial frequency splitting, although the temporal beating remains inside these domains. These experimental results may support the understanding of other systems in nature undergoing similar clustering processes.

Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic classical features with energy and control parameters. Corresponding signatures are now verified also on the quantum level for different schemes of quantization and with a variable classicality constant.

We study magnetic field evolution in flows with fluctuating in time governing parameters in electrically conducting fluid. We use a standard mean-field approach to derive equations for large-scale magnetic field for the fluctuating Arnold-Beltrami-Childress (ABC) flow as well as for the fluctuating Roberts flow. The derived mean-field dynamo equations have growing solutions with growth rate of the large-scale magnetic field which is not controlled by molecular magnetic diffusivity. Our study confirms the Zeldovich idea that the nonstationarity of the fluid flow may remove the obstacle in the large-scale dynamo action of classic stationary flows.

Denser and highly magnetized ferrofluids exhibit several non-Newtonian behaviors attributed to the formation of magnetic particle chains. We investigate the rheological and adhesive properties during tensile deformation of a confined chain-forming ferrofluid subjected to a radial magnetic field. Both the magnetoviscous contribution to the viscosity and the adhesive force are derived analytically. The response of the system to changes in the length of the chains is examined under zero and nonzero shear circumstances. Our results indicate that the existence of chains has a significant impact on the adhesive strength as well as on the viscosity of the ferrofluid, allowing it to display both shear-thinning and shear-thickening regimes. These findings open up the possibility of monitoring complex rheological responses of such fluids with the assistance of applied magnetic fields, allowing a more accurate assessment of their adhesive properties.

In this work we mimic the efficient propulsion mechanism of natural cilia by magnetically actuating thin films in a cyclic but non-reciprocating manner. By simultaneously solving the elastodynamic, magnetostatic, and fluid mechanics equations, we show that the amount of fluid propelled is proportional to the area swept by the cilia. By using the intricate interplay between film magnetization and applied field we are able to generate a pronounced asymmetry and associated flow. We delineate the functional response of the system in terms of three dimensionless parameters that capture the relative contribution of elastic, inertial, viscous, and magnetic forces.

The propagation of the kink along the curved Josephson junction is considered. It is shown that the torsion as well as curvature is responsible for the existence of the energy barrier that affects the motion of the fluxon in the junction. It is also observed that the motion of the kink in the junction can be controlled in a very simple way even in the straight junction by modulating its width.

Genetic algorithms are a standard heuristic to find states of low energy in complex state spaces as given by physical systems such as spin glasses but also in combinatorial optimization. The paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover. Many schemes have been considered in literature as possible crossover selection strategies. We show for a large class of quality measures that the best possible probability distribution for selecting individuals in each generation of the algorithm execution is a rectangular distribution over the individuals sorted by their energy values. This means uniform probabilities have to be assigned to a group of the individuals with lowest energy in the population but probabilities equal to zero to individuals which are corresponding to energy values higher than a fixed cutoff, which is equal to a certain rank in the vector sorted by the energy of the states in the current population. The considered strategy is dubbed threshold selecting. The proof applies basic arguments of Markov chains and linear optimization and makes only a few assumptions on the underlying principles and hence applies to a large class of algorithms.

We study a two-dimensional $XXZ$-Ising model on a square-hexagon (denoted for simplicity by 4–6) lattice with spin 1/2. The phase diagram at zero temperature is discussed, where five states are found, two types of ferrimagnetic states, two types of antiferromagnetic states, and one ferromagnetic state. To solve this model, we have mapped onto the eight-vertex model with union Jack interaction term, and it was verified that the model cannot be completely mapped onto eight-vertex model. However, by imposing an exact solution condition, we have found the region where the $XXZ$-Ising model on 4–6 lattice is exactly soluble with one free parameter, particularly for the case of symmetric eight-vertex model condition. In this manner we have explored the properties of the system and have analyzed the interacting competition parameters which preserve the region where there is an exact solution. Unfortunately the present model does not satisfy the free fermion condition of the eight-vertex model, unless for a trivial solution. Even so, we are able to discuss the critical point region, beyond the region of exact resolvability.

Landauer’s erasure principle is generalized to nondeterministic processes on systems having an arbitrary number of nonsymmetrical logical states. The condition that the process is applied in the same way, irrespective of the initial logical state, imposes some restrictions on the individual heat exchanges associated with each possible transition. The complete set of such restrictions are derived by a statistical analysis of the phase-space flow induced by the process. Landauer’s erasure principle can be derived from and is a special case of these.

We study a quasi-two-dimensional monolayer of granular rods fluidized by a spatially and temporally homogeneous upflow of air. By tracking the position and orientation of the particles, we characterize the dynamics of the system with sufficient resolution to observe ballistic motion at the shortest time scales. Particle anisotropy gives rise to dynamical anisotropy and superdiffusive dynamics parallel to the rod’s long axis, causing the parallel and perpendicular mean-square displacements to become diffusive on different time scales. The distributions of free times and free paths between collisions deviate from exponential behavior, underscoring the nonthermal character of the particle motion. The dynamics show evidence of rotational-translational coupling similar to that of an anisotropic Brownian particle. We model rotational-translational coupling in the single-particle dynamics with a modified Langevin model using nonthermal noise sources. This suggests a phenomenological approach to thinking about collections of self-propelling particles in terms of enhanced memory effects.

Particle motion in an unsteady peristaltic fluid flow is analyzed. The fluid is incompressible and Newtonian in a two-dimensional planar geometry. A perturbation method based on a small ratio of wave height to wavelength is used to obtain a closed-form solution for the fluid velocity field. This analytical solution is used in conjunction with an equation of motion for a small rigid sphere in nonuniform flow taking Stokes drag, virtual mass, Faxén, Basset, and gravity forces into account. Fluid streamlines and velocity profiles are calculated. Theoretical values for pumping rates are compared with available experimental data. An application to ureteral peristaltic flow is considered since fluid flow in the ureter is sometimes accompanied by particles such as stones or bacteriuria. Particle trajectories for parameters that correspond to calcium oxalates for calculosis and Escherichia coli type for bacteria are analyzed. The findings show that retrograde or reflux motion of the particles is possible and bacterial transport can occur in the upper urinary tract when there is a partial occlusion of the wave. Dilute particle mixing is also investigated, and it is found that some of the particles participate in the formation of a recirculating bolus, and some of them are delayed in transit and eventually reach the walls. This can explain the failure of clearing residuals from the upper urinary tract calculi after successful extracorporeal shock wave lithotripsy. The results may also be relevant to the transport of other physiological fluids and industrial applications in which peristaltic pumping is used.