A general procedure is discussed to formulate a coupling function capable of targeting desired responses such as synchronization, antisynchronization, and amplitude death in identical as well as mismatched chaotic oscillators. The coupling function is derived for unidirectional, mutual, and matrix type coupling. The matrix coupling, particularly, is able to induce synchronization, antisynchronization, and amplitude death simultaneously in different state variables of a response system. The applicability of the coupling is demonstrated in spiking-bursting Hindmarsh-Rose neuron model, Rössler oscillator, Lorenz system, Sprott system, and a double scroll system. We also report a scaling law that defines a process of transition to synchronization.

The integration of time-dependent quantum mechanical wave equations is a fundamental problem in computational physics and computational chemistry. The wave-function’s energy spectrum as well as its momentum spectrum impose fundamental limits on the performance of numerical algorithms for the solution of wave equations. We demonstrate how canonical transforms may be applied to negotiate these limitations and to increase the performance of numerical algorithms by up to several orders of magnitude. Our approach includes the so-called Kramers-Henneberger transform as a special case and puts forward modifications toward an improved numerical efficiency.

Assembling quantum dots (QDs) into nanoscale configurations over macroscopic dimensions is an important goal to realizing their electro-optical potential. In this Rapid Communication, we present a detailed study of a pentylcyanobiphenyl liquid crystal (LC) and a CdS QD colloidal dispersion by probing the dielectric property $\overline{\epsilon }$ and relaxation as a function of an applied ac electric field $E_{\text{ac}}$. In principle, dispersing QDs in a nematic LC medium can direct the dots to align in nearly one-dimensional chainlike structures along the nematic director and these assemblies of QDs can be directed by external electric fields. In a uniform planar aligned cell, the Fréedericksz switching of the $\text{LC}+\text{QDs}$ appears as a two-step process with the same initial switching field as the bulk but with the final $\overline{\epsilon }$ value larger than that for an aligned bulk LC. The relaxation of $\overline{\epsilon }$ immediately following the removal of $E_{\text{ac}}$ follows a single-exponential decay to its original value that is slower than the bulk but becomes progressively faster with increasing $E_{\text{ac}}$, eventually saturating. These results suggest that the arrangement of the QDs is mediated by the LC.

A deterministic overdamped ratchet driven by a periodic square driving force is shown to display chaotic behavior. The system has neither temporal nor quenched noise but the strong nonlinearity of the driving force produces a very rich bifurcation pattern with synchronized as well as chaotic regions. This pattern disappears if a sinusoidal force replaces the square force. This unexpected behavior is explained by decomposing the system into two exactly solvable subsystems, each with its own characteristic transit time, so that the ratio between the period of the driving force and the transit times can be analyzed. The transition from synchronized to chaotic motion can be explained by means of a one-dimensional Poincaré map. Our results can be experimentally confirmed in a number of systems, including the three-junction superconducting quantum interference devices ratchet, the rocking ratchet effect for cold atoms, and the Josephson vortex ratchet.

The origin of stochastic fluctuations in gene expression has received considerable attention recently. Fluctuations in gene expression are particularly pronounced in cellular systems because of the small copy number of species undergoing transitions between discrete chemical states and the small size of biological compartments. In this paper, we propose a stochastic model for gene expression regulation including several binding sites, considering elementary reactions only. The model is used to investigate the role of cooperativity on the intrinsic fluctuations of gene expression by means of master-equation formalism. We found that the Hill coefficient and the level of noise increase as the interaction energy between activators increases. Additionally, we show that the model allows one to distinguish between two cooperative binding mechanisms.

Variability in neural responses is a ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The statistical properties of the generated spikes depend on the stimulating input current. Given that real sensory neurons are driven by time-dependent signals, here we study how the interspike interval distribution of integrate-and-fire neurons depends on the evolution of the stimulus in a quasistatic limit. We obtain a closed-form expression for this distribution, and we compare it to the one obtained with numerical simulations for several time-dependent currents. For slow inputs, the quasistatic distribution provides a very good description of the data. The results obtained for the integrate-and-fire model can be extended to other nonautonomous stochastic systems where the first passage time problem has an explicit solution.

Respiration in bacteria involves a sequence of energetically coupled electron and proton transfers creating an electrochemical gradient of protons (a proton-motive force) across the inner bacterial membrane. With a simple kinetic model, we analyze a redox loop mechanism of proton-motive force generation mediated by a molecular shuttle diffusing inside the membrane. This model, which includes six electron-binding and two proton-binding sites, reflects the main features of nitrate respiration in E. coli bacteria. We describe the time evolution of the proton translocation process. We find that the electron-proton electrostatic coupling on the shuttle plays a significant role in the process of energy conversion between electron and proton components. We determine the conditions where the redox loop mechanism is able to translocate protons against the transmembrane voltage gradient above 200 mV with a thermodynamic efficiency of about 37%, in the physiologically important range of temperatures from 250 to 350 K.

A bacterial bath is a model active system consisting of a population of rodlike motile or self-propelled bacteria suspended in a fluid environment. This system can be viewed as an active, nonequilibrium version of a lyotropic liquid crystal or as a generalization of a driven diffusive system. We derive a set of phenomenological equations, which include the effects of internal force generators in the bacteria, describing the hydrodynamic flow, orientational dynamics of the bacteria, and fluctuations induced by both thermal and nonthermal noises. These equations violate the fluctuation dissipation theorem and the Onsager reciprocity relations. We use them to provide a quantitative account of results from recent microrheological experiments on bacterial baths.

We present a reformulation of modularity that allows the analysis of the community structure in networks of correlated data. The modularity preserves the probabilistic semantics of the original definition even when the network is directed, weighted, signed, and has self-loops. This is the most general condition one can find in the study of any network, in particular those defined from correlated data. We apply our results to a real network of correlated data between stores in the city of Lyon (France).

Stochastic disturbances and spikes (sudden sharp fluctuations of any system parameter), commonly observed among natural and laboratory-scale systems, can perturb the multistable dynamics significantly and become a serious impediment when the device is designed for a certain dynamical behavior. We experimentally demonstrate that suitable periodic modulation of any system parameter may efficiently control such stochastic multistability related problems. The control mechanism is verified individually with two standard models (namely, an analog circuit of Lorenz equations and a cavity-loss modulated ${\text{CO}}_2$ laser), against three externally introduced disturbing signals, (namely, white Gaussian noise, pink noise, and train of spikes). Indeed, with both the systems, it has been observed that the modulation is capable to significantly control untoward jumps to coexisting attractors that otherwise would have occurred due to either of the disturbances. These results establish the robustness and wide applicability of this control mechanism in resolving stochastic multistability related problems.

In this paper, the measurement of the heat transfer coefficient in rarefied gases is presented; these are among the first heat transfer measurements in the slip flow regime. The experimental setup is validated by comparing friction factor in the slip regime and heat transfer coefficient in the continuum regime. Experimental results suggest that the Nusselt number is a function of Reynolds and Knudsen numbers in the slip flow regime. The measured values for Nusselt numbers are smaller than that predicted by theoretical or simulation results, and can become a few orders of magnitude smaller than the theoretical values in the continuum regime. The results are repeatable and expected to be useful for further experimentation and modeling of flow in the slip and transition regimes.

We report a method of magnetic mixing wherein a “vortex” magnetic field applied to a suspension of magnetic particles creates strong homogeneous mixing throughout the fluid volume. Experiments designed to elucidate the microscopic mechanism of mixing show that the torque is quadratic in the field, decreases with field frequency, and is optimized at a vortex field angle of $\sim 55°$. Theory and simulations indicate that the field-induced formation of volatile particle chains is responsible for these phenomena. This technique has applications in microfluidic devices and is ideally suited to applications such as accelerating the binding of target biomolecules to biofunctionalized magnetic microbeads.

We demonstrate that, for the case of quasiequipartition between the velocity and the magnetic field, the Lagrangian-averaged magnetohydrodynamics (LAMHD) $\alpha$ model reproduces well both the large-scale and the small-scale properties of turbulent flows; in particular, it displays no increased (superfilter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the subfilter scales. This is in contrast to the case of the neutral fluid in which the Lagrangian-averaged Navier-Stokes $\alpha$ model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of superfilter-scale spectral properties. We argue that, as the Lorentz force breaks the conservation of circulation and enables spectrally nonlocal energy transfer (associated with Alfvén waves), it is responsible for the absence of a viscous bottleneck in magnetohydrodynamics (MHD), as compared to the fluid case. As LAMHD preserves Alfvén waves and the circulation properties of MHD, there is also no (superfilter) bottleneck found in LAMHD, making this method capable of large reductions in required numerical degrees of freedom; specifically, we find a reduction factor of $\approx 200$ when compared to a direct numerical simulation on a large grid of ${1536}^3$ points at the same Reynolds number.

Pattern formation in a miscible ferrofluid system is experimentally investigated. The experiment is performed by immersing a thin ferrofluid droplet in a cylindrical container, overfilling it with a nonmagnetic miscible fluid, and applying an in-plane radial magnetic field. Visually striking patterns are obtained whose morphologies change from circular at zero field to complex starburstlike structures at finite field. The evolution of miscible ferrofluid droplets of various initial diameters subjected to different magnetic-field strengths is considered. Proper rescaling of the experimental data indicates that the time evolution of the droplets’ area increments obeys a universal 4/3 power-law behavior at long times.

It is desirable to achieve the self-organization of a microcolumn between electrodes in a flow channel because the microcolumn can be used as a biosensor with high sensitivity. A direct simulation of a dispersed system of metallic particles in water is performed to show that a microcolumn between electrodes is formed by the application of an ac electric field. By the multiphysics coupled simulation technique between fluidics and electrostatics based on the boundary element method along with the double layer approximation, we find that microcolumns are formed by the growth of clusters perpendicular to the electrodes under the condition that the number density of particles is larger than the percolation threshold. Further, we propose a simple model that efficiently explains the time dependence of the probability of the formation of a microcolumn by considering standard collision theory and percolation theory. By this analysis, we can greatly contribute to developments in studies on the self-organization of microcolumns and biosensors.

A variational approach is used to develop a robust numerical procedure for solving the nonlinear Poisson-Boltzmann equation. Following Maggs and Rossetto [Phys. Rev. Lett. 88, 196402 (2002)], we construct an appropriate constrained free energy functional such that its Euler-Lagrange equations are equivalent to the Poisson-Boltzmann equation. This is a formulation that searches for a true minimum in function space, in contrast to previous variational approaches that rather searched for a saddle point. We then develop, implement, and test an algorithm for its numerical minimization, which is quite simple and unconditionally stable. The analytic solution for planar geometry is used for validation. Some results are presented for a charged colloidal sphere surrounded by counterions and optimizations based upon fast Fourier transforms and hierarchical preconditioning are briefly discussed.

We provide an observation suggesting a strong correlation between helicity and enstrophy in fluid turbulence. Helicity statistics were obtained in a direct numerical simulation of forced isotropic turbulence. An investigation of coherent structures revealed that intermittently large local helicity was found in the core region of the coherent rotational structures, thus showing a strong correlation with local enstrophy, not dissipation. Statistics regarding the relative helicity and the correlation between velocity and vorticity conditioned on different levels of enstrophy clearly suggest that velocity and vorticity tend to be aligned in the core of the coherent structures.

Aerodynamic performance due to forewing and hindwing interaction in gliding dragonfly flight has been studied using a multiblock lattice Boltzmann method. We find that the interactions between forewing and hindwing effectively enhance the total lift force and reduce the drag force on the wings compared to two independent wings. The interaction mechanism may be associated with the triangular camber effect by modulating the relative arrangement of the forewing and hindwing. The results obtained in this Brief Report provide physical insight into the understanding of aerodynamic behaviors for gliding dragonfly flight.

Within the framework of the Helfrich elastic theory of membranes and of differential geometry, we study the relative stability of spherical vesicles and double bubbles. We find that not only temperature but also magnetic fields can induce topological transformations between spherical vesicles and double bubbles and provide a phase diagram for the equilibrium shapes.

We investigate directed thermal heat flux across one-dimensional homogenous nonlinear lattices when no net thermal bias is present on average. A nonlinear lattice of Fermi-Pasta-Ulam-type or Lennard-Jones-type system is connected at both ends to thermal baths which are held at the same temperature on temporal average. We study two different modulations of the heat bath temperatures, namely: (i) a symmetric, harmonic ac driving of temperature of one heat bath only and (ii) a harmonic mixing drive of temperature acting on both heat baths. While for case (i) an adiabatic result for the net heat transport can be derived in terms of the temperature-dependent heat conductivity of the nonlinear lattice a similar such transport approach fails for the harmonic mixing case (ii). Then, for case (ii), not even the sign of the resulting Brownian motion induced heat flux can be predicted a priori. A nonvanishing heat flux (including a nonadiabatic reversal of flux) is detected which is the result of an induced dynamical symmetry breaking mechanism in conjunction with the nonlinearity of the lattice dynamics. Computer simulations demonstrate that the heat flux is robust against an increase of lattice sizes. The observed ratchet effect for such directed heat currents is quite sizable for our studied class of homogenous nonlinear lattice structures, thereby making this setup accessible for experimental implementation and verification.