A mechanism amenable to laminate and fold flows is identified and quantified. This laminating mechanism follows from a physical and experimental approach relying on the interlaced structure of velocity and Lagrangian acceleration. The Lagrangian acceleration being the resultant of the forces applied on particle fluids, the component of acceleration perpendicular to the velocity vector allows the quantification of a rate of change of the velocity’s direction, i.e., the local angular Lagrangian velocity, $\dot{\theta }$. The spatial variation in $\dot{\theta }$ is then used to predict and measure the lamination and folding rate. To support and illustrate this approach, three basic experimental flows, driven by electromagnetic forces, are discussed and compared. Folding rate intensities are extracted for different characteristic length scales. Also, good agreement is found between grid deformation and the prediction of lamination rate. This quantification of lamination rate opens new avenues for the design of mixers, in particular at low Reynolds numbers.

The dynamic clustering phenomenon in two-dimensional simple shear flows has been investigated using molecular dynamic simulations of systems containing binary and continuous size distributions of equal-material-density particles. Particular attention has been paid to two questions: (1) Does the presence of size nonuniformities serve to enhance or attenuate the presence of clusters? (2) Do particles of a given size preferentially segregate within the clusters? With respect to the first question, the prominence of clustered regions increases with increasing deviation from the monodisperse limit in the case of both binary and continuous size distributions. With respect to the second question, the larger particles of both binary and continuous size distributions are consistently observed to segregate within the transient clustered regions. Further investigation of granular temperatures within the clustered and dilute regions reveals that this segregation is consistent with previously observed temperature-driven segregation in steady-state systems; large particles favor the lower-temperature (clustered) regions. Moreover, observation of clustering length scales suggests that large particles may favor the center of the clustered regions, where granular temperatures are expected to reach a minimum.

We investigate the relaxation of the nematic deformation when the distorting field is switched off. We show that the usual analysis based on the diffusionlike equation does not allow a complete description of the phenomenon because it does not permit one to satisfy the initial boundary condition, at $t=0$, on the first time derivative of the nematic tilt angle. An alternative approach to the problem, taking into account the inertial properties of the nematic molecules, allows one to satisfy the initial boundary conditions on the first-order time derivative of the tilt angle. In this framework the dynamical evolution of the nematic deformation, in the initial time, depends on the inertial properties of the nematic molecules. However, the typical relaxation time is so short that, for all practical effects, the first time derivative of the tilt angle is discontinuous at $t=0$. A more realistic description involves the switching time of the distorting field. In this framework, the initial boundary condition of the first-order derivative is automatically satisfied. Our analysis shows that the description based on the diffusion equation works well when the switching time is very small with respect to the diffusion time.

The aim of our work is to study the effect of geometry variation on nucleation times and to address its role in the context of eukaryotic chemotaxis (i.e., the process which allows cells to identify and follow a gradient of chemical attractant). As a first step in this direction we study the nucleation dynamics of the two-dimensional Ising model defined on a cylindrical lattice whose radius changes as a function of time. Geometry variation is obtained by changing the relative value of the couplings between spins in the compactified (vertical) direction with respect to the horizontal one. This allows us to keep the lattice size unchanged and study in a single simulation the values of the compactification radius which change in time. We show both with theoretical arguments and numerical simulations that squeezing the geometry allows the system to speed up nucleation times even in presence of a very small energy gap between the stable and the metastable states. We then address the implications of our analysis for directional chemotaxis. The initial steps of chemotaxis can be modeled as a nucleation process occurring on the cell membrane as a consequence of the external chemical gradient (which plays the role of energy gap between the stable and metastable phases). In nature most of the cells modify their geometry by extending quasi-one-dimensional protrusions (filopodia) so as to enhance their sensitivity to chemoattractant. Our results show that this geometry variation has indeed the effect of greatly decreasing the time scale of the nucleation process even in presence of very small amounts of chemoattractants.

We study the evolution of Boolean networks as model systems for gene regulation. Inspired by biological networks, we select simultaneously for robust attractors and for the ability to respond to external inputs by changing the attractor. Mutations change the connections between the nodes and the update functions. In order to investigate the influence of the type of update functions, we perform our simulations with canalizing as well as with threshold functions. We compare the properties of the fitness landscapes that result for different versions of the selection criterion and the update functions. We find that for all studied cases the fitness landscape has a plateau with maximum fitness resulting in the fact that structurally very different networks are able to fulfill the same task and are connected by neutral paths in network (“genotype”) space. We find furthermore a connection between the attractor length and the mutational robustness, and an extremely long memory of the initial evolutionary stage.

Many types of cells can sense external ligand concentrations with cell-surface receptors at extremely high accuracy. Interestingly, ligand-bound receptors are often internalized, a process also known as receptor-mediated endocytosis. While internalization is involved in a vast number of important functions for the life of a cell, it was recently also suggested to increase the accuracy of sensing ligand as the overcounting of the same ligand molecules is reduced. Here we show, by extending simple ligand-receptor models to out-of-equilibrium thermodynamics, that internalization increases the accuracy with which cells can measure ligand concentrations in the external environment. Comparison with experimental rates of real receptors demonstrates that our model has indeed biological significance.

Nucleation processes are important for the understanding in protein dynamics. To evaluate the effect of nucleation mechanism in dimerization process, a domain-swapped dimer (Esp8) is simulated with the symmetrized Gō model and the classical Gō model. The pathways of the dimerization are analyzed with computational $\varphi$-analysis method. It is found out that some nuclei are observed in the kinetic steps of the dimeric association though the whole pathway is a process with multiple intermediate states. The key residues in the nuclei are rather similar to those observed in the monomeric folding. The differences with the monomeric cases are also discussed. These differences illustrate the effects of dimeric feature on the nucleation process. Besides, manual mutations are carried out to illustrate the importance of the interactions related to the nuclei. It is observed that the mutations in the nuclei-related interactions apparently change the dynamics while other mutations have little effect on the kinetics. All of these results outline a picture that the nucleation processes act as the fundamental steps of high-order organization of protein systems.

A distinct propagation of solitary waves in the presence of autocatalysis, diffusion, and symmetry-breaking (differential) advection, is being studied. These pulses emerge at lower reaction rates of the autocatalytic activator, i.e., when the advective flow overcomes the fast excitation and induces a fluid type “drifting” behavior, making the phenomenon unique to reaction-diffusion-advection class systems. Using the spatial dynamics analysis of a canonical model, we present the properties and the organization of such drifting pulses. The insights underly a general understanding of localized transport in simple reaction-diffusion-advection models and thus provide a background to potential chemical and biological applications.

The two-dimensional density correlation matrix is constructed for symbolic sequences using contiguous segments of arbitrary size. The multifractal spectrum obtained from this matrix motif is shown to characterize the correlations in the symbolic sequences. This method is applied to entire human chromosomes, shuffled human chromosomes, reconstructed human genomic sequences and to artificial random sequences. It is shown that all human chromosomes have common characteristics in their multifractal spectrum and deviate substantially from random and uncorrelated sequences of the same size. Small deviations are observed between the longer and the shorter chromosomes, especially for the higher (in absolute values) statistical moments. The correlations are crucial for the form of the multifractal spectrum; surrogate shuffled chromosomes present randomlike spectrum, distinctly different from the actual chromosomes. Analytical approaches based on hierarchical superposition of tensor products show that retaining pair correlations in the sequences leads to a closer representation of the genomic multifractal spectra, especially in the region of negative exponents, due to the underrepresentation of various functional units (such as the cytosine-guanine $CG$ combination and its complementary $GC$ complex). Retaining higher-order correlations in the construction of the tensor products is a way to approach closer the structure of the multifractal spectra of the actual genomic sequences. This hierarchical approach is generic and is applicable to other correlated symbolic sequences.

In this paper we study the classification of spatiotemporal pattern of one-dimensional cellular automata (CA) whereas the classification comprises CA rules including their initial conditions. We propose an exploratory analysis method based on the normalized compression distance (NCD) of spatiotemporal patterns which is used as dissimilarity measure for a hierarchical clustering. Our approach is different with respect to the following points. First, the classification of spatiotemporal pattern is comparative because the NCD evaluates explicitly the difference of compressibility among two objects, e.g., strings corresponding to spatiotemporal patterns. This is in contrast to all other measures applied so far in a similar context because they are essentially univariate. Second, Kolmogorov complexity, which underlies the NCD, was used in the classification of CA with respect to their spatiotemporal pattern. Third, our method is semiautomatic allowing us to investigate hundreds or thousands of CA rules or initial conditions simultaneously to gain insights into their organizational structure. Our numerical results are not only plausible confirming previous classification attempts but also shed light on the intricate influence of random initial conditions on the classification results.

We study the stability problem of unbounded shear flow, with velocity $U_i=S{x}_3{\delta }_{i1}$, subjected to a uniform vertical density stratification, with Brunt-Väisälä frequency $N$, and system rotation of rate $\Omega$ about an axis aligned with the spanwise $\left(x_2\right)$ direction. The evolution of plane-wave disturbances in this shear flow is governed by a nonhomogeneous second-order differential equation with time-dependent coefficients. An analytical solution is found to be described by Legendre functions in terms of the nondimensional parameter ${\sigma }_{\phi }^2=R\left(R+1\right){\text{sin}}^2\phi +R_i$, where $R=\left(2\Omega /S\right)$ is the rotation number, $\phi$ is the angle between the horizontal wave vector and the streamwise axis, and $R_i=N^2/S^2$ is the Richardson number. The long-time behavior of the solution is analyzed using the asymptotic representations of the Legendre functions. On the one hand, linear stability is analyzed in terms of exponential growth, as in a normal-mode analysis: the rotating stratified shear flow is stable if $R_i>1/4$, or if $0<R_i<1/4$ and $R\left(R+1\right)>0$, or if $R\left(R+1\right)<0<R\left(R+1\right)+R_i$ and $0<R_i<1/4$. It is unstable if $R_i<0$ and $R\left(R+1\right)+R_i<0.$ On the other hand, different behaviors for the “exponentially stable” case can coexist in different wave-space regions: some modes undergo a power-law growth or a power-law decay, while other exhibit damped oscillatory behavior. For geophysical and astrophysical applications, stability diagrams are shown for all values of $R_i$ and $R$ and an arbitrary orientation of the wave vector. Crucial contributions to spectral energies are shown to come from the $k_1=0$ mode, which corresponds to an infinite streamwise wavelength. Accordingly, two-dimensional contributions to both kinetic and potential energies are calculated analytically in this streamwise direction.

The unique properties of magnetic fluids are exploited to create a static interface between two fluids in the context of studying Rayleigh-Taylor (RT) driven mixing. Paramagnetic fluids have previously been used for studying this phenomenon [Z. Huang et al., Phys. Rev. Lett. 99, 204502 (2007)], as have ferrofluids [G. Pacitto et al., Phys. Rev. E 62, 7941 (2000)], but we propose using magnetorheological fluids instead to attain better control of the initial condition. As the motivation for using this technique is to quantify the effects of the initial condition on late time behavior of the RT instability, it is important that the initial condition be prescribed at a scale large enough to reliably measure. As a first demonstration of creating such an interface, this technique is applied to the two-dimensional (2D) instability with a single-mode sinusoidal interface. This technique has been used to study both moderate and high Atwood number systems, with successful control of the interface in an $A=1$ system being demonstrated. The nonlinear growth phase for this initial condition is examined and comparisons are made with both analytical models and published numerical and experimental work on the 2D single-mode RT instability. Measurements of the late time RT spike behavior reveal poor agreement between the experimental results and the analytical models.

We propose and test a method for controlling the size of nanoparticles, which plays a fundamental role in their electrical, optical, and mechanical properties. The method utilizes turbulent mixing, and is applicable to the fabrication of any type of nanoparticle that uses a solution environment in the preparation process. We show by well-controlled experiments on the CdS nanoparticles, which are semiconducting materials, that the average size $⟨d⟩$ of the particles decreases with Reynolds number Re.

The dynamic characteristics of strongly coupled one-component plasmas are studied within the moment approach. Our results on the dynamic structure factor and the dynamic local-field correction satisfy the sum rules and other exact relations automatically. A quantitative agreement is obtained with numerous simulation data on the plasma dynamic properties, including the dispersion and decay of collective modes. Our approach allows us to correct and complement the results previously found with other treatments.

Amplitude death is the cessation of oscillations that occurs in coupled nonlinear systems when fixed points are stabilized as a consequence of the interaction. We show here that this phenomenon is very general: it occurs in nonlinearly coupled systems in the absence of parameter mismatch or time delay although time-delayed interactions can enhance the effect. Application is made to synaptically coupled model neurons, nonlinearly coupled Rössler oscillators, as well as to networks of nonlinear oscillators with nonlinear coupling. By suitably designing the nonlinear coupling, arbitrary steady states can be stabilized.

Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles with constant speed and transitions between discreet allowed velocity directions. A new ingredient is that transitions into a given velocity state depend on spatial derivatives of other states populations, rather than on populations themselves. This feature requires the sacrifice of the single-particle character of the model, but allows to imitate the Huygens’ principle and to recover wave equations in arbitrary dimensions.

We study a competitive reaction model between two monomers $A$ and $B$ on a linear lattice. We assume that monomer $A$ can react with a nearest-neighbor monomer $A$ or $B$, but reactions between monomers of type $B$ are prohibited. We include in our model lateral interactions between monomers as well as the effects of temperature of the catalyst. The model is considered in the adsorption controlled limit, where the reaction rate is infinitely larger than the adsorption rate of the monomers. We employ site and pair mean-field approximations as well as static Monte Carlo simulations. We determine the phase diagram of the model in the plane $y_A$ versus temperature, where $y_A$ is the probability that a monomer of the type $A$ arrives at the surface. This phase diagram shows regions of active and absorbing states separated by a line of continuous phase transitions. Despite the absorbing state of the model to be strongly dependent on temperature, we show that the static critical exponents of the model belong to the same universality class of the directed percolation.

We study the unexpected high flexibility of short dsDNA which recently has been reported by a number of experiments. Via the Langevin dynamics simulation of our Breathing DNA model, first we observe the formation of bubbles within the duplex and also forks at the ends, with the size distributions independent of the contour length. We find that these local denaturations at a physiological temperature, despite their rare and transient presence, can lower the persistence length drastically for a short DNA segment in agreement with experiment.

A scheme for generating a fractal butterfly Floquet spectrum, first proposed by Wang and Gong [Phys. Rev. A 77, 031405(R) (2008)], is extended to driven SU(2) systems such as a driven two-mode Bose-Einstein condensate. A class of driven systems without a link with the Harper-model context is shown to have an intriguing butterfly Floquet spectrum. The found butterfly spectrum shows remarkable deviations from the known Hofstadter’s butterfly. In addition, the level crossings between Floquet states of the same parity and between Floquet states of different parities are studied and highlighted. The results are relevant to studies of fractal statistics, quantum chaos, and coherent destruction of tunneling, as well as the validity of mean-field descriptions of Bose-Einstein condensates.

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.