The colloidal probe technique (CPT) is used to measure distance-dependent interaction forces between polyelectrolyte layers physisorbed from $1\mathrm{M}$ $\mathrm{NaCl}$ solution in salt solutions between $0.1\mathrm{mM}$ and $1\mathrm{M}$. Both linear polycations (poly(allylamine)hydrochloride, poly-l-lysine) and linear polyanions (poly(styrenesulfonate)) are used. The repulsive interaction energies in the range between ${10}^{-7}$ and ${10}^{-4}\mathrm{J}∕{\mathrm{m}}^2$ are described by the theory of Alexander and de Gennes for surfaces covered with neutral anchored polymers. However, the brush thickness scales with molecular area and salt concentration with a power of $-1∕3$ as known from a salted brush and reaches approximately 50% of the contour length in diluted solutions. The findings are confirmed by CPT images using a gold layer as height reference.

We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the probability density of the arrival time. We explicitly calculate the path integral for a special case of dichotomous disorder and use the corresponding characteristic function to derive prominent properties of the arrival time probability density. Specifically, we establish the scaling properties of the central moments, analyze the behavior of the probability density for short, long, and intermediate distances. In order to quantify the deviation of the arrival time distribution from a Gaussian shape, we evaluate the skewness and the kurtosis.

We present experimental findings on the flow rule for granular flows on a rough inclined plane using various materials, including sand and glass beads of various sizes and four types of copper particles with different shapes. We characterize the materials by measuring $h_s$ (the thickness at which the flow subsides) as a function of the plane inclination $\theta$ on various surfaces. Measuring the surface velocity $u$ of the flow as a function of flow thickness $h$, we find that for sand and glass beads the Pouliquen flow rule $u∕\sqrt{gh}\sim \beta h∕h_s$ provides reasonable but not perfect collapse of the $u\left(h\right)$ curves measured for various $\theta$ and mean particle diameter $d$. Improved collapse is obtained for sand and glass beads by using a recently proposed scaling of the form $u∕\sqrt{gh}=\beta h{\tan }^2\theta ∕h_s{\tan }^2{\theta }_1$ where ${\theta }_1$ is the angle at which the $h_s\left(\theta \right)$ curves diverge. Measuring the slope $\beta$ for ten different sizes of sand and glass beads, we find a systematic, strong increase of $\beta$ with the divergence angle ${\theta }_1$ of $h_s$. Copper materials with different shapes are not well described by either flow rule with $u\sim h^{3∕2}$.

Fluids in which the interparticle potential has a hard core, is attractive at moderate separations, and repulsive at large separations are known to exhibit unusal phase behavior, including stable inhomogeneous phases. Here we report a joint simulation and theoretical study of such a fluid, focusing on the relationship between the liquid-vapor transition line and any new phases. The phase diagram is studied as a function of the amplitude of the attraction for a certain fixed amplitude of the long ranged repulsion. We find that the effect of the repulsion is to substitute the liquid-vapor critical point and a portion of the associated liquid-vapor transition line, by two first-order transitions. One of these transitions separates the vapor from a fluid of spherical liquidlike clusters; the other separates the liquid from a fluid of spherical voids. At low temperature, the two transition lines intersect one another and a vapor-liquid transition line at a triple point. While most integral equation theories are unable to describe the new phase transitions, the Percus-Yevick approximation does succeed in capturing the vapor-cluster transition, as well as aspects of the structure of the cluster fluid, in reasonable agreement with the simulation results.

In the present paper we consider some properties of defect modes in chiral photonic crystals with an anisotropic defect layer. We solved the problem by Ambartsumian’s layer addition method. We investigated the influence of the defect layer thickness variation and its location in the chiral photonic crystal (CPC) and also its optical axes orientation, as well as of CPC thickness variation on defect mode properties. Variations of the optical thickness of the defect layer have its impact on the defect mode linewidth and the light accumulation in the defect. We obtain that CPCs lose their base property at certain defect layer thicknesses; namely, they lose their diffraction reflection dependence on light polarization. We also show that the circular polarization handedness changes from right-handed to left-handed if the defect layer location is changed, and therefore, such systems can be used to create sources of elliptically polarized light with tunable ellipticity. Some nonreciprocity properties of such systems are investigated, too. In particular, it is also shown that such a system can work as a practically ideal wide band optical diode for circularly polarized incident light provided the defect layer thickness is properly chosen, and it can work as a narrow band diode at small defect layer thicknesses.

Random walks on simple graphs in connection with electrical resistor networks lead to the definition of Markov chains with transition probability matrix in terms of electrical conductances. We extend this definition to an effective transition matrix $P_{ij}$ to account for the probability of going from vertex $i$ to any vertex $j$ of the original connected graph $G$. Also, we present an algorithm based on the definition of this effective transition matrix among vertices in the network to extract a topological feature related to the manner by which graph $G$ has been organized. This topological feature corresponds to the communities in the graph.

Magnetic domain patterns under an oscillating field are studied theoretically by using a simple Ising-like model. We propose two ways to investigate the effects of the oscillating field. The first one leads to a model in which rapidly oscillating terms are averaged out and the model can explain the existence of the maximum amplitude of the field for the appearance of patterns. The second one leads to a model that includes the delay of the response to the field and the model suggests the existence of a traveling pattern which moves very slowly compared with the time scale of the driving field.

Mechanisms for the suppression of spatiotemporal chaos (STC) in one-dimensional driven drift-wave system to a spatially regular state by a periodic signal are investigated. In the driving wave coordinate, by transforming the system to a set of coupled oscillators (modes) moving in a periodic potential, it is found that the modes can be enslaved one by one through phase synchronization (PS) by the control signal; for some modes frequency-locking occurs while the other modes display multilooping PS without frequency-locking. Further study of the linear behavior of the modes shows that the saddle point embedded in the STC is changed to an unstable focus, which makes it possible for the imperfect PS to change to a perfect functional one, leading to the suppression of the STC.

The classical diffraction limit excludes the possibility of resolving features of an object which are spaced less than half a wavelength apart when scattering experiments are performed from the far field. However, recently it has been shown that this limit could be a consequence of the Born approximation that neglects the distortion of the probing wave as it travels through the object to be imaged. Such a distortion, which is due to the multiple scattering phenomenon, can encode unlimited resolution in the radiating component of the scattered field thus leading to super resolution. In this context, a resolution better than $\lambda$/3 has been reported in the case of elastic wave probing [F. Simonetti, Phys. Rev. E 73, 036619 (2006)], $\lambda$ being the wavelength of the wave illuminating the object. This paper demonstrates a resolution better than $\lambda ∕4$ and approaching $\lambda ∕6$ for objects immersed in a water bath probed by means of a ring transducer array that excites and detects ultrasonic pressure waves in a full view configuration. This is achieved despite the presence of a high level of noise in the measurements (the signal to noise ratio was below $0\mathrm{dB}$). Moreover, while previous papers have provided experimental evidence of super resolution for objects small compared to the wavelength, here the case of extended objects is also investigated.

We present a lattice Boltzmann algorithm based on an underlying free energy that allows the simulation of the dynamics of a multicomponent system with an arbitrary number of components. The thermodynamic properties, such as the chemical potential of each component and the pressure of the overall system, are incorporated in the model. We derived a symmetrical convection diffusion equation for each component as well as the Navier Stokes equation and continuity equation for the overall system. The algorithm was verified through simulations of binary and ternary systems. The equilibrium concentrations of components of binary and ternary systems simulated with our algorithm agree well with theoretical expectations.

We report molecular dynamics simulations on completely charged polyelectrolyte brushes grafted to two parallel surfaces. The pressure $\Pi$ is evaluated as a function of separation $D$ between the two grafting planes. For decreasing separation, $\Pi$ shows several regimes distinguished by their scaling with $D$ which reflects the different physical nature of the various regimes. At weak compression the pressure obeys the $1∕D$ power law predicted by scaling theory of an ideal gas of counterions in the osmotic brush regime. In addition we find that the brushes shrink as they approach each other trying to avoid interpenetration. At higher compressions where excluded volume interactions become important, we obtain scaling exponents between $-2$ at small grafting density ${\rho }_a$ and $-3$ at large ${\rho }_a$. This behavior indicates a transition from a brush under good solvent condition to the melt regime with increasing grafting density.

A $2\times 2$ game model implemented by a coevolution mechanism of both networks and strategy, inspired by the work of Zimmermann and Eguiluz [Phys. Rev. E72, 056118 (2005)] is established. Network adaptation is the manner in which an existing link between two agents is destroyed and how a new one is established to replace it. The strategy is defined as whether an agent offers cooperation $\left(C\right)$ or defection $\left(D\right)$. Both the networks and strategy are synchronously renovated in a simulation time step. A series of numerical experiments, considering various $2\times 2$ game structures, reveals that the proposed coevolution mechanism can solve dilemmas in several game classes. The effect of solving a dilemma means mutual-cooperation reciprocity ($R$ reciprocity), which is brought about by emerging several cooperative hub agents who have plenty of links. This effect can be primarily observed in game classes of the prisoner’s dilemma and stag hunt. The coevolution mechanism, however, seems counterproductive for game classes of leader and hero, where the alternating reciprocity (ST reciprocity) is meaningful.

Using dynamic light scattering we have investigated the time dependence of fluctuations near the critical point of phase separation in solutions of polystyrene in cyclohexane with polymer molecular weights ranging from $196000\text{to}11.4\times {10}^6\mathrm{g}{\mathrm{mol}}^{-1}$. At the lowest polymer molecular weight the dynamic correlation function follows a single-exponential decay with a decay rate that can be represented by the mode-coupling theory of critical dynamics but with a mesoscopic viscosity that characterizes the hydrodynamic environment of the polymers in the solution. At all higher polymer molecular weights two distinct dynamic modes are observed, a slow and a fast mode, that originate from a coupling of the critical concentration fluctuations with viscoelastic relaxation of the polymer chain in solutions. This coupling causes an additional slowing down of the fluctuations on top of the well-known critical slowing down expected in the absence of a coupling between the two modes. From an analysis of the time dependence of the experimental dynamic correlation functions in terms of a theory of coupling of dynamic modes we are able to determine the viscoelastic properties of the polymers in the solution. These viscoelastic properties diverge in the theta-point limit of infinite polymer molecular weight.

The dynamics of reentry is studied in a one-dimensional loop of model cardiac cells with discrete intercellular gap junction resistance $\left(R\right)$. Each cell is represented by a continuous cable with ionic current given by a modified Beeler-Reuter formulation. For $R$ below a limiting value, propagation is found to change from period-1 to quasiperiodic (QP) at a critical loop length $\left(L_{crit}\right)$ that decreases with $R$. Quasiperiodic reentry exists from $L_{crit}$ to a minimum length $\left(L_{\text{min}}\right)$, which also shortens with $R$. The decrease of $L_{crit}\left(R\right)$ is not a simple scaling, but the bifurcation can still be predicted from the slope of the restitution curve giving the duration of the action potential as a function of the diastolic interval. However, the shape of the restitution curve changes with $R$. An increase of $R$ does not seem to increase the number of possible QP solutions since, as in the continuous cable, only two QP modes of propagation were found despite an extensive search through alternative initial conditions.

There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale. However, this has been achieved in rare examples only, in particular, when involving high-speed migration of cells. One major difficulty is the lack of a suitable multiscale simulation platform, which embeds reaction diffusion of soluble substances, fast cell migration and mechanics, and, being of great importance in several tissue types, cell flow homeostasis. In this paper a step into this direction is presented by developing an agent-based mathematical model specifically designed to incorporate these features with special emphasis on high-speed cell migration. Cells are represented as elastic spheres migrating on a substrate in lattice-free space. Their movement is regulated and guided by chemoattractants that can be derived from the substrate. The diffusion of chemoattractants is considered to be slower than cell migration and, thus, to be far from equilibrium. Tissue homeostasis is not achieved by the balance of growth and death but by a flow equilibrium of cells migrating in and out of the tissue under consideration. In this sense the number and the distribution of the cells in the tissue is a result of the model and not part of the assumptions. For the purposes of demonstration of the model properties and functioning, the model is applied to a prominent example of tissue in a cellular flow equilibrium, the secondary lymphoid tissue. The experimental data on cell speed distributions in these tissues can be reproduced using reasonable mechanical parameters for the simulated cell migration in dense tissue.

We address a fundamental modeling issue in science as related to the field of dynamical systems: when is a model of a physical system a ÒgoodÓ representation? Conjugacy provides a means to determine if two systems are dynamically equivalent. We develop mathematical technology to decide when dynamics of a ÒtoyÓ model are like (although not identical to) dynamics of the physical system, since the concept of conjugacy is too rigid for such cases. We contrast the usual methodology where model quality is measured in a Banach space to our dynamically motivated notion of matching orbits as best as possible. We highlight our methods with a lower-ordered model of a “noisy” logistic map and also a simplified model of a Lorenz system such that the usual one-dimensional map model is not exactly justified in the traditional sense.

We explore the phenomenon of segregation and pattern formation in the complex system of a rotating horizontal cylinder completely filled with a dilute suspension of non-Brownian particles. A general dimensionless analysis is presented, which reveals the importance of the different dimensionless parameters involved. A detailed account of the mechanism of segregation and formation of axial bands for the case of low viscosity fluids is given. According to the analysis the axial pressure gradient associated with an inertial-mode excitation within the bounded fluid is responsible for the formation of bands in interleaving nodal planes of the excitation. The question of stability of the band patterns is addressed and a phase diagram in the appropriate dimensionless space is presented.

Astable regimes are common in nonlinear systems ranging from electrooptic devices to cardiac rhythms under environmental stress. Electrosprays exhibit three main axial regimes (dripping, pulsating, and cone-jet). It is generally accepted that the transition between the pulsating and cone-jet regimes is sudden, accompanied by an abruptly enhanced spray current. Here we present an alternative to this scenario, in which the electrospray follows a new chaotic astable path to the cone-jet regime. The astable regime could be explained as a result of transitions between a limit cycle (pulsating regime) and a fixed point (cone-jet regime) in a subcritical Andronov-Hopf bifurcation due to small external perturbations (noise). With the introduction of this regime, a broader view of the diverse axial regimes becomes possible based on nonlinear dynamics that enables their consistent classification.

It has been generally believed in literature that in nanosecond laser ablation, the condensed substrate phase contributes mass to the plasma plume through surface evaporation across the sharp interface between the condensed phase and the vapor or plasma phase. However, this will not be true when laser intensity is sufficiently high. In this case, the target temperature can be greater than the critical temperature, so that the sharp interface between the condensed and gaseous phases disappears and is smeared into a macroscopic transition layer. The substrate should contribute mass to the plasma region mainly through hydrodynamic expansion instead of surface evaporation. Based on this physical mechanism, a numerical model has been developed by solving the one-dimensional hydrodynamic equations over the entire physical domain supplemented by wide-range equations of state. It has been found that model predictions have good agreements with experimental measurement for plasma front location, temperature, and electron number density. This has provided further evidence (at least in the indirect sense), besides the above theoretical analysis, that for nanosecond laser metal ablation in air at sufficiently high intensity, the dominant physical mechanism for mass transfer from the condensed phase to the plasma plume is hydrodynamic expansion instead of surface evaporation. The developed and verified numerical model provides useful means for the investigation of nanosecond laser-induced plasma at high intensities.

We present a multicomponent lattice Boltzmann simulation for continuum fluid mechanics, paying particular attention to the component segregation part of the underlying algorithm. In the principal result of this paper, the dynamics of a component index, or phase field, is obtained for a segregation method after U. D’Ortona et al. [Phys. Rev. E 51, 3718 (1995)], due to Latva-Kokko and Rothman [Phys. Rev. E 71 056702 (2005)]. The said dynamics accord with a simulation designed to address multicomponent flow in the continuum approximation and underwrite improved simulation performance in two main ways: (i) by reducing the interfacial microcurrent activity considerably and (ii) by facilitating simulational access to regimes of flow with a low capillary number and drop Reynolds number [I. Halliday, R. Law, C. M. Care, and A. Hollis, Phys. Rev. E 73, 056708 (2006)]. The component segregation method studied, used in conjunction with Lishchuk’s method [S. V. Lishchuk, C. M. Care, and I. Halliday, Phys. Rev. E 67, 036701 (2003)], produces an interface, which is distributed in terms of its component index; however, the hydrodynamic boundary conditions which emerge are shown to support the notion of a sharp, unstructured, continuum interface.