Global feedback control of pattern formation in a wide class of systems described by the Swift-Hohenberg (SH) equation is investigated theoretically, by means of stability analysis and numerical simulations. Two cases are considered: (i) feedback control of the competition between hexagon and roll patterns described by a supercritical SH equation, and (ii) the use of feedback control to suppress the blowup in a system described by a subcritical SH equation. In case (i), it is shown that feedback control can change the hexagon and roll stability regions in the parameter space as well as cause a transition from up to down hexagons and stabilize a skewed (mixed-mode) hexagonal pattern. In case (ii), it is demonstrated that feedback control can suppress blowup and lead to the formation of spatially localized patterns in the weakly nonlinear regime. The effects of a delayed feedback are also investigated for both cases, and it is shown that delay can induce temporal oscillations as well as blowup.

In this paper, we demonstrate the efficiency of simulations via direct computation of the partition function under various macroscopic conditions, such as different temperatures or volumes. The method can compute partition functions by flattening histograms, through, for example, the Wang-Landau recursive scheme, outside the energy space. This method offers a more general and flexible framework for handling various types of ensembles, especially ones in which computation of the density of states is not convenient. It can be easily scaled to large systems, and it is flexible in incorporating Monte Carlo cluster algorithms or molecular dynamics. High efficiency is shown in simulating large Ising models, in finding ground states of simple protein models, and in studying the liquid-vapor phase transition of a simple fluid. The method is very simple to implement and we expect it to be efficient in studying complex systems with rugged energy landscapes, e.g., biological macromolecules.

Experiments on ${}^4\mathrm{He}$ films reveal an attractive Casimir-like force at the bulk $\lambda$ point and in the superfluid regime. Previous work has explained the magnitude of this force at the $\lambda$ transition and deep in the superfluid region but not the substantial attractive force immediately below the $\lambda$ point. Utilizing a simple mean-field calculation renormalized by critical fluctuations we obtain an effective Casimir force that is qualitatively consistent with the scaling function $\vartheta$ obtained by collapse of experimental data.

We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation matrix from a reference model and we show that the expected values are known also when the specific model is unknown. We propose to make use of the Kullback-Leibler distance to estimate the information extracted from a correlation matrix by correlation filtering procedures. We also show how to use this distance to measure the stability of filtering procedures with respect to statistical uncertainty. We explain the effectiveness of our method by comparing four filtering procedures, two of them being based on spectral analysis and the other two on hierarchical clustering. We compare these techniques as applied both to simulations of factor models and empirical data. We investigate the ability of these filtering procedures in recovering the correlation matrix of models from simulations. We discuss such ability in terms of both the heterogeneity of model parameters and the length of data series. We also show that the two spectral techniques are typically more informative about the sample correlation matrix than techniques based on hierarchical clustering, whereas the latter are more stable with respect to statistical uncertainty.

Recent experimental data for the complete wetting behavior of pure ${}^4\mathrm{He}$ and of ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$ mixtures exposed to solid substrates show that there is a change of the corresponding film thicknesses $L$ upon approaching thermodynamically the $\lambda$ transition and the tricritical end point, respectively, which can be attributed to critical Casimir forces $f_C$. We calculate the scaling functions $\vartheta$ of $f_C$ within models representing the corresponding universality classes. For the mixtures our analysis provides an understanding of the rich behavior of $\vartheta$ deduced from the experimental data and predicts the crossover behavior between the tricritical point and the $\lambda$ transition of pure ${}^4\mathrm{He}$ which are connected by a line of critical points. The formation of a “soft-mode” phase within the wetting films gives rise to a pronounced maximum of $f_C$ below the tricritical point as observed experimentally. Near the tricritical point we find logarithmic corrections $\sim L^{-3}(\ln L{)}^{1∕2}$ for the leading behavior of $\vartheta$ dominating the contributions from the background dispersion forces.

In the modeling of infectious disease spread within explicit social contact networks, previous studies have predominantly assumed that the effects of shifting social associations within groups are small. These models have utilized static approximations of contact networks. We examine this assumption by modeling disease spread within dynamic networks where associations shift according to individual preference based on three different measures of network centrality. The results of our investigations clearly show that this assumption may not hold in many cases. We demonstrate that these differences in association dynamics do yield significantly different disease outcomes both from each other and also from models using graph-theoretically accurate static network approximations. Further work is therefore needed to explore under which circumstances static models accurately reflect constantly shifting natural populations.

The acceleration of ions in collisionless electrostatic shocks and solitary waves, driven by ultrashort intense laser pulses in a thin solid target under different conditions, is investigated theoretically. When a shock is formed, ions with certain initial velocities inside the target can be accelerated by the electrostatic field at the shock front to twice the shock speed. When a solitary wave is formed, only ions located at the rear surface of the target can be accelerated by the solitary wave together with the sheath field formed there.

Inspired by dengue and yellow fever epidemics, we investigated the contact process (CP) in a multiscale network constituted by one-dimensional chains connected through a Barabási-Albert scale-free network. In addition to the CP dynamics inside the chains, the exchange of individuals between connected chains (travels) occurs at a constant rate. A finite epidemic threshold and an epidemic mean lifetime diverging exponentially in the subcritical phase, concomitantly with a power law divergence of the outbreak’s duration, were found. A generalized scaling function involving both regular and SF components was proposed for the quasistationary analysis and the associated critical exponents determined, demonstrating that the CP on this hybrid network and nonvanishing travel rates establishes a new universality class.

Global time-delay autosynchronization is known to control spatiotemporal turbulence in oscillatory reaction-diffusion systems. Here, we investigate the complex Ginzburg-Landau equation in the regime of spatiotemporal turbulence and study numerically how local or a combination of global and local time-delay autosynchronization can be used to suppress turbulence by inducing uniform oscillations. Numerical simulations show that while a purely local control is unsuitable to produce uniform oscillations, a mixed local and global control can be efficient and also able to create other patterns such as standing waves, amplitude death, or traveling waves.

The wall effects on the axisymmetric rise and deformation of an initially spherical gas bubble released from rest in a liquid-filled, finite circular cylinder are numerically investigated. The bulk and gas phases are considered incompressible and immiscible. The bubble motion and deformation are characterized by the Morton number (Mo), Eötvös number (Eo), Reynolds number (Re), Weber number (We), density ratio, viscosity ratio, the ratios of the cylinder height and the cylinder radius to the diameter of the initially spherical bubble ($H^{*}=H∕d_0$, $R^{*}=R∕d_0$). Bubble rise in liquids described by Eo and Mo combinations ranging from (1,0.01) to (277.5,0.092), as appropriate to various terminal state Reynolds numbers $\left({\mathrm{Re}}_T\right)$ and shapes have been studied. The range of terminal state Reynolds numbers includes $0.02<{\mathrm{Re}}_T<70$. Bubble shapes at terminal states vary from spherical to intermediate spherical-cap–skirted. The numerical procedure employs a front tracking finite difference method coupled with a level contour reconstruction of the front. This procedure ensures a smooth distribution of the front points and conserves the bubble volume. For the wide range of Eo and Mo examined, bubble motion in cylinders of height $H^{*}=8$ and $R^{*}\ge 3$, is noted to correspond to the rise in an infinite medium, both in terms of Reynolds number and shape at terminal state. In a thin cylindrical vessel (small $R^{*}$), the motion of the bubble is retarded due to increased total drag and the bubble achieves terminal conditions within a short distance from release. The wake effects on bubble rise are reduced, and elongated bubbles may occur at appropriate conditions. For a fixed volume of the bubble, increasing the cylinder radius may result in the formation of well-defined rear recirculatory wakes that are associated with lateral bulging and skirt formation. The paper includes figures of bubble shape regimes for various values of $R^{*}$, Eo, Mo, and ${\mathrm{Re}}_T$. Our predictions agree with existing results reported in the literature.

Pyrogenic silica is often used as a thickening agent in paints, pastes, adhesives, or resins. Other applications include, e.g., abrasives in chemical mechanical planarization in the microelectronics industry. In all these applications it is essential to control the state of dispersion. Sometimes, phase transitions from the liquid to the solid state are required while in other cases they have to be completely avoided for the whole shelf life. The nature and influencing parameters of the fluid-solid transition for pyrogenic silica have not been investigated so far. Most investigations deal with the phase transitions of small clay particles such as laponite. Here, we dedicate our interest to the behavior of pyrogenic silica suspensions with varying specific surface area and ionic background concentration. To get an impression of the phase transition behavior we compare our results to model laponite suspensions. We apply dynamic light scattering measurements in the backscattering regime to minimize multiple scattering contributions from concentrated pyrogenic silica suspensions. Further on we exert a decomposition of the measured autocorrelation functions into an ergodic and nonergodic contribution. The analysis of the ergodic spectrum yields two different gelation kinetics for both systems, laponite and pyrogenic silica. For laponite these are in accordance with earlier investigations. The kinetics depend on the ionic background and the solids content of the suspensions. Additionally, we used dynamic extinction spectroscopy to follow the phase transitions of pyrogenic silica on a macroscale.

Isotropic untreated indium-tin-oxide layers can cause memory alignment of nematic liquid crystals. We have demonstrated an experimental method to characterize this effect by using a micropatterned surface. We tried to imprint a high tilt on an indium-tin-oxide substrate surface. We also investigated microscopic switching behavior of a memory-induced nematic liquid crystal cell by means of a vertical field effect.

This paper presents a model of the thermoregulation system of the spadix of skunk cabbage Symplocarpus foetidus which regulates its internal temperature at around $20°\mathrm{C}$ during flowering even when the ambient air temperature drops below freezing. From the temperature responses of the spadix to changing ambient air temperature, we assumed that the thermoregulation system of the spadix is probably one of negative feedback control. The feedback signals are based on the rate of temperature change of the spadix over time. A signal is factored into the biochemical energy generator, and becomes biochemical energy, some of which becomes heat. Comparing our proposed model temperature responses and those of the living spadix, we found good agreement. In the process of engineering the model, the existence of two regulatory pathways in the thermoregulation system was simulated, and our proposed model appears to provide the necessary elements to explain the fundamental mechanism of the thermoregulation system of S. foetidus.

Applicability of time-average moiré techniques for chaotic oscillations is analyzed in this paper. Envelope function characterizing the rate of convergence of time-averaged color intensity is derived. A study of the relationship among Lyapunov exponents and gray scale color intensity provides insight into the process of chaotic contrast modulation and confirms that chaotic oscillations do not produce time-average moiré fringes.

For certain families of fluid flow, a conserved quantity—stream helicity—has been conjectured. Using examples of linked and knotted streamtubes, it has been shown that stream helicity does, in certain cases, entertain itself with a very precise topological meaning, viz., a measure of the degree of knottedness or linkage of stream tubes. As a consequence, stream helicity may emerge as a robust topological invariant.

In this paper the drag-out problem for shear-thinning liquids at variable inclination angles is considered. For this free boundary problem dimension-reduced lubrication equations are derived for the most commonly used viscosity models, namely, the power-law, Ellis, and Carreau model. For the resulting lubrication models a system of ordinary differential equations governing the steady state solutions is obtained. Phase plane analysis is used to characterize the type of possible steady state solutions and their dependence on the rheological parameters.

Calculating accurate forces within variational and diffusion Monte Carlo (VMC and DMC) methods is a very challenging problem. We derive expressions for the contribution to the Hellmann-Feynman force from nonlocal pseudopotentials for use within the VMC and DMC methods. Equilibrium bond lengths and harmonic vibrational frequencies are calculated from the Hellmann-Feynman forces and compared with those obtained from the energies at the Hartree-Fock, VMC, and pure DMC levels. Results for five small molecules show that the equilibrium bond lengths obtained from the force and energy calculations differ by less than $0.007\mathrm{\AA }$ at the DMC level.

We study the mechanical response generated by local deformations in jammed packings of rigid disks. Based on discrete element simulations we determine the critical force of the local perturbation that is needed to break the mechanical equilibrium and examine the generated displacement field. Displacements decay as a power law of the distance from the perturbation point. The decay exponent and the critical force exhibit a nontrivial dependence on the friction: Both quantities are nonmonotonic and have a sharp maximum at the friction coefficient 0.1. We find that the mechanical response properties are closely related to the problem of force indeterminacy where similar nonmonotonic behavior was observed previously. We establish a direct connection between the critical force and the ensemble of static force networks.