A recent experiment [Boncheva et al. Proc. Natl. Acad. Sci. U.S.A. 102, 3924 (2005)] introduced the possibility of initiating the self-assembly of a three-dimensional structure from a flat elastic sheet. The ultimate utility of this method for assembly depends on whether it leads to incorrect, metastable structures. Here we examine how the number of metastable states depends on the sheet shape and thickness. Using simulations and theory, we identify out-of-plane buckling as the key event leading to metastability. The buckling strain that arises from joining edges of a planar sheet can be estimated using the theory of dislocations in elastic media. The number of metastable states increases rapidly with increasing variability in the boundary curvature and decreasing sheet thickness.

The explicit solution to the spectral problem of quantum graphs found recently by Dabaghian and Blümel [Phys. Rev. E 68, 055201(R) (2003); 70, 046206 (2004); JETP Lett. 77, 530 (2003)] is used to produce an exact periodic orbit theory description for the probability distributions of spectral statistics, including the distribution for the nearest neighbor separations $s_n=k_n-k_{n-1}$, and the distribution of the spectral oscillations around the average, $\delta k_n=k_n-{\overline{k}}_n$.

Multicriticality of the gonihedric model in $2+1$ dimensions is investigated numerically. The gonihedric model is a fully frustrated Ising magnet with finely tuned plaquette-type (four-body and plaquette-diagonal) interactions, which cancel out the domain-wall surface tension. Because the quantum-mechanical fluctuation along the imaginary-time direction is simply ferromagnetic, the criticality of the $\left(2+1\right)$-dimensional gonihedric model should be an anisotropic one; that is, the respective critical indices of real-space $(\perp )$ and imaginary-time $(\Vert )$ sectors do not coincide. Extending the parameter space to control the domain-wall surface tension, we analyze the criticality in terms of the crossover (multicritical) scaling theory. By means of the numerical diagonalization for the clusters with $N\le 28$ spins, we obtained the correlation-length critical indices $\left({\nu }_{\perp },{\nu }_{\Vert }\right)=\left[0.45\left(10\right),1.04\left(27\right)\right]$, and the crossover exponent $\varphi =0.7\left(2\right)$. Our results are comparable to $\left({\nu }_{\perp },{\nu }_{\Vert }\right)=\left(0.482,1.230\right)$, and $\varphi =0.688$ obtained by Diehl and Shpot for the $\left(d,m\right)=\left(3,2\right)$ Lifshitz point with the $ϵ$-expansion method up to $O\left({ϵ}^2\right)$.

From event-driven simulations of a gravity-driven channel flow of inelastic hard disks, we show that the velocity distribution function remains close to a Gaussian for a wide range densities (even when the Knudsen number is of order 1) if the walls are smooth and the particle collisions are nearly elastic. For dense flows, a transition from a Gaussian to a power-law distribution for the high-velocity tails occurs with increasing dissipation in the center of the channel, irrespective of wall roughness. For a rough wall, the near-wall distribution functions are distinctly different from those in the bulk, even in the quasielastic limit.

By exposing two-dimensional crystals to tunable substrate potentials one can selectively manipulate the crystal’s phonon band structure. We explore this idea and study the overdamped lattice dynamics of colloidal crystals subject to commensurate substrate potentials with sinusoidal modulations in up to two spatial directions. We furthermore show that the mean-square displacement of colloids in the crystal can be understood as the Laplace transform of the phonon spectrum and discuss how our results can best be verified experimentally.

A number of recent experiments suggest that, at a given wetting speed, the dynamic contact angle formed by an advancing liquid-gas interface with a solid substrate depends on the flow field and geometry near the moving contact line. In the present work, this effect is investigated in the framework of an earlier developed theory that was based on the fact that dynamic wetting is, by its very name, a process of formation of a new liquid-solid interface (newly “wetted” solid surface) and hence should be considered not as a singular problem but as a particular case from a general class of flows with forming or/and disappearing interfaces. The results demonstrate that, in the flow configuration of curtain coating, where a liquid sheet (“curtain”) impinges onto a moving solid substrate, the actual dynamic contact angle indeed depends not only on the wetting speed and material constants of the contacting media, as in the so-called slip models, but also on the inlet velocity of the curtain, its height, and the angle between the falling curtain and the solid surface. In other words, for the same wetting speed the dynamic contact angle can be varied by manipulating the flow field and geometry near the moving contact line. The obtained results have important experimental implications: given that the dynamic contact angle is determined by the values of the surface tensions at the contact line and hence depends on the distributions of the surface parameters along the interfaces, which can be influenced by the flow field, one can use the overall flow conditions and the contact angle as a macroscopic multiparametric signal-response pair that probes the dynamics of the liquid-solid interface. This approach would allow one to investigate experimentally such properties of the interface as, for example, its equation of state and the rheological properties involved in the interface’s response to an external torque, and would help to measure its parameters, such as the coefficient of sliding friction, the surface-tension relaxation time, and so on.

We investigate the unwinding process of pure and racemized mixtures of (1-methylheptyloxycarbonyl)phenyl-$4^{\prime }$-carboctyloxy-biphenyl-4-carboxylate (MHPOOCBC) in homeotropic cells by studying (i) the optical texture under crossed polarizers and (ii) the tilted conoscopy as a function of the electric field for different temperatures. The tilted conoscopy yields biaxiality and the tilt angle for values of the latter up to 45°. We find that the unwinding process depends on the optical purity of the sample and the temperature. A cell with pure MHPOOCBC surprisingly exhibits a large positive biaxiality in the initial stages of the unwinding process. The magnitude of the positive biaxiality decreases with a decrease in the enantiomeric excess (EE) of the compound and eventually it becomes negative for a material having a low EE value. The negative biaxiality observed in a mixture with a low EE value is normal and can be explained by a double sine-Gordon equation proposed by Meyer. Microscopic observations show that the special unwinding behavior (positive biaxiality) is related to the helical fractures, that is, to the existence of discretely coiled helical structures. We show that these helical fractures arise from the existence of a narrow energy well in the synclinic position. This implies that the elastic constant near the synclinic position is significantly larger than in other positions. By adopting a semiempirical equation for the interlayer interactions which replaces the conventional equation, we successfully simulate the various unwinding behaviors. We reasonably conclude that the special interlayer interaction is due to the steric interactions between the two adjacent surfaces formed by somewhat tilted terminal parts of the molecules.

We study the hierarchical structuring of islands of stable periodic oscillations inside chaotic regions in phase diagrams of single-mode semiconductor lasers with optical injection. Phase diagrams display remarkable accumulation horizons: boundaries formed by the accumulation of infinite cascades of self-similar islands of periodic solutions of ever-increasing period. Each cascade follows a specific period-adding route. The riddling of chaotic laser phases by such networks of periodic solutions may compromise applications operating with chaotic signals such as, e.g., secure communications.

Estimating the Jacobian matrix of a nonlinear dynamical system through observed time-series data is one of the important steps in predicting future states of the time series. The Jacobian matrix is estimated using local information about divergences of nearby trajectories. Although the basic algorithm for estimating the Jacobian matrix generally works well, it often fails for short or noisy data series. In this paper, we proposed a scheme to effectively use near-neighbor information for more accurate estimation of the Jacobian matrix using the bootstrap resampling method. Then, to confirm the validity of the proposed method, we applied it to a mathematical model and several real time series. As a result, we confirmed that the proposed method greatly improves nonlinear predictability, not only for noise-corrupted mathematical models but also for real time series.

We analyze theoretically the polarization dynamics in unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs). The master VCSEL is subject to an isotropic optical feedback. The slave VCSEL is subject to an orthogonal optical injection from the master VCSEL, i.e., only the linearly polarized mode orthogonal to the dominant linearly polarized mode of the free-running slave VCSEL is injected into the slave VCSEL. This laser configuration may lead the slave VCSEL polarization to switch to that of the injected master laser field. The injected power required for polarization switching depends on the frequency detuning. We identify in the plane of the injection parameters two regions of enhanced synchronization between the injected LP mode and the corresponding slave LP mode. In the so-called region II the slave VCSEL exhibits anticorrelated dynamics in its two LP modes while in the so-called region I the slave VCSEL exhibits dynamics in only one LP mode, which corresponds to the polarization of the injected field. The two regions exhibit different synchronization properties in both the LP mode dynamics and total intensity dynamics. We furthermore analyze the dependency of the synchronization quality on the parameter mismatch between master and slave VCSELs and on the polarization switching properties of each VCSEL.

We have discovered that hydraulic jumps corresponding to obliquely inclined circular liquid jets, under certain conditions of impingement, confer a series of interesting flow patterns (including jumps with corners). These patterns are markedly different from the regular elliptical (or oblate) shaped jump profiles that are commonly observed with higher angles of jet inclination. These patterns are attributed to the changes in the spreading flow profile due to “jet-jump interaction” at relatively lower jet inclination angles. The irregular shaped jump profiles, close to the critical angle of jet inclination, are mathematically characterized by introducing the concept of an equivalent jump radius. These theoretical predictions match excellently with the experimental findings. A phenomenological explanation is also provided by drawing analogies from shock-wave interactions in compressible fluid mechanics and from twin-jet interaction mechanisms.

We describe a method for the development of the optimal spatial distributions of the porosity $\varphi$ and permeability $k$ of a large-scale porous medium. The optimal distributions are constrained by static and dynamic data. The static data that we utilize are limited data for $\varphi$ and $k$, which the method honors in the optimal model and utilizes their correlation functions in the optimization process. The dynamic data include the first-arrival (FA) times, at a number of receivers, of seismic waves that have propagated in the porous medium, and the time-dependent production rates of a fluid that flows in the medium. The method combines the simulated-annealing method with a simulator that solves numerically the three-dimensional (3D) acoustic wave equation and computes the FA times, and a second simulator that solves the 3D governing equation for the fluid’s pressure as a function of time. To our knowledge, this is the first time that an optimization method has been developed to determine simultaneously the global minima of two distinct total energy functions. As a stringent test of the method’s accuracy, we solve for flow of two immiscible fluids in the same porous medium, without using any data for the two-phase flow problem in the optimization process. We show that the optimal model, in addition to honoring the data, also yields accurate spatial distributions of $\varphi$ and $k$, as well as providing accurate quantitative predictions for the single- and two-phase flow problems. The efficiency of the computations is discussed in detail.

We derive Ewald sum formulas for potential energy and force for a system of point charges interacting with an arbitrary, long-range central potential. The system is made neutral by a uniform background of opposite charge interacting with the same potential. These formulas can be readily used in computer numerical simulations of model physical systems. In particular, expressions for the potential energy and the force have been obtained in both two and three dimensions for Coulomb and other power-law potentials, Yukawa systems, and for an electronic bilayer. We discuss numerical results and their accuracy for various systems and, based on our analysis, suggest values to be used for the parameters that appear in the Ewald sums.

We find three distinct phases; a tubular phase, a planar phase, and the spherical phase, in a triangulated fluid surface model. It is also found that these phases are separated by discontinuous transitions. The fluid surface model is investigated within the framework of the conventional curvature model by using the canonical Monte Carlo simulations with dynamical triangulations. The mechanical strength of the surface is given only by skeletons, and no two-dimensional bending energy is assumed in the Hamiltonian. The skeletons are composed of elastic linear chains and rigid junctions and form a compartmentalized structure on the surface, and for this reason the vertices of triangles can diffuse freely only inside the compartments. As a consequence, an inhomogeneous structure is introduced in the model; the surface strength inside the compartments is different from the surface strength on the compartments. However, the rotational symmetry is not influenced by the elastic skeletons; there is no specific direction on the surface. In addition to the three phases mentioned above, a collapsed phase is expected to exist in the low bending rigidity regime that was not studied here. The inhomogeneous structure and the fluidity of vertices are considered to be the origin of such a variety of phases.

In ${\mathrm{Al}}_2{\mathrm{O}}_3$ suspensions, depending on the experimental conditions, very different microstructures can be found, comprising fluidlike suspensions, a repulsive structure, and a clustered microstructure. For technical processing in ceramics, the knowledge of the microstructure is of importance, since it essentially determines the stability of a workpiece to be produced. To enlighten this topic, we investigate these suspensions under shear by means of simulations. We observe cluster formation on two different length scales: the distance of nearest neighbors and on the length scale of the system size. We find that the clustering behavior does not depend on the length scale of observation. If interparticle interactions are not attractive the particles form layers in the shear flow. The results are summarized in a stability diagram.

We have studied the nucleation kinetics of charged colloidal model systems under salt free conditions crystallizing in bcc structure covering a wide range of particle number densities $18\mathrm{\mu }{\mathrm{m}}^{-3}\le n\le 66.3\mathrm{\mu }{\mathrm{m}}^{-3}$. We employed direct video-microscopic observation of individual nucleation events to obtain time resolved nucleation rate densities. Polarization microscopy and static light scattering on the resulting solids in combination with Avrami theory is used to determine the steady state nucleation rate at high undercoolings. The final nucleation rate densities $J$ from different methods are observed to be consistent with each other. By increasing the difference in the chemical potential between melt and crystal $\mathrm{\Delta }\mathrm{\mu }$ about one order of magnitude $J$ increases from ${10}^9{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$ to ${10}^{17}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$ over approximately seven orders of magnitude. The data can be well analyzed and interpreted using classical nucleation theory (CNT) leading to a linearly increasing melt-crystal surface tension. Surprisingly, the reduced surface tension is about one order of magnitude larger compared to other system (metals; hard sphere colloids). The critical radius of the crystal nuclei is decreasing down to a very small value of 1.5 coordination shells. The determined kinetic prefactors are up to 10 orders of magnitude smaller than the prefactor calculated by CNT.

We study a phenomenological model in which the simulated packing of hard, attractive spheres on a prolate spheroid surface with convexity constraints produces structures identical to those of prolate virus capsid structures. Our simulation approach combines the traditional Monte Carlo method with a modified method of random sampling on an ellipsoidal surface and a convex hull searching algorithm. Using this approach we identify the minimum physical requirements for nonicosahedral, elongated virus capsids, such as two aberrant flock house virus particles and the prolate prohead of bacteriophage $\varphi 29$, and discuss the implication of our simulation results in the context of recent experimental findings. Our predicted structures may also be experimentally realized by the evaporation-driven assembly of colloidal spheres under appropriate conditions.

The azimuthal anchoring energy of the nematic liquid crystal 4-$n$-pentyl-$4^{\prime }$-cyanobiphenyl (5CB) on a uv-aligned polyimide substrate with in-plane order parameter $S^{\prime }=0.2$ is measured. The measurements are performed at temperature $T=24°\mathrm{C}$ using simultaneously a high accuracy reflectometric method and a high accuracy transmitted light method. With both the methods, we observe an apparent surface director rotation opposite to the orienting torque that would correspond to a negative extrapolation length. It is shown that this unusual behavior is due to the relatively high birefringence of the uv-aligned polyimide layers. Taking into account for this birefringence, we find a small but positive extrapolation length. The experimental results are interpreted in terms of a simple mesoscopic model where the nematic molecules are assumed to be rigidly attached on the polymer surface and the measured extrapolation length is entirely due to the order parameter variation in a thin interfacial layer where the nematic order parameter passes from the surface value to the bulk value within a few nematic correlation lengths. Assuming the surface order parameter is $S_0=0.37$, the correlation length of the nematic liquid crystal is estimated to be ${\xi }_c^{\prime }=2.4\pm 1\mathrm{nm}$. The corresponding thermodynamic extrapolation length is $d_e=2.8\pm 1.2\mathrm{nm}$ that corresponds to a very strong azimuthal anchoring.

In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten–type functional response and reaction diffusion. We obtain the conditions of Hopf, Turing, and wave bifurcation in a spatial domain. Furthermore, we present a theoretical analysis of evolutionary processes that involves organisms distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that the typical dynamics of population density variation is the formation of isolated groups, i.e., stripelike or spotted or coexistence of both. Our study shows that the spatially extended model has not only more complex dynamic patterns in the space, but also chaos and spiral waves. It may help us better understand the dynamics of an aquatic community in a real marine environment.