This paper deals with the computation of periodic orbits of dynamical systems up to any arbitrary precision. These very high requirements are useful, for example, in the studies of complex pole location in many physical systems. The algorithm is based on an optimized shooting method combined with a numerical ordinary differential equation (ODE) solver, tides, that uses a Taylor-series method. Nowadays, this methodology is the only one capable of reaching precision up to thousands of digits for ODEs. The method is shown to be quadratically convergent. Some numerical tests for the paradigmatic Lorenz model and the Hénon-Heiles Hamiltonian are presented, giving periodic orbits up to 1000 digits.

We study the single file diffusion of a cyclic chain of particles that cannot cross each other, in a thermal bath, with long-ranged interactions and arbitrary damping. We present simulations that exhibit new behaviors specifically associated with systems of small numbers of particles and with small damping. In order to understand those results, we present an original analysis based on the decomposition of the particles’ motion in the normal modes of the chain. Our model explains all dynamic regimes observed in our simulations and provides convincing estimates of the crossover times between those regimes.

We investigate the ion distribution and overcharging at charged interfaces with dielectric inhomogeneities in the presence of asymmetric electrolytes containing polyvalent and monovalent ions. We formulate an effective “dressed counterion” approach by integrating out the monovalent salt degrees of freedom and show that it agrees with results of explicit Monte Carlo simulations. We then apply the dressed counterion approach within the framework of the generalized strong-coupling theory, valid for polyvalent ions at low concentrations, which enables an analytical description for salt effects as well as dielectric inhomogeneities in the limit of strong Coulomb interactions. Limitations and applicability of this theory are examined by comparing the results with simulations.

We study the equilibrium textures of molecular orientation inside cylindrical fibers made of coaxial layers of bent-core smectics. We propose a free-energy model taking into account surface-like and bulk contributions—including layer-compression and electrostatic terms among others— with constant values of the material parameters. We follow the usual variational procedure of minimization of the free energy with respect to the tilt-angle profile $\theta (r)$ and obtain an Euler-Lagrange equation and its boundary condition. We solve the variational equations for the equilibrium configurations using a boundary-layer approximation and find multiple solutions. Since the equilibrium tilt profiles are found to be radially inhomogeneous, we select those with minimum distortions in order to find the lowest free-energy state. We minimize further the free energy of the system with respect to the fiber radius and find wider intervals of stability than those previously reported, depending on the balance of the material’s spontaneous polarization, elastic and electric divergence-of-polarization constants, and surface-tension coefficients. The bulk and surface-layer structures thus found could be used to calculate the allowed modes of propagation of electromagnetic waves inside the fiber.

Vesicle behavior under unbounded axial Poiseuille flow is studied analytically. Our study reveals subtle features of the dynamics. It is established that there exists a stable off-centerline steady-state solution for low enough flow strength. This solution appears as a symmetry-breaking bifurcation upon lowering the flow strength and includes slipper shapes, which are characteristic of red blood cells in the microvasculature. A stable axisymmetric solution exists for any flow strength provided the excess area is small enough. It is shown that the mechanism of the symmetry breaking depends on the geometry of the flow: The bifurcation is subcritical in axial Poiseuille flow and supercritical in planar flow.

This study explores a method to characterize the temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the time in parts of its phase space away from the synchronization state. Therefore characteristics of dynamics near this state (such as its stability properties and Lyapunov exponents or distributions of the durations of synchronized episodes) do not describe the system’s dynamics for most of the time. We consider an approach to characterize the system dynamics in this case by exploring the relationship between the phases on each cycle of oscillations. If some overall level of phase locking is present, one can quantify when and for how long phase locking is lost, and how the system returns back to the phase-locked state. We consider several examples to illustrate this approach: coupled skewed tent maps, the stability of which can be evaluated analytically; coupled Rössler and Lorenz oscillators, undergoing through different intermittency types on the way to phase synchronization; and a more complex example of coupled neurons. We show that the obtained measures can describe the differences in the dynamics and temporal structure of synchronization and desynchronization events for the systems with a similar overall level of phase locking and similar stability of the synchronized state.

It is shown that the solutions of inviscid hydrodynamical equations with suppression of all spatial Fourier modes having wave numbers in excess of a threshold $K_{\mathrm{G}}$ exhibit unexpected features. The study is carried out for both the one-dimensional Burgers equation and the two-dimensional incompressible Euler equation. For large $K_{\mathrm{G}}$ and smooth initial conditions, the first symptom of truncation, a localized short-wavelength oscillation which we call a “tyger,” is caused by a resonant interaction between fluid particle motion and truncation waves generated by small-scale features (shocks, layers with strong vorticity gradients, etc.). These tygers appear when complex-space singularities come within one Galerkin wavelength ${\lambda }_{\mathrm{G}}=2\pi /K_{\mathrm{G}}$ from the real domain and typically arise far away from preexisting small-scale structures at locations whose velocities match that of such structures. Tygers are weak and strongly localized at first—in the Burgers case at the time of appearance of the first shock their amplitudes and widths are proportional to ${K_{\mathrm{G}}}^{-2/3}$ and ${K_{\mathrm{G}}}^{-1/3}$, respectively—but grow and eventually invade the whole flow. They are thus the first manifestations of the thermalization predicted by T. D. Lee [Q. J. Appl. Math. 10, 69 (1952)]. The sudden dissipative anomaly—the presence of a finite dissipation in the limit of vanishing viscosity after a finite time $t_{\star }$—which is well known for the Burgers equation and sometimes conjectured for the three-dimensional Euler equation, has as counterpart, in the truncated case, the ability of tygers to store a finite amount of energy in the limit $K_{\mathrm{G}}\to \infty$. This leads to Reynolds stresses acting on scales larger than the Galerkin wavelength and thus prevents the flow from converging to the inviscid-limit solution. There are indications that it may eventually be possible to purge the tygers and thereby to recover the correct inviscid-limit behavior.

Using numerical simulations, we perform an extensive finite-size analysis of the transverse diffusion coefficient in a sheared 2D amorphous solid over a broad range of strain rates at temperatures up to the supercooled liquid regime. We thus obtain direct qualitative evidence for the persistence of correlations between elementary plastic events up to the vicinity of the glass transition temperature $T_g$. A quantitative analysis of the data, combined with a previous study of the $T$ and $\stackrel{·}{\gamma }$ dependence of the macroscopic stress [Phys. Rev. Lett. 105, 266001 (2010)], leads us to conclude that the average avalanche size remains essentially unaffected by temperature up to $T~0.75T_g$.

In this work we explore the effects of human mobility on the dispersion of a vector borne disease. We combine an already presented stochastic model for dengue with a simple representation of the daily motion of humans on a schematic city of $20\times 20$ blocks with 100 inhabitants in each block. The pattern of motion of the individuals is described in terms of complex networks in which links connect different blocks and the link length distribution is in accordance with recent findings on human mobility. It is shown that human mobility can turn out to be the main driving force of the disease dispersal.

We explore the Brownian dynamics in the quantum regime (by investigating the quantum Langevin and Smoluchowski equations) in terms of an effective time-independent Hamiltonian in the presence of a rapidly oscillating field. We achieve this by systematically expanding the time-dependent system-reservoir Hamiltonian in the inverse of driving frequency with a systematic time-scale separation and invoking a quantum gauge transformation within the framework of Floquet theorem.

We investigate a hard-square lattice gas on the square lattice by means of transfer-matrix and Monte Carlo methods. The size of the hard squares is equal to two lattice constants, so the simultaneous occupation of nearest-neighbor sites as well as of next-to-nearest-neighbor sites is excluded. Near saturation of the particle density, this system is known to undergo a phase transition to one out of four partially ordered phases. We find that this transition displays strong finite-size corrections to scaling and that the correlation functions deviate from isotropy to rather large distances. In contrast with an earlier study, we find that the critical temperature exponent of the transition is not Ising-like.

We have explored the role of dissipation in the scattered intensity and spectrum of resonance fluorescence from an excited two-level system in a spin bath. It has been shown that depending on the field strength a crossover temperature sets up a boundary between the coherent and incoherent intensity regimes, and at low field the scattered intensity may be coherent even at high temperature. We demonstrate the formation of a thermally induced Mollow triplet in the low-field regime.

We simultaneously measure the flow rate and the normal force on the base, near the outlet, during the discharge through an orifice of a dense packing of monosized disks driven by a conveyor belt. We find that the normal force on the base decreases even when a constant flow rate is measured. In addition, we show, by changing the mass of the disks, that pressure can be changed while the flow rate remains constant. Conversely, we are able, by changing the belt velocity, to set different flow rates for the same pressure. The experiment confirms that, contrary to what has been implicitly assumed in numerous works, the flow rate through an aperture is not controlled by the pressure in the outlet region.

There are many physical situations where particles experience external fields or are in a nonisothermal environment. Monte Carlo (MC) simulations can be useful to understand such experimental systems at steady state. Within this context, we formulate a general framework to study these systems via inhomogeneous MC simulations incorporating spatially varying temperature and gravitational fields. Using this approach we study granular materials consisting of hard spheres in an external field with either uniform or nonuniform temperature. We present comprehensive results from our MC simulations and compare these with theoretical results based on the Carnahan-Starling equation of state.

There are various arguments and models connecting the characteristic length associated with the boson peak vibrations ξ to the length scale of dynamical heterogeneity $L_{\mathrm{het}}$. ξ is usually defined as the ratio of the transverse sound velocity to the boson peak frequency. Here we present pressure, temperature, and molecular weight dependencies of ξ, estimated using light scattering, in a few molecular and polymeric glass formers. These dependencies are compared with respective dependencies of the activation volume Δ$V^{\mathrm{\#}}$ in the same materials. Good agreement is found for the pressure and molecular weight dependencies of ξ and Δ$V^{\mathrm{\#}}$ measured at the glass transition temperature $T_g$. These results provide more evidence for a possible relationship between the sensitivity of structural relaxation to density (activation volume) and the heterogeneity volume. However, contrary to the expectations for $L_{\mathrm{het}}$, ξ does not decrease with temperature above $T_g$ in most of the studied materials. The temperature dependence of ξ is compared to that of $L_{\mathrm{het}}$ in glycerol and orthoterphenyl (OTP) estimated from literature data. The analysis shows a clear difference in the behavior of ξ($T$) and Δ$V^{\mathrm{\#}}$($T$) at temperatures above $T_g$, although Δ$V^{\mathrm{\#}}$($T$)${}^{1/3}$ and $L_{\mathrm{het}}$($T$) have similar temperature dependence. Possible reasons for the observed difference are discussed.

We study random sequential adsorption (RSA) of coupled three-circle objects (consisting of two circular discs of radius $r_2$ touching the central one of radius $r_1$ making an angle $\theta$) on a two-dimensional continuum substrate. For all the objects corresponding to various values of radius ratios $r_2/r_1$ and angles $\theta$, approach of instantaneous coverage $\Theta (t)$ to the jammed state coverage $\Theta (\infty )$, is found to obey a power law $\Theta (\infty )-\Theta (t)~t^{-p}$, as expected based on general arguments. However, the observed values of exponent $p$ and jammed state coverage $\Theta (\infty )$ are found to vary with $r_2/r_1$ and $\theta$. The interplay between the degree of nonconvexity $\left|\delta \right|$ and packing efficiency $\eta$ of the object governs the saturation coverage $\Theta (\infty )$.

We reexamined the isotropic-nematic (Iso-N) phase transitions of 4-$n$-heptyl cyanobiphenyl (7CB) embedded in aerosils of silica nanoparticle dispersions using highly sensitive differential scanning calorimetry (HS-DSC), polarizing optical microscopy (POM), and retardation measurements. We found a simple and very profound relationship between the calorimetric and optical measurements; in addition to double DSC peaks, which have been observed previously, a two-step change of the retardation was clearly observed by varying temperature. From our analysis, there is no doubt that the Iso-N liquid-crystal phase transition certainly occurs in two steps, i.e., the bulk transition takes place at first and then the surface transition takes place upon cooling. We should note that the surface transition takes place below the bulk transition temperature, the opposite of what was recently observed in a polymer-dispersed liquid-crystal system.

Despite numerous attempts, understanding the thermal denaturation of DNA is still a challenge due to the lack of structural data on the transition since standard experimental approaches to DNA melting are made in solution and do not provide spatial information. We report a measurement using neutron scattering from oriented DNA fibers to determine the size of the regions that stay in the double-helix conformation as the melting temperature is approached from below. A Bragg peak from the B form of DNA is observed as a function of temperature and its width and integrated intensity are measured. These results, complemented by a differential calorimetry study of the melting of B-DNA fibers as well as electrophoresis and optical observation data, are analyzed in terms of a one-dimensional mesoscopic model of DNA.

The lateral migration of platelets in a microchannel is studied numerically where the hydrodynamic interactions between red cells, platelets, and vessel walls are resolved by the Stokes flow boundary integral equations. The simulations provide a clear physical description of the expulsion of the platelets by the velocity fluctuations in the core cellular flow toward the cell-depleted layer near the wall. The lateral migration is shown to be diffusional, and we further demonstrate, in agreement with previous experiments, that the diffusivity scales sublinearly with the shear rate if the relevant capillary number, $\mathrm{Ca}<1$, as a result of its intrinsic dependence on the deformation of red cells.

An important step in unveiling the relation between network structure and dynamics defined on networks is to detect communities, and numerous methods have been developed separately to identify community structure in different classes of networks, such as unipartite networks, bipartite networks, and directed networks. Here, we show that the finding of communities in such networks can be unified in a general framework—detection of community structure in bipartite networks. Moreover, we propose an evolutionary method for efficiently identifying communities in bipartite networks. To this end, we show that both unipartite and directed networks can be represented as bipartite networks, and their modularity is completely consistent with that for bipartite networks, the detection of modular structure on which can be reformulated as modularity maximization. To optimize the bipartite modularity, we develop a modified adaptive genetic algorithm (MAGA), which is shown to be especially efficient for community structure detection. The high efficiency of the MAGA is based on the following three improvements we make. First, we introduce a different measure for the informativeness of a locus instead of the standard deviation, which can exactly determine which loci mutate. This measure is the bias between the distribution of a locus over the current population and the uniform distribution of the locus, i.e., the Kullback-Leibler divergence between them. Second, we develop a reassignment technique for differentiating the informative state a locus has attained from the random state in the initial phase. Third, we present a modified mutation rule which by incorporating related operations can guarantee the convergence of the MAGA to the global optimum and can speed up the convergence process. Experimental results show that the MAGA outperforms existing methods in terms of modularity for both bipartite and unipartite networks.