We propose a minimal model for the emergence of a directed flow in autonomous Hamiltonian systems. It is shown that internal breaking of the spatiotemporal symmetries, via localized initial conditions, which are unbiased with respect to the transporting degree of freedom, and transient chaos conspire to form the physical mechanism for the occurrence of a current. Most importantly, after passage through the transient chaos, trajectories perform solely regular transporting motion so that the resulting current is of continual ballistic nature. This has to be distinguished from the features of transport reported previously for driven Hamiltonian systems with mixed phase space where transport is determined by intermittent behavior exhibiting power-law decay statistics of the duration of regular ballistic periods.

Recent experiments on a freely evolving dipolar vortex in a homogeneous shallow fluid layer have clearly shown the existence and evolution of complex three-dimensional (3D) flow structures. The present contribution focuses on the 3D structures of a dipolar vortex evolving in a stable shallow two-layer fluid. Experimentally, Stereoscopic Particle Image Velocimetry is used to measure instantaneously all three components of the velocity field in a horizontal plane and 3D numerical simulations provide the full 3D velocity and vorticity fields over the entire flow domain. Remarkably, the experimental results, supported by the numerical simulations, show to a large extent the same 3D structures and evolution as in the single-layer case. The numerical simulations indicate that the so-called frontal circulation in the two-layer fluid is due to deformations of the internal interface. The 3D flow structures will also affect the distribution of massless passive particles released at the free surface. With numerical studies it is shown that these passive particles tend to accumulate or deplete locally where the horizontal velocity field is not divergence-free. This is in contrast with pure two-dimensional incompressible flows where the divergence of the velocity field is zero by definition.

We study the contribution of electron-atom interaction to the equation of state for partially ionized hydrogen plasma using the cluster-virial expansion. We use the Beth-Uhlenbeck approach to calculate the second virial coefficient for the electron-atom (bound cluster) pair from the corresponding scattering phase shifts and binding energies. Experimental scattering cross-sections as well as phase shifts calculated on the basis of different pseudopotential models are used as an input for the Beth-Uhlenbeck formula. By including Pauli blocking and screening in the phase shift calculation, we generalize the cluster-virial expansion in order to cover also near solid density plasmas. We present results for the electron-atom contribution to the virial expansion and the corresponding equation of state, i.e. pressure, composition, and chemical potential as a function of density and temperature. These results are compared with semiempirical approaches to the thermodynamics of partially ionized plasmas. Avoiding any ill-founded input quantities, the Beth-Uhlenbeck second virial coefficient for the electron-atom interaction represents a benchmark for other, semiempirical approaches.

We report a new and efficient factorized algorithm for the determination of the adaptive compound mobility matrix $B$ in a stochastic quasi-Newton method (S-QN) that does not require additional potential evaluations. For one-dimensional and two-dimensional test systems, we previously showed that S-QN gives rise to efficient configurational space sampling with good thermodynamic consistency [C. D. Chau, G. J. A. Sevink, and J. G. E. M. Fraaije, J. Chem. Phys. 128, 244110 (2008)]. Potential applications of S-QN are quite ambitious, and include structure optimization, analysis of correlations and automated extraction of cooperative modes. However, the potential can only be fully exploited if the computational and memory requirements of the original algorithm are significantly reduced. In this paper, we consider a factorized mobility matrix $B=J{J}^T$ and focus on the nontrivial fundamentals of an efficient algorithm for updating the noise multiplier $J$. The new algorithm requires $\mathcal{O}\left(n^2\right)$ multiplications per time step instead of the $\mathcal{O}\left(n^3\right)$ multiplications in the original scheme due to Choleski decomposition. In a recursive form, the update scheme circumvents matrix storage and enables limited-memory implementation, in the spirit of the well-known limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method, allowing for a further reduction of the computational effort to $\mathcal{O}\left(n\right)$. We analyze in detail the performance of the factorized (FSU) and limited-memory (L-FSU) algorithms in terms of convergence and (multiscale) sampling, for an elementary but relevant system that involves multiple time and length scales. Finally, we use this analysis to formulate conditions for the simulation of the complex high-dimensional potential energy landscapes of interest.

This Brief Report shows that the Smoluchowski thermostat, a stochastic boundary condition used to mimic a diffusive gas-wall collision, produces the correct stationary nonequilibrium states. The stationary states are generated by placing an ideal gas coupled to a Smoluchowski thermostat in a constant external field. It is shown by simple numerical simulations that the resulting drift velocity is compatible with the definition of the gas particle mobility, satisfying the well-known fluctuation-dissipation theorem. As an interesting application, it is shown that species that are chemically identical but differ in surface momentum accommodation can be separated effectively in the Knudsen regime.

We analyze metastability associated with a discontinuous nonequilibrium phase transition in a stochastic lattice-gas realization of Schloegl’s second model for autocatalysis. This model realization involves spontaneous annihilation, autocatalytic creation, and diffusion of particles on a square lattice, where creation at empty sites requires an adjacent diagonal pair of particles. This model, also known as the quadratic contact process, exhibits discontinuous transition between a populated active state and a particle-free vacuum or “poisoned” state, as well as generic two-phase coexistence. The poisoned state exists for all particle annihilation rates $p>0$ and hop rates $h\ge 0$ and is an absorbing state in the sense of Markovian processes. The active or reactive steady state exists only for $p$ below a critical value, $p_{\text{e}}=p_{\text{e}}\left(h\right)$, but a metastable extension appears for a range of higher $p$ up to an effective upper spinodal point, $p_{\text{s}+}=p_{\text{s}+}\left(h\right)$ (i.e., $p_{\text{s}+}>p_{\text{e}}$). For selected $h$, we assess the location of $p_{\text{s}+}\left(h\right)$ by characterizing both the poisoning kinetics and the propagation of interfaces separating vacuum and active states as a function of $p$.

DNA-coated colloids are a popular model system for self-assembly through tunable interactions. The DNA-encoded linkages between particles theoretically allow for very high specificity, but generally no directionality or long-range interactions. We introduce a two-dimensional lattice model for particles of many different types with short-range isotropic interactions that are pairwise specific. For this class of models, of which the DNA-coated colloids are one example, we address the fundamental question whether it is possible to reliably design the interactions so that the ground state is unique and corresponds to a given crystal structure. First, we determine lower limits for the interaction range between particles, depending on the complexity of the desired pattern and the underlying lattice. Then, we introduce a proof-of-principle “recipe” for determining the pairwise interactions that exactly satisfies this minimum criterion, and we show that it is sufficient to uniquely determine the ground state for a large class of crystal structures. Finally, we verify these results using Monte Carlo simulations.

We describe experiments on drying of a hard-sphere colloidal suspension in confined geometry where a drop of the suspension is squeezed in between two circular transparent plates and allowed to dry. In this situation, the geometry controls the vapor removal rate and leads to a facilitated observation directly inside the drop. We monitor the drying kinetics of colloids of two sizes and several volume fractions; in most cases, the drying kinetics leads to the formation of a crust at the level of the meniscus which can be either crystalline or glassy, the transition between the two cases being triggered by the local deposition velocity, itself slaved to the evaporation rate. It yields a final dry state which is either polycrystalline or amorphous. The crust is also responsible for a shape instability of the quasi-two-dimensional drop shrinking upon evaporation but with a crust opposing mechanical and flow resistance, and possibly a partial adhesion on the substrate.

We present a developmental model of ocular dominance column formation that takes into account the existence of an array of intrinsically specified cytochrome oxidase blobs. We assume that there is some molecular substrate for the blobs early in development, which generates a spatially periodic modulation of experience-dependent plasticity. We determine the effects of such a modulation on a competitive Hebbian mechanism for the modification of the feedforward afferents from the left and right eyes. We show how alternating left and right eye dominated columns can develop, in which the blobs are aligned with the centers of the ocular dominance columns and receive a greater density of feedforward connections, thus becoming defined extrinsically. More generally, our results suggest that the presence of periodically distributed anatomical markers early in development could provide a mechanism for the alignment of cortical feature maps.

Zero acceleration points (ZAPs) and flow structures around them are studied in a direct numerical simulation of two-dimensional energy-cascading stationary homogeneous isotropic turbulence with an extended $k^{-5/3}$ energy spectrum. A well-defined classification of ZAPs in terms of the acceleration gradient tensor’s $\left(\nabla \mathbf{a}\right)$ invariants emerges naturally as a result of well-defined properties of and relations between these invariants at ZAPs. About half of all ZAPs are anti-ZAPs [with $\text{det}\left(\nabla \mathbf{a}\right)<0$] and the number of vortical and straining ZAPs [with $\text{det}\left(\nabla \mathbf{a}\right)>0$] is about the same. Vortical and straining ZAPs are swept by the local fluid velocity to a good statistical approximation whereas anti-ZAPs, which are present in every vortical and straining ZAP’s creation and destruction events, are not. The average lifetime of ZAPs seems to scale with the time scale of the smallest eddies in the turbulence, though ZAPs (in particular vortical ones) are able to survive up to a few integral time scales. Our ZAP classification can also be applied to extended flow regions and it turns out that vortical and straining regions are mediated by regions containing anti-ZAPs. A discussion of the length scales and sizes characterizing these regions and the distances between ZAPs is also given.

When a micron-sized water droplet impacts on a freely suspended soap film with speed $v_i$, there exists a critical impact velocity of penetration $v_C$. Droplets with $v_i<v_C$ merge and flow with the film after impacts, whereas droplets with $v_i>v_C$ tunnel through it. In all cases, the film remains intact despite the fact that the droplet radius $\left(R_0=26\mu \text{m}\right)$ is much greater than the film thickness $\left(0<h\lesssim 10\mu \text{m}\right)$. The critical velocity $v_C$ is measured as a function of $h$, and interestingly $v_C$ approaches an asymptotic value $v_{C0}\simeq 520\text{cm}/\text{s}$ in the limit $h\to 0$. This indicates that in addition to an inertial effect, a deformation or stretching energy of the film is required for penetration. Quantitatively, we found that this deformation energy corresponds to the creation of $\sim 14$ times of the cross-sectional area of the droplet $\left(14\pi R_0^2\right)$ or a critical Weber number ${\text{We}}_C\left(\equiv 2{\rho }_w{v}_{C0}^2{R}_0/\sigma \right)\simeq 44$, where ${\rho }_w$ and $\sigma$ are, respectively, the density and the surface tension of water.

We propose a general strategy for designing coupling functions in order to achieve a desired amplitude dynamics in coupled nonlinear oscillators. The target dynamics achieved by the proposed control schemes is a fixed-point motion at a desired amplitude level or a periodic motion at a desired frequency. The control schemes are illustrated with Rössler and Hindmarsh-Rose oscillators.

The distribution of a population throughout the physiological age of the individuals is very relevant information in population studies. It has been modeled by the Langevin and the Fokker-Planck equations. A major problem with these equations is that they allow the physiological age to move back in time. This paper proposes an Infinitesimally ratcheted random walk as a way to solve that problem. Two mathematical representations are proposed. One of them uses a nonlocal scalar field. The other one is local, but involves a multicomponent field of speed states. These two formulations are compared to each other and to the Fokker-Planck equation. The relevant properties are discussed. The dynamics of the mean and variance of the population age resulting from the two proposed formulations are obtained.

A dynamical analogy supported by five scale-free statistics (the Gutenberg-Richter distribution of event sizes, the distribution of interevent intervals, the Omori and inverse Omori laws, and the conditional waiting time until the next event) is shown to exist between two classes of seizures (“focal” in humans and generalized in animals) and earthquakes. Increments in excitatory interneuronal coupling in animals expose the system’s dependence on this parameter and its dynamical transmutability: moderate increases lead to power-law behavior of seizure energy and interevent times, while marked ones to scale-free (power-law) coextensive with characteristic scales and events. The coextensivity of power law and characteristic size regimes is predicted by models of coupled heterogeneous threshold oscillators of relaxation and underscores the role of coupling strength in shaping the dynamics of these systems.

We present an analysis of the anisotropic spectral energy distribution in incompressible magnetohydrodynamic turbulence permeated by a strong mean magnetic field. The turbulent flow is generated by high-resolution pseudospectral direct numerical simulations with large-scale isotropic forcing. Examining the radial energy distribution for various angles $\theta$ with respect to ${\mathbf{B}}_0$ reveals a specific structure which remains hidden when not taking axial symmetry with respect to $B_0$ into account. For each direction, starting at the forced large scales, the spectrum first exhibits an amplitude drop around a wave number $k_0$ which marks the start of a scaling range and goes on up to a dissipative wave number $k_d\left(\theta \right)$. The three-dimensional spectrum for $k\ge k_0$ is described by a single $\theta$-independent functional form $F\left(k/k_d\right)$, with the scaling law being the same in every direction. The previous properties still hold when increasing the mean field from $B_0=5$ up to $B_0=10b_{\text{rms}}$, as well as when passing from resistive to ideal flows. We conjecture that at fixed $B_0$ the direction-independent scaling regime is reached when increasing the Reynolds number above a threshold which raises with increasing $B_0$. Below that threshold critically balanced turbulence is expected.

We study a class of strongly nonlinear traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression. Until now the only traveling-wave solutions known for this class of systems were the single-hump solitary waves studied by Nesterenko in the continuum approximation limit. Instead, we directly study the discrete strongly nonlinear governing equations of motion of these media without resorting to continuum approximations or homogenization, which enables us to compute families of stable multihump traveling-wave solutions with arbitrary wavelengths. We develop systematic semianalytical approaches for computing different families of nonlinear traveling waves parametrized by spatial periodicity (wave number) and energy, and show that in a certain asymptotic limit, these wave families converge to the known single-hump solitary wave studied by Nesterenko. In addition, we demonstrate the existence of an additional class of stable strongly localized out-of-phase standing waves in perfectly homogeneous granular chains with no precompression or disorder. Until now such localized solutions were known to exist only in granular chains with strong precompression. Our findings indicate that homogeneous granular chains possess complex intrinsic nonlinear dynamics, including intrinsic nonlinear energy transfer and localization phenomena.

${\text{CoFe}}_2{\text{O}}_4$ nanoparticles are ferrimagnetic and $p\text{−}{\text{MgFe}}_2{\text{O}}_4$ nanoparticles are paramagnetic. Binary ferrofluids can be synthesized by mixing ${\text{CoFe}}_2{\text{O}}_4$ ferrofluids and $p\text{−}{\text{MgFe}}_2{\text{O}}_4$ fluids in such a way that the magnetic interaction of the ${\text{CoFe}}_2{\text{O}}_4$ particles is large enough to form field-induced chainlike aggregates. The field modulation of light transmission through films of ${\text{CoFe}}_2{\text{O}}_4\text{–}p\text{−}{\text{MgFe}}_2{\text{O}}_4$ binary ferrofluids with different values of applied magnetic field is compared with pure ${\text{CoFe}}_2{\text{O}}_4$ ferrofluids. The experimental results revealed that the light transmission coefficient of binary ferrofluids can be more intensely modulated by an external magnetic field than pure ${\text{CoFe}}_2{\text{O}}_4$ ferrofluids. These show that in the binary ferrofluids, the field-induced structure mainly arises from the ${\text{CoFe}}_2{\text{O}}_4$ nanoparticle system and the $p\text{−}{\text{MgFe}}_2{\text{O}}_4$ nanoparticles introduce a nonlinear modulation effect, even though the microstructure of $p\text{−}{\text{MgFe}}_2{\text{O}}_4$ fluids is not affected by an applied magnetic field. Using a model of magnetic bidispersal, the enhanced field modulation of the light transmission through binary ferrofluids is explained by the coupling of geometric shadowing effects from both the ${\text{CoFe}}_2{\text{O}}_4$ and $p\text{−}{\text{MgFe}}_2{\text{O}}_4$ particle systems.

The mean-square displacement (MSD) was measured by neutron scattering at various temperatures and pressures for a number of molecular glass-forming liquids. The MSD is invariant along the glass-transition line at the pressure studied, thus establishing an “intrinsic” Lindemann criterion for any given liquid. A one-to-one connection between the MSD’s temperature dependence and the liquid’s fragility is found when the MSD is evaluated on a time scale of $\sim 4\text{ns}$, but does not hold when the MSD is evaluated at shorter times. The findings are discussed in terms of the elastic model and the role of relaxations, and the correlations between slow and fast dynamics are addressed.

The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation functions in DDFT, and the lowest order approximation using scale analysis. The complete amplitude equation formalism for binary PFC is developed to describe the coupled dynamics of slowly varying complex amplitudes of structural profile, zeroth-mode average atomic density, and system concentration field. Effects of noise (corresponding to stochastic amplitude equations) and species-dependent atomic mobilities are also incorporated in this formalism. Results of a sample application to the study of surface segregation and interface intermixing in alloy heterostructures and strained layer growth are presented, showing the effects of different atomic sizes and mobilities of alloy components. A phenomenon of composition overshooting at the interface is found, which can be connected to the surface segregation and enrichment of one of the atomic components observed in recent experiments of alloying heterostructures.

The electrical polarizability $\alpha \left(\omega \right)$ of a biological cell in the presence of a layer of localized, partially bounded, charges at the two cell membrane interfaces has been calculated within the dipolar approximation. The cell is modeled in the light of the single-shell spherical model, but the results can be easily extended to shelled particles of more complex shape. Under the influence of an external electric field, the presence of these charge distributions, which added to the ones originated by the mismatch of the complex dielectric constants of the different media, produces a further dielectric relaxation, besides the one due to the usual Maxwell-Wagner effect. We explicitly find the contribution that must be added to the electrical polarizability $\alpha \left(\omega \right)$ in order to take into account the surface electrical currents originated by the localized charges free to move on the membrane surfaces. Our results, maintaining their validity whatsoever the values of the surface charge distributions and, moreover, whatsoever the values of the membrane conductivity are, extend the applicability of the model recently proposed by Prodan et al. [Biophys. J. 95, 4174 (2008)], who developed an analytical solution which offers reliable results only in the case of weak surface charge distributions and, moreover, for negligible small values of the membrane conductivity. Our approach, removing these constrains, represents a valuable improvement toward more realistic biological cell models and widens the use of dielectric relaxation methods to a larger class of biological systems.