Barchans are dunes of high mobility which have a crescent shape and propagate under conditions of unidirectional wind. However, sand dunes only appear above a critical size, which scales with the saturation distance of the sand flux [P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. 89, 264301 (2002); B. Andreotti, P. Claudin, and S. Douady, Eur. Phys. J. B 28, 321 (2002); G. Sauermann, K. Kroy, and H. J. Herrmann, Phys. Rev. E 64, 31305 (2001)]. It has been suggested by P. Hersen, S. Douady, and B. Andreotti, Phys. Rev. Lett. 89, 264301 (2002)] that this flux fetch distance is itself constant. Indeed, this could not explain the protosize of barchan dunes, which often occur in coastal areas of high litoral drift, and the scale of dunes on Mars. In the present work, we show from three-dimensional calculations of sand transport that the size and the shape of the minimal barchan dune depend on the wind friction speed and the sand flux on the area between dunes in a field. Our results explain the common appearance of barchans a few tens of centimeter high which are observed along coasts. Furthermore, we find that the rate at which grains enter saltation on Mars is one order of magnitude higher than on Earth, and is relevant to correctly obtain the minimal dune size on Mars.

Our interest goes to the different virial contributions to the equation of state of charged colloidal suspensions. Neglect of surface effects in the computation of the colloidal virial term leads to spurious and paradoxical results. This pitfall is one of the several facets of the danger of a naive implementation of the so called one component model, where the microionic degrees of freedom are integrated out to only keep in the description the mesoscopic (colloidal) degrees of freedom. On the other hand, due incorporation of wall induced forces dissolves the paradox brought forth in the naive approach, provides a consistent description, and confirms that for salt-free systems, the colloidal contribution to the pressure is dominated by the microionic one. Much emphasis is put on the no salt case but the situation with added electrolyte is also discussed.

We present a general theoretical framework to discuss mechanisms of morphogen transport and gradient formation in a cell layer. Trafficking events on the cellular scale lead to transport on larger scales. We discuss in particular the case of transcytosis where morphogens undergo repeated rounds of internalization into cells and recycling. Based on a description on the cellular scale, we derive effective nonlinear transport equations in one and two dimensions which are valid on larger scales. We derive analytic expressions for the concentration dependence of the effective diffusion coefficient and the effective degradation rate. We discuss the effects of a directional bias on morphogen transport and those of the coupling of the morphogen and receptor kinetics. Furthermore, we discuss general properties of cellular transport processes such as the robustness of gradients and relate our results to recent experiments on the morphogen Decapentaplegic (Dpp) that acts in the wing disk of the fruit fly Drosophila.

We numerically investigate the stability of one- and two-dimensional gap solitons for very long propagation distances both in self-focusing and in self-defocusing nonlinear photonic media. We demonstrate that the existence of stable solitons in the first gap requires much stronger lattices in a self-focusing than in a self-defocusing medium. Moreover, we present a one-dimensional linear stability analysis of the fundamental solitary mode in the first gap considering a self-focusing photorefractive nonlinearity.

Powdered materials of sizes ranging from nanometers to micrometers are widely used in materials science and are carefully selected to enhance the performance of a matrix. Fillers have been used in order to improve properties, such as mechanical, rheological, electrical, magnetic, thermal, etc., of the host material. Changes in the shape and size of the filler particles are known to affect and, in some cases, magnify such enhancement. This effect is usually associated with an increased probability of formation of a percolating cluster of filler particles in the matrix. In this series of papers, we will consider lattice models. Previous model calculations of percolation in polymeric systems generally did not take into account the possible difference between the size and shape of monomers and filler particles and usually neglected interactions or accounted for them in a crude fashion. In our approach, the original lattice is replaced by a recursive structure on which calculations are done exactly and interactions as well as size and shape disparities can be easily taken into account. Here, we introduce the recursive approach, describe how to derive the percolation threshold as a function of the various parameters of the problem, and apply the approach to the analysis of the effect of correlations among monodisperse particles on the percolation threshold of a system. In the second paper of the series, we tackle the issue of the effect of size and shape disparities of the particles on their percolation properties. In the last paper, we describe the effects due to the presence of a polymer matrix.

The preparation of many composites requires the intermixing of several macromolecular fluids along with the addition of rigid filler particles. These fillers are usually polydisperse and there is extensive experimental evidence that their size and shape profoundly affect the properties of the resulting material. In particular, it is generally found that the percolation threshold decreases as the size disparity between the different particles present in a system increases, and that the threshold decreases with increasing aspect ratio of the particles. Here, a recursive approach that we have recently introduced is applied to the study of the percolation of particles of different sizes and shapes, without the presence of a polymer matrix, on a lattice in various phases including metastable states. In our approach, the original lattice is replaced by a recursive structure on which calculations are done exactly and interactions as well as size and shape disparities are easily taken into account. In the previous paper of this series, we introduced the recursive approach and showed how correlations among particles of the same size can affect percolation. Before considering the complete system made of particles of various sizes and shapes embedded in a polymer matrix, in the third paper of the series, we describe here the properties of systems made of particles without any matrix. The approach appears to be extremely successful since it is able to capture most of the important features observed in experiments.

We use a recently developed lattice model of polymers to study the percolation of particles of different sizes and shapes in the presence of a polymer matrix. The polymer is modeled as an infinitely long chain to simplify the calculation but we make it more realistic by considering it semiflexible. We study the effects of the stiffness of the polymer, the size disparity of the filler particles, their aspect ratio, and the interactions between fillers and polymer on the percolation properties of the system. The lattice model is solved exactly on a recursive square Husimi lattice, which is an approximation for a square lattice. The solution represents an approximate solution for a square lattice. Our results are able to reproduce most of the experimental findings that have been observed in the literature. In particular, we observe how an increase in the size disparity of the filler particles dispersed in the matrix as well as an increase of their aspect ratio decreases the percolation threshold.

In order to understand how the performance of a liquid-crystal laser depends on the physical properties of the low molar mass nematic host, we have studied the energy threshold and slope efficiency of ten optically pumped liquid-crystal lasers based on different hosts. Specifically, this leads to a variation in the birefringence, the orientational order parameter, and the order parameter of the transition dipole moment of the dye. It is found that low threshold energies and high slope efficiencies correlate with high order parameters and large birefringences. To a first approximation this can be understood by considering analytical expressions for the threshold and slope efficiency, which are derived from the space-independent rate equations for a two-level system, in terms of the macroscopic liquid crystal properties.

Mechanical unfolding of polyproteins by force spectroscopy provides valuable insight into their free energy landscapes. Most experiments of the unfolding process have been fit to two-state and/or one dimensional models, with the details of the protein and its dynamics often subsumed into a zero-force unfolding rate and a distance $x_u^{1\mathrm{D}}$ to the transition state. We consider the entire phase space of a model protein under a constant force, and show that $x_u^{1\mathrm{D}}$ contains a sizeable contribution from exploring the full multidimensional energy landscape. This effect is greater for proteins with many degrees of freedom that are affected by force; and surprisingly, we predict that externally attached flexible linkers also contribute to the measured unfolding characteristics.

We describe the large-scale collective behavior of solutions of polar biofilaments and stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational currents. The large-scale properties of the system are described in terms of continuum equations for filament and motor densities, polarization, and alignment tensor obtained by coarse-graining the Smoluchovski equation. The possible homogeneous and inhomogeneous states of the systems are obtained as stable solutions of the dynamical equations and are characterized in terms of experimentally accessible parameters. We make contact with work by other authors and show that our model allows for an estimate of the various parameters in the hydrodynamic equations in terms of physical properties of the crosslinkers.

Measurements with an atomic force microscope (AFM) offer a direct way to probe elastic properties of lipid bilayer membranes locally: provided the underlying stress-strain relation is known, material parameters such as surface tension or bending rigidity may be deduced. In a recent experiment a pore-spanning membrane was poked with an AFM tip, yielding a linear behavior of the force-indentation curves. A theoretical model for this case is presented here which describes these curves in the framework of Helfrich theory. The linear behavior of the measurements is reproduced if one neglects the influence of adhesion between tip and membrane. Including it via an adhesion balance changes the situation significantly: force-distance curves cease to be linear, hysteresis and nonzero detachment forces can show up. The characteristics of this rich scenario are discussed in detail in this paper.

We perform a numerical study of the trajectories of spiral wave cores in excitable systems whose excitability is modulated in proportion to the integral of the activity in a sensory domain in the shape of an equilateral triangle. As a result of this domain shape having vertices opposite sides, unusual forms of lobed limit cycles occur, which are destroyed and then re-form as the domain size is varied. Some key results are also demonstrated experimentally using the light-sensitive Belousov-Zhabotinsky reaction. To characterize the observed behavior, we introduce the concept of express and stagnation zones, which are regions where the trajectory moves particularly rapidly or slowly. The location and strength of the zones far from the domain are accounted for by approximating the parts of the spiral wave crossing the domain by a series of plane waves.

Molecular dynamics simulations have been carried out to investigate the fluid wetting and flow in nanochannels whose surfaces are structured by an array of nanoscale triangular modules. We find that the surface nanostructures have a dual effect on the boundary slip and friction of the liquid nanoflow. On the one hand, the nanostructures can enhance the surface hydrophilicity for a hydrophilic liquid-solid interaction, and can increase the hydrophobicity for a hydrophobic interaction due to a nanoscale lotus effect. In particular, the nanostructured surface may show superhydrophobicity and lead to the large velocity slip of the liquid flow. On the other hand, simultaneously, the nanostructures distort the nanoscale streamlines of the liquid flow near the channel surfaces and block the nanoflow directly, which decreases the apparent slip length equivalently. The dual effect of the nanostructures on the surface wettability and the hydrodynamic disturbance results in a nonmonotonic dependence of the slip length on the nanostructure size. The simulations imply that the surface nanostructures can be applied to control the friction of liquid micro- and nanoflows.

The investigation of dust structure formed in glow discharge in an external longitudinal magnetic field with induction up to $400\mathrm{G}$ applied is presented in this work. The dust structure starts to rotate in the magnetic field. The angular-velocity magnitude is one to two orders larger than one in other discharge types. Its dependence on the magnetic field is nonmonotonic. The rotation direction inverses with an increase of the magnetic induction value up to a certain magnitude $B_0$. In close range of induction around $B_0$ and under certain conditions the rotation of the upper and lower parts of the structure in the opposite direction is observed. Rotation is caused by the ion-drag force. The inversion of rotation direction relates with the change of plasma flows in the area of their formation in stratum with the magnetic field applied. The effect of ion flows was investigated in two additional experiments on the observation of structure rotation onset and on gravity-driven probing of stratum. The angular-velocity unhomogeniety allowed us to investigate shearing and to observe melting of the dust crystal. The correlation functions approach showed the occurrence of structure transformation and its phase transition of the meltinglike type in the magnetic field.

We introduce a one-dimensional phenomenological model of a nonlocal medium featuring focusing cubic and defocusing quintic nonlocal optical nonlinearities. By means of numerical methods, we find families of solitons of two types, even-parity (fundamental) and dipole-mode (odd-parity) ones. Stability of the solitons is explored by means of computation of eigenvalues associated with modes of small perturbations, and tested in direct simulations. We find that the stability of the fundamental solitons strictly follows the Vakhitov-Kolokolov criterion, whereas the dipole solitons can be destabilized through a Hamiltonian-Hopf bifurcation. The solitons of both types may be stable in the nonlocal model with only quintic self-attractive nonlinearity, in contrast with the instability of all solitons in the local version of the quintic model.

We investigate two-dimensional (2D) states in Bose-Einstein condensates with self-attraction or self-repulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. The states trapped both in the central potential well and in remote circular troughs are studied. In the repulsive mode, a new soliton species is found, in the form of radial gap solitons. The latter solitons are completely stable if they carry zero vorticity $(l=0)$, while with $l\ne 0$ they develop a weak azimuthal modulation, which makes them rotating patterns, that persist indefinitely long. In addition, annular gap solitons may support stable azimuthal dark-soliton pairs on their crests. In remote troughs of the attractive model, stable localized states may assume a ringlike shape with weak azimuthal modulation, or shrink into solitons strongly localized in the azimuthal direction, which is explained in the framework of an averaged 1D equation with the cyclic azimuthal coordinate. Numerical simulations of the attractive model also reveal stable necklacelike patterns, built of several strongly localized peaks. Dynamics of strongly localized solitons circulating in the troughs is studied too. While the solitons with sufficiently small velocities are completely stable, fast solitons gradually decay, due to the leakage of matter into the adjacent trough, under the action of the centrifugal force. Investigation of head-on collisions between strongly localized solitons traveling in circular troughs shows that collisions between in-phase solitons in a common trough lead to collapse, while $\pi$-out-of-phase solitons bounce many times, but eventually merge into a single one, without collapsing. In-phase solitons colliding in adjacent circular troughs also tend to merge into a single soliton.

We present a method to compute harmonic vibrations that uses the structures and the forces in the structures that are obtained from a geometry optimization. It does not require any additional electronic structure calculations. The method generally takes only on the order of minutes on a regular PC, but it does not guarantee the calculation of all vibrations of a system. Tests on small adsorbates on a transition metal surface show, however, that the most relevant vibrations are obtained. An important part of the method is the inclusion of several checks to determine the reliability of its results, which gives also error estimates of the vibrational frequencies.

We study a parametrically modulated oscillator that has two stable states of vibration at half the modulation frequency ${\omega }_F$. Fluctuations of the oscillator lead to interstate switching. A comparatively weak additional field can strongly affect the switching rates because it changes the switching activation energies. The change is linear in the field amplitude. When the additional field frequency ${\omega }_d$ is ${\omega }_F∕2$, the field makes the populations of the vibrational states different, thus lifting the states symmetry. If ${\omega }_d$ differs from ${\omega }_F∕2$, the field modulates the state populations at the difference frequency, leading to fluctuation-mediated wave mixing. For an underdamped oscillator, the change of the activation energy displays characteristic resonant peaks as a function of frequency.

Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space-dependent friction and multiplicative noise and construct the corresponding Fokker-Planck equation, valid for short correlation time, with space-dependent diffusion coefficient to study the escape rate from a metastable state in the moderate- to large-damping regime. By considering the dynamics in a model cubic potential we analyze the results numerically which are in good agreement with theoretical predictions. It has been shown numerically that enhancement of the rate is possible by properly tuning the correlation time of the external noise.