The translocation of a short DNA fragment through a nanopore is addressed when the perforated membrane contains an embedded electrode. Accurate numerical solutions of the coupled Poisson, Nernst-Planck, and Stokes equations for a realistic, fully three-dimensional setup as well as analytical approximations for a simplified model are worked out. By applying a suitable voltage to the membrane electrode, the DNA can be forced to preferably traverse the pore either along the pore axis or at a small but finite distance from the pore wall.

The relationship between bilayer stability and lipid head group orientation is reported. In this work, molecular-dynamics simulations are performed to analyze the structure-property relationship of lipid biomembranes, taking into account coarse-grained model lipid interactions. The work explains the molecular scale mechanism of the phase behavior of lipid systems due to ion-lipid or anesthetic-lipid interactions, where reorientations of dipoles play a key role in modifying lipid phases and thereby alter biomembrane function. Our study demonstrates that simple dipolar reorientation is indeed sufficient in tuning a bilayer to a randomly flipped nonbilayer lamellar phase. This study may be used to assess the impact of changes in lipid phase characteristics on biomembrane structure due to the presence of anesthetics and ions.

The scaling behavior of friction between rough surfaces is a well-known phenomenon. It might be asked whether such a scaling feature also exists for friction at an atomic scale despite the absence of roughness on atomically flat surfaces. Indeed, other types of fluctuations, e.g., thermal and instrumental fluctuations, become appreciable at this length scale and can lead to scaling behavior of the measured atomic-scale friction. We investigate this using the lateral force exerted on the tip of an atomic force microscope (AFM) when the tip is dragged over the clean NaCl (001) surface in ultra-high vacuum at room temperature. Here the focus is on the fluctuations of the lateral force profile rather than its saw-tooth trend; we first eliminate the trend using the singular value decomposition technique and then explore the scaling behavior of the detrended data, which contains only fluctuations, using the multifractal detrended fluctuation analysis. The results demonstrate a scaling behavior for the friction data ranging from 0.2 to 2 nm with the Hurst exponent $H=0.61\pm 0.02$ at a $1\sigma$ confidence interval. Moreover, the dependence of the generalized Hurst exponent, $h\left(q\right)$, on the index variable $q$ confirms the multifractal or multiscaling behavior of the nanofriction data. These results prove that fluctuation of nanofriction empirical data has a multifractal behavior which deviates from white noise.

Solute dispersion in fluid flow results from the interaction between advection and diffusion. The relative contributions of these two mechanisms to mass transport are characterized by the reduced velocity $\nu$, also referred to as the Péclet number. In the absence of diffusion (i.e., when the solute diffusion coefficient $D_{\mathrm{m}}=0$ and $\nu \to \infty$), divergence-free laminar flow of an incompressible fluid results in a zero-transverse dispersion coefficient $(D_{\mathrm{T}}=0)$, both in ordered and random two-dimensional porous media. We demonstrate by numerical simulations that a more realistic realization of the condition $\nu \to \infty$ using $D_{\mathrm{m}}\ne 0$ and letting the fluid flow velocity approach infinity leads to completely different results for ordered and random two-dimensional porous media. With increasing reduced velocity, $D_{\mathrm{T}}$ approaches an asymptotic value in ordered two-dimensional porous media but grows linearly in disordered (random) structures depending on the geometrical disorder of a structure: a higher degree of heterogeneity results in a stronger growth of $D_{\mathrm{T}}$ with $\nu$. The obtained results reveal that disorder in the geometrical structure of a two-dimensional porous medium leads to a growth of $D_{\mathrm{T}}$ with $\nu$ even in a uniform pore-scale advection field; however, lateral diffusion is a prerequisite for this growth. By contrast, in ordered two-dimensional porous media the presence of lateral diffusion leads to a plateau for the transverse dispersion coefficient with increasing $\nu$.

Capillary electrophoresis techniques often involve ion-concentration shock waves in an electrolyte solution, propagating under the effect of an external electric field. These shock waves are characterized by self-sharpening gradients in ion concentrations and electrical conductivity that are collinear with the electric field. The coupling of electric field and fluid motion at the shock interface sometimes leads to an undesirable electrohydrodynamic (EHD) instability. Using linear stability analysis, we describe the motion of small-amplitude disturbances of an electrophoretic shock wave. Our analysis shows that the EHD instability results due to the competition between destabilizing electroviscous flow and stabilizing electromigration of the shock wave. The ratio of timescales corresponding to electroviscous flow and electromigration yields a threshold criterion for the onset of instability. We present a validation of this threshold criterion with published experimental data and also describe the physical mechanism underlying the EHD instability of the electrophoretic shock wave.

An experimental study was conducted to resolve previous conflicting results on water electrospray in air at atmospheric pressure. Using a small flow rate relative to that used in previous studies and a small nonmetallic nozzle, we observed stable electrospray of water in air without discharge and distinguished three distinct operating regimes for applied voltage and flow rate. The well-known cone-jet mode was observed and the general scaling law of the generated droplet size in the cone-jet mode was confirmed by direct visualization of the meniscus, jet, and generated droplets. We also observed and analyzed whipping motion in the electrified water jet.

We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first neighbors to global coupling, and a parameter ($\beta$) that allows one to scan continuously from nondelayed to one-time delayed dynamics. In the $\alpha -\varepsilon$ plane we identify periodic orbits, limit cycles, and chaotic trajectories, and describe how these structures change with delay. These features can be explained by studying the bifurcation diagrams of a two-dimensional nondelayed map. This allows us to understand the effects of one-time delays on CSSs, e.g., regularization of chaotic orbits and synchronization of short-range coupled maps, observed when the dynamics is moderately delayed. Finally, we substitute the logistic map with cubic and logarithmic maps, in order to test the robustness of our findings.

In this paper, we investigate the influence of the retarded access by a time-varying delay on the dynamics of delay systems. We show that there are two universality classes of delays, which lead to fundamental differences in dynamical quantities such as the Lyapunov spectrum. Therefore, we introduce an operator theoretic framework, where the solution operator of the delay system is decomposed into the Koopman operator describing the delay access and an operator similar to the solution operator known from systems with constant delay. The Koopman operator corresponds to an iterated map, called access map, which is defined by the iteration of the delayed argument of the delay equation. The dynamics of this one-dimensional iterated map determines the universality classes of the infinite-dimensional state dynamics governed by the delay differential equation. In this way, we connect the theory of time-delay systems with the theory of circle maps and the framework of the Koopman operator. In this paper, we extend our previous work [A. Otto, D. Müller, and G. Radons, Phys. Rev. Lett. 118, 044104 (2017)] by elaborating the mathematical details and presenting further results also on the Lyapunov vectors.

A scenario has recently been reported in which in order to stabilize complete synchronization of an oscillator network—a symmetric state—the symmetry of the system itself has to be broken by making the oscillators nonidentical. But how often does such behavior—which we term asymmetry-induced synchronization (AISync)—occur in oscillator networks? Here we present the first general scheme for constructing AISync systems and demonstrate that this behavior is the norm rather than the exception in a wide class of physical systems that can be seen as multilayer networks. Since a symmetric network in complete synchrony is the basic building block of cluster synchronization in more general networks, AISync should be common also in facilitating cluster synchronization by breaking the symmetry of the cluster subnetworks.

In the present work, motivated by generalized forms of the Hertzian dynamics associated with granular crystals, we consider the possibility of such models to give rise to both dispersive shock and rarefaction waves. Depending on the value $p$ of the nonlinearity exponent, we find that both of these possibilities are realizable. We use a quasicontinuum approximation of a generalized inviscid Burgers model in order to predict the solution profile up to times near the formation of the dispersive shock, as well as to estimate when it will occur. Beyond that time threshold, oscillations associated with the highly dispersive nature of the underlying model emerge, which cannot be captured by the quasicontinuum approximation. Our analytical characterization of the above features is complemented by systematic numerical computations.

We use large-scale computer simulations to explore the nonequilibrium aging dynamics in a microscopic model for colloidal gels. We find that gelation resulting from a kinetically arrested phase separation is accompanied by “anomalous” particle dynamics revealed by superdiffusive particle motion and compressed exponential relaxation of time correlation functions. Spatiotemporal analysis of the dynamics reveals intermittent heterogeneities producing spatial correlations over extremely large length scales. Our study is a microscopically resolved model reproducing all features of the spontaneous aging dynamics observed experimentally in soft materials.

We investigate the role of greed on the lifetime of a random-walking forager on an initially resource-rich lattice. Whenever the forager lands on a food-containing site, all the food there is eaten and the forager can hop $\mathcal{S}$ more steps without food before starving. Upon reaching an empty site, the forager comes one time unit closer to starvation. The forager is also greedy—given a choice to move to an empty or to a food-containing site in its local neighborhood, the forager moves preferentially toward food. Surprisingly, the forager lifetime varies nonmonotonically with greed, with different senses of the nonmonotonicity in one and two dimensions. Also unexpectedly, the forager lifetime in one dimension has a huge peak for very negative greed where the forager is food averse.

We present a systematic experimental study of the confinement effect on the crystallization of a monolayer of magnetized beads. The particles are millimeter-scale grains interacting through the short range magnetic dipole-dipole potential induced by an external magnetic field. The grains are confined by repulsing walls and are homogeneously distributed inside the cell. A two-dimensional (2d) Brownian motion is induced by horizontal mechanical vibrations. Therefore, the balance between magnetic interaction and agitation allows investigating 2d phases through direct visualization. The effect of both confinement size and shape on the grains' organization in the low-energy state has been investigated. Concerning the confinement shape, triangular, square, pentagonal, hexagonal, heptagonal, and circular geometries have been considered. The grain organization was analyzed after a slow cooling process. Through the measurement of the averaged bond order parameter for the different confinement geometries, it has been shown that cell geometry strongly affects the ordering of the system. Moreover, many kinds of defects, whose observation rate is linked to the geometry, have been observed: disclinations, dislocations, defects chain, and also more exotic defects such as a rosette. Finally, the influence of confinement size has been investigated and we point out that no finite-size effect occurs for a hexagonal cell, but the finite-size effect changes from one geometry to another.

In this paper we show that in the semiclassical regime of periodic potential large enough, the Stark-Wannier ladders become a dense energy spectrum because of a cascade of bifurcations while increasing the ratio between the effective nonlinearity strength and the tilt of the external field; this fact is associated to a transition from regular to quantum chaotic dynamics. The sequence of bifurcation points is explicitly given.

The living cell uses a variety of molecular receptors to read and process chemical signals that vary in space and time. We model the dynamics of such molecular level measurements as Markov processes in steady state, with a coupling between the receptor and the signal. We prove exactly that, when the signal dynamics is not perturbed by the receptors, the free energy consumed by the measurement process is lower bounded by a quantity proportional to the mutual information. Our result is completely independent of the receptor architecture and dependent on signal properties alone, and therefore holds as a general principle for molecular information processing.

We investigate the aggregation and fragmentation dynamics of tracers and inertial aggregates in random flows leading to steady-state size distributions. Our objective is to elucidate the impact of changes in aggregation rates due to differences in advection dynamics, especially with respect to the influence of inertial effects. This aggregation process is, at the same time, balanced by fragmentation triggered by local hydrodynamic stress. Our study employs an individual-particle-based model, tracking the position, velocity, and size of each aggregate. We compare the steady-state size distribution formed by tracers and inertial aggregates, characterized by different sizes and densities. On the one hand, we show that the size distributions change their shape with changes in the dilution rate of the suspension. On the other hand, we obtain that the size distributions formed with different binding strengths between monomers can be rescaled to a single form with the use of a characteristic size for both dense inertial particles and tracer monomers. Nevertheless, this last scaling relation also fails if the size distribution contains aggregates that behave as tracer-like and inertial-like, which results in a crossover between different scalings.

Equal volume mixtures of small and large polytetrafluorethylene spheres are shaken in an atmosphere of controlled humidity which allows one to also control their tribocharging. We find that the contact numbers are charge dependent: As the charge density of the beads increases, the number of same-type contacts decreases and the number of opposite-type contacts increases. This change is not caused by a global segregation of the sample. Hence, tribocharging can be a way to tune the local composition of a granular material.

A consistent formulation is presented for the direct numerical simulation of an arbitrarily shaped colloidal particle at a deformable fluidic interface. The rigid colloidal particle is decomposed into a collection of solid spherical beads and the three-phase boundaries are replaced with smoothly spreading interfaces. The major merit of the present formulation lies in the ease with which the geometrical decomposition of the colloidal particle is implemented, yet allows the dynamic simulation of intricate three-dimensional colloidal shapes in a binary fluid. The dynamics of a rodlike, a platelike, and a ringlike particle are presently tested. It is found that platelike particles attach more rapidly to a fluidic interface and are subsequently harder to dislodge when subject to an external force. Using the Bond number, i.e., the ratio of the gravitational force to the reference capillary force, a spherical particle with equal affinity for the two fluids breaks away from a fluidic interface at the critical value $\text{Bo}=0.75$. This value is in line with our numerical experiments. It is here shown that a plate and a ring of equivalent masses detach at greater critical Bond numbers approximately equal to $\text{Bo}=1.3$. Results of this study will find applications in the stabilization of emulsions by colloids and in the recovery of colloidal particles by rising bubbles.

I have developed an alternative numerical approach to study mass transfer from a stationary core-shell reservoir under channel flow conditions. I use the lattice Boltzmann method to compute both the solvent fluid flow and the diffusion and advection of the solute. I have investigated the impact of the flow by reporting mass transfer quantities such as the instantaneous solute concentration and the local Sherwood number at the surface of the reservoir. The flow is found to enhance the release of the encapsulated material, but it prevents the released material from reaching the channel walls.

We introduce and study a banded random matrix model describing sparse, long-range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and a mapping to a long-range epidemics model, we establish the phase diagram of the model. A genuine localization transition, with well defined mobility edges, appears as the hopping rate decreases slower than ${\ell }^{-2}$, where $\ell$ is the distance. Correspondingly, the decay of the localized states evolves from a standard exponential shape to a stretched exponential and finally to a $exp(-C{ln}^{\kappa }\ell )$ behavior, with $\kappa >1$.