In a thought-provoking paper, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] describe a version of the famous double-slit experiment performed with droplets bouncing on a vertically vibrated fluid surface. In the experiment, an interference pattern in the single-particle statistics is found even though it is possible to determine unambiguously which slit the walking droplet passes. Here we argue, however, that the single-particle statistics in such an experiment will be fundamentally different from the single-particle statistics of quantum mechanics. Quantum mechanical interference takes place between different classical paths with precise amplitude and phase relations. In the double-slit experiment with walking droplets, these relations are lost since one of the paths is singled out by the droplet. To support our conclusions, we have carried out our own double-slit experiment, and our results, in particular the long and variable slit passage times of the droplets, cast strong doubt on the feasibility of the interference claimed by Couder and Fort. To understand theoretically the limitations of wave-driven particle systems as analogs to quantum mechanics, we introduce a Schrödinger equation with a source term originating from a localized particle that generates a wave while being simultaneously guided by it. We show that the ensuing particle-wave dynamics can capture some characteristics of quantum mechanics such as orbital quantization. However, the particle-wave dynamics can not reproduce quantum mechanics in general, and we show that the single-particle statistics for our model in a double-slit experiment with an additional splitter plate differs qualitatively from that of quantum mechanics.

The deformation and breakup of an axisymmetric, conducting drop suspended in a nonconducting medium and subjected to an external electric field is numerically investigated here using an electrokinetic model. This model uses a combined level set-volume of fluid formulation of the deformable surfaces, along with a multiphase implementation of the Nernst-Planck equation for transport of ions, that allows for varying conductivity inside the drop. A phase diagram, based on a parametric study, is used to characterize the stability conditions. Stable drops with lower ion concentration are characterized by longer drop shapes than those achieved at higher ion concentrations. For higher drop ion concentration, greater charge accumulation is observed at drop tips. Consequently, such drops break up by pinching off rather than tip streaming. The charge contained in droplets released from unstable drops is shown to increase with drop ion concentration. These dynamic drop behaviors depend on the strength of the electric field and the concentration of ions in the drop and result from the interplay between the electric forces arising from the permittivity jump at the drop interface and the ions in the bulk.

The spectrum of x-ray Thomson scattering is proportional to the dynamic structure factor. An important contribution is the ion feature which describes elastic scattering of x rays off electrons. We apply an ab initio method for the calculation of the form factor of bound electrons, the slope of the screening cloud of free electrons, and the ion-ion structure factor in warm dense beryllium. With the presented method we can calculate the ion feature from first principles. These results will facilitate a better understanding of x-ray scattering in warm dense matter and an accurate measurement of ion temperatures which would allow determining nonequilibrium conditions, e.g., along shock propagation.

Reflection and transmission due to the incident wave in one-dimensional bead chains when there are impurities have been studied. The impurities can be any kind of material, any size, and their numbers are arbitrary. The dependence of the transmission and the reflection on the numbers and the material parameters of the impurities are given. The analytical results are given by using the inverse scattering method. Substantial reflection is observed if there is only one steel bead. However, the reflection is negligible if there are two steel beads. The reflection monotonously increases as the numbers of the steel beads increase. The reflection remains a constant when the numbers of the steel beads are so many that the length composed by the steel beads is larger than the width of the solitary wave. It can be used to detect the impurities in the beads' chain by measuring the reflection of a pulse.

Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations—matrices—acting on the data are often not accessible directly but are only represented indirectly in form of a computer routine. Such a routine implements the transformation a data vector undergoes under matrix multiplication. While efficient probing routines to estimate a matrix's diagonal or trace, based solely on such computationally affordable matrix-vector multiplications, are well known and frequently used in signal inference, there is no stochastic estimate for its determinant. We introduce a probing method for the logarithm of a determinant of a linear operator. Our method rests upon a reformulation of the log-determinant by an integral representation and the transformation of the involved terms into stochastic expressions. This stochastic determinant determination enables large-size applications in Bayesian inference, in particular evidence calculations, model comparison, and posterior determination.

Population annealing is a Monte Carlo algorithm that marries features from simulated-annealing and parallel-tempering Monte Carlo. As such, it is ideal to overcome large energy barriers in the free-energy landscape while minimizing a Hamiltonian. Thus, population-annealing Monte Carlo can be used as a heuristic to solve combinatorial optimization problems. We illustrate the capabilities of population-annealing Monte Carlo by computing ground states of the three-dimensional Ising spin glass with Gaussian disorder, while comparing to simulated-annealing and parallel-tempering Monte Carlo. Our results suggest that population annealing Monte Carlo is significantly more efficient than simulated annealing but comparable to parallel-tempering Monte Carlo for finding spin-glass ground states.

We present a multiscale model, based on molecular dynamics (MD) and kinetic Monte Carlo (kMC), to study the aggregation driven growth of colloidal particles. Coarse-grained molecular dynamics (CGMD) simulations are employed to detect key agglomeration events and calculate the corresponding rate constants. The kMC simulations employ these rate constants in a stochastic framework to track the growth of the agglomerates over longer time scales and length scales. One of the hallmarks of the model is a unique methodology to detect and characterize agglomeration events. The model accounts for individual cluster-scale effects such as change in size due to aggregation as well as local molecular-scale effects such as changes in the number of neighbors of each molecule in a colloidal cluster. Such definition of agglomeration events allows us to grow the cluster to sizes that are inaccessible to molecular simulations as well as track the shape of the growing cluster. A well-studied system, comprising fullerenes in NaCl electrolyte solution, was simulated to validate the model. Under the simulated conditions, the agglomeration process evolves from a diffusion limited cluster aggregation (DLCA) regime to percolating cluster in transition and finally to a gelation regime. Overall the data from the multiscale numerical model shows good agreement with existing theory of colloidal particle growth. Although in the present study we validated our model by specifically simulating fullerene agglomeration in electrolyte solution, the model is versatile and can be applied to a wide range of colloidal systems.

We study the restricted solid on solid model for surface growth in spatial dimension $d=2$ by means of a multisurface coding technique that allows one to produce a large number of samples in the stationary regime in a reasonable computational time. Thanks to (i) a careful finite-size scaling analysis of the critical exponents and (ii) the accurate estimate of the first three moments of the height fluctuations, we can quantify the wandering exponent with unprecedented precision: ${\chi }_{d=2}=0.3869\left(4\right)$. This figure is incompatible with the long-standing conjecture due to Kim and Koesterlitz that hypothesized ${\chi }_{d=2}=2/5$.

The accuracy of molecular signaling in biological cells and novel diagnostic devices is ultimately limited by the counting noise floor imposed by the thermal diffusion. Motivated by the fact that messenger RNA and vesicle-engulfed signaling molecules transiently bind to molecular motors and are actively transported in biological cells, we show here that the random active delivery of signaling particles to within a typical diffusion distance to the receptor generically reduces the correlation time of the counting noise. Considering a variety of signaling particle sizes from mRNA to vesicles and cell sizes from prokaryotic to eukaryotic cells, we show that the conditions for active focusing—faster and more precise signaling—are indeed compatible with observations in living cells. Our results improve the understanding of molecular cellular signaling and novel diagnostic devices.

For a certain class of isolated quantum systems, we report the existence of irreversible processes in which the energy is not dissipated. After a closed cycle in which the initial energy distribution is fully recovered, the expectation value of a symmetry-breaking observable changes from a value differing from zero in the initial state to zero in the final state. This entails the unavoidable loss of a certain amount of information and constitutes a source of irreversibility. We show that the von Neumann entropy of time-averaged equilibrium states increases in the same magnitude as a consequence of the process. We support this result by means of numerical calculations in an experimentally feasible system, the Lipkin-Meshkov-Glick model.

Systems living in complex nonequilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the continuous-time random walk (CTRW). Stochastic trajectories of a CTRW can be described in terms of the subordination of a normal diffusive process by an inverse Lévy-stable process. Here, we propose an equivalent Langevin formulation of a force-free CTRW without subordination. By introducing a different type of non-Gaussian noise, we are able to express the CTRW dynamics in terms of a single Langevin equation in physical time with additive noise. We derive the full multipoint statistics of this noise and compare it with the scaled Brownian motion (SBM), an alternative stochastic model describing subdiffusive dynamics. Interestingly, these two noises are identical up to the second order correlation functions, but different in the higher order statistics. We extend our formalism to general waiting time distributions and force fields and compare our results with those of the SBM. In the presence of external forces, our proposed noise generates a different class of stochastic processes, resembling a CTRW but with forces acting at all times.

The structure of a finite particle cluster is typically determined by total energy minimization. Here we consider the case where a cluster of soft-sphere dipoles becomes active, i.e., when the individual particles exhibit an additional self-propulsion along their dipole moments. We numerically solve the overdamped equations of motion for soft-sphere dipoles in a solvent. Starting from an initial metastable dipolar cluster, the self-propulsion generates a complex cluster dynamics. The final cluster state has in general a structure widely different to the initial one, the details depend on the model parameters and on the protocol of how the self-propulsion is turned on. The center of mass of the cluster moves on a helical path, the details of which are governed by the initial cluster magnetization. An instantaneous switch to a high self-propulsion leads to fission of the cluster. However, fission does not occur if the self-propulsion is increased slowly to high strengths. Our predictions can be verified through experiments with self-phoretic colloidal Janus particles and for macroscopic self-propelled dipoles in a highly viscous solvent.

A numerical and systematic parameter study of three-dimensional vesicle electrohydrodynamics is presented to investigate the effects of varying electric field strength and different fluid and membrane properties. The dynamics of vesicles in the presence of dc electric fields is considered, in both the presence and absence of linear shear flow. For suspended vesicles it is shown that the conductivity ratio and viscosity ratio between the interior and exterior fluids, as well as the vesicle membrane capacitance, substantially affect the minimum electric field strength required to induce a full prolate-oblate-prolate transition. In addition, there exists a critical electric field strength above which a vesicle will no longer tumble when exposed to linear shear flow.

Self-assembly is one of the most fascinating phenomena in nature and is one key component in the formation of hierarchical structures. The formation of structures depends critically on the interaction between the different constituents, and therefore the link between these interactions and the resulting structure is fundamental for the understanding of materials. We have realized a two-dimensional system of colloidal particles with tunable magnetic dipole forces. The phase formation is studied by transmission optical microscopy and a phase diagram is constructed. We report a phase transition from hexagonal to random and square arrangements when the magnetic interaction between the individual particles is tuned from antiferromagnetic to ferrimagnetic.

A trapping mechanism for propelled colloidal particles based on an inhomogeneous drive is presented and studied by means of computer simulations. In experiments this method can be realized using photophoretic Janus particles driven by a light source, which is partially blocked by a shading mask. This leads to an accumulation of particles in the passive part. An equation for an accumulation parameter is derived using the effective inhomogeneous diffusion constant generated by the inhomogeneous drive. The impact of particle interaction on the trapping mechanism is studied, as well as the interplay between passivity-induced trapping and the emergent self-clustering of systems containing a high density of active particles. The combination of both effects makes the clusters more controllable for applications.

We study the small strain elastic behavior of composite athermal fiber networks constructed by adding stiffer fibers to a cross-linked base network. We observe that if the base network is in the affine deformation regime, the composite behaves similar to a fiber-reinforced continuum. When the base network is in the nonaffine deformation regime, the stiffness of the composite increases by orders of magnitude upon the addition of a small fraction of stiff fibers. The increase is not gradual, but rather occurs in two steps. Of these, one is associated with the stiffness percolation of the network of added fibers. The other, which occurs at very small fractions of stiff fibers, is due to the percolation of perturbation zones, or “interphases,” induced in the base network by the stiff fibers, regions where the energy is stored mostly in the axial deformation mode. Their size controls the stiffening transition and depends on base network parameters and the length of added fibers. It is also shown that the perturbation field introduced in the base network by the presence of a stiff fiber is much longer ranged than in the case when the fiber is tied to a continuum of same modulus with the base network.

Transport networks play a key role across four realms of eukaryotic life: slime molds, fungi, plants, and animals. In addition to the developmental algorithms that build them, many also employ adaptive strategies to respond to stimuli, damage, and other environmental changes. We model these adapting network architectures using a generic dynamical system on weighted graphs and find in simulation that these networks ultimately develop a hierarchical organization of the final weighted architecture accompanied by the formation of a system-spanning backbone. In addition, we find that the long term equilibration dynamics exhibit behavior reminiscent of glassy systems characterized by long periods of slow changes punctuated by bursts of reorganization events.

We present results demonstrating the space charge-mediated transition between classical, diffusion-limited current and surface-conduction dominant over-limiting current in a shallow microchannel-nanochannel device. The extended space charge layer develops at the depleted microchannel-nanochannel entrance at high current and is correlated with a distinctive maximum in the dc resistance. Experimental results for a shallow surface-conduction dominated system are compared with theoretical models, allowing estimates of the effective surface charge at high voltage to be obtained. In comparison to an equilibrium estimate of the surface charge obtained from electrochemical impedance spectroscopy, it is further observed that the effective surface charge appears to change under applied voltage.

We demonstrate the role of selectivity variation in the structure of the nonequilibrium extended space charge using one-dimensional analytic and two-dimensional numerical Poisson-Nernst-Planck models for the electro-diffusive transport of a symmetric electrolyte. This provides a deeper understanding of the underlying mechanism behind a previously observed maximum in the resistance-voltage curve for a shallow micro-nanochannel interface device [Schiffbauer, Liel, Leibowitz, Park, and Yossifon, arXiv:1409.4548, Phys. Rev. E (to be published)]. The current study helps to establish a connection between parameters such as the geometry and nanochannel surface charge and the control of selectivity and resistance in the overlimiting current regime.