We modify the standard Vicsek model to clearly distinguish between intrinsic noise due to imperfect alignment between organisms and extrinsic noise due to fluid motion. We then consider the effect of a steady vortical flow, the Taylor-Green vortex, on the dynamics of the flock, for various flow speeds, with a fixed intrinsic particle speed. We pay particular attention to the morphology of the flow, and quantify its filamentarity. Strikingly, above a critical flow speed there is a pronounced increase in the filamentarity of the flock, when compared to the zero-flow case. This is due to the fact that particles appear confined to areas of low vorticity; a familiar phenomena, commonly seen in the clustering of inertial particles in vortical flows. Hence, the cooperative motion of the particles gives them an effective inertia, which is seen to have a profound effect on the morphology of the flock, in the presence of external fluid motion. Finally, we investigate the angle between the flow and the particles direction of movement and find it follows a power-law distribution.

We investigated by numerical simulations the effects of Schmidt number on passive scalar transport in forced compressible turbulence. The range of Schmidt number ($\text{Sc}$) was $\frac{1}{25}\sim 25$. In the inertial-convective range the scalar spectrum seemed to obey the $k^{-5/3}$ power law. For $\text{Sc}\gg 1$, there appeared a $k^{-1}$ power law in the viscous-convective range, while for $\text{Sc}\ll 1$, a $k^{-17/3}$ power law was identified in the inertial-diffusive range. The scaling constant computed by the mixed third-order structure function of the velocity-scalar increment showed that it grew over $\text{Sc}$, and the effect of compressibility made it smaller than the $\frac{4}{3}$ value from incompressible turbulence. At small amplitudes, the probability distribution function (PDF) of scalar fluctuations collapsed to the Gaussian distribution whereas, at large amplitudes, it decayed more quickly than Gaussian. At large scales, the PDF of scalar increment behaved similarly to that of scalar fluctuation. In contrast, at small scales it resembled the PDF of scalar gradient. Furthermore, the scalar dissipation occurring at large magnitudes was found to grow with $\text{Sc}$. Due to low molecular diffusivity, in the $\text{Sc}\gg 1$ flow the scalar field rolled up and got mixed sufficiently. However, in the $\text{Sc}\ll 1$ flow the scalar field lost the small-scale structures by high molecular diffusivity and retained only the large-scale, cloudlike structures. The spectral analysis found that the spectral densities of scalar advection and dissipation in both $\text{Sc}\gg 1$ and $\text{Sc}\ll 1$ flows probably followed the $k^{-5/3}$ scaling. This indicated that in compressible turbulence the processes of advection and dissipation except that of scalar-dilatation coupling might deferring to the Kolmogorov picture. It then showed that at high wave numbers, the magnitudes of spectral coherency in both $\text{Sc}\gg 1$ and $\text{Sc}\ll 1$ flows decayed faster than the theoretical prediction of $k^{-2/3}$ for incompressible flows. Finally, the comparison with incompressible results showed that the scalar in compressible turbulence with $\text{Sc}=1$ lacked a conspicuous bump structure in its spectrum, but was more intermittent in the dissipative range.

A general quantitative model of capillary flow in homogeneous porous media with varying cross-sectional sizes is presented. We optimize the porous structure for the minimization of the penetration time under global constraints. Programmable capillary flows with constant volumetric flow rate and linear evolution of flow distance to time are also obtained. The controlled innovative flow behaviors are derived based on a dynamic competition between capillary force and viscous resistance. A comparison of dynamic transport on the basis of the present design with Washburn's equation is presented. The regulation and maximization of flow velocity in porous materials is significant for a variety of applications including biomedical diagnostics, oil recovery, microfluidic transport, and water management of fabrics.

Two-dimensional diffusion of a rhodamine 6G fluorescent tracer molecule at the $n$-decane–water interface was studied with all-atom molecular dynamics simulations. In agreement with experimental data, we find increased mobility of the tracer at the $n$-decane–water interfaces in comparison to its mobility in bulk water. Orientational ordering of water and $n$-decane molecules near the interface is observed, and may change the interfacial viscosity as suggested to explain the experimental data. However, the restricted rotational motion of the rhodamine molecule at the interface suggests that the Saffman-Delbrück model may be a more appropriate approximation of rhodamine diffusion at $n$-decane–water interfaces, and, without any decrease in interfacial viscosity, suggests faster diffusion consistent with both experimental and simulation values.

In the paper by Abe and Okuyama [Phys. Rev. E 83, 021121 (2011)], the quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is discussed. It is claimed that the state at the beginning of the quantum Carnot cycle is pure. After that, it is apparently transmuted to a mixed state if Clausius equality is imposed. We prove that this statement is incorrect. In particular, we prove that the state at the beginning of the cycle is mixed due to the process of measuring energy.

In their Comment on the paper [Abe and Okuyama, Phys. Rev. E 83, 021121 (2011)], González-Díaz and Díaz-Solórzano discuss that the initial state of the quantum-mechanical analog of the Carnot cycle should be not in a pure state but in a mixed state due to a projective measurement of the system energy. Here, first the Comment is shown to miss the point. Then, second, multiple projective measurements are discussed as a generalization of the Comment, although they are not relevant to the work commented.

We study the effect of confinement on the mean perimeter of the convex hull of a planar Brownian motion, defined as the minimum convex polygon enclosing the trajectory. We use a minimal model where an infinite reflecting wall confines the walk to one side. We show that the mean perimeter displays a surprising minimum with respect to the starting distance to the wall and exhibits a nonanalyticity for small distances. In addition, the mean span of the trajectory in a fixed direction $\theta \in ]0,\pi /2[$, which can be shown to yield the mean perimeter by integration over $\theta$, presents these same two characteristics. This is in striking contrast to the one-dimensional case, where the mean span is an increasing analytical function. The nonmonotonicity in the two-dimensional case originates from the competition between two antagonistic effects due to the presence of the wall: reduction of the space accessible to the Brownian motion and effective repulsion.

An experimental and theoretical study of lyotropic chromonic liquid crystals (LCLCs) confined in cylinders with degenerate planar boundary conditions elucidates LCLC director configurations. When the Frank saddle-splay modulus is more than twice the twist modulus, the ground state adopts an inhomogeneous escaped-twisted configuration. Analysis of the configuration yields a large saddle-splay modulus, which violates Ericksen inequalities but not thermodynamic stability. Lastly, we observe point defects between opposite-handed domains, and we explain a preference for point defects over domain walls.

We consider cyclic Lotka-Volterra models with three and four strategies where at every interaction agents play a strategy using a time-dependent probability distribution. Agents learn from a loss by reducing the probability to play a losing strategy at the next interaction. For that, an agent is described as an urn containing $\beta$ balls of three and four types, respectively, where after a loss one of the balls corresponding to the losing strategy is replaced by a ball representing the winning strategy. Using both mean-field rate equations and numerical simulations, we investigate a range of quantities that allows us to characterize the properties of these cyclic models with time-dependent probability distributions. For the three-strategy case in a spatial setting we observe a transition from neutrally stable to stable when changing the level of discretization of the probability distribution. For large values of $\beta$, yielding a good approximation to a continuous distribution, spatially synchronized temporal oscillations dominate the system. For the four-strategy game the system is always neutrally stable, but different regimes emerge, depending on the size of the system and the level of discretization.

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014)] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the ${\ell }_1$-optimization-based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done auto-matically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudolikelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that, on various topologies and with different distribution of couplings, the decimation method outperforms the widely used ${\ell }_1$-optimization-based methods.

We investigate the critical behavior of a stochastic lattice model describing a contact process in the Sierpinski carpet with fractal dimension $d=log8/log3$. We determine the threshold of the absorbing phase transition related to the transition between a statistically stationary active and the absorbing states. Finite-size scaling analysis is used to calculate the order parameter, order parameter fluctuations, correlation length, and their critical exponents. We report that all static critical exponents interpolate between the line of the regular Euclidean lattices values and are consistent with the hyperscaling relation. However, a short-time dynamics scaling analysis shows that the dynamical critical exponent $Z$ governing the size dependence of the critical relaxation time is found to be larger then the literature values in Euclidean $d=1$ and $d=2$, suggesting a slower critical relaxation in scale-free lattices.

Using discrete particle simulations validated by experimental data acquired using the positron emission particle tracking technique, we study the efficiency of energy transfer from a vibrating wall to a system of discrete, macroscopic particles. We demonstrate that even for a fixed input energy from the wall, energy conveyed to the granular system under excitation may vary significantly dependent on the frequency and amplitude of the driving oscillations. We investigate the manner in which the efficiency with which energy is transferred to the system depends on the system variables and determine the key control parameters governing the optimization of this energy transfer. A mechanism capable of explaining our results is proposed, and the implications of our findings in the research field of granular dynamics as well as their possible utilization in industrial applications are discussed.

The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is revisited within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we present a simple method to calculate the frequencies of the normal modes, which are then used to estimate the interaction potential. The possibility that such interactions play a non-negligible role in ensuring the effective functioning of the biomolecular functions is investigated. On the basis of experimental results reported in the literature and simple numerical estimates, it is found that long-range interactions involving electromagnetic fields of frequencies ${\displaystyle 0.1–1\text{THz}}$ could be temporarily activated despite radiation losses and solvent dissipation. Moreover, the theoretical background used to derive the mentioned interactions sheds light on Fröhlich's theory of selective long-range forces between biomolecules. At variance with a long-standing belief, we show that sizable resonant long-range interactions may exist only if the interacting system is out of thermal equilibrium.

The macroscale movement behavior of a wide range of isolated migrating cells has been well characterized experimentally. Recently, attention has turned to understanding the behavior of cells in crowded environments. In such scenarios it is possible for cells to interact, inducing neighboring cells to move in order to make room for their own movements or progeny. Although the behavior of interacting cells has been modeled extensively through volume-exclusion processes, few models, thus far, have explicitly accounted for the ability of cells to actively displace each other in order to create space for themselves. In this work we consider both on- and off-lattice volume-exclusion position-jump processes in which cells are explicitly allowed to induce movements in their near neighbors in order to create space for themselves to move or proliferate into. We refer to this behavior as pushing. From these simple individual-level representations we derive continuum partial differential equations for the average occupancy of the domain. We find that, for limited amounts of pushing, comparison between the averaged individual-level simulations and the population-level model is nearly as good as in the scenario without pushing. Interestingly, we find that, in the on-lattice case, the diffusion coefficient of the population-level model is increased by pushing, whereas, for the particular off-lattice model that we investigate, the diffusion coefficient is reduced. We conclude, therefore, that it is important to consider carefully the appropriate individual-level model to use when representing complex cell-cell interactions such as pushing.

Real networks feature layers of interactions and complexity. In them, different types of nodes can interact with each other via a variety of events. Examples of this complexity are task-oriented social networks (TOSNs), where teams of people share tasks towards creating a quality artifact, such as academic research papers or software development in commercial or open source environments. Accomplishing those tasks involves both work, e.g., writing the papers or code, and communication, to discuss and coordinate. Taking into account the different types of activities and how they alternate over time can result in much more precise understanding of the TOSNs behaviors and outcomes. That calls for modeling techniques that can accommodate both node and link heterogeneity as well as temporal change. In this paper, we report on methodology for finding temporal motifs in TOSNs, limited to a system of two people and an artifact. We apply the methods to publicly available data of TOSNs from 31 Open Source Software projects. We find that these temporal motifs are enriched in the observed data. When applied to software development outcome, temporal motifs reveal a distinct dependency between collaboration and communication in the code writing process. Moreover, we show that models based on temporal motifs can be used to more precisely relate both individual developer centrality and team cohesion to programmer productivity than models based on aggregated TOSNs.

This work describes the inertial effects on the rotational behavior of an oblate spheroidal particle confined between two parallel opposite moving walls, which generate a linear shear flow. Numerical results are obtained using the lattice Boltzmann method with an external boundary force. The rotation of the particle depends on the particle Reynolds number, ${\mathrm{Re}}_p=G{d}^2{\nu }^{-1}$ ($G$ is the shear rate, $d$ is the particle diameter, $\nu$ is the kinematic viscosity), and the Stokes number, $\mathrm{St}=\alpha {\mathrm{Re}}_p$ ($\alpha$ is the solid-to-fluid density ratio), which are dimensionless quantities connected to fluid and particle inertia, respectively. The results show that two inertial effects give rise to different stable rotational states. For a neutrally buoyant particle $\left(\mathrm{St}={\mathrm{Re}}_p\right)$ at low ${\mathrm{Re}}_p$, particle inertia was found to dominate, eventually leading to a rotation about the particle's symmetry axis. The symmetry axis is in this case parallel to the vorticity direction; a rotational state called log-rolling. At high ${\mathrm{Re}}_p$, fluid inertia will dominate and the particle will remain in a steady state, where the particle symmetry axis is perpendicular to the vorticity direction and has a constant angle ${\varphi }_c$ to the flow direction. The sequence of transitions between these dynamical states were found to be dependent on density ratio $\alpha$, particle aspect ratio $r_p$, and domain size. More specifically, the present study reveals that an inclined rolling state (particle rotates around its symmetry axis, which is not aligned in the vorticity direction) appears through a pitchfork bifurcation due to the influence of periodic boundary conditions when simulated in a small domain. Furthermore, it is also found that a tumbling motion, where the particle symmetry axis rotates in the flow-gradient plane, can be a stable motion for particles with high $r_p$ and low $\alpha$.

Electrostatic or magnetostatic problems involving complex heterogeneity are nontrivial for modeling and simulation. Most existing numerical methods focus on sharp interface models and the computational cost increases with increasing complexity of the geometry. Here we develop an iterative spectral method, the bound charge successive approximation algorithm, to solve electrostatic or magnetostatic heterogeneity problems in the context of diffuse-interface modeling. As tests and verifications, this algorithm is applied to calculation of the depolarization factor of an ellipsoid, and simulation of random dielectric mixtures and the dielectophoretic motion of multiple particles. The algorithm shows excellent efficiency and the computational cost mainly depends on the permittivity or permeability contrast in the whole system, regardless of the complexity of the geometry. In particular, for evolving heterostructures the solution of bound charge in one time step can be used as input for the next, which could further significantly shorten the iteration (approximation) process, making it practical to simulate the long-range electrostatic or magnetostatic interaction in complex and evolving heterostructures.

The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time (MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.

The radical pair model has been successful in explaining behavioral characteristics of the geomagnetic compass believed to underlie the navigation capability of certain avian species. In this study, the spin dynamics of the radical pair model and decoherence therein are interpreted from a microscopic state transition point of view. This helps to elucidate the interplay between the hyperfine and Zeeman interactions that enables the avian compass and clarify the distinctive effects of nuclear and environmental decoherence on it. Three regimes have been identified for the strength of the hyperfine interaction with respect to that of the geomagnetic Zeeman. It is found that the compass is likely to function in the large hyperfine interaction regime. Using a quantum information theoretic quantifier of coherence, we find that nuclear decoherence induces new structure in the spin dynamics for intermediate hyperfine interaction strength. On the other hand, environmental decoherence—modeled by two different noise models—seems to disrupt the compass action.

Excess of probabilities of elastic processes over inelastic ones is a characteristic feature of the chaotic resonance scattering predicted by the random matrix theory (RMT). Quantitatively, this phenomenon is characterized by the elastic enhancement factor $F^{\left(\beta \right)}$ that is, essentially, a typical ratio of elastic and inelastic cross sections. Being measured experimentally, this quantity can provide important information on the character of dynamics of the complicated intermediate open system formed on the intermediate stage of various resonance scattering processes. We discuss properties of the enhancement factor in a wide scope from mesoscopoic systems as, for example, heavy nuclei to macroscopic electromagnetic analogous devices imitating two-dimensional quantum billiards. We demonstrate a substantial qualitative distinction between the elastic enhancement factor's peculiarities in these two cases. A complete analytical solution is found for the case of systems without time-reversal symmetry and only a few equivalent open scattering channels.