Ionic polymer metal composites (IPMCs) are a class of soft electroactive materials that are recently finding extensive application as mechanical sensors and energy harvesters in liquids. In their most fundamental form, IPMCs are composed of a hydrated ionomeric membrane that is sandwiched between two electrochemically deposited metal electrodes. Ionomer swelling, counterion diffusion, and the formation of electric double layers are some of the physical phenomena underpinning energy transduction in IPMCs; however, a thorough understanding of the relative influence of such phenomena is yet to be established. Here, we propose a physics-based modeling framework, based on the Poisson-Nernst-Planck system, to describe IPMC chemoelectrical response to an imposed time-varying flexural deformation. We utilize the method of matched asymptotic expansions to compute a closed-form solution for the electric potential and counterion concentration in the IPMC. The model predicts that IPMC sensing is independent of the time rate of deformation and linearly correlated to the mechanical curvature, with a coefficient of proportionality that is a function of the ionomer thickness and the temperature. Thus, our results demonstrate that the characterization of IPMC electrical impedance suffices to identify all the parameters that are relevant to sensing, in contrast with the current state of knowledge. Theoretical results are validated through experiments on patterned in-house fabricated IPMC samples that are subject to time-varying flexural deformations.

Cell-to-cell adhesion is an important aspect of malignant spreading that is often observed in images from the experimental cell biology literature. Since cell-to-cell adhesion plays an important role in controlling the movement of individual malignant cells, it is likely that cell-to-cell adhesion also influences the spatial spreading of populations of such cells. Therefore, it is important for us to develop biologically realistic simulation tools that can mimic the key features of such collective spreading processes to improve our understanding of how cell-to-cell adhesion influences the spreading of cell populations. Previous models of collective cell spreading with adhesion have used lattice-based random walk frameworks which may lead to unrealistic results, since the agents in the random walk simulations always move across an artificial underlying lattice structure. This is particularly problematic in high-density regions where it is clear that agents in the random walk align along the underlying lattice, whereas no such regular alignment is ever observed experimentally. To address these limitations, we present a lattice-free model of collective cell migration that explicitly incorporates crowding and adhesion. We derive a partial differential equation description of the discrete process and show that averaged simulation results compare very well with numerical solutions of the partial differential equation.

In an asymmetric bistable dynamical system with delayed feedback, one of the stable states is usually “stronger” than the other one: The system relaxes to it not only from close initial conditions, but also from oscillatory initial configurations which contain epochs of stay near both attractors. However, if the initial nucleus of the stronger phase is shorter than a certain critical value, it shrinks, and the weaker state is established instead. We observe this effect in a paradigmatic model and in an experiment based on a bistable semiconductor laser and characterize it in terms of scaling laws governing its asymptotic properties.

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright $N$-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave–short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions—(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components—result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.

We study the role of amplifier saturation in eliminating feedback noise in self-sustained oscillators. We extend previous works that use a saturated amplifier to quench fluctuations in the feedback magnitude, while simultaneously tuning the oscillator to an operating point at which the resonator nonlinearity cancels fluctuations in the feedback phase. We consider a generalized model which features an amplitude-dependent amplifier gain function. This allows us to determine the total oscillator phase noise in realistic configurations due to noise in both quadratures of the feedback, and to show that it is not necessary to drive the resonator to large oscillation amplitudes in order to eliminate noise in the phase of the feedback.

In this study, plane Poiseuille-Couette flow is simulated as a model for specified streamwise slip on one of the channel walls. The relative velocity between the two walls is set to be 1, 2, and 4 in viscous wall units. This is equivalent to the presence of a superhydrophobic surface at one of the channel walls that causes fluid to slip on the boundary. The results show that the streamwise slip forces turbulence in the near-wall region to tend towards a limiting one-component state. This leads to the suppression of small scale turbulence and laminarization close to the wall and then to drag reduction. The selective weakening of the streamwise vorticity close the wall and the observed decrease of turbulence kinetic energy production can then be considered as a consequence of this effect. Changes in the coherent structures, including a decrease of sweep events and increase of ejection events close to the wall where slip occurs, are also observed.

The evolution of the force distributions during the isotropic compression of two-dimensional packings of soft frictional particles is investigated numerically. Regardless of the applied deformation, the normal contact force distribution $P\left(f_n\right)$ can be fitted by the product of a power law, and a stretched exponential, while the tangential force distribution $P\left(f_t\right)$ is fitted well by a Gaussian. With increasing strain, the asymptotic behavior at large forces does not change, but both $P\left(f_n\right)$ and $P\left(f_t\right)$ exhibit a broadening, even though, when scaled with the average forces, their widths decrease. Furthermore, the distribution of friction mobilization $P\left(\eta \right)$ is a decreasing function of $\eta =|f_t|/\left(\mu f_n\right)$, except for an increased probability of fully mobilized contacts ($\eta =1$). The excess coordination number of the packings increases with the applied strain, indicating that the more a packing is compressed the more stable it becomes.

In this paper, we present the effects of memory decay on a bootstrap percolation model applied to random directed graphs (quorum percolation). The addition of decay was motivated by its natural occurrence in physical systems previously described by percolation theory, such as cultured neuronal networks, where decay originates from ionic leakage through the membrane of neurons and/or synaptic depression. Surprisingly, this feature alone appears to change the critical behavior of the percolation transition, where discontinuities are replaced by steep but finite slopes. Using different numerical approaches, we show evidence for this qualitative change even for very small decay values. In experiments where the steepest slopes can not be resolved and still appear as discontinuities, decay produces nonetheless a quantitative difference on the location of the apparent critical point. We discuss how this shift impacts network connectivity previously estimated without considering decay. In addition to this particular example, we believe that other percolation models are worth reinvestigating, taking into account similar sorts of memory decay.

Percolation theory is an approach to study the vulnerability of a system. We develop an analytical framework and analyze the percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that the damage in the network due to a failure is a continuous function of the size of the failure, i.e., the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to an abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of $n$ classic Erdős-Rényi (ER) networks, where each network depends on the same number $m$ of other networks, i.e., for a random regular network (RR) formed of interdependent ER networks. The dependency between nodes of different networks is taken as one-to-one correspondence, i.e., a node in one network can depend only on one node in the other network (no-feedback condition). In contrast to a treelike NetONet in which the size of the largest connected cluster (mutual component) depends on $n$, the loops in the RR NetONet cause the largest connected cluster to depend only on $m$ and the topology of each network but not on $n$. We also analyzed the extremely vulnerable feedback condition of coupling, where the coupling between nodes of different networks is not one-to-one correspondence. In the case of NetONet formed of ER networks, percolation only exhibits two phases, a second order phase transition and collapse, and no first order percolation transition regime is found in the case of the no-feedback condition. In the case of NetONet composed of RR networks, there exists a first order phase transition when the coupling strength $q$ (fraction of interdependency links) is large and a second order phase transition when $q$ is small. Our insight on the resilience of coupled networks might help in designing robust interdependent systems.

We examine the time-dependent behavior of a nonlinear system driven by a two-frequency forcing. By using a nonperturbative approach, we are able to derive an asymptotic expression, valid in the long-time limit, for the time average of the output variable which describes the response of the system. We identify several universal features of the asymptotic response of the system, which are independent of the details of the model. In particular, we determine an asymptotic expression for the width of the resonance observed by keeping one frequency fixed and varying the other one. We show that this width is smaller than the usually assumed Fourier width by a factor determined by the two driving frequencies, and independent of the model system parameters. Additional general features can also be identified depending on the specific symmetry properties of the system. Our results find direct application in the study of sub-Fourier signal processing with nonlinear systems.

Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of $250000000$ cells to provide topological and geometrical statistics of this important class of networks. We also report correlations between some of these topological and geometrical measures. Using these results, we are able to corroborate several conjectures regarding the properties of three-dimensional Poisson-Voronoi networks and refute others. In many cases, we provide accurate fits to these data to aid further analysis. We also demonstrate that topological measures represent powerful tools for describing cellular networks and for distinguishing among different types of networks.

The endocytotic mechanism of entry of virions into cells includes wrapping of a virion by the host membrane with subsequent formation of a vesicle covering a virion. The energy along this pathway depends on the ligand-receptor interaction and deformation of the cell membrane and underlying actin cytoskeleton. The available models describe the cytoskeleton deformation by using the conventional continuum theory of elasticity and predict that this factor often controls the repulsive part of the virion-cell interaction. This approach is, however, debatable because the size of virions is smaller than or comparable to the length scale characterizing the cytoskeleton structure. The author shows that the continuum theory appreciably (up to one order of magnitude) overestimates the cytoskeleton-deformation energy and that the scale of this energy is comparable to that of cell membrane bending.

When active matter particles such as swimming bacteria are placed in an asymmetric array of funnels, it has been shown that a ratchet effect can occur even in the absence of an external drive. Here we examine active ratchets for two-dimensional arrays of funnels or L shapes where there is also an externally applied dc drive or drift. We show that for certain conditions the ratchet effect can be strongly enhanced and it is possible to have conditions under which run-and-tumble particles with one run length move in the opposite direction from particles with a different run length. For the arrays of L shapes, we find that the application of a drift force can enhance a transverse rectification in the direction perpendicular to the drift. When particle-particle steric interactions are included, we find that the ratchet effects can be either enhanced or suppressed depending on barrier geometry, particle run length, and particle density.

The Mullins-Sekerka and the electric breakdown instabilities are well known to lead to the spontaneous formation of a variety of complex spatial structures, among them dendritic crystal shapes, and treelike electric discharge patterns. Controlling such systems by suppressing predominantly excited solutions offers the opportunity to manipulate and stabilize these patterns in a defined way for a wide range of technological applications. In this work, we employ a variational approach which enables one to systematically search for the ideal conditions under which the patterns grow, but where interfacial deformations are efficiently minimized. The effectiveness of our variational control method is illustrated via linear stability calculations on both two-dimensional and three-dimensional contour-dynamics models for crystal growth and electric discharge phenomena.

Sliding at interface during thin film buckling was reported by recent atomistic simulations. A stability analysis under the Föppl–von Kármán plate theory is performed to investigate the effect of interface sliding on the transition of a straight-sided blister to the telephone cord buckle in biaxially compressed thin films on rigid substrates. It is shown that the critical stress and the wavelength of the telephone cord buckle significantly increase as the interface sliding is noticeable in comparison with the constant values derived from previous classic analysis without interface sliding. Our theoretic analysis is further validated by results from numerical simulations based on our recently developed continuum model of nonlinear buckling. The results indicate that the wavelength variation in the telephone cord buckle observed in experiments may be due to interface sliding.

Signal propagation in neuronal dendrites represents the basis for interneuron communication and information processing in the brain. Here we take into account charge inhomogeneities arising in the vicinity of ion channels in cytoplasm and obtain a modified cable equation. We show that charge inhomogeneities acting on a millisecond time scale can lead to the appearance of propagating waves with wavelengths of hundreds of micrometers. They correspond to a certain frequency band predicting the appearance of resonant properties in brain neuron signaling. We also show that membrane potential in spiny dendrites obeys the modified cable equation suggesting a crucial role of the spines in dendritic subthreshold resonance.

The excitation energy transfer dynamics in the Fenna-Matthews-Olson complex is quantified in terms of a non-Markovianity measure based on the time evolution of the trace distance of two quantum states. We use a system description derived from experiments and different environmental fluctuation spectral functions, which are obtained either from experimental data or from molecular dynamics simulations. These exhibit, in all cases, a nontrivial structure with several peaks attributed to vibrational modes of the pigment-protein complex. Such a structured environmental spectrum can, in principle, give rise to strong non-Markovian effects. We present numerically exact real-time path-integral calculations for the transfer dynamics and find, in all cases, a monotonic decrease of the trace distance with increasing time which renders a Markovian description valid.

A theoretical framework for the description of susceptible-infected-removed (SIR) spreading processes with synergistic transmission of infection on a lattice is developed. The model incorporates explicitly the effects of time-dependence of the state of the hosts in the neighborhood of transmission events. Exact solution of the model shows that time-dependence of the state of nearest neighbors of recipient hosts is a key factor for synergistic spreading processes. It is demonstrated that the higher the connectivity of a lattice, the more prominent is the effect of synergy on spread.

Finite time Lyapunov exponents are used to determine expanding, contracting, and hyperbolic regions in computational simulations of laminar steady-state fluid flows within realistic three dimensional pore structures embedded within an impermeable matrix. These regions correspond approximately to pores where flow converges (contraction) or diverges (expansion), and to throats between pores where the flow mixes (hyperbolic). The regions are sparse and disjoint from one another, occupying only a small percentage of the pore space. Nonetheless, nearly every percolating fluid particle trajectory passes through several hyperbolic regions indicating that the effects of in-pore mixing are distributed throughout an entire pore structure. Furthermore, the observed range of fluid dynamics evidences two scales of heterogeneity within each of these flow fields. There is a larger scale that affects dispersion of fluid particle trajectories across the connected network of pores and a relatively small scale of nonuniform distributions of velocities within an individual pore.

Based on a parallel scalable library for Coulomb interactions in particle systems, a comparison between the fast multipole method (FMM), multigrid-based methods, fast Fourier transform (FFT)-based methods, and a Maxwell solver is provided for the case of three-dimensional periodic boundary conditions. These methods are directly compared with respect to complexity, scalability, performance, and accuracy. To ensure comparable conditions for all methods and to cover typical applications, we tested all methods on the same set of computers using identical benchmark systems. Our findings suggest that, depending on system size and desired accuracy, the FMM- and FFT-based methods are most efficient in performance and stability.