We use molecular-dynamics computer simulations to investigate the density, strain-rate, and shear-pressure responses of a simple model atomic fluid to transverse and longitudinal external forces. We have previously introduced a response function formalism for describing the density, strain-rate, and shear-pressure profiles in an atomic fluid when it is perturbed by a combination of longitudinal and transverse external forces that are independent of time and have a simple sinusoidal spatial variation. In this paper, we extend the application of the previously introduced formalism to consider the case of a longitudinal force composed of multiple sinusoidal components in combination with a single-component sinusoidal transverse force. We find that additional harmonics are excited in the density, strain-rate, and shear-pressure profiles due to couplings between the force components. By analyzing the density, strain-rate, and shear-pressure profiles in Fourier space, we are able to evaluate the Fourier coefficients of the response functions, which now have additional components describing the coupling relationships. Having evaluated the Fourier coefficients of the response functions, we are then able to accurately predict the density, velocity, and shear-pressure profiles for fluids that are under the influence of a longitudinal force composed of two or three sinusoidal components combined with a single-component sinusoidal transverse force. We also find that in the case of a multisinusoidal longitudinal force, it is sufficient to include only pairwise couplings between different longitudinal force components. This means that it is unnecessary to include couplings between three or more force components in the case of a longitudinal force composed of many Fourier components, and this paves the way for a highly accurate but tractable treatment of nonlocal transport phenomena in fluids with density and strain-rate inhomogeneities on the molecular length scale.

The experimental flow curves of four different yield-stress fluids with different interparticle interactions are studied near the jamming concentration. By appropriate scaling with the distance to jamming all rheology data can be collapsed onto master curves below and above jamming that meet in the shear-thinning regime and satisfy the Herschel-Bulkley and Cross equations, respectively. In spite of differing interactions in the different systems, master curves characterized by universal scaling exponents are found for the four systems. A two-state microscopic theory of heterogeneous dynamics is presented to rationalize the observed transition from Herschel-Bulkley to Cross behavior and to connect the rheological exponents to microscopic exponents for the divergence of the length and time scales of the heterogeneous dynamics. The experimental data and the microscopic theory are compared with much of the available literature data for yield-stress systems.

The magnetoviscous effect, change in viscosity with change in magnetic field strength, and the anisotropy of the magnetoviscous effect, change in viscosity with orientation of magnetic field, have been a focus of interest for four decades. A satisfactory understanding of the microscopic origin of anisotropy of the magnetoviscous effect in magnetic fluids is still a matter of debate and a field of intense research. Here, we present an extensive simulation study to understand the relation between the anisotropy of the magnetoviscous effect and the underlying change in microstructures of ferrofluids. Our results indicate that field-induced chainlike structures respond very differently depending on their orientation relative to the direction of an externally applied shear flow, which leads to a pronounced anisotropy of viscosity. In this work, we focus on three exemplary values of dipolar interaction strengths which correspond to weak, intermediate, and strong interactions between dipolar colloidal particles. We compare our simulation results with an experimental study on cobalt-based ferrofluids as well as with an existing theoretical model called the chain model. A nonmonotonic behavior in the anisotropy of the magnetoviscous effect is observed with increasing dipolar interaction strength and is explained in terms of microstructure formation.

We study a thin-film growth model with temperature activated diffusion of adsorbed particles, allowing for the formation of overhangs and pores, but without detachment of adatoms or clusters from the deposit. Simulations in one-dimensional substrates are performed for several values of the diffusion-to-deposition ratio $R$ of adatoms with a single bond and of the detachment probability $\epsilon$ per additional nearest neighbor, respectively, with activation energies are $E_s$ and $E_b$. If $R$ and $\epsilon$ independently vary, regimes of low and high porosity are separated at $0.075\le {\epsilon }_c\le 0.09$, with vanishingly small porosity below that point and finite porosity for larger $\epsilon$. Alternatively, for fixed values of $E_s$ and $E_b$ and varying temperature, the porosity has a minimum at $T_c$, and a nontrivial regime in which it increases with temperature is observed above that point. This is related to the large mobility of adatoms, resembling features of equilibrium surface roughening. In this high-temperature region, the deposit has the structure of a critical percolation cluster due to the nondesorption. The pores are regions enclosed by blobs of the corresponding percolating backbone, thus the distribution of pore size $s$ is expected to scale as $s^{-\tilde{\tau }}$ with $\tilde{\tau }\approx 1.45$, in reasonable agreement with numerical estimates. Roughening of the outer interface of the deposits suggests Villain-Lai-Das Sarma scaling below the transition. Above the transition, the roughness exponent $\alpha \approx 0.35$ is consistent with the percolation backbone structure via the relation $\alpha =2-d_B$, where $d_B$ is the backbone fractal dimension.

We study the high-velocity regime mode-I fracture instability wherein small microbranches start to appear near the main crack, using large-scale simulations. Some of the features of those microbranches have been reproduced qualitatively in smaller-scale studies [using $\mathcal{O}\left({10}^4\right)$ atoms] on both a model of an amorphous material (via the continuous random network model) and using perturbed-lattice models. In this study, larger-scale simulations $\mathrm{[}\mathcal{O}\left({10}^6\right)$ atoms] were performed using multithreading computing on a GPU device, in order to achieve more physically realistic results. First, we find that the microbranching pattern appears to be converging with the lattice width. Second, the simulations reproduce the growth of the size of a microbranch as a function of the crack velocity, as well as the increase of the amplitude of the derivative of the electrical-resistance root-mean square with respect to the time as a function of the crack velocity. In addition, the simulations yield the correct branching angle of the microbranches, and the power law exponent governing the shape of the microbranches seems to be lower than unity, so that the side cracks turn over in the direction of propagation of the main crack as seen in experiment.

The way tension propagates along a chain is a key to govern many anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the dynamical fluctuations of a segment in a long polymer during its stretching process is investigated. We show that the response, i.e., average drift, is anomalous, which is characterized by the nonlinear memory kernel, and its relation to the fluctuation is nontrivial. These features are discussed on the basis of the generalized Langevin equation, in which the role of the temporal change in spring constant due to the stress hardening is pinpointed. We carried out the molecular dynamics simulation, which supports our theory.

We demonstrate how rhythmic activity can arise in neural networks from feedforward rather than recurrent circuitry and, in so doing, we provide a mechanism capable of explaining the temporal decorrelation of $\gamma$-band oscillations. We compare the spiking activity of a delayed recurrent network of inhibitory neurons with that of a feedforward network with the same neural properties and axonal delays. Paradoxically, these very different connectivities can yield very similar spike-train statistics in response to correlated input. This happens when neurons are noisy and axonal delays are short. A Taylor expansion of the feedback network's susceptibility—or frequency-dependent gain function—can then be stopped at first order to a good approximation, thus matching the feedforward net's susceptibility. The feedback network is known to display oscillations; these oscillations imply that the spiking activity of the population is felt by all neurons within the network, leading to direct spike correlations in a given neuron. On the other hand, in the output layer of the feedforward net, the interaction between the external drive and the delayed feedforward projection of this drive by the input layer causes indirect spike correlations: spikes fired by a given output layer neuron are correlated only through the activity of the input layer neurons. High noise and short delays partially bridge the gap between these two types of correlation, yielding similar spike-train statistics for both networks. This similarity is even stronger when the delay is distributed, as confirmed by linear response theory.

Intrinsic noise arising from the stochastic opening and closing of voltage-gated ion channels has been shown experimentally and mathematically to have important effects on a neuron's function. Study of classical neuron models with stochastic ion channels is becoming increasingly important, especially in understanding a cell's ability to produce subthreshold oscillations and to respond to weak periodic stimuli. While it is known that stochastic models can produce oscillations (quasicycles) in parameter regimes where the corresponding deterministic model has only a stable fixed point, little analytical work has been done to explore these connections within the context of channel noise. Using a stochastic hybrid Morris-Lecar (ML) model, we combine a system-size expansion in ${\mathrm{K}}^{+}$ and a quasi-steady-state (QSS) approximation in persistent ${\mathrm{Na}}^{+}$ in order to derive an effective Langevin equation that preserves the low-dimensional (planar) structure of the underlying deterministic ML model. (The QSS analysis exploits the fact that persistent ${\mathrm{Na}}^{+}$ channels are fast.) By calculating the corresponding power spectrum, we determine analytically how noise significantly extends the parameter regime in which subthreshold oscillations occur.

Bird flocks are a paradigmatic example of collective motion. One of the prominent traits of flocking is the presence of long range velocity correlations between individuals, which allow them to influence each other over the large scales, keeping a high level of group coordination. A crucial question is to understand what is the mutual interaction between birds generating such nontrivial correlations. Here we use the maximum entropy (ME) approach to infer from experimental data of natural flocks the effective interactions between individuals. Compared to previous studies, we make a significant step forward as we retrieve the full functional dependence of the interaction on distance, and find that it decays exponentially over a range of a few individuals. The fact that ME gives a short-range interaction even though its experimental input is the long-range correlation function, shows that the method is able to discriminate the relevant information encoded in such correlations and single out a minimal number of effective parameters. Finally, we show how the method can be used to capture the degree of anisotropy of mutual interactions.

The article analyzes the contribution of stochastic thermal fluctuations in the attachment times of the immature T-cell receptor TCR: peptide-major-histocompatibility-complex pMHC immunological synapse bond. The key question addressed here is the following: how does a synapse bond remain stabilized in the presence of high-frequency thermal noise that potentially equates to a strong detaching force? Focusing on the average time persistence of an immature synapse, we show that the high-frequency nodes accompanying large fluctuations are counterbalanced by low-frequency nodes that evolve over longer time periods, eventually leading to signaling of the immunological synapse bond primarily decided by nodes of the latter type. Our analysis shows that such a counterintuitive behavior could be easily explained from the fact that the survival probability distribution is governed by two distinct phases, corresponding to two separate time exponents, for the two different time regimes. The relatively shorter timescales correspond to the cohesion:adhesion induced immature bond formation whereas the larger time reciprocates the association:dissociation regime leading to TCR:pMHC signaling. From an estimate of the bond survival probability, we show that, at shorter timescales, this probability $P_{\mathrm{\Delta }}\left(\tau \right)$ scales with time $\tau$ as a universal function of a rescaled noise amplitude $\frac{D}{{\mathrm{\Delta }}^2}$, such that $P_{\mathrm{\Delta }}\left(\tau \right)\sim {\tau }^{-(\frac{\mathrm{\Delta }}{\sqrt{D}}+\frac{1}{2})},\mathrm{\Delta }$ being the distance from the mean intermembrane (T cell:Antigen Presenting Cell) separation distance. The crossover from this shorter to a longer time regime leads to a universality in the dynamics, at which point the survival probability shows a different power-law scaling compared to the one at shorter timescales. In biological terms, such a crossover indicates that the TCR:pMHC bond has a survival probability with a slower decay rate than the longer LFA-1:ICAM-1 bond justifying its stability.

Measuring molecular diffusion has been used to characterize the properties of living organisms and porous materials. NMR is able to detect the diffusion process in vivo and noninvasively. The fractional motion (FM) model is appropriate to describe anomalous diffusion phenomenon in crowded environments, such as living cells. However, no FM-based NMR theory has yet been established. Here, we present a general formulation of the FM-based NMR signal under the influence of arbitrary magnetic field gradient waveforms. An explicit analytic solution of the stretched exponential decay format for NMR signals with finite-width Stejskal-Tanner bipolar pulse magnetic field gradients is presented. Signals from a numerical simulation matched well with the theoretical prediction. In vivo diffusion-weighted brain images were acquired and analyzed using the proposed theory, and the resulting parametric maps exhibit remarkable contrasts between different brain tissues.

We investigated the effects of electrostatic interactions on the rate constant $\left(k_{\mathrm{p}}\right)$ for tension-induced pore formation in lipid membranes of giant unilamellar vesicles under constant applied tension. A decrease in salt concentration in solution as well as an increase in surface charge density of the membranes increased $k_{\mathrm{p}}$. These data indicate that $k_{\mathrm{p}}$ increases as the extent of electrostatic interaction increases. We developed a theory on the effect of the electrostatic interactions on the free energy profile of the membrane containing a prepore and also on the values of $k_{\mathrm{p}}$; this theory explains the experimental results and fits the experimental data reasonably well in the presence of weak electrostatic interactions. Based on these results, we conclude that a decrease in the free energy barrier of the prepore state due to electrostatic interactions is the main factor causing an increase in $k_{\mathrm{p}}$.

Two-dimensional space-filling bearings are dense packings of disks that can rotate without slip. We consider the entire first family of bearings for loops of four disks and propose a hierarchical construction of their contact network. We provide analytic expressions for the clustering coefficient and degree distribution, revealing bipartite scale-free behavior with a tunable degree exponent depending on the bearing parameters. We also analyze their average shortest path and percolation properties.

Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. We find that the full dynamical equations for the phase dynamics of a limit-cycle oscillator array go beyond previously studied Kuramoto-type equations. We analyze the evolution of the phase field in a two-dimensional array and obtain a “phase diagram” for the resulting stationary and nonstationary patterns. Our results are of direct relevance in the context of currently emerging experiments on nano- and optomechanical oscillator arrays, as well as for any array of coupled limit-cycle oscillators that have undergone a Hopf bifurcation. The possible observation in optomechanical arrays is discussed briefly.

The quenching of oscillations in interacting systems leads to several unwanted situations, which necessitate a suitable remedy to overcome the quenching. In this connection, this work addresses a mechanism that can resurrect oscillations in a typical situation. Through both numerical and analytical studies, we show that the candidate which is capable of resurrecting oscillations is nothing but the feedback, the one which is profoundly used in dynamical control and in biotherapies. Even in the case of a rather general system, we demonstrate analytically the applicability of the technique over one of the oscillation quenched states called amplitude death states. We also discuss some of the features of this mechanism such as adaptability of the technique with the feedback of only a few of the oscillators.

Spontaneous explosive is an abrupt transition to collective behavior taking place in heterogeneous networks when the frequencies of the nodes are positively correlated with the node degree. This explosive transition was conjectured to be discontinuous. Indeed, numerical investigations reveal a hysteresis behavior associated with the transition. Here, we analyze explosive synchronization in star graphs. We show that in the thermodynamic limit the transition to (and out of) collective behavior is indeed discontinuous. The discontinuous nature of the transition is related to the nonlinear behavior of the order parameter, which in the thermodynamic limit exhibits multiple fixed points. Moreover, we unravel the hysteresis behavior in terms of the graph parameters. Our numerical results show that finite-size graphs are well described by our predictions.

The ballistic increase for the velocity of a particle in a bouncing-ball model was investigated. The phenomenon is caused by accelerating structures in phase space known as accelerator modes. They lead to a regular and monotonic increase of the velocity. Here, both regular and ballistic Fermi acceleration coexist in the dynamics, leading the dynamics to two different growth regimes. We characterized deaccelerator modes in the dynamics, corresponding to unstable points in the antisymmetric position of the accelerator modes. In control parameter space, parameter sets for which these accelerations and deaccelerations constitute structures were obtained analytically. Since the mapping is not symplectic, we found fractal basins of influence for acceleration and deacceleration bounded by the stable and unstable manifolds, where the basins affect globally the average velocity of the system.

We perform two high-resolution direct numerical simulations of stratified turbulence for Reynolds number equal to $\mathrm{Re}\approx 25000$ and Froude number, respectively, of $\mathrm{Fr}\approx 0.1$ and $\mathrm{Fr}\approx 0.03$. The flows are forced at large scale and discretized on an isotropic grid of ${2048}^3$ points. Stratification makes the flow anisotropic and introduces two extra characteristic scales with respect to homogeneous isotropic turbulence: the buoyancy scale, $L_B$, and the Ozmidov scale, ${\ell }_{\mathrm{oz}}$. The former is related to the number of layers that the flow develops in the direction of gravity, and the latter is regarded as the scale at which isotropy is recovered. The values of $L_B$ and ${\ell }_{\mathrm{oz}}$ depend on the Froude number, and their absolute and relative amplitudes affect the repartition of energy among Fourier modes in ways that are not easy to predict. By contrasting the behavior of the two simulated flows we identify some surprising similarities: After an initial transient the two flows evolve towards comparable values of the kinetic and potential enstrophy and energy dissipation rate. This is the result of the Reynolds number being large enough in both flows for the Ozmidov scale to be resolved. When properly dimensionalized, the energy dissipation rate is compatible with atmospheric observations. Further similarities emerge at large scales: The same ratio between potential and total energy $(\approx 0.1)$ is spontaneously selected by the flows, and slow modes grow monotonically in both regimes, causing a slow increase of the total energy in time. The axisymmetric total energy spectrum shows a wide variety of spectral slopes as a function of the angle between the imposed stratification and the wave vector. One-dimensional energy spectra computed in the direction parallel to gravity are flat from the forcing up to buoyancy scale. At intermediate scales a $\sim k^{-3}$ parallel spectrum develops for the $\mathrm{Fr}\approx 0.03$ run, whereas for weaker stratification, the saturation spectrum does not have enough scales to develop and instead one observes a power law compatible with Kolmogorov scaling. Finally, the spectrum of helicity is flat until $L_B$, as observed in the nocturnal planetary boundary layer.

The present paper is devoted to an experimental investigation of the cavity formed upon a single-drop impingement onto a traveling solitary surface wave on a deep pool of the same liquid. The dynamics of the cavity throughout its complete expansion and receding phase are analyzed using high-speed shadowgraphy and compared to the outcomes of drop impingements onto steady liquid surface films having equal thickness. The effects of the surface wave velocity, amplitude and phase, drop impingement velocity, and liquid viscosity on the cavity's diameter and depth evolution are accurately characterized at various time instants. The wave velocity induces a distinct and in time increasing inclination of the cavity in the wave propagation direction. In particular for strong waves an asymmetrical distribution of the radial expansion and retraction velocity along the cavity's circumference is observed. A linear dependency between the absolute Weber number and the typical length and time scales associated with the cavity's maximum depth and maximum diameter is reported.

We investigate the Rayleigh-Bénard convection under sinusoidally varying temperatures of the horizontal rigid planes bounding a laterally infinite fluid layer for the bicritical states. The problem is analogous to the well studied Faraday instability and Rayleigh-Bénard convection under gravity modulation. Under modulation, the neutral instability curve is found to alternate between the conventional harmonic and subharmonic tongues in the space of the dimensionless wave number of disturbance and the control parameter. The transition between harmonic and subharmonic critical instability responses is found to occur via a bicritical state, where the two instability responses coexist with different wave numbers. These bicritical states are found to depend upon the modulation parameters and the Prandtl number.