Sandpile models have been used to provide simple phenomenological models without incorporating the detailed features of a fully featured model. The Chapman sandpile model [Chapman et al., Phys. Rev. Lett. 86, 2814 (2001)] has been used as an analog for the behavior of a plasma edge, with mass loss events being used as analogs for edge-localized modes (ELMs). In this work we modify the Chapman sandpile model by providing for both increased and intermittent driving. We show that the behavior of the sandpile, when continuously fuelled at very high driving, can be determined analytically by a simple algorithm. We observe that the size of the largest avalanches is better reduced by increasing constant driving than by the intermittent introduction of “pellets” of sand. Using the sandpile model as a reduced model of ELMing behavior, we conject that ELM control in a fusion plasma may similarly prove more effective with increased total fuelling than with pellet addition.

We study the interface tracking characteristics of a color-gradient-based lattice Boltzmann model for immiscible flows. Investigation of the local density change in one of the fluid phases, via a Taylor series expansion of the recursive lattice Boltzmann equation, leads to the evolution equation of the order parameter that differentiates the fluids. It turns out that this interface evolution follows a conservative Allen-Cahn equation with a mobility which is independent of the fluid viscosities and surface tension. The mobility of the interface, which solely depends upon lattice speed of sound, can have a crucial effect on the physical dynamics of the interface. Further, we find that, when the equivalent lattice weights inside the segregation operator are modified, the resulting differential operators have a discretization error that is anisotropic to the leading order. As a consequence, the discretization errors in the segregation operator, which ensures a finite interface width, can act as a source of the spurious currents. These findings are supported with the help of numerical simulations.

In this Rapid Communication we report the unusual dynamics of planar, rigid, and anisotropy glass-forming molecules of unusually large size by dielectric spectroscopy by using two examples. The size of the molecules is much larger than the dipolar moiety located at the end of the longer axis of each molecule. The observed dynamics deviates strongly from the anticorrelation between ${\beta }_{\mathrm{KWW}}$ (fractional exponent of the Kohlrausch-Williams-Watts function) and dielectric strength, $\mathrm{\Delta }\varepsilon \left(T_g\right)$, established generally for small van der Waals molecular glass formers. Moreover, the dynamics of the two large molecules differ greatly, albeit the difference is the dipole moment being orthogonal or parallel to the longer axis of the molecules. The drastic variation in dielectric response of the two materials coming from different portions of the structural α-relaxation spectrum is probed by the dipole. Thus, the new behavior opens up a new research area of the dynamics and thermodynamics of nonpolymeric sizable molecules, the dielectric response of which can be varied by the design of the dipole moiety.

We study the properties of nonequilibrium systems modelled as spin models without defined Hamiltonian as the majority voter model. This model has transition probabilities that do not satisfy the condition of detailed balance. The lack of detailed balance leads to entropy production phenomena, which are a hallmark of the irreversibility. By considering that voters can diffuse on the lattice we analyze how the entropy production and how the critical properties are affected by this diffusion. We also explore two important aspects of the diffusion effects on the majority voter model by studying entropy production and entropy flux via time-dependent and steady-state simulations. This study is completed by calculating some critical exponents as function of the diffusion probability.

The expressions for entropy production, free energy, and entropy extraction rates are derived for a Brownian particle that walks in an underdamped medium. Our analysis indicates that as long as the system is driven out of equilibrium, it constantly produces entropy at the same time it extracts entropy out of the system. At steady state, the rate of entropy production ${\dot{e}}_p$ balances the rate of entropy extraction ${\dot{h}}_d$. At equilibrium both entropy production and extraction rates become zero. The entropy production and entropy extraction rates are also sensitive to time. As time progresses, both entropy production and extraction rates increase in time and saturate to constant values. Moreover, employing microscopic stochastic approach, several thermodynamic relations for different model systems are explored analytically and via numerical simulations by considering a Brownian particle that moves in overdamped medium. Our analysis indicates that the results obtained for underdamped cases quantitatively agree with overdamped cases at steady state. The fluctuation theorem is also discussed.

Using stochastic thermodynamics, the properties of interacting linear chains subject to periodic drivings are investigated. The systems are described by Fokker-Planck-Kramers equation and exact solutions are obtained as functions of the modulation frequency and strength constants. Analysis will be carried out for short and long chains. In the former case, explicit expressions are derived for a chain of two particles, in which the entropy production is written down as a bilinear function of thermodynamic forces and fluxes, whose associated Onsager coefficients are evaluated for distinct kinds of periodic drivings. The limit of long chains is analyzed by means of a protocol in which the intermediate temperatures are self-consistently chosen and the entropy production is decomposed as a sum of two individual contributions, one coming from real baths (placed at extremities of lattice) and other from self-consistent baths. Whenever the former dominates for short chains, the latter contribution prevails for long ones. The thermal reservoirs lead to a heat flux according to Fourier's law.

The first step in nonlinear time-series analysis can be selecting a delay for reconstruction. The most popular choices of this delay are the first zero of the autocovariance and the first minimum of the mutual information. An advantage of the first method arises from the robustness to noise of the autocovariance function, while an advantage of the second is that the first minimum of the mutual information provides a useful choice of delay for a wide range of nonlinear systems. We propose a method to choose a delay for frequently sampled flowlike data based on a mean local autocovariance function and compare its performance to methods based on the autocovariance and the mutual information. In addition, we compare the novel method to an established method based on cross-validatory mean-square errors of predictors corresponding to different choices of delay. The mean local autocovariance combines the versatility of the mutual information with some of the robustness to noise of the autocovariance.

Using a tight binding model, we investigate the dynamics of an exciton on a disordered extended star graph whose central site acts as an energy trap. When compared with what happens in an ordered network, our results reveal that the disorder drastically improves the excitonic absorption that becomes complete. Moreover, we show the occurrence of an optimal disorder for which the absorption time is strongly minimized, a surprising effect that originates in a disorder-induced restructuring process of the exciton eigenstates. Finally, we also show the existence of an optimal value of the absorption rate that reduces even more the absorption time. The resulting superoptimized trapping process is interpreted as a positive interplay between both the disorder and the so-called superradiance transition.

Diverse biological functions of biomembranes are made possible by their rich dynamic behaviors across multiple scales. While the potential coupling between the dynamics of differing scales may underlie the machineries regulating the biomembrane-involving processes, the mechanism and even the existence of this coupling remain an open question, despite the latter being taken for granted. Via inelastic neutron scattering, we examined dynamics across multiple scales for the lipid membranes whose dynamic behaviors were perturbed by configurational changes at two membrane regions. Surprisingly, the dynamic behavior of individual lipid molecules and their collective motions were not always coupled. This suggests that the expected causal relation between the dynamics of the differing hierarchical levels does not exist and that an apparent coupling can emerge by manipulating certain membrane configurations. The findings provide insight on biomembrane modeling and how cells might individually or concertedly control the multiscale membrane dynamics to regulate their functions.

We discuss the shear viscosity of a Newtonian solution of catalytic enzymes and substrate molecules. The enzyme is modeled as a two-state dimer consisting of two spherical domains connected with an elastic spring. The enzymatic conformational dynamics is induced by the substrate binding and such a process is represented by an additional elastic spring. Employing the Boltzmann distribution weighted by the waiting times of enzymatic species in each catalytic cycle, we obtain the shear viscosity of dilute enzyme solutions as a function of substrate concentration and its physical properties. The substrate affinity distinguishes between fast and slow enzymes, and the corresponding viscosity expressions are obtained. Furthermore, we connect the obtained viscosity with the diffusion coefficient of a tracer particle in enzyme solutions.

Thermal fusion plasmas initiated by standing whistler waves are investigated numerically by two- and one-dimensional particle-in-cell simulations. When a standing whistler wave collapses due to the wave breaking of ion plasma waves, the energy of the electromagnetic waves transfers directly to the ion kinetic energy. Here we find that ion heating by use of standing whistler waves is operational even in multidimensional simulations of multi-ion species targets, such as deuterium-tritium (DT) ices and solid ammonia borane (${\mathrm{H}}_6\mathrm{BN}$). The energy conversion efficiency to ions becomes as high as 15% of the injected laser energy, which depends significantly on the target thickness and laser pulse duration. The ion temperature could reach a few tens of keV or much higher if appropriate laser-plasma conditions are selected. DT fusion plasmas generated by this method must be useful as efficient neutron sources. Our numerical simulations suggest that the neutron generation efficiency exceeds ${10}^9$ n/J per steradian, which is beyond the current achievements of the state-of-the-art laser experiments. Standing whistler-wave heating would expand the experimental possibility for an alternative ignition design of magnetically confined laser fusion and also for more difficult fusion reactions, including the aneutronic proton-boron reaction.

We present a class of exponential integrators to compute solutions of the stochastic Schrödinger equations arising from the modeling of open quantum systems. To be able to implement the methods within the same framework as the deterministic counterpart, we express the solution using Kunita's representation. With appropriate truncations, the solution operator can be written as matrix exponentials, which can be efficiently implemented by the Krylov subspace projection. The accuracy is examined in terms of the strong convergence by comparing trajectories, and in terms of the weak convergence by comparing the density-matrix operators. We show that the local accuracy can be further improved by introducing third-order commutators in the exponential. The effectiveness of the proposed methods is tested using the example from Di Ventra et al. [J. Phys.: Condens. Matter 16, 8025 (2004)].

A potential source of subharmonic bubble emissions is revealed experimentally by high-speed imaging. When an acoustic bubble is driven at sufficiently large pressure amplitudes, energy transfer from surface to volume oscillations can lead to the triggering of subharmonic spherical oscillations. This experimental evidence is in agreement with recent theoretical modeling of nonspherical bubble dynamics accounting for nonlinear mode coupling. Implications for the monitoring of stable cavitation activity are discussed.

We study Coulomb crystals containing two ion species simultaneously confined in radio frequency traps and coupled to different thermal reservoirs located in two separate regions. We use a three-dimensional model to simulate the trapped bicrystal and show in a numerically rigorous manner the effects of the mass dependence of the trapping frequencies on the underlying nonequilibrium dynamics and the temperature profiles. By solving the classical Langevin equations of motion, we obtain the spatial probability densities of the two ion species and the kinetic temperature profiles across the axial direction of the trap in the nonequilibrium steady state. We analyze trapping conditions leading to bicrystals that exhibit ion conformations ranging from a linear chain of alternating ion species to two- and three-dimensional configurations. The results evidence the spatial segregation of the two ion species due to the mass dependence of the trapping frequencies and the increase of ion delocalization for heavier ion species and/or weaker trapping confinements. We also show the correlation between the increase of the temperature gradient in the bulk and this enhancement of ion delocalization through the trap.

The timescales of many physical, chemical, and biological processes are determined by first passage times (FPTs) of diffusion. The overwhelming majority of FPT research studies the time it takes a single diffusive searcher to find a target. However, the more relevant quantity in many systems is the time it takes the fastest searcher to find a target from a large group of searchers. This fastest FPT depends on extremely rare events and has a drastically faster timescale than the FPT of a given single searcher. In this work, we prove a simple explicit formula for every moment of the fastest FPT. The formula is remarkably universal, as it holds for $d$-dimensional diffusion processes (i) with general space-dependent diffusivities and force fields, (ii) on Riemannian manifolds, (iii) in the presence of reflecting obstacles, and (iv) with partially absorbing targets. Our results rigorously confirm, generalize, correct, and unify various conjectures and heuristics about the fastest FPT.

Molecular systems are inherently probabilistic and operate in a noisy environment, yet, despite all these uncertainties, molecular functions are surprisingly reliable and robust. The principles used by natural systems to deal with noise are still not well understood, especially in a nonhomogeneous environment where molecules can diffuse across different compartments. In this paper we show that membrane transport mechanisms have very effective properties of noise reduction. In particular, we show that active transport mechanisms (those that can transport against a gradient of concentration by using energy or by means of the concentration gradient of other substances), such as symporters and antiporters, have surprising efficiency in noise reduction, which outperforms passive diffusion mechanisms and are well below Poisson levels. We link our results to the coupled transport of potassium, sodium, and glucose to show that the noise in internal glucose level can be greatly reduced. Our results show that compartmentalization can be a highly effective mechanism of noise reduction and suggests that membrane transport could give this extra benefit, contributing to the emergence of complex compartmentalization in eukaryotes.

A method of data assimilation (DA) is employed to estimate electrophysiological parameters of neurons simultaneously with their synaptic connectivity in a small model biological network. The DA procedure is cast as an optimization, with a cost function consisting of both a measurement error and a model error term. An iterative reweighting of these terms permits a systematic method to identify the lowest minimum, within a local region of state space, on the surface of a nonconvex cost function. In the model, two sets of parameter values are associated with two particular functional modes of network activity: simultaneous firing of all neurons and a pattern-generating mode wherein the neurons burst in sequence. The DA procedure is able to recover these modes if: (i) the stimulating electrical currents have chaotic waveforms and (ii) the measurements consist of the membrane voltages of all neurons in the circuit. Further, this method is able to prune a model of unnecessarily high dimensionality to a representation that contains the maximum dimensionality required to reproduce the provided measurements. This paper offers a proof-of-concept that DA has the potential to inform laboratory designs for estimating properties in small and isolatable functional circuits.

We introduce a minimal model for a two-dimensional polar flock with nonquenched rotators and show that the rotators make the usual macroscopic long-range order of the flock more robust than the clean system. The rotators memorize the flock-information which helps in establishing the robustness. Moreover, the memory of the rotators assists in probing the moving flock. We also formulate a hydrodynamic framework for the microscopic model that makes our study comprehensive. Using linearized hydrodynamics, it is shown that the presence of such nonquenched heterogeneities increases the sound speeds of the flock. The enhanced sound speeds lead to faster convection of information and consequently the robust ordering in the system. We argue that similar nonquenched heterogeneities may be useful in monitoring and controlling large crowds.

A binary mixture of droplets and patchy colloids, where patches are arranged in tetrahedral symmetry, is studied with Metropolis Monte Carlo simulations. The colloidal patches attract droplets, while both the colloid-colloid and the droplet-droplet interactions are hard sphere like. We find stable crystal structures with atomic analogs $\mathrm{ZnS}, {\mathrm{CaF}}_2$, and fcc or hcp (face centered cubic or hexagonal close packed) of the droplets coexisting with a dispersed fluid of the colloids. The simulated crystal structures agree well with those predicted by close-packing calculations for an intermediate range of droplet-colloid size ratios. A discrepancy between the simulations and theoretical predictions occurs at low and high size ratios. The results of the simulations for mixtures with anisotropic colloid-droplet interactions reveal a richer phase diagram, with ZnS-gas and ZnS-fluid coexistence, as compared to the isotropic case. For the example of a square planar patch arrangement, we find a particular crystal structure, consisting of two interpenetrating fcc or hcp lattices with right bond angles. Such a structure has no known atomic analog. Our study of generic models of anisotropic colloid-droplet mixtures could provide a promising way towards the fabrication of novel and complex colloidal structures.