Although multi-phase-field models are applied extensively to simulate various pattern formations, their asymptotic analysis is not typically performed at a level of rigor common to their scalar counterparts. Most of the time, arguments given, such as for the justification of the selection of the bulk phases or the phasal composition of the interfaces between them, are only heuristic in nature. In particular, the reduction of the multi-phase-field models to two-phase ones, so as to ascertain the dynamical laws captured by them, can only be termed as hand waving, at best. It is also common to land the starting point of the analysis directly at a point where the binary interfaces have already formed and continue therefrom with the prediction of their instantaneous evolution. However, exactly how a given initial filling transitions to a state characterized by the presence of bulk phases separated by internal layers, and with what distribution, is rarely addressed. Moreover, a detailed and systematic study, focused on the numerical realization of the asymptotics predicted laws, has never been reported before for multi-phase-field models. In the current article, endorsing against these undesirabilities of the common presentations, a full-fledged asymptotic analysis of a multi-grain-growth phase-field model is put forth and numerically verified. However, the consideration is only limited to the analysis of binary interfaces; that of junctions (triple points, quadruple points, etc.) is deferred to a later work.

The effect of rotation on small-scale characteristics and scaling law in the mixing zone of the three-dimensional turbulent Rayleigh-Taylor instability (RTI) is investigated by the lattice Boltzmann method at small Atwood number. The mixing zone width $h\left(t\right)$, the root mean square of small scale fluctuation, the spectra, and the structure functions are obtained to analyze the rotating effect. We mainly focus on the process of the development of plumes and discuss the physical mechanism in the mixing zone in rotating and nonrotating systems. The variation of kinetic energy spectra $E_u$ and temperature energy spectra $E_{\theta }$ with the dimensionless rotation $\mathrm{\Omega }\tau$ demonstrate the suppression effect of rotation. Two scaling laws between the mixing layer width $h\left(t\right)$ and dimensionless time $t/\tau$ are obtained at various Coriolis forces($\sqrt{h\left(t\right)}\simeq t^{0.9}$ and $\sqrt{h\left(t\right)}\simeq t^{0.35}$). The rotation increasingly suppresses the growth of the mixing layer width $h\left(t\right)$. The velocity and temperature fluctuations are also suppressed by the rotation effect. The relation between the Nusselt number (Nu) and the Rayleigh number (Ra) indicates that the heat transfer is suppressed by the rotation effect in the rotating RT system. The width of the inertial subrange increasingly narrows with increasing $\mathrm{\Omega }\tau$.

We study the relaxation dynamics of a binary liquid mixture near a light-absorbing Janus particle after switching on and off illumination using experiments and theoretical models. The dynamics is controlled by the temperature gradient formed around the heated particle. Our results show that the relaxation is asymmetric: The approach to a nonequilibrium steady state is much slower than the return to thermal equilibrium. Approaching a nonequilibrium steady state after a sudden temperature change is a two-step process that overshoots the response of spatial variance of the concentration field. The initial growth of concentration fluctuations after switching on illumination follows a power law in agreement with the hydrodynamic and purely diffusive model. The energy outflow from the system after switching off illumination is well described by a stretched exponential function of time with characteristic time proportional to the ratio of the energy stored in the steady state to the total energy flux in this state.

Numerous attempts have been made to obtain earthquake statistics from a theoretical-physics perspective, but these studies mostly involve regular earthquakes. In recent years, a new category of earthquakes, referred to as slow earthquakes, has been discovered. Slow earthquakes emit only weak or no seismic signals and have different statistics than regular earthquakes. Here we propose a physical model for the tremor, which is a type of slow earthquake, introducing two competing timescales in a cellular automaton model. The proposed model reproduces some observation results for tremors, such as enduring events, moment-duration scaling, size distribution, and the power spectrum of the moment rate function.

We discuss here the application of the simultaneous block diagonalization (SBD) of matrices to the study of the stability of both complete and cluster synchronization in random (generic) networks. For both problems, we define indices that measure success (or failure) of application of the SBD technique in decoupling the stability problem into problems of lower dimensionality. We then see that in the case of random networks the extent of the dimensionality reduction achievable is the same as that produced by application of a trivial transformation.

Many species are unsustainable at small population densities (Allee effect); i.e., below the so-called Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to extinction. Here, we show how, in spatially extended habitats, dispersal can lead to a sustainable population in a region, provided the amplitude of environmental fluctuations is below an extinction threshold. We have identified two types of sustainable populations: high-density and low-density populations (through a mean-field approximation, valid in the limit of large dispersal length). Our results show that patches where population is high, low, or extinct coexist when the population is close to global extinction (even for homogeneous habitats). The extinction threshold is maximum for characteristic dispersal distances much larger than the spatial scale of synchrony of environmental fluctuations. The extinction threshold increases proportionally to the square root of the dispersal rate and decreases with the Allee threshold. The low-population-density solution can allow understanding of difficulties in recovery after harvesting. This theoretical framework provides a unique approach to address other factors, such as habitat fragmentation or harvesting, impacting population resilience to environmental fluctuations.

When blood flows through vessel networks, red blood cells (RBCs) are typically concentrated close to the vessel center line, creating a lubrication layer near the vessel wall. As RBCs bind oxygen, the width of this cell-free layer (CFL) impacts not only the blood rheology inside the vasculature, but also oxygen delivery to the tissues they perfuse and, hence, their function. Existing attempts to relate the width of the CFL to the rheological properties of the blood and the geometrical properties of the vessel are based on an analysis of the forces acting on RBCs suspended in the blood. However, the complexity of interactions in the blood makes this a challenging task. Here, we propose an alternative, two-step approach to derive such a functional relationship. First, we extend widely accepted empirical fits describing the minimum flow fraction needed for RBCs to enter a daughter vessel downstream of a microvascular bifurcation so that it depends not only on the diameter and discharge haematocrit of the parent vessel, but also on its average shear rate. Second, we propose a simple geometrical model for the minimum flow fraction based on the cross-sectional blood flow profile within the parent vessel upstream of the bifurcation—considering uniform, parabolic, and blunt velocity profiles—and derive the leading-order approximation to this model for small CFL widths. By equating the functional relationships obtained using these two approaches, we derive expressions relating the CFL width to the vessel diameter, discharge haematocrit, and mean shear rate. The resulting expressions are in good agreement with available in vivo data and represent a promising basis for future research.

The impact of nanoparticles (NPs) composed of atoms with covalent bonding is investigated numerically and theoretically. We use recent models of covalent bonding of carbon atoms and elaborate a numerical model of amorphous carbon (a-C) NPs, which may be applied for modeling soot particles. We compute the elastic moduli of the a-C material which agree well with the available data. We reveal an interesting phenomenon—stress-dependent adhesion, which refers to stress-enhanced formation of covalent bonds between contacting surfaces. We observe that the effective adhesion coefficient linearly depends on the maximal stress between the surfaces and explain this dependence. We compute the normal restitution coefficient for colliding NPs and explore the dependence of the critical velocity, demarcating bouncing and aggregative collisions, on the NP radius. Using the obtained elastic and stress-dependent adhesive coefficients we develop a theory for the critical velocity. The predictions of the theory agree very well with the simulation results.

The Fermi acceleration model describes how cosmic ray particles accelerate to great speeds by interacting with moving magnetic fields. We identify a variation of the model where light ions interact with a moving wall while undergoing pitch angle scattering through Coulomb collisions due to the presence of a heavier ionic species. The collisions introduce a stochastic component which adds complexity to the particle acceleration profile and sets it apart from collisionless Fermi acceleration models. The unusual effect captured by this simplified variation of Fermi acceleration is the nonconservation of phase space, with the possibility for a distribution of particles initially monotonically decreasing in energy to exhibit an energy peak upon compression. A peaked energy distribution might have interesting applications, such as to optimize fusion reactivity or to characterize astrophysical phenomena that exhibit nonthermal features.

In a recent paper, Lucco Castello et al. [arXiv:2107.03537] performed systematic extractions of classical one-component plasma bridge functions from molecular dynamics simulations and provided an accurate parametrization that was incorporated in their isomorph-based empirically modified hypernetted chain approach for Yukawa one-component plasmas. Here the extraction technique and parametrization strategy are described in detail, while the deficiencies of earlier efforts are discussed. The structural and thermodynamic predictions of the updated version of the integral equation theory approach are compared with extensive available simulation results revealing a truly unprecedented level of accuracy in the entire dense liquid region of the Yukawa phase diagram.

Linear irreversible thermodynamics predicts that the entropy production rate can become negative. We demonstrate this prediction for metals under AC driving whose conductivity is well described by the Drude-Sommerfeld model. We then show that these negative rates are fully compatible with stochastic thermodynamics, namely, that the entropy production does fulfill a fluctuation theorem. The analysis is concluded with the observation that the stochastic entropy production as defined by the surprisal or ignorance of the Shannon information does not agree with the phenomenological approach.

A striking and highly versatile feature of magnetic (nano)particles is their ability to be manipulated at will at a distance by external fields. In this paper, the influence of gravity on the self-assembly of dipolar particles near a surface in the presence of a strong vertical magnetic field is investigated theoretically. A rich ground-state phase diagram stems from the effects of the number of particles $N$ and gravity. Two distinct regimes are discovered for the gravity-mediated breakup of a standing chain. When $N$ is small, there is a chain fragmentation (with two widely separated repulsive chain fragments) above a critical value for the gravity, whereas for higher chains, ribbonization (with two cohesive chain fragments) sets in. In both scenarios, simple algebraic decays for the transition gravity as a function of $N$ are analytically predicted and accurately corroborate the exact numerical results. Further intricate chain fragmentations and internal ribbon transformations operate upon further increasing the gravity until all $N$ constitutive particles lie on the surface. Our findings shed additional light on various recent experiments and computer simulations on magnetic colloids and granular media.

The spontaneous generation of electrical activity underpins a number of essential physiological processes, and is observed even in tissues where specialized pacemaker cells have not been identified. The emergence of periodic oscillations in diffusively coupled assemblies of excitable and electrically passive cells (which are individually incapable of sustaining autonomous activity) has been suggested as a possible mechanism underlying such phenomena. In this paper we investigate the dynamics of such assemblies in more detail by considering simple motifs of coupled electrically active and passive cells. The resulting behavior encompasses a wide range of dynamical phenomena, including chaos. However, embedding such assemblies in a lattice yields spatiotemporal patterns that either correspond to a quiescent state or to partial or globally synchronized oscillations. The resulting reduction in dynamical complexity suggests an emergent simplicity in the collective dynamics of such large, spatially extended systems. Furthermore, we show that such patterns can be reproduced by a reduced model comprising only excitatory and oscillatory elements. Our results suggest a generalization of the mechanism by which periodic activity can emerge in a heterogeneous system comprising nonoscillatory elements by coupling them diffusively, provided their steady states in isolation are sufficiently dissimilar.

Statistical methods for reconstructing networks from repeated measurements typically assume that all measurements are generated from the same underlying network structure. This need not be the case, however. People's social networks might be different on weekdays and weekends, for instance. Brain networks may differ between healthy patients and those with dementia or other conditions. Here we describe a Bayesian analysis framework for such data that allows for the fact that network measurements may be reflective of multiple possible structures. We define a finite mixture model of the measurement process and derive a Gibbs sampling procedure that samples exactly from the full posterior distribution of model parameters. The end result is a clustering of the measured networks into groups with similar structure. We demonstrate the method on both real and synthetic network populations.

The Hawk-Dove evolutionary game offers a paradigm of the trade-offs associated with aggressive and passive behaviors. When two (or more) populations of players compete, their success or failure is measured by their frequency in the population, and the system is governed by the replicator dynamics. We develop a time-dependent optimal-adaptive control theory for this dynamical system in which the entries of the payoff matrix are dynamically altered to produce control schedules that minimize and maximize the aggressive population through a finite-time cycle. These schedules provide upper and lower bounds on the outcomes for all possible strategies since they represent two extremizers of the cost function. We then adaptively extend the optimal control schedules over multiple cycles to produce absolute maximizers and minimizers for the system.

We present a theoretical study of the transition energies $\omega$ and the oscillator strengths $gf$ for the C-like ions (with $Z$ from 14–36) subject to plasma environment for atomic transitions, which meet the spatial and temporal criteria of the Debye-Hückel (DH) approximation. Two strong dipole-allowed transitions, viz., the intrashell transition $2s2p^3{}^3{D}_1\to 2s^{2}2p^2{}^3{P}_0$, and the intershell transition $2s^{2}2p3d{}^3{D}_1\to 2s^{2}2p^2{}^3{P}_0$ are investigated in detail. We found that both $\omega$ and $gf$ increase for the intrashell transition under the Debye-Hückel screening potential $V_{DH}$ in terms of the Debye length $D$, which is linked to the ratio between the plasma density $N_e$ and its temperature $kT$. In contrast, both $\omega$ and $gf$ decrease for the intershell transition. Our theoretically estimated data have led to a general scaling feature for the change in $\omega$ of both intershell and intrashell transitions for ions with different nuclear charge $Z$. A similar general feature for the change in $gf$ is also found for the intrashell transition. However, due to the change of the electron correlations between electrons in different shells with respect to the relativistic spin-orbit interaction as $Z$ varies, the variation of $gf$ subject to the surrounding plasma is more complicated for the intershell transition. The results presented in this work may facilitate the plasma diagnostic to determine the plasma temperature and density for the astrophysical objects and the controlled fusion facilities.

Neural network potentials (NNPs) combine the computational efficiency of classical interatomic potentials with the high accuracy and flexibility of the ab initio methods used to create the training set, but can also result in unphysical predictions when employed outside their training set distribution. Estimating the epistemic uncertainty of a NNP is required in active learning or on-the-fly generation of potentials. Inspired from their use in other machine-learning applications, NNP ensembles have been used for uncertainty prediction in several studies, with the caveat that ensembles do not provide a rigorous Bayesian estimate of the uncertainty. To test whether NNP ensembles provide accurate uncertainty estimates, we train such ensembles in four different case studies and compare the predicted uncertainty with the errors on out-of-distribution validation sets. Our results indicate that NNP ensembles are often overconfident, underestimating the uncertainty of the model, and require to be calibrated for each system and architecture. We also provide evidence that Bayesian NNPs, obtained by sampling the posterior distribution of the model parameters using Monte Carlo techniques, can provide better uncertainty estimates.

Delay embeddings of time series data have emerged as a promising coordinate basis for data-driven estimation of the Koopman operator, which seeks a linear representation for observed nonlinear dynamics. Recent work has demonstrated the efficacy of dynamic mode decomposition (DMD) for obtaining finite-dimensional Koopman approximations in delay coordinates. In this paper we demonstrate how nonlinear dynamics with sparse Fourier spectra can be (i) represented by a superposition of principal component trajectories and (ii) modeled by DMD in this coordinate space. For continuous or mixed (discrete and continuous) spectra, DMD can be augmented with an external forcing term. We present a method for learning linear control models in delay coordinates while simultaneously discovering the corresponding exogenous forcing signal in a fully unsupervised manner. This extends the existing DMD with control (DMDc) algorithm to cases where a control signal is not known a priori. We provide examples to validate the learned forcing against a known ground truth and illustrate their statistical similarity. Finally, we offer a demonstration of this method applied to real-world power grid load data to show its utility for diagnostics and interpretation on systems in which somewhat periodic behavior is strongly forced by unknown and unmeasurable environmental variables.

The phenomenon of the two-state process is observed in various systems and is increasingly attracting attention, such that there is a need for a theoretical model of the process. In this paper, we present a prototypal two-state random walk (TSRW) model of a renewal process alternating between the continuous-time random walk (CTRW) state and Lévy walk (LW) state. The jump length distribution of the CTRW state is assumed to be Gaussian whereas the time distributions of the two states are both considered to follow a power law. The diffusive behavior is analyzed and discussed by calculating the mean squared displacement (MSD) analytically and numerically. The results reveal that it displays strong anomalous diffusive behaviors caused by random motions of both states, i.e., two anomalous diffusion terms coexist in the expression of the MSD, and the time distribution which has the heavier tail determines their forms. Moreover, because the two diffusion terms originate from different mechanisms, we find that the diffusion can be characterized by either the term with the largest diffusion exponent or the term with the largest diffusion coefficient at long timescales, which shows very different properties from the single-state process. In addition, the two-state nature of the process of the particle moving in a velocity field makes the TSRW model applicable to describe it. Results obtained from the two-state model reveal that the diffusion can even exhibit subdiffusive behavior, which is significantly different from known results obtained using the single-state model.