Effects of three-point direct correlation on properties of the phase field crystal (PFC) modeling are examined for the control of various ordered and disordered phases and their coexistence in both three-dimensional and two-dimensional systems. Such effects are manifested via the corresponding gradient nonlinearity in the PFC free-energy functional that is derived from classical density functional theory. Their significant impacts on the stability regimes of ordered phases, phase diagrams, and elastic properties of the system, as compared to those of the original PFC model, are revealed through systematic analyses and simulations. The nontrivial contribution from three-point direct correlation leads to the variation of the critical point of order-disorder transition to which all the phase boundaries in the temperature-density phase diagram converge. It also enables the variation and control of system elastic constants over a substantial range as needed in modeling different types of materials with the same crystalline structure but different elastic properties. The capability of this PFC approach in modeling both solid and soft matter systems is further demonstrated through the effect of three-point correlation on controlling the vapor-liquid-solid coexistence and transitions for body-centered cubic phase and on achieving the liquid-stripe or liquid-lamellar phase coexistence. All these provide a valuable and efficient method for the study of structural ordering and evolution in various types of material systems.

The gas-puff $Z$ pinch has a long history with myriad applications as an efficient neutron or x-ray source. Its simplicity as a load configuration makes it suitable for studying fundamental plasma physics phenomena such as instabilities and energy transport. For example, the implosion of cylindrical shells onto a fusion fuel are inherently susceptible to instability growth on their external surfaces; if such instabilities are unmitigated, then the consequences in terms of degraded performance can be substantial. Similarly, mitigating heat transport from a hot fuel to its colder surrounding container can make fusion conditions more easily achievable. Here we have conducted a systematic study of triple-nozzle (outer liner, inner liner, fuel) gas puffs using two-dimensional (2D) magnetohydrodynamic simulations to investigate the effect of load material on the relevant dynamics. Analogous to past studies on spherical blast waves and converging shock waves, a trend emerges linking increased radiative cooling, lower adiabatic index, and increased magneto-Rayleigh-Taylor instability growth. Notably, our results suggest that, for the present configuration, Ar radiates less than both Ne and Kr during the early stages of the implosion while mass is being swept up and perturbations begin to seed instability growth. Consequently, pinches with Ar on the outer surface exhibit more stable 2D behavior. Here we also present a parameter scan of thermonuclear neutron yield, $Y$, as a function of peak current, $I_{\mathrm{pk}}$ and dopant concentration with Ne or Ar, depending on the inner liner material. Above 6 MA, our results suggest $Y\propto I_{\mathrm{pk}}^5$ and even substantial mixing (10% by volume) of Ne into the fuel does not drastically reduce yield, suggesting an Ar/Ne/fuel configuration may reliably achieve DD thermonuclear yields of ${10}^{13}$–${10}^{14}$/cm in the 10–20 MA range.

The dynamics of the condensation process on nanostructured surfaces can be modulated substantially by tuning the surface architecture. Present study uses the mesoscopic framework of lattice Boltzmann method (LBM) to explore the role of surface morphology and cold spot temperature in determining the visual state of the condensate droplet, mode of nucleation, and associated rates of energy and mass interactions. A multiple relaxation time–(MRT)-based LBM solver, coupled with pseudopotential model, has been developed to simulate a rectangular domain of saturated vapor, housing a cold spot on the bottom rough surface. Superhydrophobicity has been achieved for certain combinations of surface parameters, with the intercolumn spacing being the most influential one. Gradual increase in the spacing modifies the nucleation mode from top through side to bottom, while the droplet changes from Cassie to Wenzel state. The Cassie drop in top nucleation mode exhibits the largest contact angle and least rate of surface heat transfer. Both types of Wenzel drops display large rate of condensation and two peaks in heat transfer, along with very short nucleation time in comparison with Cassie drops. Couple of phase diagrams have been developed combining all four scenarios of condensation predicted by the present model. One important novelty of the present study is the consideration of nonisothermal condition within LB structure. Enhancement in the degree of subcooling at the cold spot encourages greater condensation and Cassie-to-Wenzel transition.

The optical resonance problem is an eigenproblem with an exponential-growing boundary condition imposed at infinity. This inconvenient boundary condition is caused by the openness of dielectric systems, and it is explained as the effect of retardation. Following our previous work [Jiang and Xiang, Phys. Rev. A 102, 053704 (2020)] where a perfectly-matched-layer method is developed for transverse-magnetic modes, we extend the method in this paper to transverse-electric modes and apply it to study mode symmetries. The method is implemented by introducing an extra layer to absorb outgoing waves at the far-field region, based on which we derive a damping eigenequation. A finite-element-based numerical approach is developed to compute the eigenstates of the damping eigenproblem. Our method is validated by application to the circular cavity and comparison with exact analytical solutions of whispering-gallery modes. We apply the method to the elliptic cavity to study the even- and odd-symmetric optical eigenstates. We also apply the method to trace the evolution of a pair of degenerate eigenstates with cavity shapes smoothly deformed from circles to squares.

We apply the electric cell-substrate impedance sensing (ECIS) technique to monolayers of Madin-Darby canine kidney type II cells cultured on microelectrodes of different sizes. We analyze the effect of the microelectrode radius on the parameters provided by existing ECIS models. The cellular properties inferred from the models should be invariant to the change in the microelectrode radius used for the measurements, since these properties are inherent to the type of cells studied. The current standard model, the Giaever-Keese (GK) model, derived from electrical balances of a single cell extended to infinity by suitable boundary conditions, assumes an infinite microelectrode. The model is fitted to experimental data acquired with a large-radius microelectrode, which can be considered infinite for practical purposes. We compute the impedance of the other cell-covered microelectrodes from the parameters obtained with the GK model, resulting in values strongly discrepant with the experimental data for small microelectrodes. We repeat the process with the mean field (MF) model, an alternative model that depends on the microelectrode radius but not on the cell radius. In this paper we introduce the mesoscopic model, an analytical model that simultaneously includes the properties of an individual cell and the sizes of the microelectrode and the insulator (region between the microelectrode and the ground). The impedances calculated with the mesoscopic model are in excellent agreement with experimental data. Finally, the mesoscopic model reduces to the MF model when the insulator goes to infinity and to the GK model when it goes to zero.

We study the scale dependence of effective diffusion of fluid tracers, specifically, its dependence on the Péclet number, a dimensionless parameter of the ratio between advection and molecular diffusion. Here, we address the case that length and time scales on which the effective diffusion can be described are not separated from those of advection and molecular diffusion. For this, we propose an alternate method for characterizing the effective diffusivity without relying on the scale separation. For a given spatial domain inside which the effective diffusion can emerge, a time constant related to the diffusion is identified by considering the spatiotemporal evolution of a test advection-diffusion equation, where its initial condition is set at a pulse function. Then, the value of effective diffusivity is identified by minimizing the $L_{\infty }$ distance between solutions of the above test equation and the diffusion one with mean drift. With this method, for time-independent gyre and time-periodic shear flows, we numerically show the scale dependence of the effective diffusivity and its discrepancy from the classical limits that were derived on the assumption of the scale separation. The kinematic origins of the discrepancy are revealed as the development of the molecular diffusion across flow cells of the gyre and as the suppression of the drift motion due to a temporal oscillation in the shear.

A major development underlying hydrodynamic turbulence theory is the similarity decay hypothesis due to von Karman and Howarth, here extended empirically to plasma turbulence in the solar wind. In similarity decay the second-order correlation experiences a continuous transformation based on a universal functional form and a rescaling of energy and characteristic length. Solar wind turbulence follows many principles adapted from classical fluid turbulence, but previously this similarity property has not been examined explicitly. Here, we analyze an ensemble of Elsässer autocorrelation functions computed from Advanced Composition Explorer data at 1 astronomical unit (AU), and demonstrate explicitly that the two-point correlation functions undergo a collapse to a similarity form of the type anticipated from von Karman's hypothesis applied to weakly compressive magnetohydrodynamic turbulence. This provides a firm empirical basis for employing the similarity decay hypothesis to the Elsässer correlations that represent the incompressive turbulence cascade. This approach is of substantial utility in space turbulence data analysis, and for adopting von Karman-type heating rates in global and subgrid-scale dynamical modeling.

A computational model is proposed to investigate drug delivery systems in which erosion and diffusion mechanisms are participating in the drug release process. Our approach allowed us to analytically estimate the crossover point between those mechanisms through the value of the parameter $b$ $(b_c=1)$ and the scaling behavior of parameter $\tau$ on the Weibull function, $exp[-{(t/\tau )}^b]$, used to adjust drug release data in pharmaceutical literature. Numerical investigations on the size dependence of the characteristic release time $\tau$ found it to satisfy either linear or quadratic scaling relations on either erosive or diffusive regimes. Along the crossover, the characteristic time scales with the average coefficient observed on the extreme regimes (i.e., $\tau \sim L^{3/2}$), and we show that this result can be derived analytically by assuming an Arrhenius relation for the diffusion coefficient inside the capsule. Based on these relations, a phenomenological expression for the characteristic release in terms of size $L$ and erosion rate $\kappa$ is proposed, which can be useful for predicting the crossover erosion rate ${\kappa }_c$. We applied this relation to the experimental literature data for the release of acetaminophen immersed in a wax matrix and found them to be consistent with our numerical results.

We study the conditions of propagation of an initial emergent practice qualified as extremist within a population adept at a practice perceived as moderate, whether political, societal, or religious. The extremist practice is carried by an initial ultraminority of radicals (R) dispersed among conventionals (C) who are the overwhelming majority in the community. Both R and C are followers, that is, agents who, while having arguments to legitimize their current practice, are likely to switch to the other practice if given more arguments during a debate. The issue being controversial, most C tend to avoid social confrontation with R about it. They maintain a neutral indifference, assuming it is none of their business. On the contrary, R aim to convince C through an expansion strategy to spread their practice as part of a collective agenda. However, aware of being followers, they implement an appropriate strategy to maximize their expansion and determine when to force a debate with C. The effect of this asymmetry between initiating or avoiding an update debate among followers is calculated using a weighted version of the Galam model of opinion dynamics. An underlying complex landscape is obtained as a function of the respective probabilities to engage in a local discussion by R and C. It discloses zones where R inexorably expand and zones where they get extinct. The results highlight the instrumental character of the above asymmetry in providing a decisive advantage to R against C. It also points to a barrier in R initial support to reach the extension zone. In parallel, the landscape reveals a path for C to counter R expansion, pushing them back into their extinction zone. It relies on the asymmetry of C being initially a large majority which puts the required involvement of C at a rather low level.

Equations for contour dynamics of trough-shaped dark solitons are obtained for the general form of the nonlinearity function. Their self-similar solution which describes the nonlinear stage of the bending instability of dark solitons is studied in detail.

The attractive Bose-Hubbard model is applied for describing the two-exciton dynamics in a nonlinear quantum star graph. When the excitons are created on the core of the star, it is shown that the interplay between the complex architecture of the network and the nonlinearity favors the occurrence of a real quantum self-trapping. Quite weak in the small nonlinearity limit, this self-localization is enhanced as the nonlinearity increases. This feature originates in the restructuring of the two-exciton eigenstates whose localized nature intensifies with the nonlinearity. Nevertheless, the quantum self-trapping is never complete since it is impossible to localize the entire exciton density, even in the strong nonlinearity limit.

Real-world networks are often not isolated and the interdependence between different networks in a complex system is as important as the topological connectivity within individual networks. We develop a theoretical framework to study the robustness of interdependent networks under attacks with limited knowledge. A node may be attacked if it is the most connected node among a given number of potential victims. This number is referred to as the attacker's knowledge level, which joins the two ends, namely, the random failure with zero knowledge and the intentional attack with full knowledge of the network. We introduce percolation models with attacks over one layer and two layers as well as mixed site-bond percolation. Along with the discontinuous phase transition, we show the existence of a critical knowledge level, which indicates a transition of network robustness under the competition between connectivity and interdependence. It is unraveled that interdependent networks can be extremely fragile to the extent that a random failure on two layers would be more deleterious than a targeted attack with full knowledge over one layer. Moreover, we find that a balanced distribution of attack knowledge on both layers tends to be most destructive if the total knowledge is a conserved quantity.

The success of machine learning has resulted from its structured representation of data. Similar data have close internal representations as compressed codes for classification or emerged labels for clustering. We observe that the frequency of internal codes or labels follows power laws in both supervised and unsupervised learning models. This scale-invariant distribution implies that machine learning largely compresses frequent typical data, and simultaneously, differentiates many atypical data as outliers. In this study, we derive the process by which these power laws can naturally arise in machine learning. In terms of information theory, the scale-invariant representation corresponds to a maximally uncertain data grouping among possible representations that guarantee a given learning accuracy.

Transition in the propulsive performance and vortex synchronization of an oscillating foil in a combined heaving and pitching motion is numerically investigated at a range of reduced frequencies (0.16 $\le f^{*}\le$ 0.64), phase offsets ($0^{\circ }$ $\le \varphi \le$ ${315}^{\circ }$), and Reynolds number ($1000\le \text{Re}\le 16000$). Focusing on the common case of $\text{Re}=1000$, the drag to thrust transition is identified on a $\varphi -f^{*}$ phase map. Here, the range of ${90}^{\circ }$ $\le \varphi \le$ ${225}^{\circ }$ depicted a drag-dominated regime for increasing reduced frequency. However, thrust-dominated regimes were observed for $\varphi <$ ${90}^{\circ }$ and $\varphi >$ ${225}^{\circ }$, where increasing the reduced frequency led to an increased thrust production. The isoline-depicting drag-thrust boundary was further observed to coincide with transitions in the characteristic near-wake modes with increasing reduced frequency, which ranged from $\mathrm{2P}+\mathrm{2S}$ to 2P and reverse von Kármán modes. However, evaluation of the wake with changing phase offsets at individual reduced frequencies only depicted effects on the spatial configuration of the vortex structures, while the number of vortices shed in one oscillation period was unchanged. The existence of similar wake modes with significantly different propulsive performance clearly suggests that transitions of the wake topology may not always be a reliable tool for understanding propulsive mechanisms of fish swimming or development of underwater propulsion systems. We further assessed a possible route to drag production via investigation into the mean velocity fields at increasing phase offset and at intermediate reduced frequencies ranging from 0.24 to 0.40. This revealed bifurcation of a velocity jet behind the foil on account of the wake topology and dynamics of shed vortex structures. The changes posed by increasing $\varphi$ on wake structure interactions further hints at potential mechanisms that limit the achievement of optimum efficiency in underwater locomotion.

Disordered hyperuniform systems are statistically isotropic and possess no Bragg peaks like liquids and glasses, yet they suppress large-scale density fluctuations in a similar manner as in perfect crystals. The unique hyperuniform long-range order in these systems endow them with nearly optimal transport, electronic, and mechanical properties. The concept of hyperuniformity was originally introduced for many-particle systems and has subsequently been generalized to biphase heterogeneous materials such as porous media, composites, polymers, and biological tissues for unconventional property discovery. Existing methods for rendering realizations of disordered hyperuniform biphase materials reconstruction typically employ stochastic optimization such as the simulated annealing approach, which requires many iterations. Here, we propose an explicit ultraefficient method for reconstructing effectively hyperuniform biphase materials, based on the second-order non-Gaussian random fields where no additional tuning step or iteration is needed. Both the effectively hyperuniform microstructure and the latent material property field can be simultaneously generated in a single reconstruction. Moreover, our method can also incorporate hierarchical uncertainties in the heterogeneous materials, including both uncertainties in the disordered material microstructure and material property variation within each phase. The efficiency and feasibility of the proposed reconstruction method are demonstrated via a wide spectrum of examples spanning from isotropic to anisotropic, effectively hyperuniform to nonhyperuniform, and antihyperuniform systems. Our ultraefficient reconstruction method can be readily incorporated into material design, probabilistic analysis, optimization, and discovery of novel disordered hyperuniform heterogeneous materials.

Roughness and orientational order in thin films of anisotropic particles are investigated using kinetic Monte Carlo simulations on a cubic lattice. Anisotropic next-neighbor interactions between the lattice particles were chosen to mimic the effects of shape anisotropy in the interactions of disk- or rodlike molecules with van der Waals attractions. Increasing anisotropy leads first to a preferred orientation in the film (which is close to the corresponding equilibrium transition) while the qualitative mode of roughness evolution (known from isotropic systems) does not change. At strong anisotropies, an effective step-edge (Ehrlich-Schwoebel) barrier appears and a nonequilibrium roughening effect is found, accompanied by reordering in the film which can be interpreted as the nucleation and growth of domains of lying-down disks or rods. The information on order and roughness is combined into a diagram of dynamic growth modes.

For simulating incompressible two-phase fluid flows, several phase-field lattice Boltzmann (LB) methods based on the local Allen-Cahn (AC) equation have been intensively proposed in recent years. We present a local hybrid AC model for the phase-field LB method. In the proposed model, the local and nonlocal AC equations are linearly combined using a local weight assigned in the interface or bulk phase regions individually. Five numerical problems, namely diagonal translation, Zalesak's disk rotation, static bubble, two bubbles of different radii, and Rayleigh-Taylor instability, are simulated for validation. The numerical results agree well with the analytical solutions or available previous results. Additionally, the numerical dispersion and the coarsening phenomenon are considerably suppressed in the proposed model. Finally, the performance of the proposed model is validated by conducting a drainage simulation in porous media and compared with the global hybrid AC model.

The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model. This canonical model was derived perturbatively, by applying phase reduction to an ensemble of heterogeneous, globally coupled Stuart-Landau oscillators. This derivation neglects nonlinearities in the coupling constant. We show here that a comprehensive analysis requires extending the Kuramoto model up to quadratic order. This “enlarged Kuramoto model” comprises three-body (nonpairwise) interactions, which induce strikingly complex phenomenology at certain parameter values. As the coupling is increased, a secondary instability renders the synchronized state unstable, and subsequent bifurcations lead to collective chaos. An efficient numerical study of the thermodynamic limit, valid for Gaussian heterogeneity, is carried out by means of a Fourier-Hermite decomposition of the oscillator density.

An investigation of the self-consistent ambipolar charge kinetics across a negatively biased semiconducting plasma-solid interface is presented. For the specific case of a thin germanium layer with nonpolar electron-phonon scattering, sandwiched between an Ohmic contact and a collisionless argon plasma, we calculate the current-voltage characteristic and show that it is affected by the electron microphysics of the semiconductor. We also obtain the spatially and energetically resolved fluxes and charge distributions inside the layer, visualizing thereby the behavior of the charge carriers responsible for the charge transport. Albeit not quantitative, because of the crude model for the germanium band structure and the neglect of particle-nonconserving scattering processes, such as impact ionization and electron-hole recombination, which at the energies involved cannot be neglected, our results clearly indicate (i) the current through the interface is carried by rather hot carriers and (ii) the perfect absorber model, often used for the description of charge transport across plasma-solid interfaces, cannot be maintained for semiconducting interfaces.