Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where species abundances always reach a fixed point and a phase where they continuously fluctuate have been found. The dynamics when interactions are sparse, with each species interacting with only a few others, has remained largely unexplored. Here we study a system of sparse interactions, first when interactions are of constant strength and completely unidirectional, and then when adding variability and bidirectionality. We show that in this case a phase unique to the sparse setting appears in the phase diagram, where for the same control parameters different communities may reach either a fixed point or a state where the abundances of only a finite subset of species fluctuate, and we calculate the probability for each outcome. These fluctuating species are organized around short cycles in the interaction graph, and their abundances undergo large nonlinear fluctuations. We characterize the approach from this phase to a phase with extensively many fluctuating species, and show that the probability of fluctuations grows continuously to one as the transition is approached, and that the number of fluctuating species diverges. This is qualitatively distinct from the transition to extensive fluctuations coming from a fixed point phase, which is marked by a loss of linear stability. The differences are traced back to the emergent binary character of the dynamics when far from short cycles.

Laboratory granular landslides are smaller-scale, simplified, yet well-controlled versions of larger and often tragic natural landslides. Using systematic experiments and scaling analysis, we quantify the influence of grain size, fall height, and landslide volume on runout distance. We also determine the minimum landslide size required to observe this scaling, which we find is set by a combination of air drag, grain size, and fall height.

An efficient plasma compression scheme using azimuthally polarized light is proposed. Azimuthally polarized light possesses a donutlike intensity pattern, enabling it to compress and accelerate ions toward the optical axis across a wide range of parameters. When the light intensity reaches the relativistic regime of ${10}^{18}\mathrm{W}/{\mathrm{cm}}^2$, and the plasma density is below the critical density, protons can be compressed and accelerated by the toroidal soliton formed by the light. The expansion process of the soliton can be well described by the snowplow model. Three-dimensional particle-in-cell simulations show that within the soliton regime, despite the ion density exceeding ten times the critical density, the ions' energy is insufficient for efficient neutron production. When the light intensity increases to ${10}^{22}\mathrm{W}/{\mathrm{cm}}^2$, and the plasma density reaches several tens of times the critical density, deuterium ions can be compressed to thousands of times the critical density and simultaneously accelerated to the MeV level by tightly focused azimuthally polarized light during the hole-boring process. This process is far more dramatic compared to the soliton regime and can produce up to ${10}^4$ neutrons in a few light cycles. Moreover, in the subsequent beam-target stage, neutron yield is estimated to exceed ${10}^8$. Finally, we present a comparison with the results obtained using a radially polarized light to examine the influence of light polarization.

The analytical expression for the conditions of the solid-fluid phase transition, i.e., the melting curve, for two-dimensional (2D) Yukawa systems is derived theoretically from the isomorph theory. To demonstrate that the isomorph theory is applicable to 2D Yukawa systems, molecular dynamical simulations are performed under various conditions. Based on the isomorph theory, the analytical isomorphic curves of 2D Yukawa systems are derived using the local effective power-law exponent of the Yukawa potential. From the obtained analytical isomorphic curves, the melting curve of 2D Yukawa systems is directly determined using only two known melting points. The determined melting curve of 2D Yukawa systems well agrees with the previous obtained melting results using completely different approaches.

The impact of nanoscale wall roughness on rarefied gas transport is widely acknowledged, yet the associated scattering dynamics largely remain elusive. In this paper, we develop a scattering kernel for surfaces having nanoscale roughness that distinctly characterizes the two major types of interactions between gas molecules and rough surfaces. Namely these are (a) the weak perturbations arising from the thermal motion of wall atoms, essentially gas-phonon collisions, which are captured by the well-established Cercignani-Lampis model, and (b) the hard collisions owing to the irregularities of the rough, static potential energy surface, which are generally described by the fully diffuse model. Drawing an analogy between wave-surface and gas-surface scattering, a pseudo Debye-Waller factor is incorporated into the modeling as a weighting coefficient to allow the transition between smooth and rough surface conditions. The proposed scattering kernel is validated through high-fidelity molecular dynamics simulations that are performed for systems with varying roughness, temperature, and gas-surface combinations. The results indicate that the model well captures the scattering dynamics of gas molecular beams impinging on surfaces at different velocities, specifically for the accommodation coefficients and reflection patterns. Additionally, in flow and heat transport cases, it accurately predicts macroscopic quantities such as velocity slip and temperature jumps across the range of tested conditions.

Magnetic nanoparticles have emerged as a promising approach to improving cancer treatment. However, many nanoparticle designs fail in clinical trials due to a lack of understanding of how to overcome the in vivo transport barriers. To address this shortcoming, we develop a computational model aimed at the study of magnetic nanoparticles in vitro and in vivo. In this paper, we present an important building block for this overall goal, namely an efficient computational model of the in-flow capture of magnetic nanoparticles by a cylindrical permanent magnet in an idealized test setup. We use a continuum approach based on the Smoluchowski advection-diffusion equation, combined with a simple approach to consider the capture at an impenetrable boundary, and derive an analytical expression for the magnetic force of a cylindrical magnet of finite length on the nanoparticles. This provides a simple and numerically efficient way to study different magnet configurations and their influence on the nanoparticle distribution in three dimensions. Such an in silico model can increase insight into the underlying physics, help to design prototypes, and serve as a precursor to more complex systems in vivo and in silico.

This paper summarizes two related effective-temperature analyses of nonequilibrium phenomena: first, dislocations in deforming crystals and, second, chaotic behaviors of defects in thermally driven Rayleigh-Bénard hydrodynamic systems. The results are encouraging for broader applications of this statistical concept.

A binary mixture of two-different-size proliferating motile disks is studied. As growth is space limited, we focus on the conditions such that there is a coexistence of both large and small disks, or dominance of the larger disks. The study involves systematically varying some system parameters, such as diffusivities, growth rates, and self-propulsion velocities. In particular, we demonstrate that diffusing faster confers a competitive advantage, so that larger disks can in the long time coexist or even dominate the smaller ones. In the case of self-propelled disks, a coexistence regime is induced by the activity where the two types of disks show the same spatial distribution: both particles are phase separated or both are homogeneously distributed in the whole system.

Determinants are useful to represent the state of an interacting system of (effectively) repulsive and independent elements, like fermions in a quantum system and training samples in a learning problem. A computationally challenging problem is to compute the sum of powers of principal minors of a matrix which is relevant to the study of critical behaviors in quantum fermionic systems and finding a subset of maximally informative training data for a learning algorithm. Specifically, principal minors of positive square matrices can be considered as statistical weights of a random point process on the set of the matrix indices. The probability of each subset of the indices is in general proportional to a positive power of the determinant of the associated submatrix. We use Gaussian representation of the determinants for symmetric and positive matrices to estimate the partition function (or free energy) and the entropy of principal minors within the Bethe approximation. The results are expected to be asymptotically exact for diagonally dominant matrices with locally treelike structures. We consider the Laplacian matrix of random regular graphs of degree $K=2,3,4$ and exactly characterize the structure of the relevant minors in a mean-field model of such matrices. No (finite-temperature) phase transition is observed in this class of diagonally dominant matrices by increasing the positive power of the principal minors, which here plays the role of an inverse temperature.

We consider a three-dimensional lattice Abelian Higgs gauge model for a charged $N$-component scalar field $\mathit{\varphi }$, which is invariant under $\text{SO}\left(N\right)$ global transformations for generic values of the parameters. We focus on the strong-coupling regime, in which the kinetic Hamiltonian term for the gauge field is a small perturbation, which is irrelevant for the critical behavior. The Hamiltonian depends on a parameter $v$, which determines the global symmetry of the model and the symmetry of the low-temperature phases. We present renormalization-group predictions, based on a Landau-Ginzburg-Wilson effective description that relies on the identification of the appropriate order parameter and on the symmetry-breaking patterns that occur at the strong-coupling phase transitions. For $v=0$, the global symmetry group of the model is $\text{SU}\left(N\right)$; the corresponding model may undergo continuous transitions only for $N=2$. For $v\ne 0$, i.e., in the $\text{SO}\left(N\right)$ symmetric case, continuous transitions (in the Heisenberg universality class) are possible also for $N=3$ and 4. We perform Monte Carlo simulations for $N=2,3,4,6$, to verify the renormalization-group predictions. Finite-size scaling analyses of the numerical data are in full agreement.

Amplitude death has the potential to suppress unwanted oscillations in various engineering applications. However, in some engineering applications, such as dc microgrids, airfoil systems, and thermoacoustic systems, oscillation frequency is highly susceptible to external influences, leading to considerable variations. To maintain amplitude death amidst these frequency variations, we propose a design procedure that is robust against frequency variation for inducing amplitude death in delay-coupled oscillators. We first analytically derive the oscillator frequency band in which amplitude death can occur. The frequency bandwidth is maximized when the coupling strength is inversely proportional to the connection delay. Furthermore, our analysis reveals that the oscillator frequency band is influenced by the minimum eigenvalue of the normalized adjacency matrix (i.e., network topology) and that bipartite networks exhibit limited robustness to frequency variations. Our design procedure maintains the stability of amplitude death even under substantial frequency variations and is applicable to various network topologies. Numerical simulations confirm the validity of the proposed design.

Janus nanocarriers (NCs) provide promising features in interfacial applications such as targeted drug delivery. Herein, we use dissipative particle dynamics simulations to study the adhesion dynamics of NCs with Janus ligand compositions to the endothelial cell as a function of a series of effects, such as the initial orientation, ligand density, shape, and size of Janus NCs. The Janus NCs, with its long axis parallel to the endothelial glycocalyx (EG) layer, has the best penetration depth due to its lower potential energy and the lowest shell entropy loss. Among different shapes of Janus NCs, both the potential energy and the EG entropy loss control the penetration. In fact, at the parallel orientations, Janus shapes with a robust mechanical strength and larger surface area at the EG/water interface can rotate and penetrate more efficiently. An increase in the ligand density of Janus NCs increases entropy losses of both the hydrophilic and the hydrophobic ligands and decreases the potential energy. Thus, for a specific Janus NCs, functionalizing with an appropriate ligand density would help driving forces prevail over barriers of penetration into the EG layer. For a particular ligand density, once the radius of the Janus NCs exceeds the appropriate size, barriers such as hydrophobic ligands and shell entropy losses are also reinforced significantly and surpass driving forces. Our observations reveal that entropy losses for hydrophobic ligands of Janus NCs and for the shell of NCs are decisive for the adhesion and penetration of Janus NCs to endothelial cells.

We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, and study its transport through a capillary tube linking two large reservoirs. We assume that short-range interactions cause preferential adsorption of one component onto the tube's wall. The adsorption layer can become much thicker than the molecular size, which enables us to apply hydrodynamics based on a coarse-grained free-energy functional. For transport processes induced by gradients of the pressure, composition, and temperature along a cylindrical tube, we obtain the formulas of the Onsager coefficients to extend our previous results on isothermal transport, assuming the critical composition in the middle of each reservoir in the reference equilibrium state. Among the processes, we focus on thermo-osmosis—mass flow due to a temperature gradient. We explicitly derive a formula for the thermal force density, which is nonvanishing in the adsorption layer and causes thermo-osmosis. This formula for a near-critical binary fluid mixture is an extension of the conventional formula for a one-component fluid, expressed in terms of local excess enthalpy. We predict that the direction of thermo-osmotic flow of a mixture near the upper (lower) consolute point is the same as (opposite to) that of the temperature gradient, irrespective of which component is adsorbed on the wall. Our procedure would also be applied to dynamics of a soft material, whose mesoscopic inhomogeneity can be described by a coarse-grained free-energy functional.

Linear defects such as dislocations and disclinations in ordered materials attract foreign particles since they replace strong elastic distortions at the defect cores. In this work, we explore the behavior of isotropic droplets nucleating at singular disclinations in a nematic liquid crystal, predesigned by surface photopatterning. Experiments show that in the biphasic nematic-isotropic region, although the droplets are attracted to the disclination cores, their centers of mass shift away from the core centers as the temperature increases. The shift is not random, being deterministically defined by the surrounding director field. The effect is explained by the balance of interfacial anchoring and bulk elasticity. An agreement with the experiment can be achieved only if the model accounts for the disparity of the nematic elastic constants; the so-called one-constant approximation, often used in the theoretical analysis of liquid crystals, produces qualitatively wrong predictions. In particular, the experimentally observed shift towards the bend region around a +1/2 disclination core can be explained only when the bend constant is larger than the splay constant. The described dependence of the precise location of a foreign inclusion at defect cores on the elastic and surface anchoring properties can be used in rational design of microscale architectures.

In this work, we performed experiments regarding the outflow of spheres and two different types of rice-shaped particles in a quasi-two-dimensional monolayer silo with a flat bottom. We investigate the velocity and solid fraction profiles at the orifice and test whether the profiles for nonspherical particles have similar self-similar properties as in the spherical case. We find that the magnitude and shape of the velocity profiles for all three particle types are in a similar range. In contrast, the solid fraction at the orifice has a dome-shaped profile for both rice particles, whereas the profile for spherical particles is rather flat. The discharge rate determined from the velocity and solid fraction profiles describes the independently measured experimental discharge rate very well for all three investigated particle types.

We construct a formally time-reversible, one-dimensional forced Burgers equation by imposing a global constraint of energy conservation, wherein the constant viscosity is modified to a fluctuating state-dependent dissipation coefficient. The system exhibits dynamical properties which bear strong similarities with those observed for the Burgers equation and can be understood using the dynamics of the poles, shocks, and truncation effects, such as tygers. A complex interplay of these give rise to interesting statistical regimes ranging from hydrodynamic behavior to a completely thermalized warm phase. The end of the hydrodynamic regime is associated with the appearance of a shock in the solution and a continuous transition leading to a truncation-dependent state. Beyond this, the truncation effects such as tygers and the appearance of secondary discontinuity at the resonance point in the solution strongly influence the statistical properties. These disappear at the second transition, at which the global quantities exhibit a jump and attain values that are consistent with the establishment of a quasiequilibrium state characterized by energy equipartition among the Fourier modes. Our comparative analysis shows that the macroscopic statistical properties of the formally time-reversible system and the Burgers equation are equivalent in all the regimes, irrespective of the truncation effects, and this equivalence is not just limited to the hydrodynamic regime, thereby further strengthening the Gallavotti's equivalence conjecture. The properties of the system are further examined by inspecting the complex space singularities in the velocity field of the Burgers equation. Furthermore, an effective theory is proposed to describe the discontinuous transition.

When droplets approach a liquid surface, they have a tendency to merge in order to minimize surface energy. However, under certain conditions, they can exhibit a phenomenon called coalescence delay, where they remain separate for tens of milliseconds. This duration is known as the residence time or the noncoalescence time. Surprisingly, under identical parameters and initial conditions, the residence time for water droplets is not a constant value but exhibits dual peaks in its distribution. In this paper, we present the observation of the dual residence times through rigorous statistical analysis and investigate the quantitative variations in residence time by manipulating parameters such as droplet height, radius, and viscosity. Theoretical models and physical arguments are provided to explain their effects, particularly why a large viscosity or/and a small radius is detrimental to the appearance of the longer residence time peak.

Power-law distributions provide a general description of diverse natural phenomena in which events with a logarithmically increasing size occur with logarithmically decreasing probability. However, experimentally derived correlated two-dimensional information is often difficult to cleanly interpret as discrete events of defined size. Moreover, physical limitation of techniques such as those based on scanning probe microscopy, which can ideally be used to observe power-law behavior, reduce event number and thus render straightforward power-law fits even more challenging. Here we develop and compare different techniques to analyze event distributions from two-dimensional images. We show that tracking interface position allows the associated scaling parameters to be accurately extracted from both experimental and synthetic image-based datasets. We also show how these techniques can differentiate between power-law and non-power-law behavior by comparison of Hill, moments, and kernel estimators of this scaling parameter. We thus present computational tools to analyze power-law fits in two-dimensional datasets and identify the scaling parameters that best describe these distributions.

Numerical analysis of conserved field dynamics has been generally performed with pseudospectral methods. Finite differences integration, the common procedure for nonconserved field dynamics, indeed struggles to implement a conservative noise in the discrete spatial domain. In this work we present a method to generate a conservative noise in the finite differences framework, which works for any discrete topology and boundary conditions. We apply it to numerically solve the conserved Kardar-Parisi-Zhang (cKPZ) equation, widely used to describe surface roughening when the number of particles is conserved. Our numerical simulations recover the correct scaling exponents $\alpha , \beta$, and $z$ in $d=1$ and in $d=2$. To illustrate the potentiality of the method, we further consider the cKPZ equation on different kinds of nonstandard lattices and on the random Euclidean graph. This is a unique numerical study of conserved field dynamics on an irregular topology, paving the way for a broad spectrum of possible applications.

We introduce and investigate the effects of a new class of stochastic resetting protocol called subsystem resetting, whereby a subset of the system constituents in a many-body interacting system undergoes bare evolution interspersed with simultaneous resets at random times, while the remaining constituents evolve solely under the bare dynamics. Here, by reset is meant a reinitialization of the dynamics from a given state. We pursue our investigation within the ambit of the well-known Kuramoto model of coupled phase-only oscillators of distributed natural frequencies. Here, the reset protocol corresponds to a chosen set of oscillators being reset to a synchronized state at random times. We find that the mean ${\omega }_0$ of the natural frequencies plays a defining role in determining the long-time state of the system. For ${\omega }_0=0$, the system reaches a synchronized stationary state at long times, characterized by a time-independent nonzero value of the synchronization order parameter that quantifies macroscopic order in the system. Moreover, we find that resetting even an infinitesimal fraction of the total number of oscillators, in the extreme limit of infinite resetting rate, has the drastic effect of synchronizing the entire system, even in parameter regimes in which the bare evolution does not support global synchrony. By contrast, for ${\omega }_0\ne 0$, the dynamics allows at long times either a synchronized stationary state or an oscillatory synchronized state, with the latter characterized by an oscillatory behavior as a function of time of the order parameter, with a nonzero time-independent time average. Our results thus imply that the nonreset subsystem always gets synchronized at long times through the act of resetting of the reset subsystem. Our results, analytical using the Ott-Antonsen ansatz as well as those based on numerical simulations, are obtained for two representative oscillator frequency distributions, namely, a Lorentzian and a Gaussian. Given that it is easier to reset a fraction of the system constituents than the entire system, we discuss how subsystem resetting may be employed as an efficient mechanism to control attainment of global synchrony in the Kuramoto system.