The lattice kinetic scheme (LKS) is a modified version of the classical single relaxation time lattice Boltzmann method. Although used for many applications, especially when large variations in viscosity are involved, a thorough analysis of the scheme has not been provided yet. In the context of this work, the macroscopic behavior of this scheme is evaluated through the Chapman-Enskog analysis. It is shown that the additional degree of freedom provided in the scheme allows for an independent control of higher-order moments. These results are further corroborated by numerical simulations. The behavior of this numerical scheme is studied for selected external and internal flows to clarify the effect of the free parameter on the different moments of the distribution function. It is shown that it is more stable than SRT (single relaxation time) when confronted to fully periodic under-resolved simulations (especially for $\lambda \approx 1$). It can also help minimize the error coming from the viscosity-dependence of the wall position when combined with the bounce-back approach; although still present, viscosity-dependence of the wall position is reduced. Furthermore, as shown through the multiscale analysis, specific choices of the free parameter can cancel out the leading-order error. Overall, the LKS is shown to be a useful and efficient alternative to the SRT method for simulating numerically complex flows.

When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex, and obtaining a detailed physical understanding often requires case-by-case considerations. To facilitate systematic analysis, here we present a general iterative scheme for the determination of the unique external force field that yields prescribed inhomogeneous stationary or time-dependent flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one-body density distribution. Hence, compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. In equilibrium, the method allows to find the conservative force field that generates a prescribed target density profile, and hence implements the Mermin-Evans classical density functional map from density distribution to external potential. The conceptual tools developed here enable one to gain detailed physical insight into complex flow behaviour, as we demonstrate in prototypical situations.

A detailed Monte Carlo study of the satisfiability threshold for random 3-SAT has been undertaken. In combination with a monotonicity assumption we find that the threshold for random 3-SAT satisfies ${\alpha }_3\le 4.262$. If the assumption is correct, this means that the actual threshold value for $k=3$ is lower than that given by the cavity method. In contrast the latter has recently been shown to give the correct value for large $k$. Our result thus indicate that there are distinct behaviors for $k$ above and below some critical $k_c$, and the cavity method may provide a correct mean-field picture for the range above $k_c$.

We introduce the phenomenon of golden touch from myth to thermotics. We define golden touch as extending the core property to a shell with an extremely small core fraction. We obtain the requirement of golden touch by making the effective thermal conductivity of the core-shell structure equal to the thermal conductivity of the core. We summarize three types (A, B, and C) of golden touch in two dimensions, and only two types (A and B) of golden touch in three dimensions. We theoretically analyze the distinct properties of different types of golden touch by delicately designing the anisotropic thermal conductivity of the shell. Golden touch is also validated by finite-element simulations which echo the theoretical analyses. Golden touch has potential applications in thermal camouflage, thermal management, etc. Our work not only lays the foundation for golden touch in thermotics, but also provides guidance for exploring golden touch in other diffusive fields like electrostatic and magnetostatic fields.

In a network of pulse-coupled oscillators with adaptive coupling, we discover a dynamical regime which we call an “itinerant chimera.” Similarly as in classical chimera states, the network splits into two domains, the coherent and the incoherent. The drastic difference is that the composition of the domains is volatile, i.e., the oscillators demonstrate spontaneous switching between the domains. This process can be seen as traveling of the oscillators from one domain to another or as traveling of the chimera core across the network. We explore the basic features of the itinerant chimeras, such as the mean and the variance of the core size, and the oscillators lifetime within the core. We also study the scaling behavior of the system and show that the observed regime is not a finite-size effect but a key feature of the collective dynamics which persists even in large networks.

In recent years, due to the great diffusion of e-commerce, online rating platforms quickly became a common tool for purchase recommendations. However, instruments for their analysis did not evolve at the same speed. Indeed, interesting information about users' habits and tastes can be recovered just considering the bipartite network of users and products, in which links represent products' purchases and have different weights due to the score assigned to the item in users' reviews. With respect to other weighted bipartite networks, in these systems we observe a maximum possible weight per link, that limits the variability of the outcomes. In the present article we propose an entropy-based randomization method for this type of networks (i.e., bipartite rating networks) by extending the configuration model framework: the randomized network satisfies the constraints of the degree per rating, i.e., the number of given ratings received by the specified product or assigned by the single user. We first show that such a null model is able to reproduce several nontrivial features of the real network better than other null models. Then, using our model as benchmark, we project the information contained in the real system on one of the layers: To provide an interpretation of the projection obtained, we run the Louvain community detection on the obtained network and discuss the observed division in clusters. We are able to detect groups of music albums due to the consumers' taste or communities of movies due to their audience. Finally, we show that our method is also able to handle the special case of categorical bipartite networks: we consider the bipartite categorical network of scientific journals recognized for the scientific qualification in economics and statistics. In the end, from the outcome of our method, the probability that each user appreciate every product can be easily recovered. Therefore, this information may be employed in future applications to implement a more detailed recommendation system that also takes into account information regarding the topology of the observed network.

Previous research has shown that gold nanoparticles immersed in water in an optical vortex lattice formed by the perpendicular intersection of two standing light waves with a $\pi /2\mathrm{rad}$ phase difference will experience enhanced dispersion that scales with the intensity of the incident laser. We show that flexible nanoscale dumbbells (created by attaching two such gold particles by means of a polymer chain) in the same field display different types of motion depending on the chain length and field intensity. We have not disregarded the secondary optical forces due to light scattering. The dumbbells may disperse, rotate, or remain trapped. For some values of the parameters, the (enhanced) dispersion possesses a displacement distribution with exponential tails, making the motion anomalous, though Brownian.

We study the regimes of a diluted dipolar system through Monte Carlo numerical simulations in the $NVT$ ensemble. To accelerate the dynamics, several approximations and speed-up algorithms are proposed and tested. In particular, it turns out that “cluster move Monte Carlo” algorithm speeds-up to two decades faster than the traditional Monte Carlo, depending on temperature and density. We find simple-fluid, chain-fluid, ring-fluid, gel, and antiparallel columnar regimes, which are studied and characterized through positional, orientational, and thermodynamical observables.

We studied properties of monolayer films of $n$-cyanobiphenyl (with $n=5,...,8$) series of mesogens anchored on the surface of single walled boron nitride nanotube. In order to assess the impact of substrate polarization on the ordering effects we compare translational and reorientational dynamics of the films with the characteristics of analogous carbon and silicon carbide nanotube based systems. We observed significant increase of the ordering degree accompanied by increased thermal stability. This ordering is less selective than those induced by the silicon carbide nanotube, which were previously reported. The antiparallel orientation of the nearest neighboring mesogens is predominant, while the system does not exhibit any long-range spatial correlations which indicates that the size of the domains is constrained to this region. These features might be of potential importance in the design of novel optoelectronic devices.

The dynamic characteristics of a two-dimensional deformable capsule in a simple shear flow are studied with an immersed boundary-lattice Boltzmann method. Simulations are conducted by varying the Reynolds number (Re) from 0.0125 to 2000 and the dimensionless shear rate ($G$) from 0.001 to 0.5. The $G$-Re plane can be divided into four regions according to the deformation dependence on the parameters considered: viscous dominant, inertia dominant, transitional, and anomalous regions. There are four typical dynamic behaviors over the $G$-Re plane: steady deformation, prerupture state, quasisteady deformation, and continuous elongation. Analysis indicates that the pressure distribution and its variations due to the interplay of the fluid inertia force, the viscous shear stress, and the membrane elastic force determines the complex behaviors of the capsule. The effects of the bending rigidity and the internal-to-external viscosity ratio on the dynamics of the capsule are further studied. It is found that the capsule experiences smaller deformation when the higher bending rigidity is included, and the low bending rigidity does not have a remarkable influence on the capsule deformation. The capsule normally experiences smaller deformation due to the increase of the internal-to-external viscosity ratio.

Small-scale characteristics of turbulence such as velocity gradients and vorticity fluctuate rapidly in magnitude and oscillate in sign. Much work exists on the characterization of magnitude variations, but far less on sign oscillations. While in homogeneous turbulence averages performed on large scales tend to zero because of the oscillatory character, those performed on increasingly smaller scales will vary with the averaging scale in some characteristic way. This characteristic variation at high Reynolds numbers is captured by the so-called cancellation exponent, which measures how local averages tend to cancel out as the averaging scale increases, in space or time. Past experimental work suggests that the exponents in turbulence depend on whether one considers quantities in full three-dimensional (3D) space or uses their one- or two-dimensional cuts. We compute cancellation exponents of vorticity and longitudinal as well as transverse velocity gradients in isotropic turbulence at Taylor-scale Reynolds numbers up to 1300 on ${8192}^3$ grids. The 2D cuts yield the same exponents as those for full 3D, while the 1D cuts yield smaller numbers, suggesting that the results in higher dimensions are more reliable. We make the case that the presence of vortical filaments in isotropic turbulence leads to this conclusion. This effect is particularly conspicuous in magnetohydrodynamic turbulence, where an increased degree of spatial coherence develops along the direction of an imposed magnetic field.

We study the dynamics of a locally conserved energy in ergodic, local many-body quantum systems on a lattice with no additional symmetry. The resulting dynamics is well approximated by a coarse grained, classical linear functional diffusion equation for the probability of all spatial configurations of energy. This is equivalent to nonlinear stochastic hydrodynamics, describing the diffusion of energy in physical spacetime. We find the absence of nonhydrodynamic slow degrees of freedom, a nonlinear fluctuation-dissipation theorem, and the emergence of a (weakly interacting) kinetic theory for hydrodynamic modes near thermal equilibrium. The observable part of the microscopic entropy obeys the local second law of thermodynamics, and quantitatively agrees with the phenomenological predictions of hydrodynamics. Our approach naturally generalizes to ergodic systems with additional symmetries, may lead to numerical algorithms to calculate diffusion constants for lattice models, and implies sufficiency conditions for a rigorous derivation of hydrodynamics in quantum systems.

Spontaneous random mutations are an important source of variation in populations. Many evolutionary models consider mutants with a fixed fitness, chosen from a fitness distribution without considering microscopic interactions among the residents and mutants. Here, we go beyond this and consider “mutant interactors,” which lead to new interactions between the residents and invading mutants that can affect the population size and the extinction risk of populations. We model microscopic interactions between individuals by using a dynamic interaction matrix, the dimension of which increases with the emergence of a new mutant and decreases with extinction. The new interaction parameters of the mutant follow a probability distribution around the payoff entries of its ancestor. These new interactions can drive the population away from the previous equilibrium and lead to changes in the population size. Thus, the population size is an evolving property rather than an externally controlled variable. We calculate the average population size of our stochastic system over time and quantify the extinction risk of the population by the mean time to extinction.

Still under debate is the question of whether machine learning is capable of going beyond black-box modeling for complex physical systems. We investigate the generalizing and interpretability properties of learning algorithms. To this end, we use supervised and unsupervised learning to infer the phase boundaries of the active Ising model, starting from an ensemble of configurations of the system. We illustrate that unsupervised learning techniques are powerful at identifying the phase boundaries in the control parameter space, even in situations of phase coexistence. It is demonstrated that supervised learning with neural networks is capable of learning the characteristics of the phase diagram, such that the knowledge obtained at a limited set of control variables can be used to determine the phase boundaries across the phase diagram. In this way, we show that properly designed supervised learning provides predictive power to regions in the phase diagram that are not included in the training phase of the algorithm. We stress the importance of introducing interpretability methods in order to perform a physically relevant classification of the phases with deep learning.

Self-similarity and long-range correlations are the remarkable features of the Earth's surface topography. Here we develop an approach based on percolation theory to study the geometrical features of Earth. Our analysis is based on high-resolution, 1 arc min, ETOPO1 global relief records. We find some evidence for abrupt transitions that occurred during the evolution of the Earth's relief network, indicative of a continental/cluster aggregation. We apply finite-size-scaling analysis based on a coarse-graining procedure to show that the observed transition is most likely discontinuous. Furthermore, we study the percolation on two-dimensional fractional Brownian motion surfaces with Hurst exponent $H$ as a model of long-range correlated topography, which suggests that the long-range correlations may play a key role in the observed discontinuity on Earth. Our framework presented here provides a theoretical model to better understand the geometrical phase transition on Earth, and it also identifies the critical nodes that will be more exposed to global climate change in the Earth's relief network.

We study the diffusive coupling of oscillating or excitable Belousov-Zhabotinsky reaction units arranged in a square lattice array and show that for certain sizes of the units and for certain distances between the units, complex oscillation modes of individual spots occur, which manifest themselves in multi-periodic, amplitude-modulated, and multi-mode oscillations. This experimental finding can be reproduced in simulations of the FitzHugh-Nagumo model mimicking the experimental setup, suggesting that it is a generic phenomenon in systems of coupled excitable units such as excitable cell tissues or coupled oscillators such as neurons. Further analysis let us conclude that the complex oscillation modes occur close to the transition from quiescent to coupling-induced oscillations states if this transition is taking place at weak coupling strength.

It is a remarkable fact that the size of slums is similar across the globe, regardless of city, country, or culture [Friesen et al., Habitat Int. 73, 79 (2018)]. The main thesis of this paper is that this universal scale is intrinsic to the slum-city system and is independent from external factors. By interpreting reaction and diffusion as long- and short-distance migration, our paper explains this universal length scale as resulting from a Turing instability of the interaction of two social groups: poor and rich.

Neuronal network dynamics depends on network structure. In this paper we study how network topology underpins the emergence of different dynamical behaviors in neuronal networks. In particular, we consider neuronal network dynamics on Erdős-Rényi (ER) networks, regular random (RR) networks, ring lattices, and all-to-all networks. We solve analytically a neuronal network model with stochastic binary-state neurons in all the network topologies, except ring lattices. Given that apart from network structure, all four models are equivalent, this allows us to understand the role of network structure in neuronal network dynamics. While ER and RR networks are characterized by similar phase diagrams, we find strikingly different phase diagrams in the all-to-all network. Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations (with a richer repertoire of bifurcations in ER and RR compared to all-to-all networks). This suggests that local heterogeneity in the ratio between excitation and inhibition plays a crucial role on emergent dynamics. Furthermore, we also observe one subtle discrepancy between ER and RR networks, namely, ER networks undergo a neuronal activity jump at lower noise levels compared to RR networks, presumably due to the degree heterogeneity in ER networks that is absent in RR networks. Finally, a comparison between network oscillations in RR networks and ring lattices shows the importance of small-world properties in sustaining stable network oscillations.