The ordering of 2D biaxial graphene oxide (GO) particles is investigated under the application of orthogonal electric (E) and magnetic fields (B); nematic, antinematic, or biaxial nematic ordering of GO particles is selectively obtained depending on the field conditions. Particularly, a perfect biaxial nematic ordering with the highest birefringence is induced by the dual fields. Unexpectedly, the presence of B enhances the effective polarizability anisotropy, which may attribute to the enhanced steric interparticle interaction. The dual fields induce the microscopic biaxial stacking assembly of GO particles, producing grainy flocs which are not observed in a single-field condition.

We study the diffusion process in binary mixtures using transition probabilities that depend on a mean-field potential. This approach reproduces the Darken equation, a relationship between the intrinsic and the tracer diffusion coefficients, $D_A$ and $D_A^{*}$, through the thermodynamic factor $\mathrm{\Phi }$ (a function of the derivative of the activity coefficient against the molar fraction). The mean-field approach allows us to go beyond the Darken equation and separately specify the dependence of $D_A$ and $D_A^{*}$ on the thermodynamic factor. We obtain that $\mathrm{\Phi }$ appears in the expression for $D_A^{*}$, but the intrinsic diffusivity $D_A$ turns out to be independent of $\mathrm{\Phi }$. Experimental results taken from the literature on diffusion in metal alloys are consistent with this theoretical prediction.

We consider the negative-weight percolation model on directed graphs. In particular, we study the model on a two-dimensional, weighted, periodic, centered square lattice. Bond weights are taken from a distribution that allows for both positive and negative values. For a given realization of the disorder, a minimally weighted directed loop and path configuration is determined by performing a nontrivial transformation of the original lattice into a minimum-weight perfect matching problem. For this problem, fast polynomial-time algorithms are available, thus we could study large systems with high accuracy. Depending on the fraction of negatively and positively weighted bonds on the lattice, a continuous phase transition is identified and its characterizing critical exponents are estimated by means of a finite-size scaling analysis. We observe a strong change of the universality class with respect to standard directed percolation as well as with respect to undirected negative-weight percolation. Furthermore, the relation to directed polymers in random media is illustrated.

Fractional Gaussian noise (FGN) with the Hurst exponent $H$ is an important tool to model various phenomena in biophysical systems, like subdiffusion in a single protein molecule. Considering that there also exists a confined structure which can be modeled as a channel in these systems, transport and escape driven by FGN in a deformable channel are investigated in this paper. By calculating the mean velocity, and the mean first passage time (MFPT) for crossing the nearest bottleneck and the probability distribution of the final position, effects of FGN and channel structure on the system dynamics are illustrated. Our results indicate that FGN has a complex influence mechanism under different combinations of $H$ and the noise intensity. For a persistence case $(H>0.5)$, the mean velocity decreases but MFPT increases with the increase of the noise intensity and $H$. While for an antipersistence case $(H<0.5)$, when $H$ is small, the relationships among the mean velocity, MFPT and the noise intensity are exactly the opposite to persistence cases. When $H$ has a large value, the mean velocity tends to first decrease and then increase. Moreover, effects of the bottleneck and channel asymmetry are investigated. It is shown that a small $H$ and a large channel width can lead to a large mean velocity and fast crossing. Besides, a channel asymmetry can affect the system dynamics by inducing asymmetric structure and adjusting the width of bottleneck. However, the effect of the bottleneck is the main factor. Therefore, a combination of channel with wide bottleneck and FGN in an antipersistence regime is the optimal choice to promote the transport and escape. These results provide a basis for the explanation of molecular activity in living organisms and the design of particle mixture separators.

In this article we perform a thorough analysis of breathers in a one-dimensional model for a layered silicate for which there exists fossil and experimental evidence of moving excitations along the close-packed lines of the ${\mathrm{K}}^{+}$ layers. Some of these excitations are likely breathers with a small energy of about 0.2 eV as the numerically obtained breathers described in the present model. Moving breathers as exact solutions of the dynamical equations are obtained at the price of being generically associated with a plane wave, a wing, with finite amplitude, although this amplitude can be very small. We call them pterobreathers. For some frequencies the wings disappear and the solutions become exact moving breathers with no wings, showing the phenomenon of supertransmission of energy. We perform a theoretical analysis of pterobreathers in systems with substrate potential and show that they are characterized by a single frequency in the moving frame plus the frequency of the wings. We have also studied high-energy stationary breathers which transform into single and double kinks and stable multibreathers with very strong localization.

We have studied entanglement entropy and Husimi $Q$ distribution as a tool to explore chaos in the quantum two-photon Dicke model. With the increase of the energy of a system, the linear entanglement entropy of a coherent state prepared in the classical chaotic and regular regions becomes more distinguishable, and the corresponding relationship between the distribution of time-averaged entanglement entropy and the classical Poincaré section has clearly been improved. Moreover, Husimi $Q$ distribution for the initial states corresponding to the points in the chaotic region in the higher-energy system disperses more quickly than that in the lower-energy system. Our results imply that higher system energy has contributed to distinguishing between the chaotic and regular behavior in the quantum two-photon Dicke model.

Mean-field theory for networks of spiking neurons based on the so-called diffusion approximation has been used to calculate certain measures of neuronal activity which can be compared with experimental data. This includes the distribution of firing rates across the network. However, the theory in its current form applies only to networks in which there is relatively little heterogeneity in the number of incoming and outgoing connections per neuron. Here we extend this theory to include networks with arbitrary degree distributions. Furthermore, the theory takes into account correlations in the in-degree and out-degree of neurons, which would arise, e.g., in the case of networks with hublike neurons. Finally, we show that networks with broad and positively correlated degrees can generate a large-amplitude sustained response to transient stimuli which does not occur in more homogeneous networks.

The dynamics of interictal events between absence seizures and their relationship to seizures themselves are investigated by employing a neural field model of the corticothalamic system. Interictal events are modeled as being due to transient parameter excursions beyond the seizure threshold, in the present case by sufficiently temporally varying the connection strength between the cerebral cortex and the thalamus. Increasing connection strength drives the system into $\sim 3$-Hz seizure oscillations via a supercritical Hopf bifurcation once the linear instability threshold is passed. Depending on the time course of the excursion above threshold, different interictal activity event dynamics are seen in the time series of corticothalamic fields. These resemble experimental interictal time series observed via electroencephalography. It is found that the morphology of these events depends on the magnitude and duration of the excursion above threshold. For a large-amplitude excursion of short duration, events resemble interictal spikes, where one large spike is seen, followed by small damped oscillations. For a short excursion with long duration, events like observed interictal periodic sharp waves are seen. When both amplitude and duration above threshold are large, seizure oscillations are seen. Using these outcomes, proximity to seizure can be estimated and tracked.

Chemically powered self-propelled colloids generate a motor force by converting locally a source of energy into directed motion, a process that has been explored both in experiments and in computational models. The use of active colloids as building blocks for nanotechnology opens the doors to interesting applications, provided we understand the behavior of these elementary constituents. We build a consistent mesoscopic simulation model for self-propelled colloids of complex shape with the aim of resolving the coupling between their translational and rotational motion. Considering a passive $\mathsf{L}$-shaped colloidal particle, we study its Brownian dynamics and locate its center of hydrodynamics, the tracking point at which translation and rotation decouple. The active L particle displays the same circling trajectories that have been found experimentally, a result which we compare with the Brownian dynamics model. We put forward the role of hydrodynamics by comparing our results with a fluid model in which the particles' velocities are reset randomly. There, the trajectories only display random orientations. We obtain these original simulation results without any parametrization of the algorithm, which makes it a useful method for the preliminary study of active colloids, prior to experimental work.

The spectrum of the radiation of a body in equilibrium is given by Planck's law. In plasma, however, waves below the plasma frequency cannot propagate; consequently, the equilibrium radiation inside plasma is necessarily different from the Planck spectrum. We derive, using three different approaches, the spectrum for the equilibrium radiation inside plasma. We show that, while plasma effects cannot be realistically detected with technology available in the near future, there are a number of quantifiable ways in which plasma affects cosmic microwave background radiation.

We demonstrate that in the continuous limit the etching mechanism yields the Kardar-Parisi-Zhang (KPZ) equation in a ($d+1$)-dimensional space. We show that the parameters $\nu$, associated with the surface tension, and $\lambda$, associated with the nonlinear term of the KPZ equation, are not phenomenological, but rather they stem from a new probability distribution function. The Galilean invariance is recovered independently of $d$, and we illustrate this via very precise numerical simulations. We obtain firsthand the coupling parameter as a function of the probabilities. In addition, we strengthen the argument that there is no upper critical limit for the KPZ equation.

The use of two-site Lindblad dissipators to generate thermal states and study heat transport was raised to prominence by Prosen and Žnidarič [J. Stat. Mech. (2009) P02035]. Here we propose a variant of this method based on detailed balance of internal levels of the two-site Hamiltonian and characterize its performance. We study the thermalization profile in the chain, the effective temperatures achieved by different single- and two-site observables, and we also investigate the decay of two-time correlations. We find that at a large enough temperature, the steady state approaches closely a thermal state, with a relative error below $1\%$ for the inverse temperature estimated from different observables.

The speed and extent of diffusion of behaviors in social networks depends on network structure and individual preferences. The contribution of the present study is twofold. First, we introduce weighted interactions between potential adopters that depend on the similarity in their preferences and moderate the strength of social reinforcement. The reason for the extension is the existence of a confirmation bias in the way agents treat information by prioritizing evidence conforming to their opinion. As a result, individuals become less likely to be influenced by peers with relatively different preferences, reducing the overall diffusion rate under clustered networks. Second, we enrich our analysis by also considering a scale free network topology with a high degree asymmetry, motivated by its pervasiveness in online social networks. This network performs consistently well in terms of diffusion for different parameter combinations and clearly outperforms clustered networks under weighted interactions. Our results show that more realistic assumptions regarding agents' interactions shift the focus from clustering to degree distribution in the study of network structures allowing for fast and widespread behavior adoption.

An extended version of the hybrid recursive regularized lattice-Boltzmann model which incorporates external force is developed to simulate humid air flows with phase change mechanisms under the Boussinesq approximation. Mass and momentum conservation equations are solved by a regularized lattice Boltzmann approach well suited for high Reynolds number flows, whereas the energy and humidity related equations are solved by a finite volume approach. Two options are investigated to account for cloud formation in atmospheric flow simulations. The first option considers a single conservation equation for total water and an appropriate invariant variable of temperature. In the other approach, liquid and vapor are considered via two separated equations, and phase transition is accounted for via a relaxation procedure. The obtained models are then systematically validated on four well-established benchmark problems including a double diffusive Rayleigh Bénard convection of humid air, two- and three-dimensional thermal moist rising bubble under convective atmospheric environment, as well as a shallow cumulus convection in the framework of large-eddy simulation.

We study an associating lattice gas (ALG) using Monte Carlo simulation on the triangular lattice and semianalytical solutions on Husimi lattices. In this model, the molecules have an orientational degree of freedom and the interactions depend on the relative orientations of nearest-neighbor molecules, mimicking the formation of hydrogen bonds. We focus on the transition between the high-density liquid (HDL) phase and the isotropic phase in the limit of full occupancy, corresponding to chemical potential $\mu \to \infty$, which has not yet been studied systematically. Simulations yield a continuous phase transition at ${\tau }_c=k_B{T}_c/\gamma =0.4763\left(1\right)$ (where $-\gamma$ is the bond energy) between the low-temperature HDL phase, with a nonvanishing mean orientation of the molecules, and the high-temperature isotropic phase. Results for critical exponents and the Binder cumulant indicate that the transition belongs to the three-state Potts model universality class, even though the ALG Hamiltonian does not have the full permutation symmetry of the Potts model. In contrast with simulation, the Husimi lattice analyses furnish a discontinuous phase transition, characterized by a discontinuity of the nematic order parameter. The transition temperatures (${\tau }_c=0.51403$ and 0.51207 for trees built with triangles and hexagons, respectively) are slightly higher than that found via simulation. Since the Husimi lattice studies show that the ALG phase diagram features a discontinuous isotropic-HDL line for finite $\mu$, three possible scenarios arise for the triangular lattice. The first is that in the limit $\mu \to \infty$ the first-order line ends in a critical point; the second is a change in the nature of the transition at some finite chemical potential; the third is that the entire line is one of continuous phase transitions. Results from other ALG models and the fact that mean-field approximations show a discontinuous phase transition for the three-state Potts model (known to possess a continuous transition) lends some weight to the third alternative.

In a recent work [Phys. Rev. E 97, 030202(R) (2018)], Sakhr and Nieminen (SN) solved a hypothesis formulated two decades ago, according to which the local box-counting dimension $D_{\mathrm{box}}\left(r\right)$ of a given energy spectrum, or more generally of a discrete set, should exclusively depend on the nearest-neighbor spacing distribution $P\left(s\right)$ of the spectrum (set). SN found analytically this dependence, which led them to obtain closed formulas for the local box-counting dimension of Poisson spectra and of spectra belonging to Gaussian orthogonal, unitary, and symplectic ensembles. Here, first, we present a different derivation of the equation establishing the connection of $D_{\mathrm{box}}\left(r\right)$ and $P\left(s\right)$ using the concept of surrogate spectrum. Although our equation is formally different to the SN result, we prove that both are equivalent. Second, we apply our equation to solve the inverse problem of determining the functional form of $P\left(s\right)$ for spectra with real fractal structure and constant box-counting dimension $D_{\mathrm{box}}$, and we find that $P\left(s\right)$ should behave as a power-law of the spacing, with an exponent given by $-(1+D_{\mathrm{box}})$. Finally, we present four applications or consequences of this last result: First, we provide a simple algorithm able to generate random fractal spectra with prescribed and constant $D_{\mathrm{box}}$. Second, we calculate $D_{\mathrm{box}}$ for the sets given by the zeros of fractional Brownian motions, whose $P\left(s\right)$ is known to have a power-law tail. Third, we also study $D_{\mathrm{box}}\left(r\right)$ for the zeros of fractional Gaussian noises, whose $P\left(s\right)$ in known to present fat (but not power-law) tails, and that could be misinterpreted as real fractals. And finally, we present the calculation of $D_{\mathrm{box}}$ for the spectra of Fibonacci Hamiltonians, known to have fractal properties, simply by fitting their corresponding $P\left(s\right)$ to a power-law without the need of applying a box-counting algorithm.

This study investigates the tearing of a thin notched sheet when two points on the sheet are pulled apart. The concepts that determine the crack trajectory are reviewed in the general anisotropic case, in which the energy of the fracture depends on the fracture direction. When observed as a flat sheet a purely geometric “tearing vector” is defined through the location of the crack tip and the pulling points. Both Griffiths's criterion and the maximum energy release rate criterion (MERR) predict a fracture path that is parallel to the tearing vector in the isotropic case. However, for the anisotropic case, the application of the MERR leads to a crack path that deviates from the tearing vector, following a propagation direction that tends to minimize the fracture energy. In the case of strong anisotropy, it is more difficult to obtain an analytical prediction of the tearing trajectory. Thus, simple geometrical arguments are provided to give a derivation of a differential equation accounting for crack trajectory, according to the natural coordinates of the pulling, and in the case that the anisotropy is sufficiently weak. The solution derived from this analysis is in good agreement with previous experimental observations.

We study a recently derived fully relativistic kinetic model for spin-1/2 particles. First, the full set of conservation laws for energy, momentum, and angular momentum are given together with an expression for the (nonsymmetric) stress-energy tensor. Next, the thermodynamic equilibrium distribution is given in different limiting cases. Furthermore, we address the analytical complexity that arises when the spin and momentum eigenfunctions are coupled in linear theory by calculating the linear dispersion relation for such a case. Finally, we discuss the model and give some context by comparing with potentially relevant phenomena that are not included, such as radiation reaction and vacuum polarization.

Extensive Monte Carlo simulations have been performed on an Ising ferromagnet under conditions that would lead to complete wetting in a semi-infinite system. We studied an $L\times L\times D$ slab geometry with oppositely directed surface fields so that a single interface is formed and can undergo a localization-delocalization transition. Under the chosen conditions the interface position is, on average, in the middle of the slab, and its fluctuations allow a sensitive test of predictions that the effective interactions between the interface and the confining surfaces are nonlocal. The decay of distance dependent correlation functions are measured within the surface, in the middle of the slab, and between middle and the surface for slabs of varying thickness $D$. From Fourier transforms of these correlation functions a nonlinear correlation length is extracted, and its behavior is found to confirm theoretical predictions for $D>6$ lattice spacings.

High accuracy and performance of the tensor renormalization group (TRG) method have been demonstrated for the model of hard disks on a triangular lattice. We considered a sequence of models with disk diameter ranging from $a$ to $2\sqrt{3}a$, where $a$ is the lattice constant. Practically, these models are good for approximate description of thermodynamics properties of molecular layers on crystal surfaces. Theoretically, it is interesting to analyze if and how this sequence converges to the continuous model of hard disks. The dependencies of the density and heat capacity on the chemical potential were calculated with TRG and transfer-matrix (TM) methods. We benchmarked accuracy and performance of the TRG method comparing it with TM method and with exact result for the model with nearest-neighbor exclusions (1NN). The TRG method demonstrates good convergence and turns out to be superior over TM with regard to considered models. Critical values of chemical potential (${\mu }_c$) have been computed for all models. For the model with next-nearest-neighbor exclusions (2NN) the TRG and TM produce consistent results (${\mu }_c=1.75587$ and ${\mu }_c=1.75398$ correspondingly) that are also close to earlier Monte Carlo estimation by Zhang and Deng. We found that 3NN and 5NN models shows the first-order phase transition, with close values of ${\mu }_c$ (${\mu }_c=4.4488$ for 3NN and $4.4<{\mu }_c<4.5$ for 5NN). The 4NN model demonstrates continuous yet rapid phase transition with $2.65<{\mu }_c<2.7$.