We study the phase diagram in the $H-T$ plane of the potassium jarosite compound ${\mathrm{KFe}}_3$(OH)${}_6$(${\mathrm{SO}}_4$)${}_2$ for the antiferromagnetic $XY$ model with Dzyaloshinskii-Moriya (DM) interaction using the mean-field theory for different values of DM. In our approach, we obtain the tricritical point in the $H-T$ plane and the adjustment has a strong correlation with experimental data.

I study the properties of the quantum critical point of the transverse-field quantum Ising model on various fractal lattices such as the Sierpiński carpet, Sierpiński gasket, and Sierpiński tetrahedron. Using a continuous-time quantum Monte Carlo simulation method and finite-size scaling analysis, I identify the quantum critical point and investigate its scaling properties. Among others, I calculate the dynamic critical exponent and find that it is greater than one for all three structures. The fact that it deviates from one is a direct consequence of the fractal structures not being integer-dimensional regular lattices. Other critical exponents are also calculated. The exponents are different from those of the classical critical point and satisfy the quantum scaling relation, thus confirming that I have indeed found the quantum critical point. I find that the Sierpiński tetrahedron, of which the dimension is exactly 2, belongs to a different universality class than that of the two-dimensional square lattice. I conclude that the critical exponents depend on more details of the structure than just the dimension and the symmetry.

We study the effects of thermal fluctuations on symmetric tensionless heterogeneous (two-component) fluid membranes in a simple minimal model. Close to the critical point $T_c$ of the associated miscibility phase transition of the composition and for sufficiently strong curvature-composition interactions, mediated through a composition-dependent bending modulus, thermal fluctuations lead to enhancement of the effective bending modulus. Thus, the membrane conformation fluctuations will be suppressed near $T_c$, in comparison with a pure fluid membrane, for which thermal fluctuations are known to reduce the effective bending modulus at all nonzero temperatures.

A continuum theory is employed to numerically study the equilibrium orientation and defect structures of a circular cylindrical particle with flat ends under a homeotropic anchoring condition in a uniform nematic medium. Different aspect ratios of this colloidal geometry from thin discotic to long rodlike shapes and several colloidal length scales ranging from mesoscale to nanoscale are investigated. We show that the equilibrium state of this colloidal geometry is sensitive to the two geometrical parameters: aspect ratio and length scale of the particle. For a large enough mesoscopic particle, there is a specific asymptotic equilibrium angle associated to each aspect ratio. Upon reducing the particle size to nanoscale, the equilibrium angle follows a descending or ascending trend in such a way that the equilibrium angle of a particle with the aspect ratio bigger than 1:1 (a discotic particle) goes to a parallel alignment with respect to the far-field nematic, whereas the equilibrium angle for a particle with the aspect ratio 1:1 and smaller (a rodlike particle) tends toward a perpendicular alignment to the uniform nematic direction. The discrepancy between the equilibrium angles of the mesoscopic and nanoscopic particles originates from the significant differences between their defect structures. The possible defect structures related to mesoscopic and nanoscopic colloidal particles of this geometry are also introduced.

In the present paper, we analyze local field potentials (LFPs) recorded from the secondary motor cortex (M2) and primary visual cortex (V1) of freely moving mice reared in environmental enrichment (EE) and standard condition (SC). We focus on the scaling properties of the signals by using an integrated approach combining three different techniques: the Higuchi method, detrended fluctuation analysis, and power spectrum. Each technique provides direct or indirect estimations of the Hurst exponent $H$ and this prevents spurious identification of scaling properties in time-series analysis. It is well known that the power spectrum of an LFP signal scales as $1/f^{\beta }$ with $\beta >0$. Our results indicate the existence of a particular power spectrum scaling law $1/f^{\beta }$ with $\beta <0$ for low frequencies ($f<4$ Hz) for both SC and EE rearing conditions. This type of scaling behavior is associated to the presence of anticorrelation in the corresponding LFP signals. Moreover, since EE is an experimental protocol based on the enhancement of sensorimotor stimulation, we study the possible effects of EE on the scaling properties of secondary motor cortex (M2) and primary visual cortex (V1). Notably, the difference between Hurst's exponents in EE and SC for individual cortical regions (M2) and (V1) is not statistically significant. On the other hand, using the detrended cross-correlation coefficient, we find that EE significantly reduces the functional coupling between secondary motor cortex (M2) and visual cortex (V1).

The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space and time we find that if two particles arrive symmetrically in a plane at a large angle, then (i) radial repulsion and (ii) linear self-propelling toward a fixed preferred speed are sufficient for them to depart at a smaller angle. For this local gain of momentum explicit velocity alignment is not necessary, nor are adhesion or attraction, inelasticity or anisotropy of the particles, or nonlinear drag. With many particles obeying these microscopic rules of motion we find that their spatial confinement to a square with periodic boundaries (which is an indirect form of attraction) leads to stable macroscopic ordering. As a function of the strength of added noise we see—at finite system sizes—a critical slowing down close to the order-disorder boundary and a discontinuous transition. After varying the density of particles at constant system size and varying the size of the system with constant particle density we predict that in the infinite system size (or density) limit the hysteresis loop disappears and the transition becomes continuous. We note that animals, humans, drones, etc., tend to move asynchronously and are often more responsive to motion than positions. Thus, for them velocity-based continuous models can provide higher precision than coordinate-based models. An additional characteristic and realistic feature of the model is that convergence to the ordered state is fastest at a finite density, which is in contrast to models applying (discontinuous) explicit velocity alignments and discretized time. To summarize, we find that the investigated model can provide a minimal description of flocking.

A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that $p^{\prime }\left(v\right)<0$ is a sufficient condition for instability, while $p^{\prime }\left(v\right)>0$ is a necessary condition for stability; here, $v$ is the soliton velocity and $p=P/N$, where $P$ and $N$ are the soliton momentum and norm, respectively. To date, the curve $p\left(v\right)$ was calculated approximately by a collective coordinate theory, and the criterion was confirmed by simulations. The goal of this paper is to calculate $p\left(v\right)$ exactly for several classes and cases of the generalized NLSE: a soliton moving in a real potential, in particular a time-dependent ramp potential, and a time-dependent confining quadratic potential, where the nonlinearity in the NLSE also has a time-dependent coefficient. Moreover, we investigate a logarithmic and a cubic NLSE with a time-independent quadratic potential well. In the latter case, there is a bisoliton solution that consists of two solitons with asymmetric shapes, forming a bound state in which the shapes and the separation distance oscillate. Finally, we consider a cubic NLSE with parametric driving. In all cases, the $p\left(v\right)$ curve is calculated either analytically or numerically, and the stability criterion is confirmed.

Direct numerical simulation is used to study the air flow between two vertical plates maintained at different temperatures. The periodic dimensions of the plates are small so as to accommodate only one flow structure, which consists of a convection roll with oblique vorticity braids. At lower Rayleigh numbers, the roll and the braids grow and shrink alternatively following a cyclical process. As the Rayleigh number is increased, the flow becomes temporally chaotic through a period-doubling cascade. Windows corresponding to multiperiodic regimes and interior crises are observed. As the Rayleigh number is further increased, the structure intermittently switches between two vertical positions, which is seen to correspond to an “attractor-merging” crisis. The chaotic flow dynamics are characterized and the corresponding physical mechanisms are identified. We show that some of the flow key features, such as the chaotic oscillation and intermittency, can be captured by a low-order model.

Surface tension profiles in vertical soap films are experimentally investigated. Measurements are performed by introducing deformable elastic objets in the films. The shape adopted by those objects once set in the film is related to the surface tension value at a given vertical position by numerically solving the adapted elasticity equations. We show that the observed dependency of the surface tension versus the vertical position is predicted by simple modeling that takes into account the mechanical equilibrium of the films coupled to previous thickness measurements.

Fluxon dynamics in the dc-biased array of asymmetric three-junction superconducting quantum interference devices (SQUIDs) is investigated. The array of SQUIDs is described by the discrete double sine-Gordon equation. It appears that this equation possesses a finite set of velocities at which the fluxon propagates with the constant shape and without radiation. The signatures of these velocities appear on the respective current-voltage characteristics of the array as inaccessible voltage intervals (gaps). The critical depinning current has a clear minimum as a function of the asymmetry parameter (the ratio of the critical currents of the left and right junctions of the SQUID), which coincides with the minimum of the Peierls-Nabarro potential.

We study dense and highly polydisperse emulsions at droplet volume fractions $\varphi \ge 0.65$. We apply oscillatory shear and observe droplet motion using confocal microscopy. The presence of droplets with sizes several times the mean size dramatically changes the motion of smaller droplets. Both affine and nonaffine droplet motions are observed, with the more nonaffine motion exhibited by the smaller droplets which are pushed around by the larger droplets. Droplet motions are correlated over length scales from one to four times the mean droplet diameter, with larger length scales corresponding to higher strain amplitudes (up to strains of about 6%).

Epilepsy, refractory status epilepticus, and depolarization block are pathological brain activities whose mechanisms are poorly understood. Using a generic mathematical model of seizure activity, we show that these activities coexist under certain conditions spanning the range of possible brain activities. We perform a detailed bifurcation analysis and predict strategies to escape from some of the pathological states. Experimental results using rodent data provide support of the model, highlighting the concept that these pathological activities belong to the endogenous repertoire of brain activities.

A new dynamic line, the Frenkel line, has recently been proposed to separate the supercritical state into rigid-liquid and nonrigid gaslike fluid. The location of the Frenkel line on the phase diagram is unknown for real fluids. Here we map the Frenkel line for three important systems: ${\mathrm{CO}}_2,{\mathrm{H}}_2\mathrm{O}$, and ${\mathrm{CH}}_4$. This provides an important demarcation on the phase diagram of these systems, the demarcation that separates two distinct physical states with liquidlike and gaslike properties. We find that the Frenkel line can have a similar trend as the melting line above the critical pressure. Moreover, we discuss the relationship between unexplained solubility maxima and Frenkel line, and we propose that the Frenkel line corresponds to the optimal conditions for solubility.

The steady state of a Brownian particle diffusing in an arbitrary potential under the stochastic resetting mechanism has been studied. We show that there are different classes of nonequilibrium steady states depending on the nature of the potential. In the stable potential landscape, the system attains a well-defined steady state; however, the existence of the steady state for the unstable landscape is constrained. We have also investigated the transient properties of the propagator towards the steady state under the stochastic resetting mechanism. Finally, we have done numerical simulations to verify our analytical results.

Effects of the presence of ions, at moderate to high concentrations, on dynamical properties of water molecules are investigated through classical molecular dynamics simulations using two well-known nonpolarizable water models. Simulations reveal that the presence of magnesium chloride (${\mathrm{MgCl}}_2$) induces perturbations in the hydrogen bond network of water leading to the formation of bulklike domains with ‘‘defect sites'’ on boundaries of such domains: water molecules at such defect sites have less number of hydrogen bonds than those in bulk water. Reorientational autocorrelation functions for dipole vectors of such defect water molecules are computed at different concentrations of ions and compared with system of pure water. Earlier experimental and simulation studies indicate significant differences in reorientational dynamics for water molecules in the first hydration shell of many dissolved ions. Results of this study suggest that defect water molecules, which are beyond the first hydration shells of ions, also experience significant slowing of reorientation times as a function of concentration in the case of ${\mathrm{MgCl}}_2$. However, addition of cesium chloride (CsCl) to water does not perturb the hydrogen bond network of water significantly even at higher concentrations. This difference in behavior between ${\mathrm{MgCl}}_2$ and CsCl is consistent with the well-known Hofmeister series.

By considering general Markov stochastic dynamics and its coarse graining, we study the framework of stochastic thermodynamics for the original and reduced descriptions corresponding to different scales. We are especially concerned with the case where the irreversible entropy production has a finite difference between the scales. We find that the sum of the increment of the nonequilibrium entropy and the excess part of the entropy production, which are key quantities in the construction of steady-state thermodynamics, is essentially kept invariant with respect to the change in the scales of description. This general result justifies experimental approaches toward steady-state thermodynamics based on coarse-grained variables. We demonstrate our result in a mesoscopic heat engine system.

Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of random walks on temporal networks. Here we theoretically study two types of event-driven random walks on a stochastic temporal network model that produces arbitrary distributions of interevent times. In the so-called active random walk, the interevent time is reinitialized on all links upon each movement of the walker. In the so-called passive random walk, the interevent time is reinitialized only on the link that has been used the last time, and it is a type of correlated random walk. We find that the steady state is always the uniform density for the passive random walk. In contrast, for the active random walk, it increases or decreases with the node's degree depending on the distribution of interevent times. The mean recurrence time of a node is inversely proportional to the degree for both active and passive random walks. Furthermore, the mean recurrence time does or does not depend on the distribution of interevent times for the active and passive random walks, respectively.