We consider correlated Lévy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties. We introduce a geometric parameter $\alpha$, playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a single-long-jump approximation, we analytically determine the long-time asymptotic behavior of the moments of the probability distribution as a function of $\alpha$ and of the dynamic exponent $z$ associated with the scaling length of the process. We show that our scaling analysis also applies to experimentally relevant quantities such as escape-time and transmission probabilities. Extensive numerical simulations corroborate our results which, in general, are different from those pertaining to uncorrelated Lévy-walk models.

The dependence of the dynamics of open quantum systems upon initial correlations between the system and environment is an utterly important yet poorly understood subject. For technical convenience most prior studies assume factorizable initial states where the system and its environments are uncorrelated, but these conditions are not very realistic and give rise to peculiar behaviors. One distinct feature is the rapid buildup or a sudden jolt of physical quantities immediately after the system is brought in contact with its environments. The ultimate cause of this is an initial imbalance between system-environment correlations and coupling. In this paper we demonstrate explicitly how to avoid these unphysical behaviors by proper adjustments of correlations and/or the coupling, for setups of both theoretical and experimental interest. We provide simple analytical results in terms of quantities that appear in linear (as opposed to affine) master equations derived for factorized initial states.

We analyze the partition function of the dimer model on an $\mathcal{M}\times \mathcal{N}$ triangular lattice wrapped on a torus obtained by Fendley, Moessner, and Sondhi [Phys. Rev. B 66, 214513 (2002)]. From a finite-size analysis we have found that the dimer model on such a lattice can be described by a conformal field theory having a central charge $c=-2$. The shift exponent for the specific heat is found to depend on the parity of the number of lattice sites $\mathcal{N}$ along a given lattice axis: e.g., for odd $\mathcal{N}$ we obtain the shift exponent $\lambda =1$, while for even $\mathcal{N}$ it is infinite ($\lambda =\infty$). In the former case, therefore, the finite-size specific-heat pseudocritical point is size dependent, while in the latter case it coincides with the critical point of the thermodynamic limit.

We study the critical behavior of the free energy and the thermodynamic Casimir force in a $L_{\parallel }^{d-1}\times L$ block geometry in $2<d<4$ dimensions with aspect ratio $\rho =L/L_{\parallel }$ on the basis of the $O\left(n\right)$ symmetric ${\varphi }^4$ lattice model with periodic boundary conditions and with isotropic short-range interactions. Exact results are derived in the large-$n$ limit describing the geometric crossover from film ($\rho =0$) over cubic ($\rho =1$) to cylindrical ($\rho =\infty$) geometries. For $n=1$, three perturbation approaches in the minimal renormalization scheme at fixed $d$ are presented that cover both the central finite-size regime near $T_c$ for $1/4\lesssim \rho \lesssim 3$ and the region well above and below $T_c$. At bulk $T_c$, we predict the critical Casimir force in the vertical $\left(L\right)$ direction to be negative (attractive) for a slab ($\rho <1$), positive (repulsive) for a rod ($\rho >1$), and zero for a cube $(\rho =1)$. Our results for finite-size scaling functions agree well with Monte Carlo data for the three-dimensional Ising model by Hasenbusch for $\rho =1$ and by Vasilyev et al. for $\rho =1/6$ above, at, and below $T_c$.

We investigate domain competition occurring during aggregate growth under ballistic deposition on a one-dimensional substrate by kinetic Monte Carlo simulations. In order to capture adsorbate molecules being deposited vertically, domains grow tall by extending their branches laterally and suppress the growth of neighboring short domains. When molecules are deposited on a flat substrate and frozen at the deposition site, the population density of domains, $\rho$, decreases by a power law as $\rho \sim h^{-2/3}$ at height $h$. In contrast, if the effect of surface diffusion is taken into account, the domain density decreases rapidly as $\rho \sim 1/h$.

On a substrate patterned with an array of nanopillars, domains growing from pillar tops tend to envelop those growing from gaps between pillars. To completely suppress the growth of domains in gaps, pillar periodicity $\lambda$ should be smaller than a critical value ${\lambda }_c$. We estimate this value approximately using the slope angle and the aspect ratio of a single isolated domain.

We report a detailed analysis of optical trapping of low index particles in liquid crystals under experimental conditions that prevent the effect of conventional trapping originated by optical gradient forces. The observation of stable, long-range trapping shows that this phenomenon in liquid crystals is regulated by a completely different mechanism than in isotropic media. In particular, the role of the nonlocality of optical reorientation is highlighted by showing the dependence of the trapping force on the size of the reoriented area. A model based on the actual form of the Gaussian focused beam impinging on the liquid-crystalline medium in the trapping experiment is also reported, with good agreement with experimental data.

A model with solution viscoelasticity is proposed to explain the ratchetlike stretching of DNA by a symmetric ac electric field in polymer solutions. In this model, DNA is stretched by the interaction between the fluid elasticity and the oscillatory flow induced by DNA. Predictions of the model are confirmed by DNA stretching experiments performed in various polymer solutions and the corresponding rheological measurements of the solutions. In particular, experiments have verified that a net migration of stretched DNA in polymer solutions can be induced by a zero-mean asymmetric ac electric field. This last finding cannot be explained by other existing models.

Recent experiments suggest that lipid bilayer membranes may be viscoelastic. We present a generalized “Saffman-Einstein” relation that may be used to determine the linear viscoelastic shear modulus from single-bead microrheology experiments on membranes. We show that viscoelastic parameters can also be extracted from membrane domain flicker spectroscopy experiments. Contributions from fluid inertia are expected to be negligible in both microrheology and domain flicker spectroscopy experiments, but can create a “long-time tail” in the membrane velocity autocorrelation function. In a viscous membrane, this tail crosses over from $t^{-1}$ at intermediate times, as in a two-dimensional fluid, to $t^{-3/2}$ at long times, as in a three-dimensional fluid. If the membrane is viscoelastic, the velocity autocorrelation function may be negative at intermediate times.

The diffusion coefficient of an inclusion in a liquid membrane is investigated by taking into account the interaction between membranes and bulk solvents of arbitrary thickness. As illustrative examples, the diffusion coefficients of two types of inclusions, a circular domain composed of fluid with the same viscosity as the host membrane and that of a polymer chain embedded in the membrane, are studied. The diffusion coefficients are expressed in terms of the hydrodynamic screening lengths, which vary according to the solvent thickness. When the membrane fluid is dragged by the solvent of finite thickness, via stick boundary conditions, multiple hydrodynamic screening lengths together with the weight factors to the diffusion coefficients are obtained from the characteristic equation. The conditions for which the diffusion coefficients can be approximated by the expression including only a single hydrodynamic screening length are also shown.

By employing natural time analysis, we analyze the worldwide seismicity and study the existence of correlations between earthquake magnitudes. We find that global seismicity exhibits nontrivial magnitude correlations for earthquake magnitudes greater than $M_{w}6.5$.

The random-force (Larkin) model of a directed elastic string subject to quenched random forces in the transverse directions has been a paradigm in the statistical physics of disordered systems. In this Brief Report, we investigate a modified version of the above model where the total transverse force along the polymer contour and the related total torque, in each realization of disorder, vanish. We discuss the merits of adding these constraints and show that they leave the qualitative behavior in the strong stretching regime unchanged, but they reduce the effects of the random force by significant numerical prefactors. We also show that a transverse random force effectively makes the filament softer to compression by inducing undulations. We calculate the related linear compression coefficient in both the usual and the constrained random-force model.

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units.

Experiments demonstrate the amplification of 351 nm laser light in a hot dense plasma similar to those in inertial confinement fusion ignition experiments. A seed beam interacts with one or two counter-propagating pump beams, each with an intensity of $1.2\times {10}^{15}$ W/cm${}^2$ at 351 nm, crossing the seed at 24.8° at the position where the flow is Mach 1, allowing resonant stimulation of ion acoustic waves. Results show that the energy and power transferred to the seed are increased with two pumps beyond the level that occurs with a single pump, demonstrating that, under conditions similar to ignition experiments where each beam has a low gain exponent, the total scatter produced by the multiple beams can be significantly larger than that of the individual beams. It is further demonstrated that the amplification is greatly reduced when the pump polarization is orthogonal to the seed, as expected from models of stimulated scatter.

Existence, stability, and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel two-dimensional (2D) lattices, are investigated. The system with the onsite cubic self-focusing nonlinearity is modeled by the pair of discrete nonlinear Schrödinger equations linearly coupled at the single site. Symmetric, antisymmetric, and asymmetric complexes are constructed by means of the variational approximation (VA) and numerical methods. The VA demonstrates that the antisymmetric soliton complexes exist in the entire parameter space, while the symmetric and asymmetric modes can be found below a critical value of the coupling parameter. Numerical results confirm these predictions. The symmetric complexes are destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which gives rise to stable asymmetric modes. The antisymmetric complexes are subject to oscillatory and exponentially instabilities in narrow parametric regions. In bistability areas, stable antisymmetric solitons coexist with either symmetric or asymmetric ones.

The excitation of plasmons in a metallic nanostructure represents a feasible and practical approach for manipulating the propagation and absorption of light at the subwavelength scale. Of particular interest is the coupling between plasmons, which can be used to facilitate the spectral tunability and tailor the optical response of the structure. In this paper, we study the coupling between two highly localized plasmonic modes: gap plasmon polariton mode and magnetic polariton mode, supported by a metallic-dielectric multilayer structure. The strong coupling gives rise to the formation of hybrid plasmon modes and large mode splitting. These hybrid modes result in unique spectral-directional absorption characteristics in the structure. The findings hold promise in applications such as photonic and energy conversion systems as well as the design of plasmonic nanodevices.

Monte Carlo simulations using entropic sampling to estimate the number of configurations of a given energy are a valuable alternative to traditional methods. We introduce tomographic entropic sampling, a scheme which uses multiple studies, starting from different regions of configuration space, to yield precise estimates of the number of configurations over the full range of energies, without dividing the latter into subsets or windows. Applied to the Ising model on the square lattice, the method yields the critical temperature to an accuracy of about $0.01\%$, and critical exponents to $1\%$ or better. Predictions for system sizes $L=10$–160, for the temperature of the specific heat maximum, and of the specific heat at the critical temperature, are in very close agreement with exact results. For the Ising model on the simple cubic lattice the critical temperature is given to within $0.003\%$ of the best available estimate; the exponent ratios $\beta /\nu$ and $\gamma /\nu$ are given to within about $0.04\%$ and $1\%$, respectively, of the literature values. In both two and three dimensions, results for the antiferromagnetic critical point are fully consistent with those of the ferromagnetic transition. Application to the lattice gas with nearest-neighbor exclusion on the square lattice again yields the critical chemical potential and exponent ratios $\beta /\nu$ and $\gamma /\nu$ to good precision.

The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favor groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and, although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, which has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviors, we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model by generalizing the bounded confidence rule, which is common to many continuous opinion models, to what we called confidence rules. In that work we have found that the mean field version of this model (corresponding to a complete network) allows for stationary states where noninteracting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions for certain confidence rules. Moreover, we show that the model does not become inactive; that is, the opinions keep changing, even in the stationary regime. This is an important result in the context of understanding how a rule that breeds local conformity is still able to sustain global diversity while avoiding a frozen stationary state. We also provide results that give some insights on how this behavior approaches the mean field behavior as the networks are changed.

The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well described by the power-law form with the decay exponent $\tau =2.06\left(2\right)$, followed by a hump. We then use the finite-size scaling method to make all the distributions at various system sizes up to $N=2^{37}$ collapse perfectly onto a scaling curve characterized solely by the single exponent $\tau$. We also observe that the instant of that collapse converges to a well-defined percolation threshold from below as $N\to \infty$. Based on these observations, we show that the explosive percolation transition in the model should be continuous, contrary to the widely spread belief of its discontinuity.

We investigate the statistical anisotropy and Gaussianity of temperature fluctuations of Cosmic Microwave Background (CMB) radiation data from the Wilkinson Microwave Anisotropy Probe survey, using the Multifractal Detrended Fluctuation Analysis, Rescaled Range, and Scaled Windowed Variance methods. Multifractal Detrended Fluctuation Analysis shows that CMB fluctuations has a long-range correlation function with a multifractal behavior. By comparing the shuffled and surrogate series of CMB data, we conclude that the multifractality nature of the temperature fluctuation of CMB radiation is mainly due to the long-range correlations, and the map is consistent with a Gaussian distribution.

We theoretically investigate the thermophoretic force on spherical particles in binary monatomic gas mixtures in the free molecular regime. Based on gas kinetic theory and by considering the gas-particle interactions, we derive the analytical formulas of the thermophoretic force for two limiting gas-particle collision models; namely, specular and diffuse scattering scenarios. The formulas are consistent with those in simple gases and apply to both micro- and nanoparticles; for the latter the intermolecular interactions are important. As an example, the thermophoretic force on Ag nanoparticles in He-Ar mixtures is illustrated.