We study a random-walk infiltration (RWI) model, in homogeneous and in fractal media, with small localized sources at their boundaries. In this model, particles released at a source, maintained at a constant density value, execute unbiased random walks over a lattice; a model that represents solute infiltration by diffusion into a medium in contact with a reservoir of fixed concentration. A scaling approach shows that the infiltrated length, area, or volume evolves in time as the number of distinct sites visited by a single random walker in the same medium. This is consistent with numerical simulations of the lattice model and exact and numerical solutions of the corresponding diffusion equation. In a Sierpinski carpet, the infiltrated area is expected to evolve as $t^{D_F/D_W}$ (Alexander-Orbach relation), where $D_F$ is the fractal dimension of the medium and $D_W$ is the random-walk dimension; the numerical integration of the diffusion equation supports this result with very good accuracy and improves results of lattice random-walk simulations. In a Menger sponge in which $D_F>D_W$ (i.e., a fractal with a dimension close to 3), a linear time increase of the infiltrated volume is theoretically predicted and confirmed numerically. Thus, no evidence of fractality can be observed in measurements of infiltrated volumes or masses in media where random walks are not recurrent, although the tracer diffusion is anomalous. We compare our findings with results for a fluid infiltration model in which the pressure head is constant at the source and the front displacement is driven by the local gradient of that head. Exact solutions in two and three dimensions and numerical results in a carpet show that this type of fluid infiltration is in the same universality class of RWI, with an equivalence between the head and the particle concentration. These results set a relation between different infiltration processes with localized sources and the recurrence properties of random walks in the same media.

We study the $\mathcal{PT}$-symmetric periodic layered structure with the modulated Kerr nonlinearity. We demonstrate that such systems can be transformed from the full to the broken $\mathcal{PT}$ symmetry or in the opposite direction. These transitions in the periodic structure with a finite length may be observed indirectly with the help of the dependence of the transmitted wave intensity on the incident wave intensity. Furthermore, the bistability properties depend on a gain and loss value and the choice of an input surface. The reduction of a feedback between counterpropagating waves is the main impact of the complex $\mathcal{PT}$-symmetric refractive index variation on a bistability curve.

We present a technique for obtaining an effective packing fraction for discontinuous shear thickening suspensions near a critical point. It uses a measurable quantity that diverges at the critical point—in this case the inverse of the shear rate ${\dot{\gamma }}_c^{-1}$ at the onset of discontinuous shear thickening—as a proxy for packing fraction $\varphi$. We obtain an effective packing fraction for cornstarch and water by fitting ${\dot{\gamma }}_c^{-1}\left(\varphi \right)$ and then invert the function to obtain ${\varphi }_{\mathrm{eff}}\left({\dot{\gamma }}_c\right)$. We further include the dependence of ${\dot{\gamma }}_c^{-1}$ on the rheometer gap $d$ to obtain the function ${\varphi }_{\mathrm{eff}}({\dot{\gamma }}_c,d)$. This effective packing fraction ${\varphi }_{\mathrm{eff}}$ has better resolution near the critical point than the raw measured packing fraction $\varphi$ by as much as an order of magnitude. Furthermore, ${\varphi }_{\mathrm{eff}}$ normalized by the critical packing fraction ${\varphi }_c$ can be used to compare rheology data for cornstarch and water suspensions from different laboratory environments with different temperature and humidity. This technique can be straightforwardly generalized to improve resolution in any system with a diverging quantity near a critical point.

It is shown that photons of the prolonged emission recorded by the Gamma-Ray Observation of Winter Thunderclouds (GROWTH) experiment on January 13, 2012 [D. Umemoto et al., Phys. Rev E 93, 021201(R) (2016)] could be emitted by ball lightning and generated by annihilation of positrons which arose mainly due to production of the ${\beta }^{+}$-active isotopes by the sharp γ-ray flash, accompanying the formation of ball lightning, and production of electron-positron pairs by photons from ball lightning. The model of ball lightning is based on the assumption that ball lightning has a core consisting of clouds of electrons and almost totally ionized ions which oscillate with respect to each other.

In confined systems, such as the inside of a biological cell, the outer boundary or wall can affect the dynamics of internal particles. In many cases of interest both the internal particle and outer wall are approximately spherical. Therefore, quantifying the wall effects from an outer spherical boundary on the motion of an internal eccentric sphere is very useful. However, when the two spheres are not concentric, the problem becomes nontrivial. In this paper we improve existing analytical methods to evaluate these wall effects and then train a feed-forward artificial neural network within a broader model. The final model generally performed with $\sim 0.001\%$ error within the training domain and $\sim 0.05\%$ when the outer spherical wall was extrapolated to an infinite plane. Through this model, the wall effects of an outer spherical boundary on the arbitrary motion of an internal sphere for all experimentally achievable configurations can now be conveniently and efficiently determined.

Symmetries play a conspicuous role in the large-scale behavior of critical systems. In equilibrium they allow us to classify asymptotics into different universality classes, and out of equilibrium, they sometimes emerge as collective properties which are not explicit in the “bare” interactions. Here we elucidate the emergence of an up-down symmetry in the asymptotic behavior of the stochastic scalar Burgers equation in one and two dimensions, manifested by the occurrence of Gaussian fluctuations even within the time regime controlled by nonlinearities. This robustness of Gaussian behavior contradicts naive expectations due to the detailed relation—including the lack of up-down symmetry—between the Burgers equation and the Kardar-Parisi-Zhang equation, which paradigmatically displays non-Gaussian fluctuations described by Tracy-Widom distributions. We reach our conclusions via a dynamic renormalization group study of the field statistics, confirmed by direct evaluation of the field probability distribution function from numerical simulations of the dynamical equation.

Many inference problems undergo phase transitions as a function of the signal-to-noise ratio, a prominent example of this phenomenon being found in the stochastic block model (SBM) that generates a random graph with a hidden community structure. Some of these phase transitions affect the information-theoretic optimal (but possibly computationally expensive) estimation procedure, others concern the behavior of efficient iterative algorithms. A computational gap opens when the phase transitions for these two aspects do not coincide, leading to a hard phase in which optimal inference is computationally challenging. In this paper we refine this description in two ways. From a qualitative perspective, we emphasize the existence of more generic phase diagrams with a hybrid-hard phase, in which it is computationally easy to reach a nontrivial inference accuracy but computationally hard to match the information-theoretic optimal one. We support this discussion by quantitative expansions of the functional cavity equations that describe inference problems on sparse graphs, around their trivial solution. These expansions shed light on the existence of hybrid-hard phases, for a large class of planted constraint satisfaction problems, and on the question of the tightness of the Kesten-Stigum (KS) bound for the associated tree reconstruction problem. Our results show that the instability of the trivial fixed point is not generic evidence for the Bayes optimality of the message-passing algorithms. We clarify in particular the status of the symmetric SBM with four communities and of the tree reconstruction of the associated Potts model: In the assortative (ferromagnetic) case the KS bound is always tight, whereas in the disassortative (antiferromagnetic) case we exhibit an explicit criterion involving the degree distribution that separates a large-degree regime where the KS bound is tight and a low-degree regime where it is not. We also investigate the SBM with two communities of different sizes, also known as the asymmetric Ising model, and describe quantitatively its computational gap as a function of its asymmetry, as well as a version of the SBM with two groups of $q_1$ and $q_2$ communities. We complement this study with numerical simulations of the belief propagation iterative algorithm, confirming that its behavior on large samples is well described by the cavity method.

We study random sequential adsorption of particles from a pool onto a one-dimensional substrate following ballistic deposition rules with separate nucleation and growth processes occurring simultaneously. Nucleation describes the formation of point-sized seeds, and after a seed is sown, it acts as an attractor and grows in size by the addition of grains of a fixed size. At each time step either an already-nucleated seed can increase in size, or a new seed may be nucleated. We incorporate a parameter $m$ to describe the relative rates of growth to nucleation. We solve the model analytically to obtain a gap size distribution function and a general expression for the jamming coverage as a function of $m$. We show that the jamming coverage $\theta \left(m\right)$ reaches its maximum value of $\theta \left(m\right)=1$ in the limit $m\to \infty$ following a power-law $\theta \left(\infty \right)-\theta \left(m\right)\sim K{m}^{-1/2}$ for some constant $K$. We also perform an extensive Monte Carlo simulation and find good agreement between analytic and numerical results.

Recent advances have demonstrated the effectiveness of a machine-learning approach known as “reservoir computing” for model-free prediction of chaotic systems. We find that a well-trained reservoir computer can synchronize with its learned chaotic systems by linking them with a common signal. A necessary condition for achieving this synchronization is the negative values of the sub-Lyapunov exponents. Remarkably, we show that by sending just a scalar signal, one can achieve synchronism in trained reservoir computers and a cascading synchronization among chaotic systems and their fitted reservoir computers. Moreover, we demonstrate that this synchronization is maintained even in the presence of a parameter mismatch. Our findings possibly provide a path for accurate production of all expected signals in unknown chaotic systems using just one observational measure.

The Duffing oscillator is a paradigm of bistable oscillatory motion in physics, engineering, and biology. Time series of such oscillations are often observed experimentally in a nonlinear system excited by a spontaneously fluctuating force. One is then interested in estimating effective parameter values of the stochastic Duffing model from these observations—a task that has not yielded to simple means of analysis. To this end we derive theoretical formulas for the statistics of the Duffing oscillator's time series. Expanding on our analytical results, we introduce methods of statistical inference for the parameter values of the stochastic Duffing model. By applying our method to time series from stochastic simulations, we accurately reconstruct the underlying Duffing oscillator. This approach is quite straightforward—similar techniques are used with linear Langevin models—and can be applied to time series of bistable oscillations that are frequently observed in experiments.

We perform a systematic and detailed study of the glass transition in highly asymmetric binary mixtures of colloidal hard spheres, combining differential dynamic microscopy experiments, event-driven molecular dynamics simulations, and theoretical calculations, exploring the whole state diagram and determining the self-dynamics and collective dynamics of both species. Two distinct glassy states involving different dynamical arrest transitions are consistently described, namely, a double glass with the simultaneous arrest of the self-dynamics and collective dynamics of both species, and a single glass of large particles in which the self-dynamics of the small species remains ergodic. In the single-glass scenario, spatial modulations in the collective dynamics of both species occur due to the structure of the large spheres, a feature not observed in the double-glass domain. The theoretical results, obtained within the self-consistent generalized Langevin equation formalism, are in agreement with both simulations and experimental data, thus providing a stringent validation of this theoretical framework in the description of dynamical arrest in highly asymmetric mixtures. Our findings are summarized in a state diagram that classifies the various amorphous states of highly asymmetric mixtures by their dynamical arrest mechanisms.

Exploiting the relative entropy of coherence, we isolate the coherent contribution in the energetics of a driven nonequilibrium quantum system. We prove that a division of the irreversible work can be made into a coherent and incoherent part. This provides an operational criterion for quantifying the coherent contribution in a generic nonequilibrium transformation on a closed quantum system. We then study such a contribution in two physical models of a driven qubit and kicked rotor. In addition, we also show that coherence generation is connected to the nonadiabaticity of a processes, for which it gives the dominant contribution for slow-enough transformations. The amount of generated coherence in the energy eigenbasis is equivalent to the change in diagonal entropy, and here we show that it fulfills a fluctuation theorem.

We propose a quadratic unconstrained binary optimization (QUBO) formulation of rectified-linear-unit (ReLU) type functions. Different from the $q$-loss function proposed by Denchev et al. [in Proceedings of the 29th International Conference on Machine Learning, Edinburgh, edited by J. Langford and J. Pineau (Omnipress, Madison, USA, 2012)], a simple discussion based on the Legendre duality is not sufficient to obtain the QUBO formulation of ReLU-type functions. In addition to the Legendre duality, we employ the Wolfe duality, and the QUBO formulation of ReLU type is derived. The QUBO formulation is available in Ising-type annealing methods, including quantum annealing machines.

This work presents a thermodynamic analysis of the ballistic heat equation from two viewpoints: classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). A formula for calculating the entropy within the framework of EIT for the ballistic heat equation is derived. The entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and that the entropy production can be negative. The results obtained for EIT show that the entropy is a monotonic function and that the entropy production is nonnegative. A comparison between the entropy behaviors predicted for the ballistic, for the ordinary Fourier-based, and for the hyperbolic heat equation is made. A crucial difference of the asymptotic behavior of the entropy for the ballistic heat equation is shown. It is argued that mathematical time reversibility of the partial differential ballistic heat equation is not consistent with its physical irreversibility. The processes described by the ballistic heat equation are irreversible because of the entropy increase.

We investigate the dynamics of interacting quantum planar rotors as the building blocks of gear trains and nanomachinery operating in the quantum regime. Contrary to a classical hard-gear scenario of rigidly interlocked teeth, we consider the coherent contactless coupling through a finite interlocking potential, and we study the transmission of motion from one externally driven gear to the next as a function of the coupling parameters and gear profile. The transmission is assessed in terms of transferred angular momentum and transferred mechanical work. We highlight the quantum features of the model such as quantum state revivals in the interlocked rotation and interference-enhanced transmission, which could be observed in prospective rotational optomechanics experiments.

We present further developments of the auxiliary master equation approach (AMEA), a numerical method to simulate many-body quantum systems in as well as out of equilibrium and apply it to the interacting resonant level model to benchmark the new developments. In particular, our results are obtained by employing the stochastic wave functions method to solve the auxiliary open quantum system arising within AMEA. This development allows us to reach extremely low wall times for the calculation of correlation functions with respect to previous implementations of AMEA. An additional significant improvement is obtained by extrapolating a series of results obtained by increasing the number of auxiliary bath sites, $N_B$, used within the auxiliary open quantum system formally to the limit of $N_B\to \infty$. Results for the current-voltage characteristics and for equilibrium correlation functions are compared with the one obtained by exact and matrix-product states–based approaches. Further, we complement this benchmark by the presentation of spectral functions for higher temperatures where we find different behaviors around zero frequency depending on the hybridization strength.

We investigate the directed momentum current in the quantum kicked rotor model with $\mathcal{PT}$-symmetric deriving potential. For the quantum nonresonance case, the values of quasienergy become complex when the strength of the imaginary part of the kicking potential exceeds a threshold value, which demonstrates the appearance of the spontaneous $\mathcal{PT}$ symmetry breaking. In the vicinity of the transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasienergy are significantly large. Above the transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of “quantized” increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results.

Percolation is a fundamental concept that has brought new understanding of the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much fewer interlinks than the connections within each layer. For these kinds of structures, both continuous and abrupt phase transitions are observed in the size of the giant component. The continuous (second-order) transition corresponds to the formation of a giant cluster inside one layer and has a well-defined percolation threshold. The abrupt transition instead corresponds to the merger of coexisting giant clusters among different layers and is characterized by a remarkable uncertainty in the percolation threshold, which in turns causes an anomalous behavior of the observed susceptibility. We develop a simple mathematical model able to describe this phenomenon, using a susceptibility measure that defines the range where the abrupt transition is more likely to occur. Finite-size scaling analysis in the abrupt region supports the hypothesis of a genuine first-order phase transition.

Concentrated poly($N$-isopropylacrylamide) (pNIPAM) microgel suspensions at a fixed temperature below the deswelling transition of pNIPAM exhibit spontaneous particle deswelling. The microgels deswell before they are in direct contact and in polydisperse suspensions this deswelling is most pronounced for the largest microgel particles; as a consequence, the polydispersity of the suspension is reduced. Recently, we presented a model for this spontaneous deswelling that is based on the presence of counterions originating from charged groups on the surface of the pNIPAM microgels [A. Scotti et al., Proc. Natl. Acad. Sci. USA 113, 5576 (2016)]. Here we present numerical Poisson-Boltzmann calculations of the electrostatic potential and osmotic pressure inside and outside a pNIPAM microgel that could trigger the observed deswelling at high particle concentrations.