Linear and nonlinear response formulas taking into account all Casimir invariants are derived without use of angle-action variables of a single-particle (mean-field) Hamiltonian. This article deals mainly with the Vlasov system in a spatially inhomogeneous quasistationary state whose associating single-particle Hamiltonian is not integrable and has only one integral of the motion, the Hamiltonian itself. The basic strategy is to restrict the form of perturbation so that it keeps Casimir invariants within a linear order, and the single particle's probabilistic density function is smooth with respect to the single particle's Hamiltonian. The theory is applied for a spatially two-dimensional system and is confirmed by numerical simulations. A nonlinear response formula is also derived in a similar manner.

We report a new effect of a cascade replication of dissipative solitons from a single one. It is discussed in the framework of a common model based on the one-dimensional cubic-quintic complex Ginzburg-Landau equation in which an additional linear term is introduced to account the perturbation from a particular potential of externally applied force. The effect is demonstrated on the light beams propagating through a planar waveguide. The waveguide consists of a nonlinear layer able to guide dissipative solitons and a magneto-optic substrate. In the waveguide an externally applied force is considered to be an inhomogeneous magnetic field which is induced by modulated electric currents flowing along a set of conducting wires adjusted on the top of the waveguide.

Multilayer networks are widespread in natural and manmade systems. Key properties of these networks are their spectral and eigenfunction characteristics, as they determine the critical properties of many dynamics occurring on top of them. Here, we numerically demonstrate that the normalized localization length $\beta$ of the eigenfunctions of multilayer random networks follows a simple scaling law given by $\beta =x^{*}/(1+x^{*})$, with $x^{*}=\gamma {(b_{\mathrm{eff}}^2/L)}^{\delta }$, $\delta \sim 1$, and $b_{\mathrm{eff}}$ being the effective bandwidth of the adjacency matrix of the network, whose size is $L$. The scaling law for $\beta$, that we validate on real-world networks, might help to better understand criticality in multilayer networks and to predict the eigenfunction localization properties of them.

In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.

Collective leadership and herding may arise in standard models of opinion dynamics as an interplay of a strong separation of time scales within the population and its hierarchical organization. Using the voter model as a simple opinion formation model, we show that, in the herding phase, a group of agents become effectively the leaders of the dynamics while the rest of the population follow blindly their opinion. Interestingly, in some cases such herding dynamics accelerates the time to consensus, which then becomes size independent or, on the contrary, makes the consensus nearly impossible. These behaviors have important consequences when an external noise is added to the system that makes consensus (absorbing) states to disappear. We analyze this model, which shows an interesting phase diagram, with a purely diffusive phase, a herding (or two-states) phase, and mixed phases where both behaviors are possible.

A mixture of two selenium-containing compounds, 80 wt. % AS657 and 20 wt. % AS620, are studied with two complementary methods, electric-field-induced birefringence (EFIB) and microbeam resonant x-ray scattering ($\mu \mathrm{RXS}$). The mixture shows the typical phase sequence of Sm-$C_A^{*}$–$\frac{1}{3}$–$\frac{1}{2}$–Sm-$C^{*}$–Sm-$C_{\alpha }^{*}$–Sm-$A$, where $\frac{1}{3}$ and $\frac{1}{2}$ are two prototypal ferrielectric and antiferroelectric subphases with three- and four-layer unit cells, respectively. Here we designate the subphase as its $q_T$ number defined by the ratio of $\left[F\right]/\left(\right[F]+[A\left]\right)$, where $\left[F\right]$ and $\left[A\right]$ are the numbers of synclinic ferroelectric and anticlinic antiferroelectric orderings in the unit cell, respectively. The electric field vs temperature phase diagram with EFIB contours indicates the emergence of three additional subphases, an antiferroelectric one between Sm-$C_A^{*}$ and $\frac{1}{3}$ and antiferroelectric and apparently ferrielectric ones between $\frac{1}{3}$ and $\frac{1}{2}$. The simplest probable $q_T$'s for these additional subphases are $\frac{1}{4}, \frac{2}{5}$, and $\frac{3}{7}$, respectively, in the order of increasing temperature. The $\mu \mathrm{RXS}$ profiles indicate that antiferroelectric $\frac{1}{4}$ and $\frac{2}{5}$ approximately have the eight-layer ($FAAAFAAA$) and ten-layer ($FAFAAFAFAA$) Ising unit cells, respectively. The remaining subphase may be ferrielectric $\frac{3}{7}$ with a seven-layer unit cell, although the evidence is partial. These experimental results are compared with the phenomenological Landau model [P. V. Dolganov and E. I. Kats, Liq. Cryst. Rev. 1, 127 (2014)] and the quasimolecular model [A. V. Emelyanenko and M. A. Osipov, Phys. Rev. E 68, 051703 (2003)].

We report on a theoretical and experimental investigation of the normal contact of stretched neo-Hookean substrates with rigid spherical probes. Starting from a published formulation of surface Green's function for incremental displacements on a prestretched, neo-Hookean, substrate [J. Mech. Phys. Solids 56, 2957 (2008)], a model is derived for both adhesive and nonadhesive contacts. The shape of the elliptical contact area together with the contact load and the contact stiffness are predicted as a function of the in-plane stretch ratios ${\lambda }_x$ and ${\lambda }_y$ of the substrate. The validity of this model is assessed by contact experiments carried out using an uniaxally stretched silicone rubber. For stretch ratio below about 1.25, a good agreement is observed between theory and experiments. Above this threshold, some deviations from the theoretical predictions are induced as a result of the departure of the mechanical response of the silicone rubber from the neo-Hokeean description embedded in the model.

Ultracold plasmas (UCPs) provide a well-controlled system for studying multiple aspects in plasma physics that include collisions and strong-coupling effects. By applying a short electric field pulse to an UCP, a plasma electron center-of-mass oscillation can be initiated. For accessible parameter ranges, the damping rate of this oscillation is determined by the electron-ion collision rate. We performed measurements of the oscillation damping rate with such parameters and compared the measured rates to both a molecular dynamics (MD) simulation that includes strong-coupling effects and a Monte Carlo binary collision simulation designed to predict the damping rate including only weak-coupling considerations. We found agreement between the experimentally measured damping rate and the MD result. This agreement did require including the influence of a previously unreported UCP heating mechanism whereby the presence of a dc electric field during ionization increased the electron temperature, but estimations and simulations indicate that such a heating mechanism should be present for our parameters. The measured damping rate at our coldest electron temperature conditions was much faster than the weak-coupling prediction obtained from the Monte Carlo binary collision simulation, which indicates the presence of a significant strong-coupling influence. The density averaged electron strong-coupling parameter $\mathrm{\Gamma }$ measured at our coldest electron temperature conditions was 0.35(8).

To emphasize the importance of the kinetic boundary condition for micro- to nanoscale flow, we present an ad hoc kinetic boundary condition suitable for torturous geological porous media. We found that the kinetic boundary condition is one of the essential features which should be supplemented to the standard lattice Boltzmann scheme in order to obtain accurate continuum observables. The claim is validated using a channel flow setup by showing the agreement of mass flux with analytical value. Further, using a homogeneous porous structure, the importance of the kinetic boundary condition is shown by comparing the permeability correction factor with the analytical value. Finally, the proposed alternate to the kinetic boundary condition is validated by showing its capability to capture the basic feature of the kinetic boundary condition.

We apply the singular value decomposition (SVD) method, based on normal-mode analysis, to decompose the spectra of finite random matrices of standard Gaussian ensembles in trend and fluctuation modes. We use the fact that the fluctuation modes are scale invariant and follow a power law, to characterize the transition between the extreme regular and chaotic cases. Thereby, we quantify the quantum chaos in systems described by random matrix theory in a direct way, without performing any previous unfolding procedure, and therefore, avoiding possible artifacts.

We investigate the role of different aperiodic sequences in the dynamics of single quantum particles in discrete space and time. For this we consider three aperiodic sequences, namely, the Fibonacci, Thue-Morse, and Rudin-Shapiro sequences, as examples of tilings the diffraction spectra of which have pure point, singular continuous, and absolutely continuous support, respectively. Our interest is to understand how the order, intrinsically introduced by the deterministic rule used to generate the aperiodic sequences, is reflected in the dynamical properties of the quantum system. For this system we consider a single particle undergoing a discrete-time quantum walk (DTQW), where the aperiodic sequences are used to distribute the coin operations at different lattice positions (inhomogeneous DTQW) or by applying the same coin operation at all lattice sites at a given time but choosing different coin operation at each time step according to the chosen aperiodic sequence (time dependent DTQW). We study the energy spectra and the spreading of an initially localized wave packet for different cases, finding that in the case of Fibonacci and Thue-Morse tilings the system is superdiffusive, whereas in the Rudin-Shapiro case it is strongly subdiffusive. Trying to understand this behavior in terms of the energy spectra, we look at the survival amplitude as a function of time. By means of the echo we present strong evidence that, although the three orderings are very different as evidenced by their diffraction spectra, the energy spectra are all singular continuous except for the inhomogeneous DTQW with the Rudin-Shapiro sequence where it is discrete. This is in agreement with the observed strong localization both in real space and in the Hilbert space. Our paper is particularly interesting because quantum walks can be engineered in laboratories by means of ultracold gases or in optical waveguides, and therefore would be a perfect playground to study singular continuous energy spectra in a completely controlled quantum setup.

We experimentally investigate magnetic surface swimmers on water. These objects self-assemble from ferromagnetic microparticles and a nonmagnetic disk. They are floating on the liquid surface due to interface tension and move under the influence of a harmonically oscillating homogeneous magnetic field oriented vertically, which is distinguished by its amplitude and frequency. The speed of the surface swimmers strongly depends on these parameters. The functional dependencies between speed and amplitude and between speed and frequency are investigated by independently varying both control parameters. In the first case, the data obtained are in good agreement with the predicted scaling while there are some deviations in the latter case. Moreover, due to the interplay between the surface bound swimmers and the ascending liquid meniscus at the edge of the experimental vessel, different dynamics can be realized. We observe periodic and quasiperiodic trajectories in a circular vessel and aperiodic trajectories in a vessel shaped like a Bunimovich stadium.

We present the experimental analysis of the instabilities generated on a large drop of liquid metal by a time-dependent magnetic field. The study is done exploring the range of tiny values of the control parameter (the ratio between the Lorentz forces and inertia) avoiding nonlinear effects. Two different instabilities break the symmetries generating spatial patterns that appear without a threshold for some specific frequencies (up to the experimental precision) and have been observed for parameter values two orders of magnitude lower than in previously published experiments [J. Fluid Mech. 239, 383 (1992)]. One of the instabilities corresponds to a boundary condition oscillation that generates surface waves and breaks the azimuthal symmetry. The other corresponds to a parametric forcing through a modulation of the Lorentz force. The competition between these two mechanisms produces time-dependent patterns near codimension-2 points.

The properties of a bound electron system immersed in a plasma environment are strongly modified by the surrounding plasma. The modification of an essential quantity, the ionization energy, is described by the electronic and ionic self-energies, including dynamical screening within the framework of the quantum statistical theory. Introducing the ionic dynamical structure factor as the indicator for the ionic microfield, we demonstrate that ionic correlations and fluctuations play a critical role in determining the ionization potential depression. This is, in particular, true for mixtures of different ions with large mass and charge asymmetry. The ionization potential depression is calculated for dense aluminum plasmas as well as for a CH plasma and compared to the experimental data and more phenomenological approaches used so far.

We present a method of deriving a boundary condition for diffusion at a thin membrane from experimental data. Based on experimental results obtained for normal diffusion of ethanol in water, we show that the derived boundary condition at a membrane contains a term with a Riemann-Liouville fractional time derivative of order $\frac{1}{2}$. Such a form of the boundary condition shows that a transfer of particles through a thin membrane is a “long-memory process.” The presented method is an example that an important part of the mathematical model of physical processes may be derived directly from experimental data.

For fluctuating currents in nonequilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales. This generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite time scales are not accessible. Importantly, often this finite-time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long-time limit. We illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle.

In this paper, we focus on the control of the mean-field equilibrium of nonlinear networks of the Langevin type in the limit of small noise. Using iterative linear approximations, we derive a formula that prescribes a control strategy in order to displace the equilibrium state of a given system and remarkably find that the control function has a “universal” form under certain physical conditions. This result can be employed to define universal protocols useful, for example, in the optimal work extraction from a given reservoir. Generalizations and limits of application of the method are discussed.

We study the thermal phase transition of the fourfold degenerate phases (the plaquette and single-stripe states) in the two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical Ashkin-Teller-like behavior is identified both in the plaquette phase region and the single-stripe phase region. The four-state Potts critical end points differentiating the continuous transitions from the first-order ones are estimated based on finite-size-scaling analyses. Furthermore, a similar behavior of the transition to the fourfold single-stripe phase is also observed in the anisotropic triangular Ising model. Thus, this work clearly demonstrates that the transitions to the fourfold degenerate states of two-dimensional Ising antiferromagnets exhibit similar transition behavior.