The motion of a rigid, spinning disk on a flat surface ends with a dissipation-induced finite-time singularity. The problem of finding the dominant energy absorption mechanism during the last phase of the motion generated a lively debate during the past two decades. Various candidates including air drag and different types of friction have been considered, nevertheless impacts have not been examined until now. We investigate the effect of impacts caused by geometric imperfections of the disk and of the underlying flat surface, through analyzing the dynamics of polygonal disks with unilateral point contacts. Similarly to earlier works, we determine the rate of energy absorption under the assumption of a regular pattern of motion analogous to precession-free motion of a rolling disk. In addition, we demonstrate that the asymptotic stability of this motion depends on parameters of the impact model. In the case of instability, the emerging irregular motion is investigated numerically. We conclude that there exists a range of model parameters (small radii of gyration or small restitution coefficients) in which absorption by impacts dominates all previously investigated mechanisms during the last phase of motion. Nevertheless the parameter values associated with a homogeneous disk on a hard surface are typically not in this range, hence the effect of impacts is in that case not dominant.

We consider pressure-driven flows in wide microchannels, and discuss how a transverse shear, generated by misaligned superhydrophobic walls, impacts cross-sectional spreading of Brownian particles. We show that such a transverse shear can induce an advective superdiffusion, which strongly enhances dispersion of particles compared to a normal diffusion, and that maximal cross-sectional spreading corresponds to a crossover between its subballistic and superballistic regimes. This allows us to argue that an advective superdiffusion can be used for boosting dispersion of particles at smaller Péclet numbers compared to known concepts of passive microfluidic mixing. This implies that our superdiffusion scenario allows one efficient mixing of much smaller particles or using much thinner microchannels than methods, which are currently being exploited.

Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable bifurcations of the underlying vector field. Here, we report a different situation, corresponding to a fluctuating system approaching a bifurcation, where both effects collaborate. We show that the problem can be reduced to a single control parameter governing the competition between deterministic and stochastic effects. Two asymptotic regimes are identified: When the control parameter is small (e.g., small noise), deviations from the deterministic case are well described by the Freidlin-Wentzell theory. In particular, escapes over the potential barrier are very rare events. When the parameter is large (e.g., large noise), such events become typical. Unlike pure noise-induced transitions, the distribution of the escape time is peaked around a value which is asymptotically predicted by an adiabatic approximation. We show that the two regimes are characterized by qualitatively different reacting trajectories with algebraic and exponential divergences, respectively.

Two distinct transition points have been observed in a problem of lattice percolation studied using a system of pulsating disks. Sites on a regular lattice are occupied by circular disks whose radii vary sinusoidally within $[0,R_0]$ starting from a random distribution of phase angles. A lattice bond is said to be connected when its two end disks overlap with each other. Depending on the difference of the phase angles of these disks, a bond may be termed as dead or live. While a dead bond can never be connected, a live bond is connected at least once in a complete time period. Two different time scales can be associated with such a system, leading to two transition points. Namely, a percolation transition occurs at $R_{0c}=0.908\left(5\right)$ when a spanning cluster of connected bonds emerges in the system. Here, information propagates across the system instantly, i.e., with infinite speed. Secondly, there exists another transition point $R_0^{*}=0.5907\left(3\right)$ where the giant cluster of live bonds spans the lattice. In this case the information takes finite time to propagate across the system through the dynamical evolution of finite-size clusters. This passage time diverges as $R_0\to R_0^{*}$ from above. Both the transitions exhibit the critical behavior of ordinary percolation transition. The entire scenario is robust with respect to the distribution of frequencies of the individual disks. This study may be relevant in the context of wireless sensor networks.

We study universal critical adsorption on a solid sphere and a solid cylinder in a fluid at bulk criticality, where preferential adsorption occurs. We use a local functional theory proposed by Fisher et al. [M. E. Fisher and P. G. de Gennes, C. R. Acad. Sci. Paris Ser. B 287, 207 (1978); M. E. Fisher and H. Au-Yang, Physica A 101, 255 (1980)]. We calculate the mean order parameter profile $\psi \left(r\right)$, where $r$ is the distance from the sphere center and the cylinder axis, respectively. The resultant differential equation for $\psi \left(r\right)$ is solved exactly around a sphere and numerically around a cylinder. A strong adsorption regime is realized except for very small surface field $h_1$, where the surface order parameter $\psi \left(a\right)$ is determined by $h_1$ and is independent of the radius $a$. If $r$ considerably exceeds $a, \psi \left(r\right)$ decays as $r^{-(1+\eta )}$ for a sphere and $r^{-(1+\eta )/2}$ for a cylinder in three dimensions, where $\eta$ is the critical exponent in the order parameter correlation at bulk criticality.

The Clausius inequality form of the second law of thermodynamics relates information changes (entropy) to changes in the first moment of the energy (heat and indirectly also work). Are there similar relations between other moments of the energy distribution, and other information measures, or is the Clausius inequality a one of a kind instance of the energy-information paradigm? If there are additional relations, can they be used to make predictions on measurable quantities? Changes in the energy distribution beyond the first moment (average heat or work) are especially important in small systems which are often very far from thermal equilibrium. The additional energy-information relations (AEIR's), here derived, provide positive answers to the two questions above and add another layer to the fundamental connection between energy and information. To illustrate the utility of the new AEIR's, we find scenarios where the AEIR's yield tighter constraints on performance (e.g., in thermal machines) compared to the second law. To obtain the AEIR's we use the Bregman divergence—a mathematical tool found to be highly suitable for energy-information studies. The quantum version of the AEIR's provides a thermodynamic meaning to various quantum coherence measures. It is intriguing to fully map the regime of validity of the AEIR's and extend the present results to more general scenarios including continuous systems and particles exchange with the baths.

Lyapunov exponents characterize the chaotic nature of dynamical systems by quantifying the growth rate of uncertainty associated with the imperfect measurement of initial conditions. Finite-time estimates of the exponent, however, experience fluctuations due to both the initial condition and the stochastic nature of the dynamical path. The scale of these fluctuations is governed by the Lyapunov susceptibility, the finiteness of which typically provides a sufficient condition for the law of large numbers to apply. Here, we obtain a formally exact expression for this susceptibility in terms of the Ruelle dynamical $\zeta$ function for one-dimensional systems. We further show that, for systems governed by sequences of random matrices, the cycle expansion of the $\zeta$ function enables systematic computations of the Lyapunov susceptibility and of its higher-moment generalizations. The method is here applied to a class of dynamical models that maps to static disordered spin chains with interactions stretching over a varying distance and is tested against Monte Carlo simulations.

The dynamics of a large array of coupled semiconductor lasers is studied numerically for a nonlocal coupling scheme. Our focus is on chimera states, a self-organized spatiotemporal pattern of coexisting coherence and incoherence. In laser systems, such states have been previously found for global and nearest-neighbor coupling, mainly in small networks. The technological advantage of large arrays has motivated us to study a system of 200 nonlocally coupled lasers with respect to the emerging collective dynamics. Moreover, the nonlocal nature of the coupling allows us to obtain robust chimera states with multiple (in)coherent domains. The crucial parameters are the coupling strength, the coupling phase and the range of the nonlocal interaction. We find that multiclustered chimera states exist in a wide region of the parameter space and we provide quantitative characterization for the obtained spatiotemporal patterns. By proposing two different experimental setups for the realization of the nonlocal coupling scheme, we are confident that our results can be confirmed in the laboratory.

Synchronization properties of chaotic dynamics in two mutually coupled semiconductor lasers with optical feedback embedded in a photonic integrated circuit are investigated from the point of view of their dynamical content. A phenomenon in which the two lasers can show qualitatively different synchronization properties according to the frequency range of investigation and their nonlinear dynamics is identified and termed dynamics-dependent synchronization. In-phase synchronization is observed for original signals and antiphase synchronization is observed for low-pass filtered signals in the case where one of the lasers shows chaotic oscillations while the other laser exhibits low-frequency fluctuations dynamics. The experimental conditions causing the synchronization states to vary according to the considered frequency interval are studied and the key roles of asymmetric coupling strength and injection currents are clarified.

Ecosystems are commonly conceptualized as networks of interacting species. However, partitioning natural diversity of organisms into discrete units is notoriously problematic and mounting experimental evidence raises the intriguing question whether this perspective is appropriate for the microbial world. Here an alternative formalism is proposed that does not require postulating the existence of species as fundamental ecological variables and provides a naturally hierarchical description of community dynamics. This formalism allows approaching the species problem from the opposite direction. While the classical models treat a world of imperfectly clustered organism types as a perturbation around well-clustered species, the presented approach allows gradually adding structure to a fully disordered background. The relevance of this theoretical construct for describing highly diverse natural ecosystems is discussed.

Chiral smectic-$A$ liquid crystal elastomers are rubbery materials composed of a lamellar arrangement of liquid crystalline mesogens. It has been shown experimentally that these materials shear when subjected to an electric field due to the electrically induced tilt of the director. Experiments have also shown that shearing a chiral smectic-$A$ elastomer gives rise to a polarization. Roughly, the shear force tilts the directors which, in turn, induce electric dipoles. This paper builds on previous works and models the electromechanical response of smectic-$A$ elastomers using free energy contributions that are associated with the lamellar structure, the relative tilt between the director and the layer normal, and the coupling between the director and the electric field. To illustrate the merit of the proposed model, two cases are considered—a deformation induced polarization and an electrically induced deformation. The predictions according to these two models qualitatively agree with experimental findings. Finally, a cylinder composed of helical smectic layers is also considered. It is shown that the electromechanical response varies as a function of the helix angle.

We study the adsorption of a fluid in the grand canonical ensemble occurring at a planar heterogeneous wall which is decorated with a chemical stripe of width $L$. We suppose that the material of the stripe strongly preferentially adsorbs the liquid in contrast to the outer material which is only partially wet. This competition leads to the nucleation of a droplet of liquid on the stripe, the height $h_m$ and shape of which (at bulk two-phase coexistence) has been predicted previously using mesoscopic interfacial Hamiltonian theory. We test these predictions using a microscopic Fundamental Measure Density Functional Theory which incorporates short-ranged fluid-fluid and fully long-ranged wall-fluid interactions. Our model functional accurately describes packing effects not captured by the interfacial Hamiltonian but still we show that there is excellent agreement with the predictions $h_m\approx L^{1/2}$ and for the scaled circular shape of the drop even for $L$ as small as 50 molecular diameters. For smaller stripes the droplet height is considerably lower than that predicted by the mesoscopic interfacial theory. Phase transitions for droplet configurations occurring on substrates with multiple stripes are also discussed.

Like and oppositely charged particles or dust grains in linear shear flows are often driven to collide with one another by fluid and/or electrostatic forces, which can strongly influence particle-size distribution evolution. In gaseous media, collisions in shear are further complicated because particle inertia can influence differential motion. Expressions for the collision rate coefficient have not been developed previously which simultaneously account for the influences of linear shear, particle inertia, and electrostatic interactions. Here, we determine the collision rate coefficient accounting for the aforementioned effects by determining the collision area, i.e., the area of the plane perpendicular to the shear flow defining the relative initial locations of particles which will collide with one another. Integration of the particle flux over this area yields the collision rate. Collision rate calculations are parametrized as an enhancement factor, i.e., the ratio of the collision rate considering potential interactions and inertia to the traditional collision rate considering laminar shear only. For particles of constant surface charge density, the enhancement factor is found dependent only on the Stokes number (quantifying particle inertia), the electrostatic energy to shear energy ratio, and the ratio of colliding particle radii. Enhancement factors are determined for Stokes numbers in the 0–10 range and energy ratios up to 5. Calculations show that the influences of both electrostatic interactions and inertia are significant; for inertialess ($\mathrm{St}=0$) equal-sized and oppositely charged particles, we find that even at energy ratios as low as 0.2, enhancement factors are in excess of 2. For the same situation but like-charged particles, enhancement factors fall below 0.5. Increasing the Stokes number acts to mitigate the influence of electrostatic potentials for both like and oppositely charged particles; i.e., inertia reduces the enhancement factor for oppositely charged particles and increases it for like-charged particles. Uniquely, at elevated Stokes numbers with attractive potentials we find collisionless “pockets” within the collision area, which are regions completely bounded by the collision area but within which collisions do not occur. Regression equations to results are provided, enabling calculation of the enhancement factor as a function of energy ratio and Stokes number. In total, this study both leads to insight into the collision dynamics of finite-inertia, charged particles in shear flows, and provides a means to simply calculate the particle-particle collision rate coefficient.

We present a new acceleration mechanism for electrons taking place during the interaction of an ultrashort, nonrelativistic laser pulse with a plasma generated at the surface of a solid density target. In our experiments, the plasma is created by a laser pulse with femtosecond duration and an energy of about 1 mJ focused to intensities of above ${10}^{17}\text{W}/{\mathrm{cm}}^2$. We observe that the electron energies acquired by this mechanism exceed the ponderomotive potential of the laser by an order of magnitude. This result was reproduced and quantitatively confirmed by particle-in-cell simulations, which further revealed that the observed electron acceleration is based on quasistatic electric fields caused by the space charges of ponderomotively preaccelerated electrons. This acceleration process is examined in more detail by a simplified numerical model, which allows a qualitative explanation of the final electron energies.

The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with a wide range of applications have been proposed. However, popular implementations of DMD suffer from observation noise on random dynamical systems and generate inaccurate estimation of the spectra of the stochastic Koopman operator. In this paper, we propose subspace DMD as an algorithm for the Koopman analysis of random dynamical systems with observation noise. Subspace DMD first computes the orthogonal projection of future snapshots to the space of past snapshots and then estimates the spectra of a linear model, and its output converges to the spectra of the stochastic Koopman operator under standard assumptions. We investigate the empirical performance of subspace DMD with several dynamical systems and show its utility for the Koopman analysis of random dynamical systems.

Monte Carlo simulations and Wertheim's thermodynamic perturbation theory (TPT) are used to predict the phase diagram and percolation curve for the simple two-dimensional Mercedes-Benz (MB) model of water. The MB model of water is quite popular for explaining water properties, but the phase diagram has not been reported till now. In the MB model, water molecules are modeled as two-dimensional Lennard-Jones disks, with three orientation-dependent hydrogen-bonding arms, arranged as in the MB logo. The liquid part of the phase space is explored using grand canonical Monte Carlo simulations and two versions of Wertheim's TPT for associative fluids, which have been used before to predict the properties of the simple MB model. We find that the theory reproduces well the physical properties of hot water but is less successful at capturing the more structured hydrogen bonding that occurs in cold water. In addition to reporting the phase diagram and percolation curve of the model, it is shown that the improved TPT predicts the phase diagram rather well, while the standard one predicts a phase transition at lower temperatures. For the percolation line, both versions have problems predicting the correct position of the line at high temperatures.

We study experimentally and theoretically the steady-state dynamics of a simple stochastic electronic system featuring two resistor-capacitor circuits coupled by a third capacitor. The resistors are subject to thermal noises at real temperatures. The voltage fluctuation across each resistor can be compared to a one-dimensional Brownian motion. However, the collective dynamical behavior, when the resistors are subject to distinct thermal baths, is identical to that of a Brownian gyrator, as first proposed by Filliger and Reimann [Phys. Rev. Lett. 99, 230602 (2007)]. The average gyrating dynamics is originated from the absence of detailed balance due to unequal thermal baths. We look into the details of this stochastic gyrating dynamics, its dependences on the temperature difference and coupling strength, and the mechanism of heat transfer through this simple electronic circuit. Our work affirms the general principle and the possibility of a Brownian ratchet working near room temperature scale.

There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, $H\left(p\right)=-{\sum }_i{p}_{i}log{p}_i$. For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as $S_{\mathrm{EXT}}$ for extensive entropy, $S_{\mathrm{IT}}$ for the source information rate in information theory, and $S_{\mathrm{MEP}}$ for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

We studied the Ehrenfest urn model in which particles in the same urn interact with each other. Depending on the nature of interaction, the system undergoes a first- or second-order phase transition. The relaxation time to the equilibrium state, the Poincaré cycles of the equilibrium state and the most far-from-equilibrium state, and the duration time of the states during first-order phase transition are calculated. It was shown that the scaling behavior the Poincaré cycles could serve as an indication to the nature of phase transition, and the behavior of the ratio of duration time of the states could be strong evidence of the metastability during first-order phase transition.

In this work, we study resonance energy transfer from an impulsively loaded strongly nonlinear oscillator to a weakly coupled linear attachment with a slowly time-decaying stiffness. It is shown that even in the absence of external periodic forcing both oscillators may exhibit the resonance phenomenon, with the permanent response enhancement of the linear oscillator and the corresponding response reduction of the nonlinear actuator. This effect is said to be internal autoresonance. The influence of the system parameters on the emergence and stability of autoresonance is investigated both analytically and numerically.