We construct an analytic model for the electrostatic Debye layer formed at a plasma-liquid interface by combining the Gouy-Chapman theory for the liquid with a simple parabolic band model for the plasma sheath. The model predicts a nonlinear scaling between the plasma current density and the solution ionic strength, and we confirmed this behavior with measurements using a liquid-anode plasma. Plots of the measured current density as a function of ionic strength collapse the data and curve fits yield a plasma electron density of $\sim {10}^{19}{\mathrm{m}}^{-3}$ and an electric field of $\sim {10}^4\mathrm{V}/\mathrm{m}$ on the liquid side of the interface. Because our theory is based firmly on fundamental physics, we believe it can be widely applied to many emerging technologies involving the interaction of low-temperature, nonequilibrium plasma with aqueous media, including plasma medicine and various plasma chemical synthesis techniques.

Advanced chain-growth computer simulation methodologies have been employed for a systematic statistical analysis of the critical behavior of a polymer adsorbing at a substrate. We use finite-size scaling techniques to investigate the solvent-quality dependence of critical exponents, critical temperature, and the structure of the phase diagram. Our study covers all solvent effects from the limit of super-self-avoiding walks, characterized by effective monomer-monomer repulsion, to poor solvent conditions that enable the formation of compact polymer structures. The results significantly benefit from taking into account corrections to scaling.

Out of thermal equilibrium, an environment imposes effective mechanical forces on nanofabricated devices as well as on microscopic chemical or biological systems. Here we address the question of how to calculate these forces together with the response of the system from first principles. We show that an ideal gaslike environment, even near thermal equilibrium, can enforce a specific steady state on the system by creating effective potentials in otherwise homogeneous space. An example of stable and unstable rectifications of thermal fluctuations is presented using a modified Feynman-Smoluchowski ratchet with two degrees of freedom. Moreover, the stability of a steady configuration depends on its chiral symmetry. The transition rate probabilities and the corresponding kinetic equations are derived for a complex mechanical system with arbitrary degrees of freedom. This work, therefore, extends the applicability of mechanical systems as a toy model playground of statistical physics for active and living matter with multiple degrees of freedom.

We investigate the formation of localized domains through front pinning in a periodically forced, bistable semiconductor laser with long-delayed optoelectronic feedback. At difference with 1D spatially extended systems, the transition from the pinning to the propagation regime occurs via two separated bifurcations, each corresponding to the unpinning of one of the fronts surrounding the localized domain. The bifurcation splitting is systematically explored, unveiling the crucial role played by the forcing frequency. The experimental results are reproduced and interpreted by means of a prototypical model of our system.

Exact solutions for the elastic and thermodynamic properties for the wormlike chain model are elaborated in terms of Mathieu functions. The smearing of the classical Euler buckling instability for clamped polymers is analyzed for the force-extension relation. Interestingly, at strong compression forces the thermal fluctuations lead to larger elongations than for the elastic rod. The susceptibility defined as the derivative of the force-extension relation displays a prominent maximum at a force that approaches the critical Euler buckling force as the persistence length is increased. We also evaluate the excess entropy and heat capacity induced by the compression and find that they vary nonmonotonically with the load. These findings are corroborated by pseudo-Brownian simulations.

We present a comprehensive study of concentrated emulsions flowing in microfluidic channels, one wall of which is patterned with micron-size equally spaced grooves oriented perpendicularly to the flow direction. We find a scaling law describing the roughness-induced fluidization as a function of the density of the grooves, thus fluidization can be predicted and quantitatively regulated. This suggests common scenarios for droplet trapping and release, potentially applicable for other jammed systems as well. Numerical simulations confirm these views and provide a direct link between fluidization and the spatial distribution of plastic rearrangements.

Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Tóth et al., J. Phys.: Condens. Matter 26, 055001 (2014)], which is based on combining fluctuating hydrodynamics with the phase-field crystal theory. We show that in this hydrodynamic approach not only homogeneous and heterogeneous nucleation processes are accessible, but also growth front nucleation, which leads to the formation of new (differently oriented) grains at the solid-liquid front in highly undercooled systems. Formation of dislocations at the solid-liquid interface and interference of density waves ahead of the crystallization front are responsible for the appearance of the new orientations at the growth front that lead to spherulite-like nanostructures.

Mean-field-based Lagrangian framework is developed for the fluid turbulence theory, which enables physically objective discussions, especially, of the history effect. Mean flow serves as a purely geometrical object of Lie group theory, providing useful operations to measure the objective rate and history integration of the general tensor field. The proposed framework is applied, on the one hand, to one-point closure model, yielding an objective expression of the turbulence viscoelastic effect. Application to two-point closure, on the other hand, is also discussed, where natural extension of known Lagrangian correlation is discovered on the basis of an extended covariance group.

We study the statistics of the power $P$ dissipated by waves propagating in a one-dimensional disordered medium with damping coefficient $\nu$. An operator imposes the wave amplitude at one end, therefore injecting a power $P$ that balances dissipation. The typical realization of $P$ vanishes for $\nu \to 0$: Disorder leads to localization and total reflection of the wave energy back to the emitter, with negligible losses. More surprisingly, the mean dissipated power $〈P〉$ averaged over the disorder reaches a finite limit for $\nu \to 0$. We show that this “anomalous dissipation” ${lim}_{\nu \to 0}〈P〉$ is directly given by the integrated density of states of the undamped system. In some cases, this allows us to compute the anomalous dissipation exactly, using properties of the undamped system only. As an example, we compute the anomalous dissipation for weak correlated disorder and for Gaussian white noise of arbitrary strength. Although the focus is on the singular limit $\nu \to 0$, we finally show that this approach is easily extended to arbitrary $\nu$.

The two-dimensional Ising model with a slit is studied. The slit free energy is defined, in which the bulk term, edge terms, and corner terms other than that of the slit are canceled. The bond propagation algorithm is used to calculate the free energy, internal energy, and heat capacity numerically. At the critical point, the slit free energy has a logarithmic correction $L^{-1}lnL$, in addition to the correction $lnL$, where $L$ is the typical length of the system. The fitted coefficients of these terms agree with the conformal field theory very well. The integral constant and extrapolation length, which are pending in the conformal field theory, are obtained. In the slit internal energy, the leading term is proportional to $L$. There is a correction term, ${ln}^{2}L$, that has a geometry-independent coefficient, the exact value of which is conjectured to be $-\sqrt{2}/\left(2{\pi }^2\right)$. The leading term in the slit heat capacity is proportional to $L^2$. There is also a ${ln}^{2}L$ term; however, its coefficient depends on the geometry. In the infinitely long strip limit, its exact value is conjectured to be $5/{\pi }^2$. Near the critical point, for different size lattices, the rescaled slit free energies, internal energies, and heat capacities collapse onto the corresponding universal curves. According to the scaling and conformal field theory, the leading term of the slit free energy should be $-\frac{c}{8}ln\left|t\right|$ for $L\left|t\right|\gg 1$ and $\left|t\right|\ll 1$, where $t$ is the reduced temperature. The amplitude $\frac{c}{8}$ is universal, and $c$ is the central charge. Our results validate these predictions qualitatively. For $L\left|t\right|\gg 1$ and $\left|t\right|\ll 1$, the slit internal energy and heat capacity scale as $t^{-1}$ and $t^{-2}$, respectively.

Lévy flights and Lévy walks serve as two paradigms of random walks resembling common features but also bearing fundamental differences. One of the main dissimilarities is the discontinuity versus continuity of their trajectories and infinite versus finite propagation velocity. As a consequence, a well-developed theory of Lévy flights is associated with their pathological physical properties, which in turn are resolved by the concept of Lévy walks. Here, we explore Lévy flight and Lévy walk models on bounded domains, examining their differences and analogies. We investigate analytically and numerically whether and under which conditions both approaches yield similar results in terms of selected statistical observables characterizing the motion: the survival probability, mean first passage time, and stationary probability density functions. It is demonstrated that the similarity of the models is affected by the type of boundary conditions and the value of the stability index defining the asymptotics of the jump length distribution.

We investigate multiple random walks traversing independently and concurrently on complex networks and introduce the concept of mean first parallel passage time (MFPPT) to quantify their search efficiency. The mean first parallel passage time represents the expected time required to find a given target by one or some of the multiple walkers. We develop a general theory that allows us to calculate the MFPPT analytically. Interestingly, we find that the global MFPPT follows a harmonic law with respect to the global mean first passage times of the associated walkers. Remarkably, when the properties of multiple walkers are identical, the global MFPPT decays in a power law manner with an exponent of unity, irrespective of network structure. These findings are confirmed by numerical and theoretical results on various synthetic and real networks. The harmonic law reveals a universal principle governing multiple random walks on networks that uncovers the contribution and role of the combined walkers in a target search. Our paradigm is also applicable to a broad range of random search processes.

We analyze the equilibrium spatial distribution of surface temperatures of patterned surfaces. The surface is exposed to a constant external heat flux and has a fixed internal temperature that is coupled to the outside heat fluxes by finite heat conductivity across the surface. It is assumed that the temperatures are sufficiently high so that the thermal wavelength (a few microns at room temperature) is short compared to all geometric length scales of the surface patterns. Hence the radiosity method can be employed. A recursive multiple scattering method is developed that enables rapid convergence to equilibrium temperatures. While the temperature distributions show distinct dependence on the detailed surface shapes (cuboids and cylinder are studied), we demonstrate robust universal relations between the mean and the standard deviation of the temperature distributions and quantities that characterize overall geometric features of the surface shape.

We define and study one-dimensional model of irreversible aggregation of particles obeying a discrete-time kinetics, which is a special limit of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. The model allows for clusters of particles to translate as a whole entity one site to the right with the same probability as single particles do. A particle and a cluster, as well as two clusters, irreversibly aggregate whenever they become nearest neighbors. Nonequilibrium stationary phases appear under the balance of injection and ejection of particles. By extensive Monte Carlo simulations it is established that the phase diagram in the plane of the injection-ejection probabilities consists of three stationary phases: a multiparticle (MP) one, a completely filled (CF) phase, and a “mixed” (MP+CF) one. The transitions between these phases are: an unusual transition between MP and CF with jump discontinuity in both the bulk density and the current, a conventional first-order transition with a jump in the bulk density between MP and MP+CF, and a continuous clustering-type transition from MP to CF, which takes place throughout the MP+CF phase between them. By the data collapse method a finite-size scaling function for the current and bulk density is obtained near the unusual phase transition line. A diverging correlation length, associated with that transition, is identified and interpreted as the size of the largest cluster. The model allows for a future extension to account for possible cluster fragmentation.

We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide an ideal basis for the experimental study of problems originating from the field of quantum chaos and random matrix theory. Our objective is to demonstrate that this is true only for short-range fluctuation properties in the spectra, whereas the observation of deviations in the long-range fluctuations is typical for quantum graphs. This may be attributed to the unavoidable occurrence of short periodic orbits, which explore only the individual bonds forming a graph and thus do not sense the chaoticity of its dynamics. In order to corroborate our supposition, we performed numerous experimental and corresponding numerical studies of long-range fluctuations in terms of the number variance and the power spectrum. Furthermore, we evaluated length spectra and compared them to semiclassical ones obtained from the exact trace formula for quantum graphs.

Prominent changes in neuronal dynamics have previously been attributed to a specific switch in onset bifurcation, the Bogdanov-Takens (BT) point. This study unveils another, relevant and so far underestimated transition point: the saddle-node-loop bifurcation, which can be reached by several parameters, including capacitance, leak conductance, and temperature. This bifurcation turns out to induce even more drastic changes in synchronization than the BT transition. This result arises from a direct effect of the saddle-node-loop bifurcation on the limit cycle and hence spike dynamics. In contrast, the BT bifurcation exerts its immediate influence upon the subthreshold dynamics and hence only indirectly relates to spiking. We specifically demonstrate that the saddle-node-loop bifurcation (i) ubiquitously occurs in planar neuron models with a saddle node on invariant cycle onset bifurcation, and (ii) results in a symmetry breaking of the system's phase-response curve. The latter entails an increase in synchronization range in pulse-coupled oscillators, such as neurons. The derived bifurcation structure is of interest in any system for which a relaxation limit is admissible, such as Josephson junctions and chemical oscillators.

We introduce a coarse-grained stochastic model for the spontaneous activity of neuronal cultures to explain the phenomenon of noise focusing, which entails localization of the noise activity in excitable networks with metric correlations. The system is modeled as a continuum excitable medium with a state-dependent spatial coupling that accounts for the dynamics of synaptic connections. The most salient feature is the emergence at the mesoscale of a vector field $\mathbf{V}\left(\mathbf{r}\right)$, which acts as an advective carrier of the noise. This entails an explicit symmetry breaking of isotropy and homogeneity that stems from the amplification of the quenched fluctuations of the network by the activity avalanches, concomitant with the excitable dynamics. We discuss the microscopic interpretation of $\mathbf{V}\left(\mathbf{r}\right)$ and propose an explicit construction of it. The coarse-grained model shows excellent agreement with simulations at the network level. The generic nature of the observed phenomena is discussed.

Stability principles for bilayer complex plasmas are studied. To mimic bilayer crystals and identify the main melting mechanism of such structures, a simple binary-chain model is employed. This approach provides adequate representation of the collective effects and accurate description of the interaction nonreciprocity, associated with the wake-mediated interparticle forces. It is shown that the wake-induced coupling of the wave modes sustained in different crystalline layers can trigger the dynamical instability. Furthermore, the mode coupling is demonstrated to be a universal instability mechanism, operating also in bilayer fluids. General stability criteria for the crystalline and fluid bilayers are derived.

We study the response of a two-level quantum system to a chirp signal, using both numerical and analytical methods. The numerical method is based on numerical solutions of the Schrödinger solution of the two-level system, while the analytical method is based on an approximate solution of the same equations. We find that when two-level systems are perturbed by a chirp signal, the peak population of the initially unpopulated state exhibits a high sensitivity to frequency modulation rate. We also find that the aforementioned sensitivity depends on the strength of the forcing, and weaker forcings result in a higher sensitivity, where the frequency modulation rate required to produce the same reduction in peak population would be lower. We discuss potential applications of this result in the field of microwave power transmission, as it shows applying fast frequency modulation to transmitted microwaves used for power transmission could decrease unintended absorption of microwaves by organic tissue.

In the infinite configuration network the links between nodes are assigned randomly with the only restriction that the degree distribution has to match a predefined function. This work presents a simple equation that gives for an arbitrary degree distribution the corresponding size distribution of connected components. This equation is suitable for fast and stable numerical computations up to the machine precision. The analytical analysis reveals that the asymptote of the component size distribution is completely defined by only a few parameters of the degree distribution: the first three moments, scale, and exponent (if applicable). When the degree distribution features a heavy tail, multiple asymptotic modes are observed in the component size distribution that, in turn, may or may not feature a heavy tail.