In this paper, we study the effect of solutal Marangoni convection (SMC) on the microstructure evolution in a monotectic system, using the convective Cahn-Hilliard and Navier-Stokes equations with a capillary tensor contributed by the chemical concentration gradient. At first, we simulate the spontaneous motion of two distant droplets induced by SMC and compare our results with an analytical solution. We then compute the coalescence of two droplets in contact and coarsening of two distant droplets considering different sizes. We further study the influence of SMC on the evolution of phase separation processes inside the spinodal region for Fe-50 at %Sn and Fe-40 at %Sn alloys. In the former case, we rationalize our results using Fourier spectra and in the latter case, we compare the size distribution of droplets with the LSW theory.

A model describing the nonsymmetrical laser-pulse propagation in capillary tubes with inner radius smoothly varying with the capillary length is proposed. Using this model, the use of capillaries with specially profiled entrance sections (particularly cone matching elements) for improving the coupling of the laser energy into a capillary and avoiding capillary ablation is analyzed. It is shown that cone entrances with a sufficiently small angle (${\alpha }_{\text{cone}}\lesssim 10$ mrad) help decrease the longitudinal energy flux and ablation of the entrance face of a capillary, but do not remove the requirements on the precision of laser-pulse focusing necessary to obtain regular laser fields, characterized by a symmetrical intensity distribution, centered on the capillary axis. To achieve regular laser fields without strong transverse gradients, the angle between the laser and capillary axes has to be smaller than 1 mrad for capillaries with an inner radius of the order of tens of microns.

Using a granular-mechanics code, we study the impact of a sphere into a porous adhesive granular target, consisting of monodisperse silica grains. The model includes elastic repulsive, adhesive, and dissipative forces, as well as sliding, rolling, and twisting friction. Impact velocities of up to 30 m/s and target filling factors (densities) between 19$\%$ and 35$\%$ have been systematically studied. We find that the projectile is stopped by an effective drag force which is proportional to the square of its velocity. Target adhesion influences projectile stopping only below a critical velocity, which increases with adhesion. The penetration depth depends approximately logarithmically on the impact velocity and is inversely proportional to the target density. The excavated crater is of conical form and is surrounded by a compaction zone whose width increases but whose maximum value decreases with increasing target density. Grain ejection increases in proportion with impactor velocity. Grains are ejected which have originally been buried to a depth of $8R_{\mathrm{grain}}$ below the surface; the angular distribution favors oblique ejection with a maximum around ${45}^{\circ }$. The velocity distribution of ejected grains features a broad low-velocity maximum around 0.5–1 m/s but exhibits a high-velocity tail up to $\sim$15$\%$ of the projectile impact velocity.

Hydrated interfaces are ubiquitous in biology and appear on all length scales from ions and individual molecules to membranes and cellular networks. In vivo, they comprise a high degree of self-organization and complex entanglement, which limits their experimental accessibility by smearing out the individual phenomenology. The Langmuir technique, however, allows the examination of defined interfaces, the controllable thermodynamic state of which enables one to explore the proper state diagrams. Here we demonstrate that voltage and pressure pulses simultaneously propagate along monolayers comprised of either native pork brain or synthetic lipids. The excitation of pulses is conducted by the application of small droplets of acetic acid and monitored subsequently employing time-resolved Wilhelmy plate and Kelvin probe measurements. The isothermal state diagrams of the monolayers for both lateral pressure and surface potential are experimentally recorded, enabling us to predict dynamic voltage pulse amplitudes of 0.1–3 mV based on the assumption of static mechanoelectrical coupling. We show that the underlying physics for such propagating pulses is the same for synthetic and natural extracted (pork brain) lipids and that the measured propagation velocities and pulse amplitudes depend on the compressibility of the interface. Given the ubiquitous presence of hydrated interfaces in biology, our experimental findings seem to support a fundamentally new mechanism for the propagation of signals and communication pathways in biology (signaling), which is based neither on protein-protein or receptor-ligand interaction nor diffusion.

We analytically study bond percolation on hyperbolic lattices obtained by tiling a hyperbolic plane with constant negative Gaussian curvature. The quantity of our main concern is $p_{c2}$, the value of occupation probability where a unique unbounded cluster begins to emerge. By applying the substitution method to known bounds of the order-5 pentagonal tiling, we show that $p_{c2}\ge 0.382508$ for the order-5 square tiling, $p_{c2}\ge 0.472043$ for its dual, and $p_{c2}\ge 0.275768$ for the order-5-4 rhombille tiling.

The observation of a well-developed treelike string structure supported by a gas flow in a three-dimensional dc complex plasma is presented. The dynamically stable strings, comprising 10–20 particles, were up to 5 mm long. The experiments were performed using neon gas at a pressure of 100 Pa and melamine-formaldehyde particles with a diameter of 3.43 $\mu$m. Inside the discharge glass tube a nozzle had been built in to supply the controllable gas (plasma) flux intensity distribution along the tube. The walls of the nozzle were transparent for the laser light illuminating the particles. That gave the opportunity to closely study the particle dynamics deep inside the nozzle.

We study theoretically the generation of a continuous-wave signal by two weakly coupled delay-line oscillators. In such oscillators, the cavity length is longer than the wavelength of the signal. We show by using an analytical solution and comprehensive numerical simulations that in delay-line oscillators, the dynamics of the amplitude response cannot be neglected even when the coupling between the oscillators is weak. Therefore, weakly coupled delay-line oscillators cannot be accurately modeled by using coupled phase-oscillator models. In particular, we show that synchronization between the oscillators can be obtained in cases that are not allowed by coupled phase-oscillator models. We study the stability of the continuous-wave solutions. In delay-line oscillators, several cavity modes can potentially oscillate. To ensure stability, the bandwidth of the delay-line oscillator should be limited. We show that the weakly coupled delay-line oscillator model that is described in this paper can be used to accurately model the synchronization between two weakly coupled optoelectronic oscillators. A very good quantitative agreement is obtained between a comprehensive numerical model to study optoelectronic oscillators and the model results given in this paper.

Front propagation in heterogeneous bistable media is studied using the Schlögl model as a representative example. Spatially periodic modulations in the parameters of the bistable kinetics are taken into account perturbatively. Depending on the ratio $L/l$ ($L$ is the spatial period of the heterogeneity, $l$ is the front width), appropriate singular perturbation techniques are applied to derive an ordinary differential equation for the position of the front in the presence of the heterogeneities. From this equation, the dependence of the average propagation speed on $L/l$ as well as on the modulation amplitude is calculated. The analytical results obtained predict velocity overshoot, different cases of propagation failure, and the propagation speed for very large spatial periods in quantitative agreement with the results of direct numerical simulations of the underlying reaction-diffusion equation.

In this study, we develop a saturation-dependent treatment of dispersion in porous media using concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculate spatial solute distributions as a function of time and calculate arrival time distributions as a function of system size. Our previous results correctly predict the range of observed dispersivity values over ten orders of magnitude in experimental length scale, but that theory contains no explicit dependence on porosity or relative saturation. This omission complicates comparisons with experimental results for dispersion, which are often conducted at saturation less than 1. We now make specific comparisons of our predictions for the arrival time distribution with experiments on a single column over a range of saturations. This comparison suggests that the most important predictor of such distributions as a function of saturation is not the value of the saturation per se, but the applicability of either random or invasion percolation models, depending on experimental conditions.

To produce high-power coherent electromagnetic radiation at frequencies from microwaves up to terahertz, the radiation sources should have interaction circuits of large cross sections, i.e., the sources should operate in high-order modes. In such devices, the excitation of higher-order parasitic modes near cutoff where the group velocity is small and, hence, start currents are low can be a serious problem. The problem is especially severe in the sources of coherent, phase-controlled radiation, i.e., the amplifiers or phase-locked oscillators. This problem was studied earlier [Nusinovich, Sinitsyn, and Antonsen, Phys. Rev. E 82, 046404 (2010)] for the case of electron focusing by strong guiding magnetic fields. For many applications it is desirable to minimize these focusing fields. Therefore in this paper we analyze the problem of excitation of parasitic modes near cutoff in forward-wave amplifiers with weak focusing fields. First, we study the large-signal operation of such a device with a signal wave only. Then, we analyze the self-excitation conditions of parasitic waves near cutoff in the presence of the signal wave. It is shown that the main effect is the suppression of the parasitic wave in large-signal regimes. At the same time, there is a region of device parameters where the presence of signal waves can enhance excitation of parasitic modes. The role of focusing fields in such effects is studied.

We investigate analytically the subwavelength plasmonic lattice solitons excited in an optical plasmonic waveguide consisting of a chain of nanorods embedded in a Kerr nonlinear optical medium with strong near-field interactions. A nonlinear lattice equation with onsite and intersite nonlinear terms describing the plasmon wave propagating along the chain is derived. Stability analysis predicts that modulation instability can occur and that, correspondingly, conditions for localized modes will exist. We analyze the nonlinear excitations for genuine discreteness and nonlinearity enhanced by the fields strongly confined in the nanosized dielectric gaps. Based on a quasidiscreteness approach, we obtain a nonlinear Schrödinger equation and find that the system supports bright and dark soliton solutions in different frequency bands. It is also shown that the existence of different solitons depends strongly on the type of nonlinearity of the embedded medium.

The Boltzmann distribution is commonly used as a prior probability in Bayesian data analysis. Examples include the Ising model in statistical image analysis and the canonical ensemble based on molecular dynamics force fields in protein structure calculation. These models involve a temperature or weighting factor that needs to be inferred from the data. Bayesian inference stipulates to determine the temperature based on the model evidence. This is challenging because the model evidence, a ratio of two high-dimensional normalization integrals, cannot be calculated analytically. We outline a replica-exchange Monte Carlo scheme that allows us to estimate the model evidence by use of multiple histogram reweighting. The method is illustrated for an Ising model and examples in protein structure determination.

The effects of disorder on the critical behavior of the $q$-state Potts model in noninteger dimensions are studied by comparison of deterministic and random fractals sharing the same dimensions in the framework of a discrete scale invariance. We carried out intensive Monte Carlo simulations. In the case of a fractal dimension slightly smaller than two $d_f\simeq 1.974636$, we give evidence that the disorder structured by discrete scale invariance does not change the first order transition associated with the deterministic case when $q=7$. Furthermore the study of the high value $q=14$ shows that the transition is a second order one both for deterministic and random scale invariance, but that their behavior belongs to different university classes.

We present a finite-size scaling study of the phase transition in the two-dimensional Potts model modified by random bond disorder, in which the average is taken over quantities calculated at quasicritical temperatures of individual disorder configurations. We used the recently proposed equilibrium-like invaded cluster algorithm, which allows us to examine separately the fluctuations in the thermodynamical ensemble from the fluctuations induced by changing the disorder configuration. We point out the crucial role of the spatial inhomogeneities on all scales for the critical behavior of the system. These inhomogeneities are formed by “dressing” of the disorder via critical correlations and are demonstrated to exist for any system size despite the critical fluctuations in thermodynamical ensemble. Such inhomogeneities were previously not thought to be relevant in disorder-altered classical systems when critical temperature is finite. However, we confirm that only by averaging at quasicritical temperatures of each disorder configuration is the thermal critical exponent $y_{\tau }$ not obscured by the influence of the aforementioned spatial inhomogeneities.

For transport processes in geometrically restricted domains, the mean first-passage time (MFPT) admits a general scaling dependence on space parameters for diffusion, anomalous diffusion, and diffusion in disordered or fractal media. For transport in self-similar fractal structures, we obtain an expression for the source-target distance dependence of the MFPT that exhibits both the leading power-law behavior, depending on the Hausdorff and spectral dimension of the fractal, as well as small log-periodic oscillations that are a clear and definitive signal of the underlying fractal structure. We also present refined numerical results for the Sierpinski gasket that confirm this oscillatory behavior.

A combination of analytical calculations and Monte Carlo simulations is used to find the ground-state structures in monodisperse ferrofluid monolayers under the influence of an external magnetic field. We study two different regimes, where (i) the direction of an external field is perpendicular to the monolayer plane and (ii) an external magnetic field is in the plane. In the field perpendicular to the plane we observe a transition from an ideal ferroparticle ring to a hexagonal structure. The analytical value of the critical field strength needed for this transition is obtained and shown for relatively large systems to be independent of the number of particles. For smaller systems the value of the critical field is system-size dependent and grows fast to its asymptotic value with increasing number of particles. In the case where the magnetic field is aligned parallel to the layer plane, the critical field needed to break a ring and to create a new ground-state structure, namely a ferroparticle chain, is much smaller than in the case where a field is applied perpendicularly to the plane. The analytical expression for the asymptotic critical field in case of in-plane field is found to be a decreasing function of the total particle number in a system. We characterize both transitions to be of the first-order-type transition, with magnetic susceptibility diverging near the critical point. Our studies show that the domination of the in-plane correlations of dipoles within the ferroparticle ring results in much lower magnetic in-plane susceptibility in comparison to the one perpendicular to the plane.

We study the stability of random scale-free networks to degree-dependent attacks. We present analytical and numerical results to compute the critical fraction $p_c$ of nodes that need to be removed for destroying the network under this attack for different attack parameters. We study the effect of different defense strategies, based on the addition of a constant number of links on network robustness. We test defense strategies based on adding links to either low degree, middegree or high degree nodes. We find using analytical results and simulations that the middegree nodes defense strategy leads to the largest improvement to the network robustness against degree-based attacks. We also test these defense strategies on an internet autonomous systems map and obtain similar results.

A nonlinear analysis for the finite amplitude electron acoustic wave (EAW) is considered in a collisional plasma. The fluid model is used to describe the two-temperature electron species in a fixed ion background. In general, in electron-ion plasma, the presence of wave nonlinearity, dispersion, and dissipation (arising from fluid viscosity) give rise to the Korteweg–de Vries Burgers (KdVB) equation which exhibits shock wave. In this work, it is shown that the dissipation due to the collision between electron and ion in the presence of collective phenomena (plasma current) can also introduce an anomalous dissipation that causes the Burgers term and thus leads to the generation of electron acoustic shock wave. Both analytical and numerical analysis show the formation of transient shock wave. Relevance of the results are discussed in the context of space plasma.

Copper and silver wires are subjected to pulsed high current densities producing high density metal plasma in the sub-eV regime with atmospheric air as a background gas. Numerical simulation via application of the one-dimensional magnetohydrodynamic partial differential equations solved simultaneously with the constraining circuit equations is presented. The simulations require accurate knowledge of the material equation of state (EOS) and transport properties; the LANL sesame database is applied for the EOS in all cases. Two electrical conductivity models are applied. First, the Lee-More-Desjarlais (LMD) and its modification, the quantum LMD (QLMD) conductivity, which have been well proven at higher temperatures, are applied. Simulations with the LMD and QLMD data indicate that the conductivity data as well as the MHD methodology are accurate in the sub-eV regime of interest. A less computationally involved, empirical conductivity model is applied in the same regime to explore its temperature-density range of applicability compared to the more sophisticated model.

The rogue waves in a resonant erbium-doped fiber system governed by a coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the breather solutions of the normalized slowly varying amplitude of the complex field envelope $E$, polarization $p$, and population inversion $\eta$. The $n$-order breather solutions of the three fields are constructed using a Darboux transformation (DT) by assuming periodic seed solutions. Moreover, the $n$-order rogue waves are given by determinant forms with $n+3$ free parameters. Furthermore, the possible connection between our rouge waves and the generation of supercontinuum generation is discussed.