We present magneto-optic measurements on two materials that form the recently discovered twist-bend nematic ($N_{\mathrm{tb}}$) phase. This intriguing state of matter represents a fluid phase that is orientationally anisotropic in three directions and also exhibits translational order with periodicity several times larger than the molecular size. $N_{\mathrm{tb}}$ materials may also spontaneously form a visible, macroscopic stripe texture. We show that the optical stripe texture can be persistently inhibited by a magnetic field, and a 25$T$ external magnetic field depresses the $N$-$N_{\mathrm{tb}}$ phase transition temperature by almost 1${}^{\circ }$C. We propose a quantitative mechanism to account for this shift and suggest a Helfrich-Hurault-type mechanism for the optical stripe formation.

The Lavalette function is generalized to a two-exponent function in order to represent data looking like a sigmoid on semilogarithmic plots. A Mandelbrot trick is suggested for further investigations, if more fit parameters are needed. The analyzed data is that of the number of adherents to the main religions in the 20th century.

In this work we propose a subtle change in Axelrod's model for the dissemination of culture. The mechanism consists of excluding from the set of potentially interacting neighbors those that would never possibly exchange. Although the alteration proposed does not alter the state space topologically, it yields significant qualitative changes, specifically the emergence of surface tension, driving the system in some cases to metastable states. The transient behavior is considerably richer, and cultural regions become stable leading to the formation of different spatiotemporal patterns. A metastable “glassy” phase emerges between the globalized phase and the disordered, multicultural phase.

We consider the stability of position control of traveling waves in reaction-diffusion systems as proposed in Löber and Engel [Phys. Rev. Lett. 112, 148305 (2014)]. Instead of analyzing the controlled reaction-diffusion system, stability is studied on the reduced level of the equation of motion for the position over time of perturbed traveling waves. We find an interval of perturbations of initial conditions for which position control is stable. This interval can be interpreted as a localized region where traveling waves are susceptible to perturbations. For stationary solutions of reaction-diffusion systems with reflection symmetry, this region does not exist. Analytical results are in qualitative agreement with numerical simulations of the controlled Schlögl model.

Horizontal vibration applied to the support of a simple pendulum can deviate from the equilibrium position of the pendulum to a nonvertical position. A similar phenomenon is expected when a liquid-vapor interface is subjected to strong horizontal vibration. Beyond a threshold value of vibrational velocity the interface should attain an equilibrium position at an angle to the initial horizontal position. In the present paper experimental investigation of this phenomenon is carried out in a magnetic levitation device to study the effect of the vibration parameters, gravity acceleration, and the liquid-vapor density on the interface position. The results compare well with the theoretical expression derived by Wolf [G. H. Wolf, Z. Phys. B 227, 291 (1969)].

It has been recently emphasized that the angle of maximum wave amplitude $\alpha$ in the wake of a disturbance of finite size can be significantly narrower than the maximum value ${\alpha }_K={sin}^{-1}(1/3)\simeq 19.{47}^{\circ }$ predicted by the classical analysis of Kelvin. For axisymmetric disturbance, a simple argument based on the Cauchy-Poisson initial-value problem suggests that the wake angle decreases following a Mach-like law at large velocity, $\alpha \simeq {\text{Fr}}_L^{-1}$, where ${\text{Fr}}_L=U/\sqrt{gL}$ is the Froude number based on the disturbance velocity $U$, its size $L$, and gravity $g$. In this paper we extend this analysis to the case of nonaxisymmetric disturbances, relevant to real ships. We find that, for intermediate Froude numbers, the wake angle follows an intermediate scaling law $\alpha \simeq {\text{Fr}}_L^{-2}$, in agreement with the recent prediction of Noblesse et al. [Eur. J. Mech. B/Fluids 46, 164 (2014)]. We show that beyond a critical Froude number, which scales as $A^{1/2}$ (where $A$ is the length-to-width aspect ratio of the disturbance), the asymptotic scaling $\alpha \simeq {\text{Fr}}_B^{-1}$ holds, where now ${\text{Fr}}_B=A^{1/2}{\text{Fr}}_L$ is the Froude number based on the disturbance width. We propose a simple model for this transition, and provide a regime diagram of the scaling of the wake angle as a function of parameters $(A,{\text{Fr}}_L)$.

The effect of the secondary fluid enclosed in the indentations of a superhydrophobic surface on electro-osmotic flow is investigated. We derive analytical expressions for the net electro-osmotic flow over periodically structured surfaces, accounting for the influence of dissipation within the secondary fluid as well as for the role of charges at the fluid-fluid interfaces that are generated by auxiliary electrodes. Specifically, for a surface with rectangular grooves, the electro-osmotic flow velocity is related to the geometric parameters of the surface and the viscosity of an arbitrary secondary fluid filling the grooves. The results suggest that on specific superhydrophobic surfaces a flow enhancement by more than two orders of magnitude compared to unstructured surfaces can be expected.

The collision of wake bubbles behind two counterpropagating laser pulses in rarefied plasma is investigated using particle-in-cell simulation. Special attention is paid to the highly nonlinear dynamics of the electrons in the interaction region. It is found that, as the two bubbles approach each other and collide, the electrons in the interaction region first oscillate in a periodic fashion, forming a quasistationary dense electron density ripple with fairly regular spatial structure. At longer times, the electron motion becomes chaotic, and the density grating is gradually smeared. The electrons escape in the transverse direction, and eventually the two bubbles merge to form a single one. The transition of the electron motion from regular to chaotic is confirmed by analytical modeling using test electrons moving in counterpropagating planar electromagnetic waves. The findings shed light on the dynamics of wake-bubble collisions and the complex behavior induced by multiple laser pulses in plasmas.

We analyze the probability distribution for entropy production rates of trajectories evolving on a class of out-of-equilibrium kinetic networks. These networks can serve as simple models for driven dynamical systems, where energy fluxes typically result in nonequilibrium dynamics. By analyzing the fluctuations in the entropy production, we demonstrate the emergence, in a large system size limit, of a dynamic phase transition between two distinct dynamical regimes.

We study the effect of ultrastrong coupling on the transport of heat. In particular, we present a condition for optimal rectification, i.e., flow of heat in one direction and complete isolation in the opposite direction. We show that the strong-coupling formalism is necessary for correctly describing heat flow in a wide range of parameters, including moderate to low couplings. We present a situation in which the strong-coupling formalism predicts optimal rectification whereas the phenomenological approach predicts no heat flow in any direction, for the same parameter values.

A forced Korteweg–de Vries (KdV) equation is derived to describe weakly nonlinear, shallow-water surface wave propagation over nontrivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced KdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition, whereas amplitude remains constant.

Higher-order terms of dielectrophoretic (DEP) force are commonly ignored by invoking the simplifying dipole approximation. Concurrently, the trend towards micro- and nano-electrode structures in DEP design is bringing about an increasing number of instances where the approximation is expected to lose reliability. The case is severe for nonspherical particles (the shape of many biological particles) due to the shape-dependent nature of dielectric polarization. However, there is a lack of analytical means to determine multipole moments of nonspherical particles, numerical calculations of the same are regarded as unreliable, and there is a prevalence for higher-order force considerations to be ignored. As a result, the dipole approximation is used and/or nonspherical particles are approximated as spheres. This work proves the inefficacy of current qualitative criteria for the reliability of the dipole approximation and presents a quantitative substitute, with verified accuracy, that enables precise determination of the extent to which the dipole approximation would be reliable, and if found unreliable, corrects the approximation by adding second- and third-order terms of the DEP force. The effects of field nonuniformity, electrode design, and particle shape and aspect ratio on the significance of higher-order DEP forces is quantitatively analyzed. The results show that higher-order DEP forces are indeed of substantially increased significance for nonspherical particles; in the cases examined in this work, multipolar terms are seen to constitute more than 40% of the total force on ellipsoidal and cylindrical particles. It is further shown that approximating nonspherical particles as spheres of similar dimensions is subject to substantial error. Last, the substantial importance of the electrode design in influencing higher-order forces is shown.

A system defined by two coupled Ising models, with a bimodal random field acting in one of them, is investigated. The interactions among variables of each Ising system are infinite ranged, a limit where mean field becomes exact. This model is studied at zero temperature, as well as for finite temperatures, representing physical situations which are appropriate for describing real systems, such as plastic crystals. A very rich critical behavior is found, depending directly on the particular choices of the temperature, couplings, and random-field strengths. Phase diagrams exhibiting ordered, partially ordered, and disordered phases are analyzed, showing the sequence of transitions through all these phases, similarly to what occurs in plastic crystals. Due to the wide variety of critical phenomena presented by the model, its usefulness for describing critical behavior in other substances is also expected.

Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering exponent $\Omega$ of the background aperiodic sequence: If $\Omega <0$, the diffusion is normal and the distribution is extended. If $\Omega >0$, the diffusion is ultraslow and the distribution is localized. If $\Omega =0$, the diffusion is anomalous and the distribution is singular, which shows its complex and hierarchical structure. Multifractal analyses are performed in order to characterize these distributions. Extended, localized, and singular distributions are clearly distinguished only by the finite-size scaling behavior of ${\alpha }_{\min }$ and $f\left({\alpha }_{\min }\right)$. The multifractal spectrum of the singular distribution agrees well with that of a simple partitioning process.

Starting from the geometrical interpretation of the Rényi entropy, we introduce further extensive generalizations and study their properties. In particular, we found the probability distribution function obtained by the MaxEnt principle with generalized entropies. We prove that for a large class of dynamical systems subject to random perturbations, including particle transport in random media, these entropies play the role of Liapunov functionals. Some physical examples, which can be treated by the generalized Rényi entropies, are also illustrated.

We present an application of the Grassmann algebra to the problem of the monomer-dimer statistics on a two-dimensional square lattice. The exact partition function, or total number of possible configurations, of a system of dimers with a finite set of $n$ monomers at fixed positions can be expressed via a quadratic fermionic theory. We give an answer in terms of a product of two pfaffians and the solution is closely related to the Kasteleyn result of the pure dimer problem. Correlation functions are in agreement with previous results, both for monomers on the boundary, where a simple exact expression is available in the discrete and continuous case, and in the bulk where the expression is evaluated numerically.

We study a network model that couples the dynamics of link states with the evolution of the network topology. The state of each link, either $A$ or $B$, is updated according to the majority rule or zero-temperature Glauber dynamics, in which links adopt the state of the majority of their neighboring links in the network. Additionally, a link that is in a local minority is rewired to a randomly chosen node. While large systems evolving under the majority rule alone always fall into disordered topological traps composed by frustrated links, any amount of rewiring is able to drive the network to complete order, by relinking frustrated links and so releasing the system from traps. However, depending on the relative rate of the majority rule and the rewiring processes, the system evolves towards different ordered absorbing configurations: either a one-component network with all links in the same state or a network fragmented in two components with opposite states. For low rewiring rates and finite-size networks there is a domain of bistability between fragmented and nonfragmented final states. Finite-size scaling indicates that fragmentation is the only possible scenario for large systems and any nonzero rate of rewiring.

We numerically investigate the pool boiling of one-component fluids with a focus on the effects of surface wettability on the single-bubble dynamics. We employed the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], a diffuse-interface model for liquid-vapor flows involving liquid-vapor transition in nonuniform temperature fields. We first perform simulations for bubbles on homogeneous surfaces. We find that an increase in either the contact angle or the surface superheating can enhance the bubble spreading over the heating surface and increase the bubble departure diameter as well and therefore facilitate the transition into film boiling. We then examine the dynamics of bubbles on patterned surfaces, which incorporate the advantages of both hydrophobic and hydrophilic surfaces. The central hydrophobic region increases the thermodynamic probability of bubble nucleation while the surrounding hydrophilic region hinders the continuous bubble spreading by pinning the contact line at the hydrophobic-hydrophilic intersection. This leads to a small bubble departure diameter and therefore prevents the transition from nucleate boiling into film boiling. With the bubble nucleation probability increased and the bubble departure facilitated, the efficiency of heat transfer on such patterned surfaces is highly enhanced, as observed experimentally [Int. J. Heat Mass Transfer 57, 733 (2013)]. In addition, the stick-slip motion of contact line on patterned surfaces is demonstrated in one-component fluids, with the effect weakened by surface superheating.

We employ an effective field theory (EFT) approach to study thermal Casimir interactions between objects bound to a fluctuating fluid surface or interface dominated by surface tension, with a focus on the effects of particle anisotropy. The EFT prescription disentangles the constraints imposed by the particles' boundaries from the calculation of the interaction free energy by constructing an equivalent point particle description. The finite-size information is captured in a derivative expansion that encodes the particles' response to external fields. The coefficients of the expansion terms correspond to generalized tensorial polarizabilities and are found by matching the results of a linear response boundary value problem computed in both the full and effective theories. We demonstrate the versatility of the EFT approach by constructing the general effective Hamiltonian for a collection of particles of arbitrary shapes. Taking advantage of the conformal symmetry of the Hamiltonian, we discuss a straightforward conformal mapping procedure to systematically determine the polarizabilities and derive a complete description for elliptical particles. We compute the pairwise interaction energies to several orders for nonidentical ellipses as well as their leading-order triplet interactions and discuss the resulting preferred pair and multibody configurations. Furthermore, we elaborate on the complications that arise with pinned particle boundary conditions and show that the powerlike corrections expected from dimensional analysis are exponentially suppressed by the leading-order interaction energies.