Velazquez and Curilef [J. Stat. Mech. (2010) P02002; J. Stat. Mech. (2010) P04026] have proposed a methodology to extend Monte Carlo algorithms that are based on canonical ensemble. According to our previous study, their proposal allows us to overcome slow sampling problems in systems that undergo any type of temperature-driven phase transition. After a comprehensive review about ideas and connections of this framework, we discuss the application of a reweighting technique to improve the accuracy of microcanonical calculations, specifically, the well-known multihistograms method of Ferrenberg and Swendsen [Phys. Rev. Lett. 63, 1195 (1989)]. As an example of application, we reconsider the study of the four-state Potts model on the square lattice $L\times L$ with periodic boundary conditions. This analysis allows us to detect the existence of a very small latent heat per site $q_L$ during the occurrence of temperature-driven phase transition of this model, whose size dependence seems to follow a power law $q_L\left(L\right)\propto {(1/L)}^z$ with exponent $z\simeq 0$.$26\pm 0$.02. Discussed is the compatibility of these results with the continuous character of temperature-driven phase transition when $L\to +\infty$.

We present a method that reconstructs both the links and their relative coupling strength of bidirectional weighted networks. Our method requires only measurements of node dynamics as input. Using several examples, we demonstrate that our method can give accurate results for weighted random and weighted scale-free networks with both linear and nonlinear dynamics.

The role of spatially correlated mechanical elements in the failure behavior of heterogeneous materials represented by fiber bundle models (FBMs) was evaluated systematically for different load redistribution rules. Increasing the range of spatial correlation for FBMs with local load sharing is marked by a transition from ductilelike failure characteristics into brittlelike failure. The study identified a global failure criterion based on macroscopic properties (external load and cumulative damage) that is independent of spatial correlation or load redistribution rules. This general metric could be applied to assess the mechanical stability of complex and heterogeneous systems and thus provide an important component for early warning of a class of geophysical ruptures.

We consider a system of conformist and contrarian oscillators coupled locally in a three-dimensional cubic lattice and explore collective behavior of the system. The conformist oscillators attractively interact with the neighbor oscillators and therefore tend to be aligned with the neighbors' phase. The contrarian oscillators interact repulsively with the neighbors and therefore tend to be out of phase with them. In this paper, we investigate whether many peculiar dynamics that have been observed in the mean-field system with global coupling can emerge even with local coupling. In particular, we pay attention to the possibility that a traveling wave may arise. We find that the traveling wave occurs due to coupling asymmetry and not by global coupling; this observation confirms that the global coupling is not essential to the occurrence of a traveling wave in the system. The traveling wave can be a mechanism for the coherent rhythm generation of the circadian clock or of hormone secretion in biological systems under local coupling.

The development of tractable nonequilibrium simulation methods represents a bottleneck for efforts to describe the functional dynamics that occur within living cells. We here employ a nonequilibrium approach called the $\lambda$ ensemble to characterize the dissipative dynamics of a simple Markovian network driven by an external potential. In the highly dissipative regime brought about by the $\lambda$ bias, we observe a dynamical structure characteristic of cellular architectures: The entropy production drives a damped oscillator over state populations in the network. We illustrate the properties of such oscillations in weakly and strongly driven regimes, and we discuss how control structures associated with the “dynamical phase transition” in the system can be related to switches and oscillators in cellular dynamics.

We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent approximate effective time-independent scenario, whereby the system is rendered integrable. The time evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peaklike features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the nonintegrable map corresponding to the actual time-dependent system in the nonchaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the nonchaotic regime at both the quantum and classical level.

We carry out an extensive and high-resolution direct numerical simulation of homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy; (b) modify the fluid energy spectrum in both inverse- and forward-cascade régimes; (c) reduce small-scale intermittency; (d) suppress regions of high vorticity and strain rate; and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies and propose new experiments.

The quantum hydrodynamic (QHD) model of charged spin-1/2 particles contains physical quantities defined for all particles of a species including particles with spin-up and with spin-down. Different populations of states with different spin directions are included in the spin density (the magnetization). In this paper I derive a QHD model, which separately describes spin-up electrons and spin-down electrons. Hence electrons with different projections of spins on the preferable direction are considered as two different species of particles. It is shown that the numbers of particles with different spin directions do not conserve. Hence the continuity equations contain sources of particles. These sources are caused by the interactions of the spins with the magnetic field. Terms of similar nature arise in the Euler equation. The $z$ projection of the spin density is no longer an independent variable. It is proportional to the difference between the concentrations of the electrons with spin-up and the electrons with spin-down. The propagation of waves in the magnetized plasmas of degenerate electrons is considered. Two regimes for the ion dynamics, the motionless ions and the motion of the degenerate ions as the single species with no account of the spin dynamics, are considered. It is shown that this form of the QHD equations gives all solutions obtained from the traditional form of QHD equations with no distinction of spin-up and spin-down states. But it also reveals a soundlike solution called the spin-electron acoustic wave. Coincidence of most solutions is expected since this derivation was started with the same basic equation: the Pauli equation. Solutions arise due to the different Fermi pressures for the spin-up electrons and the spin-down electrons in the magnetic field. The results are applied to degenerate electron gas of paramagnetic and ferromagnetic metals in the external magnetic field. The dispersion of the spin-electron acoustic waves in the partially spin-polarized degenerate neutron matter are also considered.

It is demonstrated how the static electron-electron structure factor in warm dense matter can be obtained from density functional theory in combination with quantum Monte Carlo data. In contrast to theories assuming well-separated bound and free states, this ab initio approach yields also valid results for systems close to the Mott transition (pressure ionization), where bound states are strongly modified and merge with the continuum. The approach is applied to x-ray Thomson scattering and compared to predictions of the Chihara formula whereby we use the ion-ion and electron-ion structure from the same simulations. The results show significant deviations of the screening cloud from the often applied Debye-like form.

Spectral reshaping and nonuniform phase delay associated with an electromagnetic pulse propagating in a temporally dispersive medium may lead to interesting observations in which the group velocity becomes superluminal or even negative. In such cases, the finite bandwidth of the superluminal region implies the inevitable existence of a cutoff distance beyond which a superluminal pulse becomes subluminal. In this paper, we derive a closed-form analytic expression to estimate this cutoff distance in abnormal dispersive media with gain. Moreover, the method of steepest descent is used to track the time-frequency dynamics associated with the evolution of the center of mass of a superluminal pulse to the subluminal regime. This evolution takes place at longer propagation depths as a result of the subluminal components affecting the behavior of the pulse. Finally, the analysis presents the fundamental limitations of superluminal propagation in light of factors such as the medium depth, pulse width, and the medium dispersion strength.

We have reproduced the experiment of acoustic monitoring of spontaneous popping of single soap bubbles standing in air reported by Ding et al. [Phys. Rev. E 75, 041601 (2007)]. By using a single microphone and two different signal acquisition systems recording in parallel the signal at the microphone output, among them the system used by Ding et al., we have experimentally evidenced that the acoustic precursors of bubble popping events detected by Ding et al. actually result from an acausal artifact of the signal processing performed by their acquisition system which lies outside of its prescribed working frequency range. No acoustic precursor of popping could be evidenced with the microphone used in these experiments, whose sensitivity is $1\mathrm{V}{\mathrm{Pa}}^{-1}$ and frequency range is 500 Hz–100 kHz.

We reported on the sound pressure generated by aqueous foam bursts in our paper [Ding et al., Phys. Rev. E 75, 041601 (2007)]. Blanc et al., [Phys. Rev. E 91, 036401 (2015)] found that sound from one of three mechanisms of bubble burst (the prepopping) actually results from an acausal artifact of the signal processing performed by their acquisition system which lies outside of its prescribed working frequency range. We examined the same hardware used in our paper and found that the frequency range is not the cause of the artifact. The prepopping sound was a result from a built-in finite impulse response filter of analog-to-digital converters in the Brüel & Kjær data acquisition system.

We explore the crystallization of charged colloidal particles in a nonpolar solvent mixture. We simultaneously charge the particles and add counterions to the solution with aerosol-OT (AOT) reverse micelles. At low AOT concentrations, the charged particles crystallize into body-centered-cubic (bcc) or face-centered-cubic (fcc) Wigner crystals; at high AOT concentrations, the increased screening drives a thus far unobserved reentrant melting transition. We observe an unexpected scaling of the data with particle size, and account for all behavior with a model that quantitatively predicts both the reentrant melting and the data collapse.

We discuss the basic principles of self-organization of a finite number of charged particles interacting via the $1/r$ Coulomb potential in disk geometry. The analysis is based on the cyclic symmetry and periodicity of the Coulomb interaction between particles located on several rings. As a result, a system of equations is derived, which allows us readily to determine with high accuracy the equilibrium configurations of a few hundred charged particles. For $n\gtrsim 200$, we predict the formation of a hexagonal core and valence circular rings for the centered configurations.

Beads-on-string patterns have been experimentally observed in solid cylinders for a wide range of material properties and structural lengths, from millimetric soft gels to nanometric hard fibers. In this work, we combine theoretical analysis and numerical tools to investigate the formation and nonlinear dynamics of such beaded structures. We show that this morphological transition is driven by elastocapillarity, i.e., a complex interplay between the effects of surface tension and bulk elasticity. Unlike buckling or wrinkling, the presence of an axial elongation is found here to favor the onset of fiber beading, in agreement with existing experimental results on electrospun fibers, hydrogels, and nerves. Our results also prove that the applied stretch can be used in fabrication techniques to control the morphology of the emerging beads-on-string patterns. Such quantitative predictions open the way for several applications, from tissue engineering to the design of stretchable electronics and the microfabrication of functionalized surfaces.

In the field of soft matter research, the characteristic behavior of both nematic–isotropic ($N-I$) and smectic-$A\mathrm{nematic}(\mathrm{Sm}\text{−}AN)$ phase transitions has gained considerable attention due to their several attractive features. In this work, a high-resolution measurement of optical birefringence $\left(\Delta n\right)$ has been performed to probe the critical behavior at the $N-I$ and $\mathrm{Sm}\text{−}AN$ phase transitions in a binary system comprising the rodlike octylcyanobiphenyl and a laterally methyl substituted hockey-stick-shaped mesogen, 4-(3-$n$-decyloxy-2-methyl-phenyliminomethyl)phenyl 4-$n$-dodecyloxycinnamate. For the investigated mixtures, the critical exponent $\beta$ related to the limiting behavior of the nematic order parameter close to the $N-I$ phase transition has come out to be in good conformity with the tricritical hypothesis. Moreover, the yielded effective critical exponents (${\alpha }^{\prime }$, ${\beta }^{\prime }$, ${\gamma }^{\prime }$) characterizing the critical fluctuation near the $\mathrm{Sm}\text{−}AN$ phase transition have appeared to be nonuniversal in nature. With increasing hockey-stick-shaped dopant concentration, the $\mathrm{Sm}\text{−}AN$ phase transition demonstrates a strong tendency to be driven towards a first-order nature. Such a behavior has been accounted for by considering a modification of the effective intermolecular interactions and hence the related coupling between the nematic and smectic order parameters, caused by the introduction of the angular mesogenic molecules.

The dynamics of a spiking neuron approaching threshold is investigated in the framework of Markov-chain models describing the random state-transitions of the underlying ion-channel proteins. We characterize subthreshold channel-noise-induced transmembrane potential fluctuations in both type-I (integrator) and type-II (resonator) parametrizations of the classic conductance-based Hodgkin-Huxley equations. As each neuron approaches spiking threshold from below, numerical simulations of stochastic trajectories demonstrate pronounced growth in amplitude simultaneous with decay in frequency of membrane voltage fluctuations induced by ion-channel state transitions. To explore this progression of fluctuation statistics, we approximate the exact Markov treatment with a 12-variable channel-based stochastic differential equation (SDE) and its Ornstein-Uhlenbeck (OU) linearization and show excellent agreement between Markov and SDE numerical simulations. Predictions of the OU theory with respect to membrane potential fluctuation variance, autocorrelation, correlation time, and spectral density are also in agreement and illustrate the close connection between the eigenvalue structure of the associated deterministic bifurcations and the observed behavior of the noisy Markov traces on close approach to threshold for both integrator and resonator point-neuron varieties.

A detailed quantitative analysis of the specific heat in the 0.5- to 200-K temperature range for almost dry L-cysteine and its dimer, L-cystine, amino acids is presented. We report the occurrence of a sharp first-order transition at $\sim 76$ K for L-cysteine associated with the thiol group ordering which was successfully modeled with the two-dimensional Ising model. We demonstrated that quantum rotors, two-level systems (TLS), Einstein oscillators, and acoustic phonons (the Debye model) are essential ingredients to correctly describe the overall experimental data. Our analysis pointed out the absence of the TLS contribution to the low temperature specific heat of L-cysteine. This result was similar to that found in other noncrystalline amorphous materials, e.g., amorphous silicon, low density amorphous water, and ultrastable glasses. L-cystine presented an unusual nonlinear acoustic dispersion relation $\omega \left(q\right)=v{q}^{0.95}$ and a Maxwell-Boltzmann–type distribution of tunneling barriers. The presence of Einstein oscillators with ${\Theta }_E\sim 70$ K was common in both systems and adequately modeled the boson peak contributions.

We study pattern formation in planar fluid systems driven by intermolecular cohesion (which manifests as a line tension) and dipole-dipole repulsion, which are observed in physical systems including ferrofluids in Hele-Shaw cells and Langmuir layers. When the dipolar repulsion is sufficiently strong, domains undergo forked branching reminiscent of viscous fingering. A known difficulty with these models is that the energy associated with dipole-dipole interactions is singular at small distances. Following previous work, we demonstrate how to ameliorate this singularity and show that in the macroscopic limit only the scale of the microscopic details relative to the macroscopic extent of a system is relevant and develop an expression for the system energy that depends only on a generalized line tension $\Lambda$ that in turn depends logarithmically on that scale. We conduct numerical studies that use energy minimization to find equilibrium states. Following the subcritical bifurcations from the circle, we find a few highly symmetric stable shapes, but nothing that resembles the observed diversity of experimental and dynamically simulated domains. The application of a weak random background to the energy landscape stabilizes a wide range of domain morphologies recovering the diversity observed experimentally. With this technique, we generate a large sample of qualitatively realistic shapes and use them to create an empirical model for extracting $\Lambda$ with high accuracy using only a shape's perimeter and morphology.