Molecular dynamics of the antiferroelectric liquid crystal 4′-(octyloxy)biphenyl-4-carboxylate2-fluoro-4-[(octyl-2-yloxy)carbonyl]phenyl (abbreviated as D16) was investigated using different nuclear magnetic resonance (NMR) techniques. D16 molecules form a smectic-${C_{\alpha }}^{*}$ phase $\left(\mathrm{Sm}{C_{\alpha }}^{*}\right)$ in an extremely wide temperature range (∼10 °C). Due to a small tilt of the molecules, this phase is characterized by short switching times, important for new photonic applications. The proton spin-lattice relaxation times were measured in isotropic (Iso), smectic-$A$ ($\text{Sm}A)$, and $\mathrm{Sm}{C_{\alpha }}^{*}$ phases over a wide frequency range of five decades, with conventional and fast field-cycling NMR techniques. This approach allowed a comparison of the essential processes of molecular dynamics taking place in these phases. On the basis of NMR relaxometry measurements, we present a description of the motional behavior of liquid crystal molecules forming $\mathrm{Sm}{C_{\alpha }}^{*}$. Pretransitional effects were observed in wide temperature ranges in both the isotropic and $\text{Sm}A$ phases in D16. The ${}^1\mathrm{H}$ fast field-cycling NMR measurements were supplemented with NMR diffusometry and ${}^{19}\mathrm{F}$ NMR spectroscopy.

Amorphous packings prepared in the vicinity of the jamming transition play a central role in theoretical studies of the vibrational spectrum of glasses. Two mean-field theories predict that the vibrational density of states $g\left(\omega \right)$ obeys a characteristic power law, $g\left(\omega \right)\sim {\omega }^2$, called the non-Debye scaling in the low-frequency region. Numerical studies have, however, reported that this scaling breaks down at low frequencies, due to finite-dimensional effects. In this study, we prepare amorphous packings of up to $128000$ particles in spatial dimensions from $d=3$ to $d=9$ to characterize the range of validity of the non-Debye scaling. Our numerical results suggest that the non-Debye scaling is obeyed down to a frequency that gradually decreases as $d$ increases, and possibly vanishes for large $d$, in agreement with mean-field predictions. We also show that the prestress is an efficient control parameter to quantitatively compare packings across different spatial dimensions.

We first derive the exact dispersion relation for viscous Rayleigh-Taylor instability in the presence of a horizontal magnetic field using a decomposition method, and we find that the horizontal magnetic field contributes to the generation of vorticity inside the flow, thereby further distorting the velocity field. This differs from the previous view of the horizontal magnetic field behaving as a surface-tension-like force that does not produce any vorticity in inviscid flow. Vorticity transport is also investigated. The well-known approximate dispersion relation yields growth rates based on an irrotational approximation with a maximum error of 19% in comparison with the exact rates. Furthermore, we investigate the physics of the viscous Richtmyer-Meshkov instability in the presence of a magnetic field, and we find that the presence of the magnetic field leads to the generation of more eigenvalues, thereby modifying the motion of the interface. Comparisons confirm that the viscosity and magnetic field both play fundamental roles in interface behavior, and it is clarified that the behaviors of the interface for viscous Richtmyer–Meshkov instability become in agreement with the numerical simulations. The dependences of the eigenvalues on the viscosities and densities of the fluids, as well as on the magnetic field, are also discussed. Finally, we analyze the evolution of the decay modes to investigate the rotationality of the velocity fields.

We present an in-depth analysis of an ultrafast electron trajectory type that produces attosecond electromagnetic pulses in both the reflected and forward directions during normal incidence, relativistic laser-plasma interactions. Our particle-in-cell simulation results show that for a target which is opaque to the frequency of the driving laser pulse the emission trajectory is synchrotronlike but differs significantly from the previously identified figure-eight type which produces bright attosecond bursts exclusively in the reflected direction. The origin and characteristics of this trajectory type are explained in terms of the driving electromagnetic fields, the opacity of the plasma, and the conservation of canonical momentum.

The autoregressive neural networks are emerging as a powerful computational tool to solve relevant problems in classical and quantum mechanics. One of their appealing functionalities is that, after they have learned a probability distribution from a dataset, they allow exact and efficient sampling of typical system configurations. Here we employ a neural autoregressive distribution estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a paradigmatic classical model of spin-glass theory, namely, the two-dimensional Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately mimic the Boltzmann distribution using unsupervised learning from system configurations generated using standard MCMC algorithms. The trained NADE is then employed as smart proposal distribution for the Metropolis-Hastings algorithm. This allows us to perform efficient MCMC simulations, which provide unbiased results even if the expectation value corresponding to the probability distribution learned by the NADE is not exact. Notably, we implement a sequential tempering procedure, whereby a NADE trained at a higher temperature is iteratively employed as proposal distribution in a MCMC simulation run at a slightly lower temperature. This allows one to efficiently simulate the spin-glass model even in the low-temperature regime, avoiding the divergent correlation times that plague MCMC simulations driven by local-update algorithms. Furthermore, we show that the NADE-driven simulations quickly sample ground-state configurations, paving the way to their future utilization to tackle binary optimization problems.

The stable transport of migrating eukaryotic cells is essential in organ development and repair processes. However, the mechanism that preserves transport stability over long distances in organs is not fully understood. As the driving mechanism of cell migration, the expressions of heterophilic cell-cell adhesion between moving cells and scaffolding tissue have been observed in such transport. In this paper, we theoretically investigate this heterophilic adhesion, which is persistently polarized in the migrating cell, as a possible transport stabilization mechanism. The adhesion was examined on the basis of the cellular Potts model, and our results confirm the stabilization of the transport to be an effect of the persistence.

We study the rheological signatures of departure from equilibrium in two-dimensional viscous fluids with and without internal spin. Under the assumption of isotropy, we provide the most general linear constitutive relations for stress and couple stress in terms of the velocity and spin fields. Invoking Onsager's regression hypothesis for fluctuations about steady states, we derive the Green-Kubo formulas relating the transport coefficients to time-correlation functions of the fluctuating stress. In doing so, we show that one of the nonequilibrium transport coefficients, the odd viscosity, requires time-reversal symmetry breaking in the case of systems without internal spin. However, the Green-Kubo relations for systems with internal spin also show that there is a possibility for nonvanishing odd viscosity even when time-reversal symmetry is preserved. Furthermore, we find that breakdown of equipartition in nonequilibrium steady states results in the decoupling of the two rotational viscosities relating the vorticity and the internal spin.

We report flocking in the dry active granular matter of millimeter-sized two-step-tapered rods without an intervening medium. The system undergoes the flocking phase transition at a threshold area fraction of $\sim 0.12$ having high orientational correlations between the particles. However, the one-step-tapered rods do not flock and are used as the motile dissenters in the flock-forming granular matter. At the critical fraction of dissenters of $\sim 0.3$, the flocking order of the system gets completely destroyed. The variance of the system's order parameter shows a maximum near the dissenter fraction $f\sim 0.05$, suggesting a finite-size crossover between the ordered and disordered phases. Our experiments bring out the disruption of the cooperative behavior in heterogeneous active systems with possible implications in real-life examples.

The dynamics of supercooled liquids and plastically deformed amorphous solids is known to be dominated by the structure of their rough energy landscapes. Recent experiments and simulations on amorphous solids subjected to oscillatory shear at athermal conditions have shown that for small strain amplitudes these systems reach limit cycles of different periodicities after a transient. However, for larger strain amplitudes the transients become longer and for strain amplitudes exceeding a critical value the system reaches a diffusive steady state. This behavior cannot be explained using the current mean-field models of amorphous plasticity. Here we show that this phenomenology can be described and explained using a simple model of forced dynamics on a multidimensional random energy landscape. In this model, the existence of limit cycles can be ascribed to confinement of the dynamics to a small part of the energy landscape which leads to self-intersection of state-space trajectories and the transition to the diffusive regime for larger forcing amplitudes occurs when the forcing overcomes this confinement.

We study the dynamics of ideal phototactic swimmers in a steady two-dimensional model flow with transport barriers. We consider a distant light source, in which case the self-propulsion velocity of the swimmers is, at any instant, along a predetermined direction. The probability of transport along that direction emerges from the competing effects of the swimmers' self-propulsion and the flow's transport barriers. For swimmers bounded to have the same time average self-propulsion speed, temporal modulation of that speed increases the probability of escaping due to the formation of a stochastic layer which fosters transport. We use separatrix-map techniques to calculate the gain in the probability of escaping.

Scope is the response of Lagrangian flow topologies of three-dimensional time-periodic flows consisting of spheroidal invariant surfaces to perturbation. Such invariant surfaces generically accommodate nonintegrable Hamiltonian dynamics and, in consequence, intrasurface topologies composed of islands and chaotic seas. Computational studies predict a response to arbitrary perturbation that is dramatically different from the classical case of toroidal invariant surfaces: said islands and chaotic seas evolve into tubes and shells, respectively, that merge into “tube-and-shell” structures consisting of two shells connected via (a) tube(s) by a mechanism termed “resonance-induced merger” (RIM). This paper provides conclusive experimental proof of RIM and advances the corresponding structures as the physical topology of realistic flows with spheroidal invariant surfaces; the underlying unperturbed state is a singular limit that exists only for ideal conditions and cannot be achieved in a physical experiment. This paper furthermore expands existing theory on certain instances of RIM to a comprehensive theory (supported by experiments) that explains all observed instances of this phenomenon. This theory reveals that RIM ensues from perturbed periodic lines via three possible scenarios: truncation of tubes by (i) manifolds of isolated periodic points emerging near elliptic lines or by either (ii) local or (iii) global segmentation of periodic lines into elliptic and hyperbolic parts. The RIM scenario for local segmentation includes a perturbation-induced change from elliptic to hyperbolic dynamics near degenerate points on entirely elliptic lines (denoted “virtual local segmentation”). This theory furthermore demonstrates that RIM indeed accomplishes tube-shell merger by exposing the existence of invariant surfaces that smoothly extend from the tubes into the chaotic shells. These phenomena set the response to perturbation—and physical topology—of flows with spheroidal invariant surfaces fundamentally apart from flows with toroidal invariant surfaces. Its entirely kinematic nature and reliance solely on continuity and solenoidality of the velocity field render the comprehensive theory and its findings universal and generically applicable for (arbitrary perturbation of) basically any incompressible flow—in fact any smooth solenoidal vector field—accommodating spheroidal invariant surfaces.

Full-waveform inversion (FWI) is a wave-equation-based methodology to estimate the subsurface physical parameters that honor the geologic structures. Classically, FWI is formulated as a local optimization problem, in which the misfit function, to be minimized, is based on the least-squares distance between the observed data and the modeled data (residuals or errors). From a probabilistic maximum-likelihood viewpoint, the minimization of the least-squares distance assumes a Gaussian distribution for the residuals, which obeys Gauss's error law. However, in real situations, the error is seldom Gaussian and therefore it is necessary to explore alternative misfit functions based on non-Gaussian error laws. In this way, starting from the $\kappa$-generalized exponential function, we propose a misfit function based on the $\kappa$-generalized Gaussian probability distribution, associated with the Kaniadakis statistics (or $\kappa$-statistics), which we call $\kappa$-FWI. In this study, we perform numerical simulations on a realistic acoustic velocity model, considering two noisy data scenarios. In the first one, we considered Gaussian noisy data, while in the second one, we considered realistic noisy data with outliers. The results show that the $\kappa$-FWI outperforms the least-squares FWI, providing better parameter estimation of the subsurface, especially in situations where the seismic data are very noisy and with outliers, independently of the $\kappa$-parameter. Although the $\kappa$-parameter does not affect the quality of the results, it is important for the fast convergence of FWI.

We analyze the morphology of the modern urban skyline in terms of its roughness properties. This is facilitated by a database of ${10}^7$ building heights in cities throughout the Netherlands which allows us to compute the asymptotic height difference correlation function in each city. We find that in cities for which the height correlations display power-law scaling as a function of distance between the buildings, the corresponding roughness exponents are commensurate to the Edwards-Wilkinson and Kardar-Parisi-Zhang equations for kinetic roughening. Based on analogy to discrete deposition models, we argue that these two limiting classes emerge because of possible height restriction rules for buildings in some cities.

Transport of particle beams in plasmas is widely employed in fundamental research, industry, and medicine. Due to the high inertia of ion beams, their transport in plasmas is usually assumed to be stable. Here we report the focusing and flapping of intense slab proton beams transporting through large-scale plasmas by using a recently developed kinetic particle-in-cell simulation code. The beam self-focusing effect in the simulation is prominent and agrees well with previous experiments and theories. Moreover, the beam can curve and flap like turbulence as the beam density increases. Simulation and analysis indicate that the self-generated magnetic fields, produced by movement of collisional plasmas, are the dominant driver of such behaviors. By analyzing the spatial growth rate of magnetic energy and energy deposition of injected proton beams, it is found that the focusing and flapping are significantly determined by the injected beam densities and energies. In addition, a remarkable nonlinear beam energy loss is observed. Our research might find application in inertial confinement fusion and also might be of interest to the laboratory astrophysics community.

We study the dynamics of the branching and annihilating process with long-range interactions. Static particles generate an offspring and annihilate upon contact. The branching distance is supposed to follow a Lévy-like power-law distribution with $P\left(r\right)\propto 1/r^{\alpha }$. We analyze the long term behavior of the mean particles number and its fluctuations as a function of the parameter $\alpha$ that controls the range of the branching process. We show that the dynamic exponent associated with the particle number fluctuations varies continuously for $\alpha <4$ while the particle number exponent only changes for $\alpha <3$. A crossover from extreme value Frechet (at $\alpha =3$) and Gumbell (for $2<\alpha <3$) distributions is developed, similar to the one reported in recent experiments with cw-pumped random fiber lasers presenting underlying gain and Lévy processes. We report the dependence of the relevant dynamical power-law exponents on $\alpha$ showing that explosive growth takes place for $\alpha \le 2$. Further, the average occupation number distribution is shown to evolve from the standard Fermi-Dirac form to the generalized one within the context of nonextensive statistics.

We study a linear Langevin dynamics driven by an additive non-Markovian symmetrical dichotomic noise. It is shown that when the statistics of the time intervals between noise transitions is characterized by two well differentiated timescales, the stationary distribution may develop multimodality (bi- and trimodality). The underlying effects that lead to a probability concentration in different points include intermittence and also a dynamical locking of realizations. Our results are supported by numerical simulations as well as by an exact treatment obtained from a Markovian embedding of the full dynamics, which leads to a third-order differential equation for the stationary distribution.

We study the Ising model on the square lattice $\left({\mathbb{Z}}^2\right)$ and show, via numerical simulation, that allowing interactions between spins separated by distances 1 and $m$ (two ranges), the critical temperature, $T_c\left(m\right)$, converges monotonically to the critical temperature of the Ising model on ${\mathbb{Z}}^4$ as $m\to \infty$. Only interactions between spins located in directions parallel to each coordinate axis are considered. We also simulated the model with interactions between spins at distances of 1, $m$, and $u$ (three ranges), with $u$ a multiple of $m$; in this case our results indicate that $T_c(m,u)$ converges to the critical temperature of the model on ${\mathbb{Z}}^6$. For percolation, analogous results were proven for the critical probability $p_c$ [B. N. B. de Lima, R. P. Sanchis, and R. W. C. Silva, Stochast. Process. Appl. 121, 2043 (2011)].

Motivated by the classical expressions of the mean-square displacement and the velocity autocorrelation function of Brownian particles either suspended in a Newtonian viscous fluid or trapped in a harmonic potential, we show that for all timescales the mean-square displacement of Brownian microspheres with mass $m$ and radius $R$ suspended in any linear, isotropic viscoelastic material is identical to the creep compliance of a linear mechanical network that is a parallel connection of the linear viscoelastic material with an inerter with distributed inertance $m_R=\frac{m}{6\pi R}$. The synthesis of this mechanical network leads to the statement of a viscous-viscoelastic correspondence principle for Brownian motion which simplifies appreciably the calculations of the mean-square displacement and the velocity autocorrelation function of Brownian particles suspended in viscoelastic materials where inertia effects are non-negligible at longer timescales. The viscous-viscoelastic correspondence principle established in this paper by introducing the concept of the inerter is equivalent to the viscous-viscoelastic analogy adopted by Mason and Weitz [T. G. Mason and D. A. Weitz, Phys. Rev. Lett. 74, 1250 (1995)].

We study theoretically the emergence of localized states of vegetation close to the onset of desertification. These states are formed through the locking of vegetation fronts, connecting a uniform vegetation state with a bare soil state, which occurs nearby the Maxwell point of the system. To study these structures we consider a universal model of vegetation dynamics in drylands, which has been obtained as the normal form for different vegetation models. Close to the Maxwell point localized gaps and spots of vegetation exist and undergo collapsed snaking. The presence of gaps strongly suggest that the ecosystem may undergo a recovering process. In contrast, the presence of spots may indicate that the ecosystem is close to desertification.