The persistence of a transition state structure in systems driven by time-dependent environments allows the application of modern reaction rate theories to solution-phase and nonequilibrium chemical reactions. However, identifying this structure is problematic in driven systems and has been limited by theories built on series expansion about a saddle point. Recently, it has been shown that to obtain formally exact rates for reactions in thermal environments, a transition state trajectory must be constructed. Here, using optimized Lagrangian descriptors [G. T. Craven and R. Hernandez, Phys. Rev. Lett. 115, 148301 (2015)], we obtain this so-called distinguished trajectory and the associated moving reaction manifolds on model energy surfaces subject to various driving and dissipative conditions. In particular, we demonstrate that this is exact for harmonic barriers in one dimension and this verification gives impetus to the application of Lagrangian descriptor-based methods in diverse classes of chemical reactions. The development of these objects is paramount in the theory of reaction dynamics as the transition state structure and its underlying network of manifolds directly dictate reactivity and selectivity.

We propose an efficient and accurate measure for ranking spreaders and identifying the influential ones in spreading processes in networks. While the edges determine the connections among the nodes, their specific role in spreading should be considered explicitly. An edge connecting nodes $i$ and $j$ may differ in its importance for spreading from $i$ to $j$ and from $j$ to $i$. The key issue is whether node $j$, after infected by $i$ through the edge, would reach out to other nodes that $i$ itself could not reach directly. It becomes necessary to invoke two unequal weights $w_{ij}$ and $w_{ji}$ characterizing the importance of an edge according to the neighborhoods of nodes $i$ and $j$. The total asymmetric directional weights originating from a node leads to a novel measure $s_i$, which quantifies the impact of the node in spreading processes. An $s$-shell decomposition scheme further assigns an $s$-shell index or weighted coreness to the nodes. The effectiveness and accuracy of rankings based on $s_i$ and the weighted coreness are demonstrated by applying them to nine real-world networks. Results show that they generally outperform rankings based on the nodes' degree and $k$-shell index while maintaining a low computational complexity. Our work represents a crucial step towards understanding and controlling the spread of diseases, rumors, information, trends, and innovations in networks.

A two-dimensional continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model incorporates stress and deformation tensors, which can be compared with experimental data. Focusing on the interplay between cell shape changes and cell rearrangements, we elucidated dynamical behavior underlying passive relaxation, active contraction-elongation, and tissue shear flow, including a mechanism for contraction-elongation, whereby tissue flows perpendicularly to the axis of cell elongation. This study provides an integrated scheme for the understanding of the orchestration of morphogenetic processes in individual cells to achieve epithelial tissue morphogenesis.

It is well known that translocation events of a polymer or rod through pores or narrower parts of micro- and nanochannels have a stochastic nature due to the Brownian motion. However, it is not clear whether the objects of interest need to have a larger size than the entrance to exhibit the deviation from the dynamics of the surrounding fluid. We show by numerical analysis that the particle injection into the narrower part of the channel is affected by thermal fluctuation, where the particles have spherical symmetry and are smaller than the height of the constriction. The Péclet number (Pe) is the order parameter that governs the phenomena, which clarifies the spatio-temporal significance of Brownian motion compared to hydrodynamics. Furthermore, we find that there exists an optimal condition of Pe to attain the highest flow rate of particles relative to the dispersant fluid flow. Our finding is important in science and technology from nanopore DNA sequencers and lab-on-a-chip devices to filtration by porous materials and chromatography.

The Sagdeev-Zaslavski (SZ) equation for wave turbulence is analytically derived, both in terms of a generating function and of a multipoint probability density function (PDF), for weakly interacting waves with initial random phases. When the initial amplitudes are also random, a one-point PDF equation is derived. Such analytical calculations remarkably agree with results obtained in totally different fashions. Numerical investigations of the two-dimensional nonlinear Schrödinger equation (NLSE) and of a vibrating plate prove the following: (i) Generic Hamiltonian four-wave systems rapidly attain a random distribution of phases independently of the slower dynamics of the amplitudes, vindicating the hypothesis of initially random phases. (ii) Relaxation of the Fourier amplitudes to the predicted stationary distribution (exponential) happens on a faster time scale than relaxation of the spectrum (Rayleigh-Jeans distribution). (iii) The PDF equation correctly describes dynamics under different forcings: The NLSE has an exponential PDF corresponding to a quasi-Gaussian solution, as the vibrating plates, that also shows some intermittency at very strong forcings.

Diffusion in natural and engineered media is quantified in terms of stochastic models for the heterogeneity-induced fluctuations of particle motion. However, fundamental properties such as ergodicity and self-averaging and their dependence on the disorder distribution are often not known. Here, we investigate these questions for diffusion in quenched disordered media characterized by spatially varying retardation properties, which account for particle retention due to physical or chemical interactions with the medium. We link self-averaging and ergodicity to the disorder sampling efficiency $R_n$, which quantifies the number of disorder realizations a noise ensemble may sample in a single disorder realization. Diffusion for disorder scenarios characterized by a finite mean transition time is ergodic and self-averaging for any dimension. The strength of the sample to sample fluctuations decreases with increasing spatial dimension. For an infinite mean transition time, particle motion is weakly ergodicity breaking in any dimension because single particles cannot sample the heterogeneity spectrum in finite time. However, even though the noise ensemble is not representative of the single-particle time statistics, subdiffusive motion in $q\ge 2$ dimensions is self-averaging, which means that the noise ensemble in a single realization samples a representative part of the heterogeneity spectrum.

Real nonsymmetric matrices may have either real or complex conjugate eigenvalues. These matrices can be seen to be pseudosymmetric as $\eta M{\eta }^{-1}=M^t$, where the metric $\eta$ could be secular (a constant matrix) or depending upon the matrix elements of $M$. Here we construct ensembles of a large number $N$ of pseudosymmetric $n\times n$ $(n$ large) matrices using $\mathcal{N}[n(n+1)/2\le \mathcal{N}\le n^2]$ independent and identically distributed random numbers as their elements. Based on our numerical calculations, we conjecture that for these ensembles the nearest level spacing distributions [NLSDs, $p\left(s\right)]$ are sub-Wigner as $p_{abc}\left(s\right)=as{e}^{-b{s}^c}(0<c<2)$ and the distributions of their eigenvalues fit well to $D\left(\epsilon \right)=A\left[\text{tanh}\right\{(\epsilon +B)/C\}-\text{tanh}\{(\epsilon -B)/C\left\}\right]$ (exceptions also discussed). These sub-Wigner NLSDs are encountered in Anderson metal-insulator transition and topological transitions in a Josephson junction. Interestingly, $p\left(s\right)$ for $c=1$ is called semi-Poisson, and we show that it lies close to the form $p\left(s\right)=0.59s{K}_0\left(0.45s^2\right)$ derived for the case of $2\times 2$ pseudosymmetric matrix where the eigenvalues are most aptly conditionally real, $E_{1,2}=a\pm \sqrt{b^2-c^2}$, which represent characteristic coalescing of eigenvalues in parity-time (PT) -symmetric systems.

We study the role of hydrodynamic interactions in the collective behavior of collections of microscopic active particles suspended in a fluid. We introduce a calculational framework that allows us to separate the different contributions to their collective dynamics from hydrodynamic interactions on different length scales. Hence we are able to systematically show that lubrication forces when the particles are very close to each other play as important a role as long-range hydrodynamic interactions in determining their many-body behavior. We find that motility-induced phase separation is suppressed by near-field interactions, leading to open gel-like clusters rather than dense clusters. Interestingly, we find a globally polar ordered phase appears for neutral swimmers with no force dipole that is enhanced by near-field lubrication forces in which the collision process rather than long-range interaction dominates the alignment mechanism.

Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Several studies have recently conjectured that in the RSA of rectangular needles, or $k$-mers, on a square lattice, percolation is impossible if the needles are sufficiently long ($k$ of order of several thousand). We refute these claims and present rigorous proof that in any jammed configuration of nonoverlapping, fixed-length, horizontal, or vertical needles on a square lattice, all clusters are percolating clusters.

The Jarzynski equality is one of the most influential results in the field of nonequilibrium statistical mechanics. This celebrated equality allow the calculation of equilibrium free-energy differences from work distributions of nonequilibrium processes. In practice, such calculations often suffer from poor convergence due to the need to sample rare events. Here we examine if the inclusion of measurement and feedback can improve the convergence of nonequilibrium free-energy calculations. A modified version of the Jarzynski equality in which realizations with a given outcome are kept, while others are discarded, is used. We find that discarding realizations with unwanted outcomes can result in improved convergence compared to calculations based on the Jarzynski equality. We argue that the observed improved convergence is closely related to Bennett's acceptance ratio method, which was developed without any reference to measurements or feedback.

We study the coupling of a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation to a separate, advection-only transport process. We find that an infinitesimal coupling can cause a finite change in the speed and shape of the reaction front, indicating the fragility of the FKPP model with respect to such a perturbation. The front dynamics can be mapped to an effective FKPP equation only at sufficiently fast diffusion or large coupling strength. We also discover conditions when the front width diverges and when its speed is insensitive to the coupling. At zero diffusion in our mean-field description, the downwind front speed goes to a finite value as the coupling goes to zero.

A lossless nonlinear $LC$ transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear $LC$ transmission networks.

Reduced motor control is one of the most frequent features associated with aging and disease. Nonlinear and fractal analyses have proved to be useful in investigating human physiological alterations with age and disease. Similar findings have not been established for any of the model organisms typically studied by biologists, though. If the physiology of a simpler model organism displays the same characteristics, this fact would open a new research window on the control mechanisms that organisms use to regulate physiological processes during aging and stress. Here, we use a recently introduced animal-tracking technology to simultaneously follow tens of Caenorhabdits elegans for several hours and use tools from fractal physiology to quantitatively evaluate the effects of aging and temperature stress on nematode motility. Similar to human physiological signals, scaling analysis reveals long-range correlations in numerous motility variables, fractal properties in behavioral shifts, and fluctuation dynamics over a wide range of timescales. These properties change as a result of a superposition of age and stress-related adaptive mechanisms that regulate motility.

Metallic glasses (MGs) have so far attracted considerable attention for their applications as bulk materials. However, new physics and applications often emerge by dimensional reduction from three dimensions (3D) to two dimensions (2D). Here, we study, by molecular dynamics simulations, how the liquid-to-glass transition of a binary $\mathrm{C}{\mathrm{u}}_{50}\mathrm{Z}{\mathrm{r}}_{50}$ MG is affected by spatial dimensionality. We find clear evidence that crystal-like structural ordering controls both dynamic heterogeneity and slow dynamics, and thus plays a crucial role in the formation of the 2DMG. Although the 2DMG reproduces the dynamical behaviors of its 3D counterpart by considering Mermin-Wagner-type fluctuations specific to 2D, this atomic-scale structural mechanism is essentially different from that for the 3DMG in which icosahedral clusters incompatible with crystallographic symmetry play a key role in glassy behaviors. Our finding provides a structural mechanism for the formation of 2DMGs, which cannot be inferred from the knowledge of 3DMGs. The results suggest a structural basis for the glass transition in 2DMG and provide possible explanations for some previous experimental observations in ultrathin film MGs.

The polarization exchange effect in a twisted-nematic Fabry-Pérot resonator is experimentally confirmed in the regimes of both uniform and electric-field-deformed twisted structures. The polarization of output light in the transmission peaks is shown to be linear rather than elliptical. The polarization deflection from the nematic director grows from $0^{\circ }$ to ${90}^{\circ }$ angle and exchanges the longitudinal and transverse directions. Untwisting of a nematic by a voltage leads to the rotation of the polarization plane of light passing through the resonator. The polarization exchange effect allows using the investigated resonator as a spectral-selective linear polarizer with the voltage-controlled rotation of the polarization plane.

We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute activated surface diffusion, which is represented by a sequence of random hops to neighboring lattice sites with a maximum of $G$ hop attempts ($G\gg 1$), a detachment probability $\epsilon <1$ per neighboring particle, and a no-desorption condition. Computer simulations show the formation of a compact wetting layer followed by the growth of branched deposits. The maximal thickness $z_c$ of that layer increases with $G$ but is weakly affected by $\epsilon$. A scaling approach describes the crossover from smooth film growth to unstable growth and predicts $z_c\sim G^{\gamma }$, with $\gamma =1/\left[2\left(1-\nu \right)\right]\approx 0.43$, where $\nu \approx 0.30$ is the inverse of the dynamical exponent of the Villain-Lai-Das Sarma equation that describes the initial roughening. Using previous results for related deposition models, the thickness $z_c$ can be predicted as a function of an activation energy for terrace surface diffusion and the temperature, and the small effects of the parameter $\epsilon$ are justified. These predictions are confirmed by the numerical results with good accuracy. We discuss possible applications, with a particular focus on the growth of multifuncional structures with stacking layers of different porosity.

We present numerical and experimental results on the mass flow rate during the discharge of three-dimensional silos filled with a bidisperse mixture of grains of different sizes. We analyzed the influence of the ratio between coarse and fine particles on the profile of volume fraction and velocity across the orifice. By using numerical simulations, we have shown that the velocity profile has the same shape as that in the monodisperse case and is insensitive to the composition of the mixture. On the contrary, the volume fraction profile is strongly affected by the composition of the mixture. Assuming that an effective particle size can be introduced to characterize the mixture, we have shown that previous expression for the mass flow rate of monodisperse particles can be used for binary mixtures. A comparison with Beverloo's correlation is also presented.

The numerical investigation of convective flows in the radial force field caused by an oscillating electric field between spherical surfaces has been performed. A temperature difference ($T_1>T_2$) as well as a radial force field triggers a fluid flow similar to the Rayleigh-Bénard convection. The onset of convective flow has been studied by means of the linear stability analysis as a function of the radius ratio $\eta =R_1/R_2$. The influence of the temperature-dependent viscosity has been investigated in detail. We found that a varying viscosity contrast $\beta =\nu \left(T_2\right)/\nu \left(T_1\right)$ between $\beta =1$ (constant viscosity) and $\beta =50$ decreases the critical Rayleigh number by a factor of 6. Additionally, we perform a bifurcation analysis based on numerical simulations which have been calculated using a modified pseudospectral code. Numerical results have been compared with the GeoFlow experiment which is located on the International Space Station (ISS). Nonturbulent three-dimensional structures are found in the numerically predicted parameter regime. Furthermore, we observed multiple stable solutions in both experiments and numerical simulations, respectively.

This study focuses on grid refinement techniques for the direct simulation of aeroacoustics, when using weakly compressible lattice Boltzmann models, such as the D3Q19 athermal velocity set. When it comes to direct noise computation, very small errors on the density or pressure field may have great negative consequences. Even strong acoustic density fluctuations have indeed a clearly lower amplitude than the hydrodynamic ones. This work deals with such very weak spurious fluctuations that emerge when a vortical structure crosses a refinement interface, which may contaminate the resulting aeroacoustic field. We show through an extensive literature review that, within the framework described above, this issue has never been addressed before. To tackle this problem, we develop an alternative algorithm and compare its behavior to a classical one, which fits our in-house vertex-centered data structure. Our main idea relies on a directional splitting of the continuous discrete velocity Boltzmann equation, followed by an integration over specific characteristics. This method can be seen as a specific coupling between finite difference and lattice Boltzmann, locally on the interface between the two grids. The method is assessed considering two cases: an acoustic pulse and a convected vortex. We show how very small errors on the density field arise and propagate throughout the domain when a vortical flow crosses the refinement interface. We also show that an increased free stream Mach number (but still within the weakly compressible regime) strongly deteriorates the situation, although the magnitude of the errors may remain negligible for purely aerodynamic studies. A drastically reduced level of error for the near-field spurious noise is obtained with our approach, especially for under-resolved simulations, a situation that is crucial for industrial applications. Thus, the vortex case is proved useful for aeroacoustic validations of any grid refinement algorithm.