We propose a theory to account for the NMR relaxation of water protons in situations in which the fluid is confined to porous structures exhibiting a scarce distribution of paramagnetic centers on their surface. Though much of what is stated and assumed concerns the response of water, the model has sufficiently general features to be able to explain proton relaxation of other polar fluids under similar conditions. One of the main results of the paper is to show that the local anisotropy introduced by the dominant dipolar coupling in the relaxation rates of active surface elements induces a measurable dependence on sample orientation in the overall relaxation rates of the saturating fluid provided its confining structure is not statistically isotropic. Measurements of ${\mathsf{T}}_1$ proton relaxation on water saturating microcapillary tubes are performed to reveal the effect.

New data for the reflectivity of shock-compressed xenon plasmas at pressures of 10–12 GPa at large incident angles are presented. In addition, measurements have been performed at different densities. These data allow to analyze the free-electron density profile across the shock wave front. Assuming a Fermi-like density profile, the width of the front layer is inferred. The reflectivity coefficients for the $s$- and $p$-polarized waves are calculated. The influence of atoms, which was taken into account on the level of the collision frequency, proves to be essential for the understanding of the reflection process. Subsequently, a unique density profile is sufficient to obtain good agreement with the experimental data at different incident angles and at all investigated optical laser frequencies. Reflectivity measurements for different densities allow to determine the dependence of shock-front density profiles on the plasma parameters. As a result, it was found that the width of the front layer increases with decreasing density.

In this paper, a phase-field method under the framework of discrete unified gas-kinetic scheme (DUGKS) for incompressible multiphase fluid flows is proposed. Two kinetic models are constructed to solve the conservative Allen-Cahn equation that accounts for the interface behavior and the incompressible hydrodynamic equations that govern the flow field, respectively. With a truncated equilibrium distribution function as well as a temporal derivative added to the source term, the macroscopic governing equations can be exactly recovered from the kinetic models through the Chapman-Enskog analysis. Calculation of source terms involving high-order derivatives existed in the quasi-incompressible model is simplified. A series of benchmark cases including four interface-capturing tests and four binary flow tests are carried out. Results compared to that of the lattice Boltzmann method (LBM) have been obtained. A convergence rate of second order can be guaranteed in the test of interface diagonal translation. The capability of the present method to track the interface that undergoes a severe deformation has been verified. Stationary bubble and spinodal decomposition problems, both with a density ratio as high as 1000, are conducted and reliable solutions have been provided. The layered Poiseuille flow with a large viscosity ratio is simulated and numerical results agree well with the analytical solutions. Variation of positions of the bubble front and spike tip during the evolution of Rayleigh-Taylor instability has been predicted precisely. However, the detailed depiction of complicated interface patterns appearing during the evolution process is failed, which is mainly caused by the relatively large numerical dissipation of DUGKS compared to that of LBM. A high-order DUGKS is needed to overcome this problem.

A large number of real networks show abrupt phase transition phenomena in response to environmental changes. In this case, cascading phenomena can induce drastic and discontinuous changes in the system state and lead to collapse. Although complex network theory has been used to investigate these drastic events, we are still unable to predict them effectively. We here analyze collapse phenomena by proposing a minimal two-state dynamic on a complex network and introducing the effect of local connectivities on the evolution of network nodes. We find that a heterogeneous system of interconnected components presents a mixed response to stress and can serve as a control indicator. In particular, before the critical transition point is reached a severe loss of low-degree nodes is observed, masked by the minimal failure of higher-degree nodes. Accordingly, we suggest that a significant reduction in less connected nodes can indicate impending global failure.

We study quantum dynamics in the framework of repeated interactions between a system and a stream of identical probes. We present a coarse-grained master equation that captures the system's dynamics in the natural regime where interactions with different probes do not overlap, but it is otherwise valid for arbitrary values of the interaction strength and mean interaction time. We then apply it to some specific examples. For probes prepared in Gibbs states, such channels have been used to describe thermalization: while this is the case for many choices of parameters, for others one finds out-of-equilibrium states including inverted Gibbs and maximally mixed states. Gapless probes can be interpreted as performing an indirect measurement, and we study the energy transfer associated with this measurement.

We study numerically the length distribution of the longest increasing subsequence (LIS) for random permutations and one-dimensional random walks. Using sophisticated large-deviation algorithms, we are able to obtain very large parts of the distribution, especially also covering probabilities smaller than ${10}^{-1000}$. This enables us to verify for the length of the LIS of random permutations the analytically known asymptotics of the rate function and even the whole Tracy-Widom distribution. We observe a rather fast convergence in the larger than typical part to this limiting distribution. For the length $L$ of LIS of random walks no analytical results are known to us. We test a proposed scaling law and observe convergence of the tails into a collapse for increasing system size. Further, we obtain estimates for the leading-order behavior of the rate functions in both tails.

To investigate the proliferation and invasion of a tumor within an inhomogeneous matrix, we studied the spatiotemporal dynamics of two types of growth-diffusion systems (GDSs) with logistic or Allee growth occurring on a two-dimensional square site percolation lattice via numerical computation and finite-size scaling approaches. A critical percolation threshold exists in the two systems, but becomes obscure with an increasing Allee effect in Allee growth. The two systems evidently differ in their short-time spatiotemporal patterns: The tumor number density in the logistic model grows and spreads continuously and subdiffusively or weakly superdiffusively while that in the Allee model does so discretely and strongly superdiffusively. This difference is attributed to a lack of cooperation between sites for growth and diffusion in the logistic model as compared to its Allee counterpart. The Allee growth pattern is characterized by a rougher border and more inhomogeneous interior than its logistic counterpart. Judging from their growth-diffusion feature in combination with a clinical image analysis, we conclude that Allee growth is more suitable for modeling the proliferation and invasion of an early-stage malignant tumor than is logistic growth. A phase diagram that correlates a tumor's growth and diffusion on a percolation lattice with a site occupation fraction and Allee effect was established to reveal the sensitivity on proliferation and spreading of a tumor towards the above parameters. The Allee effect was also found to induce diverse dynamic features on its short-time growth and diffusion in the GDS, which brings in an opposite trend toward a tumor's growth and diffusion.

Temporal correlations in neuronal spike trains are known to introduce redundancy to stimulus encoding. However, exact methods to describe how these correlations impact neural information transmission quantitatively are lacking. Here, we provide a general measure for the information carried by correlated rate modulations only, neglecting other spike correlations, and use it to investigate the effect of rate correlations on encoding redundancy. We derive it analytically by calculating the mutual information between a time-correlated, rate modulating signal and the resulting spikes of Poisson neurons. Whereas this information is determined by spike autocorrelations only, the redundancy in information encoding due to rate correlations depends on both the distribution and the autocorrelation of the rate histogram. We further demonstrate that at very small signal strengths the information carried by rate correlated spikes becomes identical to that of independent spikes, in effect measuring the signal modulation depth. In contrast, a vanishing signal correlation time maximizes information but does not generally yield the information of independent spikes. Overall, our study sheds light on the role of signal-induced temporal correlations for neural coding, by providing insight into how signal features shape redundancy and by establishing mathematical links between existing methods.

Using numerical simulations, we examine the dynamics of driven two-dimensional bidisperse disks flowing over quenched disorder. The system exhibits a series of distinct dynamical phases as a function of applied driving force and packing fraction, including a phase-separated state as well as a smectic state with liquid-like or polycrystalline features. At low driving forces, we find a clogged phase with an isotropic density distribution, while at intermediate driving forces the disks separate into bands of high and low densities with either liquid-like or polycrystalline structure in the high-density bands. In addition to the density phase separation, we find that in some cases there is a fractionation of the disk species, particularly when the disk size ratio is large. The species phase-separated regimes form a variety of patterns such as large disks separated by chains of smaller disks. Our results show that the formation of laning states can be enhanced by tuning the ratio of disk radius of the two species, due to the clumping of small disks in the interstitial regions between the large disks. This system could be experimentally realized using sterically interacting colloidal particles suspended in a viscous fluid driven over random pinning arrays or granular matter suspended in fluid moving over a random landscape.

We study the dynamics of a thin liquid film on a compliant substrate in the presence of thermocapillary effect. A set of long-wave equations are derived to investigate the effects of fluid gravity $\left(G\right)$, fluid inertia (Re), and Marangoni stresses (Ma) on the dynamics of the liquid film and the compliant substrate. By performing linear stability analysis and time-dependent computations of the long-wave equations, we examine two different cases: thin-film flows on a horizontally compliant substrate $(\beta =0$, where $\beta$ is the inclined angle) and down a vertically compliant substrate $\left(\beta =\pi /2\right)$, respectively. For $\beta =0$, we neglect fluid inertia and identify two different modes: (1) sinuous mode, where the deformations of liquid-air and liquid-substrate interfaces are in phase, which is induced by the fluid gravity, and (2) varicose mode, where the deformations of two interfaces are in phase opposition, which is induced by the Marangoni stresses. For $\beta =\pi /2$, we consider a weak fluid inertia and only observe the varicose mode driven by fluid inertia and Marangoni stresses. However, because the gravity direction is parallel to the substrate, the fluid gravity modifies the varicose mode, making the deformations of two interfaces out of phase. In particular, we also seek the nonlinear traveling-wave solutions in the case of $\beta =\pi /2$, revealing that fluid inertia and/or heating effect enhance the height and speed of the traveling waves. In both cases, the introduction of a strong wall heating gives rise to large deformations of both the thin liquid film and the compliant substrate.

Using the renormalization-group approach, we consider an analytic theory describing the formation of a self-focusing structure of a laser beam in a plasma with relativistic nonlinearity for a given radial intensity distribution at the entrance and derive approximate analytic solutions. We study three stationary self-focused waveguide propagation modes with respect to controlling laser-plasma parameters for a Gaussian radial intensity distribution at the plasma boundary. The proposed theory specifies the domains and their boundaries on the plane of the controlling parameters where (1) self-trapping, (2) self-focusing on the axis, and (3) tubular self-focusing solutions occur. We review the concept of the critical power and show that it must be correlated to the form of the entering light pulse and its value corresponding to the minimum power that admits self-channeling can be significantly lower than the widely used value $17({\omega }^2/{\omega }_{\mathrm{pe}}^2)$ GW.

We study the dynamics of one-dimensional (1D) interacting particles simulated with the event-chain Monte Carlo algorithm (ECMC). We argue that previous versions of the algorithm suffer from a mismatch in the factor potential between different particle pairs (factors) and show that in 1D models, this mismatch is overcome by factor fields. ECMC with factor fields is motivated, in 1D, for the harmonic model, and validated for the Lennard-Jones model as well as for hard spheres. In 1D particle systems with short-range interactions, autocorrelation times generally scale with the second power of the system size for reversible Monte Carlo dynamics, and with its first power for regular ECMC and for molecular dynamics. We show, using simulations, that the autocorrelation time grows only with the square root of the system size for ECMC with factor fields. Mixing times, which bound the time to reach equilibrium from an arbitrary initial configuration, grow with the first power of the system size.

The time-dependent solution of the Fokker-Planck equation with bistable potentials is considered in terms of the eigenfunctions and eigenvalues of the linear Fokker-Planck operator. The Fokker-Planck equation is the high friction limit of the corresponding Kramers' equation. Two different potentials are considered defined with a constant diffusion coefficient, $\epsilon$, and position-dependent drift coefficients. The smallest nonzero eigenvalue of the Fokker-Planck operator, ${\lambda }_1$, provides the long-time rate coefficient for the transformation of the different species in the two stable states. A novel pseudospectral method with nonclassical polynomials is applied to this class of systems. The convergence of the eigenvalues and eigenfunctions of the Fokker-Planck operator versus the number of basis functions is studied and compared with previous results. The results are consistent with Kramers' theory, and a linear relationship between $ln{\lambda }_1$ and $1/\epsilon$ for sufficiently small $\epsilon$ values is verified. A comparison with analytic approximations to ${\lambda }_1$ is provided.

Thermal rectification and heat amplification are investigated in a nonequilibrium V-type three-level system with quantum interference. By applying the Redfield master equation combined with full counting statistics, we analyze the steady-state heat transport. The noise-induced interference is found to be able to rectify the heat current, which paves a new way to design quantum thermal rectifier. Within the three-reservoir setup, the heat amplification is clearly identified far from equilibrium, which is in absence of the negative differential thermal conductance.

Algorithms for community detection are usually stochastic, leading to different partitions for different choices of random seeds. Consensus clustering has proven to be an effective technique to derive more stable and accurate partitions than the ones obtained by the direct application of the algorithm. However, the procedure requires the calculation of the consensus matrix, which can be quite dense if (some of) the clusters of the input partitions are large. Consequently, the complexity can get dangerously close to quadratic, which makes the technique inapplicable on large graphs. Here, we present a fast variant of consensus clustering, which calculates the consensus matrix only on the links of the original graph and on a comparable number of additional node pairs, suitably chosen. This brings the complexity down to linear, while the performance remains comparable as the full technique. Therefore, our fast consensus clustering procedure can be applied on networks with millions of nodes and links.

Motivated by the observation of the storage of excess elastic free energy, prestress, in cross-linked semiflexible networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random potential. The random potential, which represents the effect of cross-linking to other filaments, is assumed to have a finite correlation length $\xi$ and mean strength $V_0$. We examine statistical distribution of curvature in filament with thermal persistence length ${\ell }_P$ and length $L_0$ in the limit in which ${\ell }_P\gg L_0$. We compare our theoretical predictions to finite-element Brownian dynamics simulations. Finally, we comment on the validity of replica field techniques in addressing these questions.

Equilibrium and nonequilibrium molecular dynamics (MD) are used to investigate the thermal conductivity of binary hard-sphere fluids. It is found that the thermal conductivity of a mixture can not only lie outside the series and parallel bounds set by their pure component values, but can lie beyond even the pure component fluid values. The MD simulations verify that revised Enskog theory can accurately predict nonequilibrium thermal conductivities at low densities and this theory is applied to explore the model parameter space. Only certain mass and size ratios are found to exhibit conductivity enhancements above the parallel bounds and dehancement below the series bounds. The anomalous dehancement is experimentally accessible in helium-hydrogen gas mixtures and a review of the literature confirms the existence of mixture thermal conductivity below the series bound and even below the pure fluid values, in accordance with the predictions of revised Enskog theory. The results reported here may reignite the debate in the nanofluid literature on the possible existence of anomalous thermal conductivities outside the series and parallel bounds as this Rapid Communication demonstrates they are a fundamental feature of even simple fluids.

Liquid Sn droplets were irradiated with shaped bursts of picosecond laser pulses. The shapes of the deforming droplets following the impact of the recoil pressure induced by these bursts were imaged using a high-speed shadowgraph system. The rupture time ${\tilde{t}}_b$ of the droplet expanding as a thin fluid film was measured for each case. A Rayleigh-Taylor instability analysis is done in order to determine the dependences governing ${\tilde{t}}_b$. The evidence supports the hypothesis that the initial perturbations of the developing Rayleigh-Taylor instabilities are on the order of the ablation depth and that there is a lower cutoff wavelength of these initial perturbations of $\sim 10\mu \mathrm{m}$.

We investigate size effects in phononic energy transport in a system of two nanoparticles interconnected by a molecule and attached to thermal contacts also by molecules. In the considered closed system, the nanoparticles and contacts are described by ensembles of finite numbers of harmonic oscillators within the Drude-Ullersma model. The macroscopic character of the contacts is simulated by a large value of the ratio $\mathrm{\Delta }/{\mathrm{\Delta }}_{\mathrm{B}}=n$ ($n>100)$ of mode spacings $\mathrm{\Delta }$ and ${\mathrm{\Delta }}_{\mathrm{B}}$ corresponding to the nanoparticles and contacts, respectively. Quasistatic energy transport on the timescale ${\mathrm{\Delta }}^{-1}$ is investigated. Equations describing the dynamics of the averaged eigenmode energies that belong to the nanoparticles and contacts are derived and solved. The resulting expressions for the energy current exiting (entering) the contacts as well as the energy current between the nanoparticles are obtained and investigated. The latter current accounts for energy accumulation by (depletion from) the nanoparticles. The finite size effects result in reversibility features and peculiarities at time moments $t=2\pi \ell {\mathrm{\Delta }}^{-1}$ for non-negative integers $\ell$. They are qualitatively the same as in a previously studied system of two equal nanoparticles mediated by a molecule, despite the presence of the macroscopic contacts. The thermal conductance of the whole nanojunction is derived and explored. The energy currents and thermal conductance of the nanojunction in a case when its parameters are known from the experiment are computed using the developed model.

In this paper, we apply machine learning methods to study phase transitions in certain statistical mechanical models on the two-dimensional lattices, whose transitions involve nonlocal or topological properties, including site and bond percolations, the $XY$ model, and the generalized $XY$ model. We find that using just one hidden layer in a fully connected neural network, the percolation transition can be learned and the data collapse by using the average output layer gives correct estimate of the critical exponent $\nu$. We also study the Berezinskii-Kosterlitz-Thouless transition, which involves binding and unbinding of topological defects, vortices and antivortices, in the classical $XY$ model. The generalized $XY$ model contains richer phases, such as the nematic phase, the paramagnetic and the quasi-long-range ferromagnetic phases, and we also apply machine learning method to it. We obtain a consistent phase diagram from the network trained with only data along the temperature axis at two particular parameter $\mathrm{\Delta }$ values, where $\mathrm{\Delta }$ is the relative weight of pure $XY$ coupling. Aside from using the spin configurations (either angles or spin components) as the input information in a convolutional neural network, we devise a feature engineering approach using the histograms of the spin orientations in order to train the network to learn the three phases in the generalized $XY$ model and demonstrate that it indeed works. The trained network by using system size $L\times L$ can be used to the phase diagram for other sizes ($L^{\prime }\times L^{\prime }$, where $L^{\prime }\ne L$) without any further training.