Molecular dynamics simulations are used to investigate the rate and temperature dependence of the slip length in thin liquid films confined by smooth, thermal substrates. In our setup, the heat generated in a force-driven flow is removed by the thermostat applied on several wall layers away from liquid-solid interfaces. We found that for both high and low wall-fluid interaction (WFI) energies, the temperature of the fluid phase rises significantly as the shear rate increases. Surprisingly, with increasing shear rate, the slip length approaches a constant value from above for high WFI energies and from below for low WFI energies. The two distinct trends of the rate-dependent slip length are rationalized by examining $S({\mathbf{G}}_1)$, the height of the main peak of the in-plane structure factor of the first fluid layer (FFL) together with $D_{\mathrm{WF}}$, which is the average distance between the wall and FFL. The results of numerical simulations demonstrate that reduced values of the structure factor, $S({\mathbf{G}}_1)$, correlate with the enhanced slip, while smaller distances $D_{\mathrm{WF}}$ indicate that fluid atoms penetrate deeper into the surface potential leading to larger friction and smaller slip. Interestingly, at the lowest WFI energy, the combined effect of the increase of $S({\mathbf{G}}_1)$ and decrease of $D_{\mathrm{WF}}$ with increasing shear rate results in a dramatic reduction of the slip length.

Motivated by the modeling of the temporal structure of the velocity field in a highly turbulent flow, we propose and study a linear stochastic differential equation that involves the ingredients of an Ornstein-Uhlenbeck process, supplemented by a fractional Gaussian noise, of parameter $H$, regularized over a (small) time scale $\epsilon >0$. A peculiar correlation between these two plays a key role in the establishment of the statistical properties of its solution. We show that this solution reaches a stationary regime, which marginals, including variance and increment variance, remain bounded when $\epsilon \to 0$. In particular, in this limit, for any $H\in ]0,1[$, we show that the increment variance behaves at small scales as the one of a fractional Brownian motion of same parameter $H$. From the theoretical side, this approach appears especially well suited to deal with the (very) rough case $H<1/2$, including the boundary value $H=0$, and to design simple and efficient numerical simulations.

Approximate analytical methods are presented to calculate the overall orthotropic hydraulic permeability of a flow with low Reynolds number, passing through a bundle of parallel circular cylinders. Two particular distributions are considered: (i) arrays with ordered rectangular lattices and (ii) irregular nonrandom distributions for which the unit cell cross sections are elliptical. The standard unit cell models, originally developed by Happel and Kuwabara for a random distribution of cylinders, are adapted to the case of nonrandom distributions. The drag force on a representative cylinder in a direction perpendicular to its axis is obtained based on the standard unit cell model: the actual unit cell of rectangular or elliptical cross section is replaced with an “equivalent” cylindrical unit cell of diameter equal to the maximum width of the actual unit cell. Using the obtained drag forces and referring back to the original geometry of the unit cell, closed-form approximate expressions for the overall permeabilities in the perpendicular directions are obtained. Numerical comparisons with more sophisticated approaches confirm the good efficiency of the presented approach, especially in the range of low solid volume fraction, i.e., of high porosity. Previous studies have revealed that, for the parallel fluid flow, the variation of permeability with aspect ratio (or in general the lateral arrangement) of parallel cylinders is generally weak. These observations suggest that Happel's model for parallel permeability in a random distribution of cylinders could be a good approximation for parallel permeabilities in nonrandom distributions with the same volume fraction.

Sintering—or coalescence—of viscous droplets is an essential process in many natural and industrial scenarios. Current physical models of the dynamics of sintering are limited by the lack of an explicit account of the evolution of microstructural geometry. Here, we use high-speed time-resolved x-ray tomography to image the evolving geometry of a sintering system of viscous droplets, and use lattice Boltzmann simulations of creeping fluid flow through the reconstructed pore space to determine its permeability. We identify and characterize a topological inversion, from spherical droplets in a continuous interstitial gas, to isolated bubbles in a continuous liquid. We find that the topological inversion is associated with a transition in permeability-porosity behavior, from Stokes permeability at high porosity, to percolation theory at low porosity. We use these findings to construct a unified physical description that reconciles previously incompatible models for the evolution of porosity and permeability during sintering.

Presented here are observations that demonstrate how the deformation of millimetric cavitation bubbles by a uniform pressure gradient quenches single-collapse luminescence. Our innovative measurement system captures a broad luminescence spectrum (wavelength range, 300–900 nm) from the individual collapses of laser-induced bubbles in water. By varying the bubble size, driving pressure, and perceived gravity level aboard parabolic flights, we probed the limit from aspherical to highly spherical bubble collapses. Luminescence was detected for bubbles of maximum radii within the previously uncovered range, $R_0=1.5$–6 mm, for laser-induced bubbles. The relative luminescence energy was found to rapidly decrease as a function of the bubble asymmetry quantified by the anisotropy parameter $\zeta$, which is the dimensionless equivalent of the Kelvin impulse. As established previously, $\zeta$ also dictates the characteristic parameters of bubble-driven microjets. The threshold of $\zeta$ beyond which no luminescence is observed in our experiment closely coincides with the threshold where the microjets visibly pierce the bubble and drive a vapor jet during the rebound. The individual fitted blackbody temperatures range between $T_{\mathrm{lum}}=7000$ and $T_{\mathrm{lum}}=11500$ K but do not show any clear trend as a function of $\zeta$. Time-resolved measurements using a high-speed photodetector disclose multiple luminescence events at each bubble collapse. The averaged full width at half-maximum of the pulse is found to scale with $R_0$ and to range between 10 and 20 ns.

The Weibel instability from counterstreaming plasma flows is a basic process highly relevant for collisionless shock formation in astrophysics. In this paper we investigate, via two- and three-dimensional simulations, suitable configurations for laboratory investigations of the ion Weibel instability (IWI) driven by a fast quasineutral plasma flow launched into the target via the radiation pressure of an ultra-high-intensity laser pulse (“hole-boring” process). The use of S-polarized light at oblique incidence is found to be an optimal configuration for driving IWI, as it prevents the development of surface rippling observed at normal incidence that would lead to strong electron heating and would favor competing instabilities. Conditions for the evolution of IWI into a collisionless shock are also investigated.

Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to the fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a technique based on mode-elimination renormalization group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner in which we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.

The loop extrusion theory assumes that protein factors, such as cohesin rings, act as molecular motors that extrude chromatin loops. However, recent single molecule experiments have shown that cohesin does not show motor activity. To predict the physical mechanism involved in loop extrusion, we here theoretically analyze the dynamics of cohesin rings on a loop, where a cohesin loader is in the middle and unloaders at the ends. Cohesin monomers bind to the loader rather frequently and cohesin dimers bind to this site only occasionally. Our theory predicts that a cohesin dimer extrudes loops by the osmotic pressure of cohesin monomers on the chromatin fiber between the two connected rings. With this mechanism, the frequency of the interactions between chromatin segments depends on the loading and unloading rates of dimers at the corresponding sites.

In this paper, we show that diffusion phenomena in three-dimensional discontinuous media can be described as a random walk by two simple interface-correction methods, namely step-balance and fictitious-velocity corrections, which are completely different in a physical picture but equivalent in that the continuity of the random walk at interfaces is considered. In both corrections, asymmetric interface permeability of a random walker, which comes from ensuring the continuity, causes apparent confinement of the walker in higher-diffusivity layers for benchmark tests on heat diffusion in two-phase multilayered systems. Effective thermal conductivities (walker diffusivities) computed from the trajectories are in excellent agreement with the series and parallel conduction formulas, indicating the equivalence of the two corrections and the importance of ensuring the continuity of a random walk at interfaces.

To extend the continuous-time quantum walk (CTQW) to simulate $P$ distinguishable particles on a graph $G$ composed of $N$ vertices, the Hamiltonian of the system is expanded to act on an $N^P$-dimensional Hilbert space, in effect, simulating the multiparticle CTQW on graph $G$ via a single-particle CTQW propagating on the Cartesian graph product $G^{\square P}$. The properties of the Cartesian graph product have been well studied, and classical simulation of multiparticle CTQWs are common in the literature. However, the above approach is generally applied as is when simulating indistinguishable particles, with the particle statistics then applied to the propagated $N^P$ state vector to determine walker probabilities. We address the following question: How can we modify the underlying graph structure $G^{\square P}$ in order to simulate multiple interacting fermionic CTQWs with a reduction in the size of the state space? In this paper, we present an algorithm for systematically removing “redundant” and forbidden quantum states from consideration, which provides a significant reduction in the effective dimension of the Hilbert space of the fermionic CTQW. As a result, as the number of interacting fermions in the system increases, the classical computational resources required no longer increases exponentially for fixed $N$.

We consider a ring of phase oscillators with nonlocal coupling strength and heterogeneous phase lags. We analyze the effects of heterogeneity in the phase lags on the existence and stability of a variety of steady states. A nonlocal coupling with heterogeneous phase lags that allows the system to be solved analytically is suggested and the stability of solutions along the Ott-Antonsen invariant manifold is explored. We present a complete bifurcation diagram for stationary patterns including the uniform drift and modulated drift states as well as chimera state, which reveals that the stable modulated drift state and a continuum of metastable drift states could occur due to the heterogeneity of the phase lags. We verify our theoretical results using the direct numerical simulations of the model system.

Simplicial complexes are now a popular alternative to networks when it comes to describing the structure of complex systems, primarily because they encode multinode interactions explicitly. With this new description comes the need for principled null models that allow for easy comparison with empirical data. We propose a natural candidate, the simplicial configuration model. The core of our contribution is an efficient and uniform Markov chain Monte Carlo sampler for this model. We demonstrate its usefulness in a short case study by investigating the topology of three real systems and their randomized counterparts (using their Betti numbers). For two out of three systems, the model allows us to reject the hypothesis that there is no organization beyond the local scale.

Perturbation analysis of neural field theory is used to derive eigenmodes of neural activity on a cortical hemisphere, which have previously been calculated numerically and found to be close analogs of spherical harmonics, despite heavy cortical folding. The present perturbation method treats cortical folding as a first-order perturbation from a spherical geometry. The first nine spatial eigenmodes on a population-averaged cortical hemisphere are derived and compared with previous numerical solutions. These eigenmodes contribute most to brain activity patterns such as those seen in electroencephalography and functional magnetic resonance imaging. The eigenvalues of these eigenmodes are found to agree with the previous numerical solutions to within their uncertainties. Also in agreement with the previous numerics, all eigenmodes are found to closely resemble spherical harmonics. The first seven eigenmodes exhibit a one-to-one correspondence with their numerical counterparts, with overlaps that are close to unity. The next two eigenmodes overlap the corresponding pair of numerical eigenmodes, having been rotated within the subspace spanned by that pair, likely due to second-order effects. The spatial orientations of the eigenmodes are found to be fixed by gross cortical shape rather than finer-scale cortical properties, which is consistent with the observed intersubject consistency of functional connectivity patterns. However, the eigenvalues depend more sensitively on finer-scale cortical structure, implying that the eigenfrequencies and consequent dynamical properties of functional connectivity depend more strongly on details of individual cortical folding. Overall, these results imply that well-established tools from perturbation theory and spherical harmonic analysis can be used to calculate the main properties and dynamics of low-order brain eigenmodes.

We discuss a deviation of the fluctuation-dissipation relation (FDR) in a driven superdiffusive system as exemplified by polymer stretching. The superdiffusion is found by monitoring momentum transfer to a tracer, which is a conjugate observable with the position. Molecular-dynamics simulation demonstrates that the FDR deviates during the nonequilibrium transient process. We then propose nonequilibrium mode analysis for superdiffusion, which is a counterpart to that for driven subdiffusion. The mode analysis yields results that are in qualitative agreement with the simulation results, suggesting that the fluctuations of the stiffness in the system from initial equilibrium to stretching account for the FDR deviation.

In this paper, we demonstrate the presence of a photonic band gap for a diamond lattice structure made of particles with normal anchoring inside a cholesteric liquid crystal. As is typical for liquid crystals (LCs), there is considerable contrast between the dielectric constant parallel ${\epsilon }_{\parallel }$ and perpendicular ${\epsilon }_{\perp }$ to the director, with ${\epsilon }_{\parallel }/{\epsilon }_{\perp }\sim 4$ here. It is shown that the size of the photonic band gap is directly related to the size of colloidal particles and the contrast between the dielectric constant in the particles and the extreme values of $\epsilon$ in the LC medium (one needs either $\epsilon$ in the particle much smaller than ${\epsilon }_{\perp } or$ much bigger than ${\epsilon }_{\parallel }$). No opening is seen in the band diagrams for small particles. For larger particles a partial gap opens when the particles are composed of very low dielectric material but never a complete gap. On the other hand, a complete gap starts to be revealed when the size of the colloidal particles is increased and when a high dielectric constant is used for filling inside the particles. The maximum size of the gap is observed when the particles are large enough so that their surfaces overlap.

General quadratic Hamiltonian models, describing the interaction between liquid-crystal molecules (typically with $D_{2h}$ symmetry), take into account couplings between their uniaxial and biaxial tensors. While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram (contravening in some regions of model parameter space), the predictions of mean-field theory, and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase. The free-energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes. On the one hand, these profiles account for the unusual thermal behavior of the biaxial order parameter under significant destabilizing influence from the cross terms. On the other, they also allude to the possibility that in real systems, these complexities might indeed be inhibiting the formation of a low-temperature biaxial order itself—perhaps reflecting the difficulties in their ready realization in the laboratory.

Experiments in several laboratories have demonstrated that identical materials brought into repeated contact generate unexplained and growing surface charge domains. Here we show that the growth of charge from these experiments can be fitted to a previously developed first-principles model for contact charging based on feedback of random surface polarizations. Surprisingly this mechanism, which leads to exponential growth in colliding granular beds, can also explain nonexponential growth of surface charging, as well as predicting spatiotemporal growth of charge domains and their dependencies on material parameters.

The positioning, adsorption, and movement of water on substrates is dependent upon the chemical nature and arrangement of the atoms of the surface. Therefore the behavior of water molecules on a substrate is a reflection of properties of the surface. Based on this premise, graphene and gold substrates were chosen to study this subject from a molecular perspective. In this work, the structural and dynamical behaviors of a water nanodroplet on Au (100) and the graphene interfaces have been studied by molecular dynamics simulation. The results have shown how the structural and dynamical behaviors of water molecules at the interface reflect the characteristics of these surfaces. The results have demonstrated that residence time and hydrogen bonds’ lifetime at the water-Au (100) interface are bigger than at the water-graphene interface. Energy contour map analysis indicates a more uniform surface energy on graphene than on the gold surface. The obtained results illustrate that water clusters on gold and graphene form tetramer and hexamer structures, respectively. Furthermore, the water molecules are more ordered on the gold surface than on graphene. The study of hydrogen bonds showed that the order, stability, and the number of hydrogen bonds is higher on the gold surface. The positioning pattern of water molecules is also similar to the arrangement of gold atoms while no regularity was observed on graphene. The study of dynamical behavior of water molecules revealed that the movement of water on gold is much less than on graphene which is in agreement with the strong water-gold interaction in comparison to the water-graphene interaction.