We developed an analytical theoretical method to determine the microscopical structure of weakly to moderately sheared colloidal suspensions in dilute conditions. The microstructure is described by the static structure factor, obtained by solving the stationary two-body Smoluchowski advection-diffusion equation. The singularly perturbed partial differential equation problem is solved by performing an angular averaging over the extensional and compressing sectors and by the rigorous application of boundary-layer theory (intermediate asymptotics). This allows us to expand the solution to a higher order in Péclet with respect to previous methods. The scheme is independent of the type of interaction potential. We apply it to the example of charge-stabilized colloidal particles interacting via the repulsive Yukawa potential and study the distortion of the structure factor. It is predicted that the distortion is larger at small wave vectors $k$ and its dependence on Pe is a simple power law. At increasing Pe, the main peak of the structure factor displays a broadening and shift toward lower $k$ in the extensional sectors, which indicates shear-induced spreading out of particle correlations and neighbor particles locally being dragged away from the reference one. In the compressing sectors, instead, a narrowing and shift toward high $k$ is predicted, reflecting shear-induced ordering near contact and concomitant depletion in the medium range. An overall narrowing of the peak is also predicted for the structure factor averaged over the whole solid angle. Calculations are also performed for hard spheres, showing good overall agreement with experimental data. It is also shown that the shear-induced structure factor distortion is orders of magnitude larger for the Yukawa repulsion than for the hard spheres.

Direct numerical simulations of electroconvection instability near an ion-selective surface are conducted using a mesoscopic lattice Boltzmann method (LBM). An electrohydrodynamic model of ion transport and fluid flow is presented. We numerically solve the Poisson-Nernst-Planck equations for the electric field and the Navier-Stokes equations for the flow field. The results cover Ohmic, limiting, and overlimiting current regimes, and they are in good agreement with the asymptotic analytical solution for the relationship between current and voltage. The influences of different ion transport mechanisms on the voltage-current relationship are discussed. The results reveal that the electroconvection mechanism is as important as other ion transport mechanisms in electrohydrodynamic flow. By comparing the contribution of different regions in the numerical domain, we find that the flow in the extended space charge layer is dominated by electroconvection. We also study the influences of multiple driving parameters, and the electrohydrodynamic coupling constant plays a dominant role in triggering convective instability. The flow pattern and ion concentration distribution are described in detail. Moreover, the route of flow from steady state to periodic oscillation and then to chaos is discussed.

Selective withdrawal is a desired phenomenon in transferring oil from large caverns in the U.S. Strategic Petroleum Reserve (SPR), because entrainment of oil at the time during withdrawal poses a risk of contaminating the environment. Motivated to understand selective withdrawal in an SPR-like orientation, we performed experiments in order to investigate the critical submergence depth as a function of critical flow rate. For the experiments, a tube was positioned through a liquid-liquid interface that draws the lower liquid upward, avoiding entrainment of the upper fluid. Analysis of the normal stress balance across the interface produced a Weber number, utilizing dynamic pressure scaling, that predicted the transition to entrainment. Additionally, an inviscid flow analysis was performed assuming an ellipsoidal control volume surface that produced a linear relationship between the Weber number and the scaled critical submergence depth. This analytical model was validated using the experimental data, resulting in a robust model for predicting transition from selective withdrawal to entrainment.

We model a class of discrete-time information ratchet with a finite tape and explore its thermodynamic consequence as a Maxwell demon. We found that, although it supports the operational regime of an engine or eraser, it cannot typically sustain these thermodynamic functionalities due to eventual equilibration as a result of the finite information capacity of the tape. Nonetheless, cumulative work can be accrued or expended through successive tape scans and we prove that at all time the ratchet obeys the information processing second law (IPSL). Unlike the IPSL for the infinite-tape ratchet which operates only at the stationary state, the IPSL here is applicable also at the transient phase of the ratchet operation. We explore two ratchet designs with the single-state perturbed coin (PC) ratchet being the simplest ratchet without memory, while the double-state modified Boyd's (MB) ratchet is the simplest ratchet with memory. Our analysis shows that the MB ratchet can harness correlation to accumulate more work by having a larger time constant to reach steady state relative to the PC ratchet.

We investigate the phase diagram and the nature of the phase transitions of three-dimensional lattice gauge-Higgs models obtained by gauging the ${\mathbb{Z}}_N$ subgroup of the global ${\mathbb{Z}}_q$ invariance group of the ${\mathbb{Z}}_q$ clock model ($N$ is a submultiple of $q$). The phase diagram is generally characterized by the presence of three different phases, separated by three distinct transition lines. We investigate the critical behavior along the two transition lines characterized by the ordering of the scalar field. Along the transition line separating the disordered-confined phase from the ordered-deconfined phase, standard arguments within the Landau-Ginzburg-Wilson framework predict that the behavior is the same as in a generic ferromagnetic model with ${\mathbb{Z}}_p$ global symmetry, $p$ being the ratio $q/N$. Thus, continuous transitions belong to the Ising and to the O(2) universality class for $p=2$ and $p\ge 4$, respectively, while for $p=3$ only first-order transitions are possible. The results of Monte Carlo simulations confirm these predictions. There is also a second transition line, which separates two phases in which gauge fields are essentially ordered. Along this line we observe the same critical behavior as in the ${\mathbb{Z}}_q$ clock model, as it occurs in the absence of gauge fields.

We investigate the thermal relaxation of an ideal gas from a nonequilibrium stationary state. The gas is enclosed between two walls, which initially have different temperatures. After making one of the walls adiabatic, the system returns to equilibrium. We notice two distinct modes of heat transport and associated timescales: one connected with a traveling heat front and the other with internal energy diffusion. At the heat front, which moves at the speed of sound, pressure, temperature, and density change abruptly, leaving lower values behind. This is unlike a shock wave, a sound wave, or a thermal wave. The front moves multiple times between the walls and is the dominant heat transport mode until surpassed by diffusion. We found that it can constitute an order 1 factor in shaping the dynamics of the outflow of internal energy. We found that cooling such a system is quicker than heating, and that hotter bodies cool down quicker than colder ones. The latter is known as the Mpemba effect.

The bulk viscosity of dilute argon gas is calculated using molecular dynamics simulations in the temperature range 150–500 K and is found to be proportional to density squared in the investigated range of densities 0.001–1 kg ${\mathrm{m}}^{-3}$. A comparison of the results obtained using Lennard-Jones and Tang-Toennies models of pair interaction potential reveals that the value of the bulk viscosity coefficient is sensitive to the choice of the pair interaction model. The inclusion of the Axilrod-Teller-Muto three-body interaction in the model does not noticeably affect the values of the bulk viscosity in dilute states, contrary to the previously investigated case of dense fluids.

We analyze the dynamics of quantum supercooled liquids in terms of tagged particle dynamics. Unlike the classical case, uncertainty in the position of a particle in quantum liquid leads to qualitative changes. We demonstrate these effects in the dynamics of the first two moments of displacements, namely, the mean-squared displacement, $\langle \mathrm{\Delta }{r}^2\left(t\right)\rangle$, and $\langle \mathrm{\Delta }{r}^4\left(t\right)\rangle$. Results are presented for a hard-sphere liquid using mode-coupling theory formulation and simulation on a binary Lennard-Jones liquid. As the quantumness (controlled by the de Broglie thermal wavelength) is increased, a nonzero value of the moments at zero time leads to significant deviations from the classical behavior in the initial dynamics. Initial displacement shows ballistic behavior $\langle \mathrm{\Delta }{r}^2\left(t\right)\rangle \sim t^2$, but, as a result of large uncertainty in the position, the dynamical effects become weaker with increasing quantumness over this timescale.

We numerically study turbulent Rayleigh-Bénard (RB) convection under spatial temperature modulation, where the bottom temperature varies sinusoidally around a mean value in space. Both two- and three-dimensional simulations are performed over the Rayleigh number range ${10}^7\le \text{Ra}\le {10}^{10}$ and the wave number range $1\le k\le 120$ at fixed Prandtl number $\text{Pr}=0.7$. It is demonstrated that spatial temperature modulation with small wave numbers can enhance the global heat transfer (characterized by the Nusselt number $\text{Nu}$) in the turbulent regime, while $\text{Nu}$ is close to that in standard RB convection in the case of large wave numbers. Further, we propose two characteristic modulation length scales: one is the penetration depth ${\delta }_k$ above which spatial modulation is negligible, the other is the inversion depth ${\delta }_{k2}$ below which there exists a stable inverse temperature gradient. Based on the relative thickness of the thermal boundary layer (BL) ${\delta }_{\mathrm{th}}$ compared with these two length scales, the underlying modulation mechanism is physically explained and three regimes are identified: (1) an unperturbed BL regime (${\delta }_k<{\delta }_{\mathrm{th}}$), in which the modulation effect does not penetrate through the thermal BL and $\text{Nu}$ is nearly unchanged; (2) a partially modulated BL regime (${\delta }_{k2}<{\delta }_{\mathrm{th}}<{\delta }_k$), in which hot spots trigger more plume emissions from the thermal BL, resulting in $\text{Nu}$ enhancement; and (3) a fully modulated BL regime (${\delta }_{\mathrm{th}}<{\delta }_{k2}$), in which the stable temperature inversion over the cold phases begins to affect convective flows, which alters the trend of $\text{Nu}$ enhancement.

In this paper, a lattice Boltzmann method (LBM) for the fluid-structure interaction of an incompressible neo-Hookean medium is proposed. The objective is to use the lattice Boltzmann method to model the fluid and the solid domains at the same time, and thus avoid coupling two solvers, one for the fluid and one for the structure. The specific case of a neo-Hookean incompressible medium allows us to use a Eulerian formulation for the structure problem, which resembles the Navier-Stokes equation. Then, a macroscopic multiphase equation can be used to model the fluid and structure problems together. Next, the LBM approach is deduced from this macroscopic multiphase formulation of the fluid-structure interaction problem. It consists in extending the LBM to the solid domain by adding a tensor term in the equilibrium function of the collision operator. The effect of the added tensor term is to cancel in the solid domain the viscous fluid constraints and add neo-Hookean constraints. Thus, only the third moment of the LBM is modified, the first two being conserved, and only the constraints in the macroscopic Navier-Stokes equation are changed. The LBM scheme obtained can then model the interaction of a fluid and a structure composed of an incompressible neo-Hookean medium with a single solver for the fluid and the solid. Two additional equations are used, one to track the fluid and solid domains with the Cahn-Hilliard equation, and the other to compute the solid displacement field by a finite-difference scheme. The proposed method is applied successfully on three cases from the literature.

Flow of viscoelastic polymer solutions in curved channels exhibits instability caused by the elastic nature of polymers even at low Reynolds numbers. However, scaling of the onset of this purely elastic instability in semidilute polymer solutions has not been previously reported. Here we experimentally investigate the flow of highly elastic polymer solutions above their overlap concentrations using pressure measurements and particle image velocimetry. We demonstrate that the onset of instability can be scaled by including shear dependent rheological properties of the polymer solutions in the nonlinear stability analysis. As a result, a universal criterion as function of normalized polymer concentration is provided for scaling the onset of purely elastic instability in the semidilute regime regardless of the type and molecular weight of the polymer.

We consider finite-dimensional systems of linear stochastic differential equations ${\partial }_t{x}_k\left(t\right)=A_{kp}\left(t\right)x_p\left(t\right)$, $\mathbf{A}\left(t\right)$ being a stationary continuous statistically isotropic stochastic process with values in real $d\times d$ matrices. We suppose that the laws of $\mathbf{A}\left(t\right)$ satisfy the large-deviation principle. For these systems, we find exact expressions for the Lyapunov and generalized Lyapunov exponents and show that they are determined in a precise way only by the rate function of the diagonal elements of $\mathbf{A}$.

SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton, Proctor, and Kutz, Proc. Natl. Acad. Sci. USA 113, 3932 (2016)]. In this article, we propose an extension of the SINDy method that learns systems of differential equations in cases where some of the variables are not observed. Our extension is based on regressing a higher order time derivative of a target variable onto a dictionary of functions that includes lower order time derivatives of the target variable. We evaluate our method by measuring the prediction accuracy of the learned dynamical systems on synthetic data and on a real data set of temperature time series provided by the Réseau de Transport d'Électricité. Our method provides high quality short-term forecasts and it is orders of magnitude faster than competing methods for learning differential equations with latent variables.

We identify the poles and zeros of the scattering matrix of a simple quantum graph by means of systematic measurement and analysis of Wigner, transmission, and reflection complex time delays. We examine the ring graph because it displays both shape and Feshbach resonances, the latter of which arises from an embedded eigenstate on the real frequency axis. Our analysis provides a unified understanding of the so-called shape, Feshbach, electromagnetically induced transparency, and Fano resonances on the basis of the distribution of poles and zeros of the scattering matrix in the complex frequency plane. It also provides a first-principles understanding of sharp resonant scattering features and associated large time delay in a variety of practical devices, including photonic microring resonators, microwave ring resonators, and mesoscopic ring-shaped conductor devices. Our analysis involves use of the reflection time difference, as well as a comprehensive use of complex time delay, to analyze experimental scattering data.

We propose a coupled phase oscillator model with inertia and study the vortex motion in the model when the external force is applied at the boundaries. The vortex exhibits a glide motion when the external force is larger than a critical value. We find a transition from the pair annihilation to passing for the collision of the vortex and antivortex when the external force is changed. In the parameter range of the passing, a single vortex exhibits a reciprocal motion, which leads to desynchronization. When the external force is further increased, the multiplication of vortices occurs and the jump of the frequency profile increases. The desynchronization induced by the vortex motion is analogous to the plastic flow induced by the dislocation motion under the shear stress in solids. In perfect crystals without dislocations, the plastic flow hardly occurs. We further show that a vortex ring is generated when a vortex line passes through an impurity region, which corresponds to the Orowan loop in the theory of plasticity.

We discuss a cellular automaton simulating the process of reaching Heider balance in a fully connected network. The dynamics of the automaton is defined by a deterministic, synchronous, and global update rule. The dynamics has a very rich spectrum of attractors including fixed points and limit cycles, the length and number of which change with the size of the system. In this paper we concentrate on a class of limit cycles that preserve energy spectrum of the consecutive states. We call such limit cycles perfect. Consecutive states in a perfect cycle are separated from each other by the same Hamming distance. Also the Hamming distance between any two states separated by $k$ steps in a perfect cycle is the same for all such pairs of states. The states of a perfect cycle form a very symmetric trajectory in the configuration space. We argue that the symmetry of the trajectories is rooted in the permutation symmetry of vertices of the network and a local symmetry of a certain energy function measuring the level of balance and frustration of triads.

From two-dimensional (2D) numerical simulations of the motion of a circular intruder into a dry granular packing, we provide evidence for a specific force term in the case of unsteady motion in addition to the force corresponding to a steady motion. We show that this additional term is proportional to the acceleration of the intruder relative to the grains as the added-mass force known for simple fluids. This force term corresponds to a variation in the kinetic energy of the surrounding flow and is characterized by a coefficient $C_{AM}$ which is intrinsically linked to the nature of the granular media. An analytical calculation of the added-mass coefficient $C_{AM}$ is developed based on the specific velocity field known for 2D granular flow around a cylinder. The theoretical value is shown to depend on the grain-cylinder size ratio, in good agreement with the measurements from our unsteady simulations.

The interaction of a high-frequency laser with plasma in the presence of an inhomogeneous external magnetic field has been studied here with the help of particle-in-cell simulations. It has been shown that the laser enters the plasma as an extraordinary wave (X-wave), where the electric field of the wave oscillates perpendicular to both the external magnetic field and propagation direction and as it travels through the plasma, its dispersion property changes due to the inhomogeneity of the externally applied magnetic field. Our study shows that the X-wave's electromagnetic energy is converted to an electrostatic mode as it encounters the upper-hybrid (UH) resonance layer. In the later stage of the evolution, this electrostatic wave breaks and converts its energy to electron kinetic energy. Our study reveals two additional processes involved in decay of the electrostatic mode at the UH resonance layer. We have shown that the energy of the electrostatic mode at the upper-hybrid resonance layer also converts to a low-frequency lower-hybrid mode and high-frequency electromagnetic harmonic radiations. The dependence of energy conversion processes on the gradient of the external magnetic field has also been studied and analyzed.