We study numerically the collective dynamics of self-rotating non-aligning particles by considering a monolayer of spheres driven by constant clockwise or counterclockwise torques. We show that hydrodynamic interactions alter the emergence of large-scale dynamical patterns compared to those observed in dry systems. In dilute suspensions, the flow stirred by the rotors induces clustering of opposite-spin rotors, while at higher densities same-spin rotors phase separate. Above a critical rotor density, dynamic hexagonal crystals form. Our findings underscore the importance of inclusion of the many-body, long-range hydrodynamic interactions in predicting the phase behavior of active particles.PACS numbers: 47.57. 47.63.mf, 83.10.Tv, 64.75.Xc Systems of motile and interacting units can exhibit non-equilibrium phenomena such as self-organization and directed motion at large scales [1]. Theoretical studies of active matter report clustering [2], phase separations [3][4][5] and rotating structures [6]. Some of these phenomena have been observed in experiments of bacterial suspensions [7] or chemically-activated motile colloids [8].The collective motion of translating units such as bacteria has received much interest [1]. On the other hand, little is known about spinning units, partly because such systems were realized experimentally only recently. Active rotation of particles can be achieved using external forcing such as rotating magnetic fields [9,10], uniform electric fields (the Quincke rotation effect) [11] or chemical reactions [12]. Self-assembly from polymers by motile bacteria can create micro-rotors [13]. In biological systems, the dancing volvox [14], uniflagellar algae C. reinhardtii [15] and bacteria T. majus [16] exhibit rotorlike behaviors. Rising interest in rotor systems generated theoretical studies exploring rotor pair dynamics [17,18], non-equilibrium structure formation [19], dynamics at interfaces [20,21], rheology of suspensions [22,23], and phase separation driven by active rotation [24,25].Models of the collective behavior of active matter often neglect particle motion due to the flow stirred by the other particles [4,5,24,26], tacitly assuming that the observed phase behavior of the "dry" system would persist in a system with fluid motion. However in the viscosity-dominated world of colloidal-size particles, hydrodynamic interaction generates a long-range correlation, which can play an important role in the self-organization in many-body systems [27][28][29]. For example, in the studies of micro-swimmers, it was found that the hydrodynamic interactions determine the collective motion of squirmers (self-propelled spheres with no aligning interaction) [30] and the recently observed self-organization of bacteria into a macro-scale bidirectional vortex when confined inside a drop [31] can only be explained by accounting for the fluid-mediated interactions [32]. It is the hydrodynamic interactions that cause two point rotors spinning in the opposite direction to translate [18] or undergo complex...

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Fully three-dimensional numerical simulations of concentrated suspensions of O(1000) particles in a Couette flow at zero Reynolds number are performed with the goal of determining the wall effects on concentrated suspensions of non-colloidal particles. The simulations, based on the force-coupling method, are performed for 0.2 6 φ 6 0.4 and 10 < L y /a < 30, where φ denotes the volume fraction and L y and a are, respectively, the channel height and the particle radius. It is shown that the suspensions can be divided into three regions depending on the microstructures; the wall region where a structured particle layering is dominant, the core region in which the suspension field is quasi-homogeneous, and the buffer region which shows the characteristics of both the particle layer and the shear structure. The width of the inhomogeneous region (wall and buffer) is a function of φ and not sensitive to L y /a, once L y /a is larger than a threshold. Rheological properties in the inhomogeneous and quasi-homogeneous regions are investigated. The particle stresses are compared with previous rheological models.

This paper presents a numerical study of the dynamic self-assembly of neutrally buoyant particles rotating in a plane in a viscous fluid. The particles experience simultaneously a magnetic torque that drives their individual spinning motion, a magnetic attraction toward the center of the domain, and flow-induced interactions. A hydrodynamic repulsion balances the centripetal attraction of the magnetized particles and leads to the formation of an aggregate of several particles that rotates with a precession velocity related to the inter-particle distance. This dynamic self-assembly is stable (but not stationary) and the morphology depends on the number of particles. The repulsion force between the particles is shown to be the result of the secondary flow generated by each particle at low but nonzero Reynolds number. Comparisons are made with analogous experiments of spinning disks at a liquid–air interface, where it is found that the variation in the characteristic scales of the aggregate with the rotation rate of individual particles are consistent with the numerical results.

The Lagrangian dispersion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Lagrangian velocity and acceleration along a particle trajectory are computed by employing several interpolation schemes. Among the schemes tested, the four-point Hermite interpolation in the homogeneous directions combined with Chebyshev polynomials in the wall-normal direction seems to produce most reliable Lagrangian statistics. Inhomogeneity of Lagrangian statistics in turbulent boundary layer is investigated by releasing many particles at several different wall-normal locations and tracking those particles. The fluid particle dispersion and Lagrangian structure function of velocity are investigated for the Kolmogorov similarity. The behavior of the Lagrangian integral time scales, Kolmogorov constants a 0 and C 0 of the velocity structure function near the wall are discussed. The intermittent behavior of the fluid particle acceleration is also examined by kurtosis of the Lagrangian structure function. Finally, the effect of the initial particle location on the dispersion is analyzed by the probability density function of particle position at several downstream locations.

We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Short-Term Memory (LSTM) network. It is shown that, when the numerical discretization is used, the function estimation problem can be solved by a multi-label classification problem. A penalized maximum log likelihood method is proposed to impose a smoothness condition in the prediction of the probability distribution. We show that the time evolution of the probability distribution can be computed by a high-dimensional integration of the transition probability of the LSTM internal states. A Monte Carlo algorithm to approximate the high-dimensional integration is outlined. The behavior of DE-LSTM is thoroughly investigated by using the Ornstein-Uhlenbeck process and noisy observations of nonlinear dynamical systems; Mackey-Glass time series and forced Van der Pol oscillator. It is shown that DE-LSTM makes a good prediction of the probability distribution without assuming any distributional properties of the stochastic process. For a multiple-step forecast of the Mackey-Glass time series, the prediction uncertainty, denoted by the 95% confidence interval, first grows, then dynamically adjusts following the evolution of the system, while in the simulation of the forced Van der Pol oscillator, the prediction uncertainty does not grow in time even for a 3,000-step forecast.

Volume leakage has recently been identified as a major threat to the security of cryptographic cloud-based data structures by Kellaris et al. [CCS'16] (see also the attacks in Grubbs et al. [CCS'18] and Lacharité et al. [S&P'18]). In this work, we focus on volume-hiding implementations of encrypted multi-maps as first considered by Kamara and Moataz [Eurocrypt'19]. Encrypted multi-maps consist of outsourcing the storage of a multi-map to an untrusted server, such as a cloud storage system, while maintaining the ability to perform private queries. Volume-hiding encrypted multi-maps ensure that the number of responses (volume) for any query remains hidden from the adversarial server. As a result, volume-hiding schemes can prevent leakage attacks that leverage the adversary's knowledge of the number of query responses to compromise privacy.We present both conceptual and algorithmic contributions towards volume-hiding encrypted multi-maps. We introduce the first formal definition of volume-hiding leakage functions. In terms of design, we present the first volume-hiding encrypted multi-map dprfMM whose storage and query complexity are both asymptotically optimal. Furthermore, we experimentally show that our construction is practically efficient. Our server storage is smaller than the best previous construction while we improve query complexity by a factor of 10-16x.In addition, we introduce the notion of differentially private volume-hiding leakage functions which strikes a better, tunable balance between privacy and efficiency. To accompany our new notion, we present a differentially private volume-hiding encrypted multimap dpMM whose query complexity is the volume of the queried key plus an additional logarithmic factor. This is a significant improvement compared to all previous volume-hiding schemes whose query overhead was the maximum volume of any key. In natural settings, our construction improves the average query overhead by a factor of 150-240x over the previous best volume-hiding construction even when considering small privacy budget of ϵ = 0.2.• Security and privacy → Management and querying of encrypted data;

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