Point-source inertial particle dispersion

We study a model of aligning self-propelled disks that nonreciprocally reorient the self-propulsion directions along the interparticle separation and towards the other disks. In the limit of small inertia and large softness, where conventional motility-induced phase separation is absent, we demonstrate that the homogeneous system at a small area fraction phase-separates into clusters and a low-density phase that, eventually, reenters the homogeneous phase with a monotonic increase in alignment strength. The disks inside the clusters move with a finite space-dependent speed, constantly shuttling between clusters through the surrounding low-density homogeneous phase while maintaining the hexatic structure properties within the clusters. The area fraction gradually increases from the periphery towards the center of the clusters with a negligible correlation of the velocity and propulsion direction inside the clusters. The novel collective behavior of reentrant phase separation is found to follow from both the limits of hard disks and extremely small inertia, tending towards the overdamped limit. However, important differences in the structural and dynamical properties are shown in the limit of hard disks and extremely small inertia, as compared to that for soft disks at finite inertia. We show that the cluster phase is associated with an effective temperature for a wide range of values of alignment strength, whereas an effective temperature is associated with the specific range of alignment in the low-density phase. We believe that the reentrant phase behavior in the limit of small area fraction and the remarkable properties of the clusters should be useful in understanding a wide range of physics issues, ranging from clogging and unclogging to information exchange and transport, in biological and synthetic self-propelled systems.

We derive a priori error estimates for the standard Galerkin and streamline diffusion finite element methods for the Fermi pencil-beam equation obtained from a fully three-dimensional Fokker–Planck equation in space and velocity variables. For a constant transport cross-section, there is a closed form analytic solution available for the Fermi equation with a data as product of Dirac functions. Our objective is to study the case of nonconstant, nonincreasing transport cross-section. Therefore we start with a theoretical, that is, a priori, error analysis for a Fermi model with modified initial data in L2. Then we construct semi-streamline-diffusion and characteristic streamline-diffusion schemes and consider an adaptive algorithm for local mesh refinements. To derive the stability estimates, for simplicity, we rely on the assumption of nonincreasing transport cross-section. Different numerical examples, in two space dimensions are justifying the theoretical results. Implementations show significant reduction of the computational error by using such adaptive procedure.

Abstract

Global attractors for gradient flows in metric spaces

Critical exponent for evolution equations in modulation spaces

This work presents measurements and analysis of sand particle velocities over a subaqueous dune with median sand diameter of 0.85 mm. Time‐lapse images of the mobile bed and an automated particle image velocimetry (PIV)‐based cross‐correlation method are used to obtain mean velocity of sand particles. This technique is shown to be consistent with measurements obtained with manual tracing. The measurements indicate an increase in mean particle velocity over a dune slope. Three regions are distinguished over the dune slope: (1) region of fluctuating particle velocity, (2) region of increasing particle velocity, and (3) region of maximum particle velocity. The observations are aligned with experimental and numerical modelling studies, indicating fluctuations in flow velocity over a dune stoss slope. We furthermore show that the standard deviation of the mean particle velocity is affected by the slope location and decreases from the lower slope towards the upper slope. The particle velocity variability is discussed in the context of general onset and cessation of sediment transport, the effect of the reattachment zone, sweep‐transport events, and the existence of superimposed bedforms. With this work we bridge the gap between measurements of bedload transport at the particle‐scale and at the bedform‐scale. © 2019 John Wiley & Sons, Ltd.

Nonuniform irradiation conditions (NUIC) of a photovoltaic (PV) array pose a major challenge to optimal power utilization due to multiple power peaks (consisting of multiple local peaks and one global peak) in power-voltage (P-V) characteristics. This paper proposes an adaptive velocity particle swarm optimization (AVPSO) algorithm for tracking the global maximum of the multiple peak P-V characteristics. The AVPSO algorithm continuously adjusts individual particle's weight factor and cognitive acceleration coefficient, depending upon its distance from the global best position during the tracking process. The advantage of the adaptive weight factor is reduced power oscillations in the region of global best position, while adaptive cognitive factor prevents the particles from getting trapped in local minima. Thus, the adaptive nature of the particle's velocity improves the global maximum power point tracking (GMPPT) time and power yield. Another feature involves limiting the particle's velocity to avoid skipping intermediate peaks. Additionally, AVPSO also includes the ability to sort particle's positions in each iteration, which prevents large changes in the PV voltage, thereby reducing the control effort of a PV voltage controller. The effectiveness of the proposed GMPPT algorithm is investigated for static and dynamic performance under different NUIC patterns and mitigation of local minima trapping issues through analysis, simulations, and extensive hardware experiments.

A general local existence theorem for quasi-linear evolution equations in nonreflexive banach spaces

Singularly perturbed evolution equations in Banach spaces

This Chapter makes use of the vector-valued distributions and ultra-distributions of Chapter 7. From the point of view of evolution boundary value problems, we assume the knowledge of the essentials of Chapter 3 and of the beginning of Chapter 4.

On the divergence problem in calculating particle velocities in dilute dispersions of identical spheres

The velocity distribution for a vibrated granular material is determined in the dilute limit where the frequency of particle collisions with the vibrating surface is large compared to the frequency of binary collisions. The particle motion is driven by the source of energy due to particle collisions with the vibrating surface, and two dissipation mechanisms\char21{}inelastic collisions and air drag\char22{}are considered. In the latter case, a general form for the drag force is assumed. First, the distribution function for the vertical velocity for a single particle colliding with a vibrating surface is determined in the limit where the dissipation during a collision due to inelasticity or between successive collisions due to drag is small compared to the energy of a particle. In addition, two types of amplitude functions for the velocity of the surface, symmetric and asymmetric about zero velocity, are considered. In all cases, differential equations for the distribution of velocities at the vibrating surface are obtained using a flux balance condition in velocity space, and these are solved to determine the distribution function. It is found that the distribution function is a Gaussian distribution when the dissipation is due to inelastic collisions and the amplitude function is symmetric, and the mean square velocity scales as $[〈{U}^{2}{〉}_{S}/(1\ensuremath{-}{e}^{2})],$ where $〈{U}^{2}{〉}_{S}$ is the mean square velocity of the vibrating surface and e is the coefficient of restitution. The distribution function is very different from a Gaussian when the dissipation is due to air drag and the amplitude function is symmetric, and the mean square velocity scales as $(〈{U}^{2}{〉}_{S}g/{\ensuremath{\mu}}_{m}{)}^{1/(m+2)}$ when the acceleration due to the fluid drag is $\ensuremath{-}{\ensuremath{\mu}}_{m}{u}_{y}|{u}_{y}{|}^{m\ensuremath{-}1},$ where g is the acceleration due to gravity. For an asymmetric amplitude function, the distribution function at the vibrating surface is found to be sharply peaked around $[\ifmmode\pm\else\textpm\fi{}2〈U{〉}_{S}/(1\ensuremath{-}e)]$ when the dissipation is due to inelastic collisions, and around $\ifmmode\pm\else\textpm\fi{}[(m+2)〈U{〉}_{S}g/{\ensuremath{\mu}}_{m}{]}^{1/(m+1)}$ when the dissipation is due to fluid drag, where $〈U{〉}_{S}$ is the mean velocity of the surface. The distribution functions are compared with numerical simulations of a particle colliding with a vibrating surface, and excellent agreement is found with no adjustable parameters. The distribution function for a two-dimensional vibrated granular material that includes the first effect of binary collisions is determined for the system with dissipation due to inelastic collisions and the amplitude function for the velocity of the vibrating surface is symmetric in the limit ${\ensuremath{\delta}}_{I}\ensuremath{\equiv}(2nr)/(1\ensuremath{-}e)\ensuremath{\ll}1.$ Here, n is the number of particles per unit width and r is the particle radius. In this limit, an asymptotic analysis is used about the limit where there are no binary collisions. It is found that the distribution function has a power-law divergence proportional to $|{u}_{x}{|}^{(c{\ensuremath{\delta}}_{I}\ensuremath{-}1)}$ in the limit ${u}_{x}\ensuremath{\rightarrow}0,$ where ${u}_{x}$ is the horizontal velocity. The constant c and the moments of the distribution function are evaluated from the conservation equation in velocity space. It is found that the mean square velocity in the horizontal direction scales as $O({\ensuremath{\delta}}_{I}T),$ and the nontrivial third moments of the velocity distribution scale as $O({\ensuremath{\delta}}_{I}{\ensuremath{\epsilon}}_{I}{T}^{3/2})$ where ${\ensuremath{\epsilon}}_{I}=(1\ensuremath{-}{e)}^{1/2}.$ Here, $T=[2〈{U}^{2}{〉}_{S}/(1\ensuremath{-}e)]$ is the mean square velocity of the particles.

Positions of particles' centers of gravity and folding centers were analyzed for individual dust particles in snow on a high mountain in Japan. Bias of dust particles' centers of gravity was observed: L1 (the longest distance from the center of gravity to the boundary of particles) is 5% (of L1, on average) longer than L2 (1/2 of the longest axis of particles), suggesting that a preferential orientation exists for particles settling heavy side down. Applying that preferential orientation of settling particles to Ginoux's model, the settling velocity for ellipsoids with Reynolds numbers lower than 2 was estimated. The results show that, for long‐range transport particles, settling velocity of spherical particles is lower than that of ellipsoids with equal surface area. Our results also indicate that, away from the source regions, dust particles are essentially spherical, which considerably simplify the calculation of settling velocity in transport and of radiative transfer models.

The evolution equations in real space and time corresponding to a class of anomalous diffusion processes are examined. As special cases, evolution equations corresponding to stable processes are derived using the theory of generalized functions, recovering some known results differently interpreted, and an evolution law for stable processes of order unity.

We describe the implementation of a 3d Lagrangian particle tracking (LPT) system based on event-based vision (EBV) sensors and demonstrate its application for the near-wall characterization of a turbulent boundary layer (TBL) in air. The viscous sublayer of the TBL is illuminated by a thin light sheet that grazes the surface of a glass window inserted into the flat wall of the wind tunnel wall. The data simultaneously captured by three synchronized EBV-cameras is used to reconstruct the 3d particle tracks within 0.4 mm of the wall on a field of view of 12.0 mm by 7.5 mm. The velocity and position of particles within the viscous sub-layer permit the estimation of the local, unsteady wall shear stress vector under the assumption of linearity between particle velocity and wall shear stress. Thereby, 2d distributions and higher order statistics of the unsteady wall shear stress are obtained. The systematic underestimation of the spanwise shear stress fluctuation can be explained on the basis of DNS data; a methodology for its mitigation is proposed. The employed EBV hardware coupled with suited LPT algorithms provide data quality on par with currently used, considerably more expensive, high-speed framing cameras.