arXiv subjects

Jeffrey S. Marshall

Publications and source records attributed to Jeffrey S. Marshall.

4 recordsLinked to original sources

arXiv2018

Exponential Scaling in Early-stage Agglomeration of Adhesive Particles in Turbulence

We carry out direct numerical simulation together with an adhesive discrete element method calculation (DNS-DEM) to investigate agglomeration of particles in homogeneous isotropic turbulence (HIT). We report an exponential-form scaling for the size distribution of early-stage agglomerates, which is valid across a wide range of particle inertia and inter-particle adhesion values. Such scaling allows one to quantify the state of agglomeration using a single scale parameter. An agglomeration kernel is then constructed containing the information of agglomerate structures and the sticking probability. An explicit relationship between the sticking probability and microscale particle properties is also proposed based on the scaling analysis of the equation for head-on collisions. Our results extend Smoluchowski's theory to the condition of non-coalescing solid adhesive particles and can reproduce DNS-DEM results with a simple one-dimensional simulation.

physics.flu-dyn↗

arXiv2015

A Simple Model for Long-Range Interacting Pendula

We show that the Hamiltonian mean field (HMF) model describes the equilibrium behavior of a system of long pendula with flat bobs that are coupled through long-range interactions (charged or self gravitating). We solve for the canonical partition function in the coordinate frame of the pendula angles. The Hamiltonian in the angles coordinate frame looks similar to the form of the HMF model but with the inclusion of an index dependent phase in the interaction term. We also show interesting non-equilibrium behavior of the pendula angles, namely that a quasistationary clustered state can exist when pendula angles are initially ordered by their index.

physics.class-ph↗

arXiv2014

Nonlinear Dynamics of Particles Excited by an Electric Curtain

The use of the electric curtain (EC) has been proposed for manipulation and control of particles in various applications. The EC studied in this paper is called the 2-phase EC, which consists of a series of long parallel electrodes embedded in a thin dielectric surface. The EC is driven by an oscillating electric potential of a sinusoidal form where the phase difference of the electric potential between neighboring electrodes is 180 degrees. We investigate the one- and two-dimensional nonlinear dynamics of a particle in an EC field. The form of the dimensionless equations of motion is codimension two, where the dimensionless control parameters are the interaction amplitude ($A$) and damping coefficient ($β$). Our focus on the one-dimensional EC is primarily on a case of fixed $β$ and relatively small $A$, which is characteristic of typical experimental conditions. We study the nonlinear behaviors of the one-dimensional EC through the analysis of bifurcations of fixed points. We analyze these bifurcations by using Floquet theory to determine the stability of the limit cycles associated with the fixed points in the Poincaré sections. Some of the bifurcations lead to chaotic trajectories where we then determine the strength of chaos in phase space by calculating the largest Lyapunov exponent. In the study of the two-dimensional EC we independently look at bifurcation diagrams of variations in $A$ with fixed $β$ and variations in $β$ with fixed $A$. Under certain values of $β$ and $A$, we find that no stable trajectories above the surface exists; such chaotic trajectories are described by a chaotic attractor, for which the the largest Lyapunov exponent is found. We show the well-known stable oscillations between two electrodes come into existence for variations in $A$ and the transitions between several distinct regimes of stable motion for variations in $β$.

nlin.CD↗

arXiv2014

Computational Studies of Multiple-Particle Nonlinear Dynamics in a Spatio-Temporally periodic potential

The spatio-temporally periodic (STP) potential is interesting in Physics due to the intimate coupling between its time and spatial components. In this paper we begin with a brief discussion of the dynamical behaviors of a single particle in a STP potential and then examine the dynamics of multiple particles interacting in a STP potential via the electric Coulomb potential. For the multiple particle case, we focus on the occurrence of bifurcations when the amplitude of the STP potential varies. It is found that the particle concentration of the system plays an important role; the type of bifurcations that occur and the number of attractors present in the Poincaré sections depend on whether the number of particles in the simulation is even or odd. In addition to the nonlinear dynamical approach we also discuss dependence of the squared fractional deviation of particles kinetic energy of the multiple particle system on the amplitude of the STP potential which can be used to elucidate certain transitions of states; this approach is simple and useful particularly for experimental studies of complicated interacting systems.

nlin.CD↗