ABSTRACT
We propose a computational framework for the self-consistent dynamics of a microsphere system driven by a pulsed acoustic field in an ideal fluid. Our framework combines a molecular dynamics integrator describing the dynamics of the microsphere system with a time-dependent integral equation solver for the acoustic field that makes use of fields represented as surface expansions in spherical harmonic basis functions. The presented approach allows us to describe the interparticle interaction induced by the field as well as the dynamics of trapping in counter-propagating acoustic pulses. The integral equation formulation leads to equations of motion for the microspheres describing the effect of nondissipative drag forces. We show (1) that the field-induced interactions between the microspheres give rise to effective dipolar interactions, with effective dipoles defined by their velocities and (2) that the dominant effect of an ultrasound pulse through a cloud of microspheres gives rise mainly to a translation of the system, though we also observe both expansion and contraction of the cloud determined by the initial system geometry.
ABSTRACT
Integral equation-based analysis of scattering from dielectric objects has been a topic of research for many decades. Different integral equation formulations, discretization methods, and comparative data of their relative advantages have been well studied. Traditional discretization methods typically rely on a tight coupling between the underlying geometry discretization and the approximation function space that is defined on this discretization. As a result, it is difficult to stitch together different approximation spaces or nonconformal domains or match basis sets to local physics. Furthermore, the basis sets most commonly used in discretizing dielectric boundary integral operators impose limits on the variety of integral equation formulations that can be employed. We recently published a methodology [J. Opt. Soc. Am. A28, 328 (2011)10.1364/JOSAA.28.000328JOAOD61084-7529] that overcomes several of these bottlenecks. In the present paper, we introduce several extensions to these concepts for dielectric scattering problems. Specifically, we present a method that (i) uses mixed higher order local geometric descriptions and (ii) mixes multiple basis sets defined on this geometry, including higher order polynomials and classical Rao-Wilton-Glisson functions. Furthermore, we provide a unified description of different integral equation formulations that can be used for the analysis of scattering from dielectric objects, and show that the present approach admits a larger range of formulations than existing methods. A number of results demonstrating the efficiency of the method (in terms of accuracy and capability) together with applicability to different formulations are presented.
