Restitution coefficient dependence of the pressure of a macroscopic active particle

Active matter systems serve as a paradigm for diverse nonequilibrium phenomena. Macroscopic realizations of active particles may exhibit inelastic collisions. We study the restitution coefficient dependence of the pressure exerted by a single bristlebot, a type of macroscopic driven particle with hopping dynamics. The finite hopping time allows for low- and high-drag parameter regimes. For low drag, the bristlebot pushes the wall with a momentum transfer rate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mover accent="true"> <a:mi>I</a:mi> <a:mo>̇</a:mo> </a:mover> </a:math> that satisfies <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mover accent="true"> <c:mi>I</c:mi> <c:mo>̇</c:mo> </c:mover> <c:mo>≃</c:mo> <c:mi>F</c:mi> </c:mrow> </c:math> , where <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>F</e:mi> </e:math> is the active force, in agreement with results for soft (elastic) walls. In the high-drag regime, we find <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mover accent="true"> <f:mi>I</f:mi> <f:mo>̇</f:mo> </f:mover> <f:mo>∝</f:mo> <f:mrow> <f:mo>(</f:mo> <f:mn>1</f:mn> <f:mo>+</f:mo> <f:mi>r</f:mi> <f:mo>)</f:mo> </f:mrow> <f:mi>F</f:mi> </f:mrow> </f:math> , showing dependence on the coefficient of restitution <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>r</h:mi> </h:math> . This behavior can be understood analytically by studying the periodic solutions of a simple one-dimensional model. Numerical simulations show that the transition between two regimes also exists for highly active two-dimensional particles.