Defects in vibrated monolayers of equilateral triangular prisms

We present experimental results in which a quasimonolayer of grains, shaped as equilateral triangular prisms, is vertically vibrated within circular and square confining cavities. The system exhibits a fluid phase characterized by sixfold orientational order. However, the specific geometries of the cavities frustrate this order, leading to the excitation of topological defects that adhere to topological principles. We analyze the distribution of topological charges of these defects and their evolution as a function of the container geometry. In particular, we find that in the circular cavity, both the number and charge of defects remain constant in the steady-state regime, with only defects of charge <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> being excited. In contrast, within the square cavity—with the same topology as the circular cavity—some defects become pinned to the corners of the cavity, developing charges of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mo>+</b:mo> <b:mn>1</b:mn> </b:mrow> </b:math> or <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mo>+</c:mo> <c:mn>2</c:mn> </c:mrow> </c:math> . Additionally, free defects with charges of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mo>±</d:mo> <d:mn>1</d:mn> </d:mrow> </d:math> can be excited. Notably, dynamic events occur, such as the fusion of two defects or the creation of two defects from a single one. These events are governed by the conservation of total charge within the cavity and give rise to various system configurations, with rapid transitions between them. The observed dynamic fluctuations in topological charge are remarkable, influenced by both particle shape and cavity geometry. This system of vertically vibrated (dissipative) granular monolayers presents a unique and simple platform for studying topological phenomena, with potential implications for topological effects in equilibrium-oriented fluids.