Boundary effects on classical liquid density fluctuations

In this paper, we study quantum vacuum fluctuation effects on the mass density of a classical liquid arising from conical topology an effective idealized cosmic string spacetime, as well mixed, Dirichlet, and Neumann boundary conditions in Minkowski spacetime. context, consider phonon field representing excitations density, which obeys Klein-Gordon equation with sound velocity replaced by light velocity. is subject to quasi-periodic condition. Moreover, Dirichlet are applied one also two parallel planes. We, thus, each case, obtain closed analytic expressions for two-point function renormalized mean-squared liquid. We point out specific characteristics latter plotting their graphs.