0000000000425929
AUTHOR
S Butera
Casimir Energies in a One-Dimensional Cavity with a Fluctuating Boundary
We consider a massless scalar field in a one-dimensional cavity with one fixed and one mobile wall. We assume that the mobile wall is also subjected to a harmonic potential, and its mechanical degrees of freedom are treated quantum-mechanically. The wall's position has thus quantum fluctuations around the equilibrium position. The possible motion of the wall makes the cavity length variable, and this gives rise to a wall-field interaction and an effective interaction between the modes of the cavity. We use an effective Hamiltonian, originally introduced by C. K. Law, to describe our system in terms of field modes relative to the equilibrium position of the mobile wall. We obtain by perturba…
Fractional calculus for the solution of non-linear stochastic oscillators with viscous dampers devices
Fluid viscoelastic dampers are of great interest in different fields of engineering. Examples of their applications can be found in seismic mitigation design of structures or in vibration absorption in airplane suspension. Such devices introduce a non-linear dissipative term in the equation of motion and therefore, the solution of even a single degree of freedom system excited by a white noise process, becomes prohibitive. The solution is usually obtained by approximated methods, like the stochastic linearization technique. In this paper it is shown that, by means of fractional operators, it is possible to find the solution of oscillators provided with fluid viscoelastic devices, approachin…