In this work, we study the nonequilibrium statistical properties of the relaxation dynamics of a nanoparticle trapped in a harmonic potential. We report an exact time-dependent analytical solution to the Langevin dynamics that arises from the stochastic differential equation of our system's energy in the underdamped regime. By utilizing this stochastic thermodynamics approach, we are able to completely describe the heat exchange process between the nanoparticle and the surrounding environment. As an important consequence of our results, we observe the validity of the heat exchange fluctuation theorem (XFT) in our setup, which holds for systems arbitrarily far from equilibrium conditions. By extending our results for the case of N noninterating nanoparticles, we perform analytical asymptotic limits and direct numerical simulations that corroborate our analytical predictions.
We investigate a quasi-two-dimensional system composed of an initially circular ferrofluid droplet surrounded by a nonmagnetic fluid of higher density. These immiscible fluids flow in a rotating Hele-Shaw cell, under the influence of an in-plane radial magnetic field. We focus on the situation in which destabilizing bulk magnetic field effects are balanced by stabilizing centrifugal forces. In this framing, we consider the interplay of capillary and magnetic normal traction effects in determining the fluid-fluid interface morphology. By employing a vortex-sheet formalism, we have been able to find a family of exact stationary N-fold polygonal shape solutions for the interface. A weakly nonlinear theory is then used to verify that such exact interfacial solutions are in fact stable.
The study of reversible, functional, and controllable adhesives is a matter of considerable practical interest, and academic research. We report the adhesive response of a magnetorheological fluid confined between two parallel plates under a probe-tack test, when it is subjected to an applied magnetic field. Our analytical approach is based on a Darcy-like law formulation which considers a magnetic field-dependent yield stress behavior. The adhesion force is calculated in closed form for two different configurations produced by a Helmholtz coils setup: uniform perpendicular, and nonuniform radial magnetic fields. In both cases, we verify that adhesion force is hugely increased as a result of the field-dependent nature of the yield stress. This provides a versatile way to obtain a shear resistant, tough structural adhesive through magnetic means.
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