First-passage time for randomly flashing diffusion

Noisy oscillator: Random mass and random damping

The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of energy to the oscillator and its dissipation to the surrounding environment. A random mass implies that the surrounding molecules not only collide with the oscillator but may also adhere to it, thereby changing its mass. We present general formulas for the first two moments and address the question of mean and energetic stabilities. The phenomenon of stochastic resonance, i.e., the expansion due to the noise of a system response to an external periodic signal, is considered for separate and joint action of two sources of noise and their characteristics.

Universal equivalence of mean first-passage time and Kramers rate

We prove that for an arbitrary time-homogeneous stochastic process, Kramers's flux-over-population rate is identical to the inverse of the associated mean first-passage time. In this way the mean first-passage time problem can be treated without making use of the adjoint equation in conjunction with cumbersome boundary conditions.

Single-particle tracking: applications to membrane dynamics

Measurements of trajectories of individual proteins or lipids in the plasma membrane of cells show a variety of types of motion. Brownian motion is observed, but many of the particles undergo non-Brownian motion, including directed motion, confined motion, and anomalous diffusion. The variety of motion leads to significant effects on the kinetics of reactions among membrane-bound species and requires a revision of existing views of membrane structure and dynamics.