Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that obtained by Green. An equation with a nonlinear friction term for Brownian motion turns out to be an example of the general results. A key method in our derivation is to use different discretization schemes in a path integral formulation and the corresponding Langevin equation, which also leads to a consistent understanding of apparently different expressions for the path integral in previous studies.
We consider the dynamics of a freely movable wall of mass $M$ with one degree
of freedom that separates a long tube into two regions, each of which is filled
with rarefied gas particles of mass $m$. The gases are initially prepared at
equal pressure but different temperatures, and we assume that the pressure and
temperature of gas particles before colliding with the wall are kept constant
over time in each region. We elucidate the energetics of the setup on the basis
of the local detailed balance condition, and then derive the expression for the
heat transferred from each gas to the wall. Furthermore, by using the
condition, we obtain the linear response formula for the steady velocity of the
wall and steady energy flux through the wall. Using perturbation expansion in a
small parameter $\epsilon\equiv\sqrt{m/M}$, we calculate the steady velocity up
to order $\epsilon$.Comment: 17 pages, 2 figure
A procedure for the clonal propagation ofPaeonia lactiflora Pall. cvs. Takinoyosooi and Sarah Bernhardt through shoot tip culture is described. Half strength Murashige and Shoog (1962) medium supplemented with 0.5 mg/l 6-benzylaminopurine plus 1 mg/l gibberellic acid promoted formation and growth of axillary buds. Continuous shoot multiplication was achieved by vertically splitting the shoot axis and subsequent division of elongated axillary shoots every 36 days. High frequency (57-100%) of rooting was obtained on paper-bridge liquid medium supplemented with 1 mg/l indole-3-butyric acid. Half of the rooted plantlets were established on porous soil. Thus, 700 and 300 plants of cv. Takinoyosooi and Sarah Bernhardt could be theoretically obtained from a single bud in one year.
We study the friction coefficient of a macroscopic sphere in a viscous fluid at low Reynolds number. First, Kirkwood's formula for the friction coefficient is reviewed on the basis of the Hamiltonian description of particle systems. According to this formula, the friction coefficient is expressed in terms of the stress correlation on the surface of the macroscopic sphere. Then, with the aid of large deviation theory, we relate the surface stress correlation to the stress correlation in the bulk of the fluid, where the latter is characterized by the viscosity in the Green-Kubo formula. By combining Kirkwood's formula and the Green-Kubo formula in large deviation theory, we derive Stokes' law without explicitly employing the hydrodynamic equations.
We consider a freely movable solid that separates a long tube into two regions, each of which is filled with a dilute gas. The gases in each region are initially prepared at the same pressure but different temperatures. Under the assumption that the pressure and temperatures of gas particles before colliding with the solid are kept constant over time, we show that temperature gaps appearing on the solid surface generate a force. We provide a quantitative estimation of the force, which turns out to be large enough to be observed by a macroscopic measurement.
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