Strong friction

The ohmic case is the most complex. A particular result is that the system is localised in one of the wells at T = 0, for sufficiently strong friction, viz. rj > nhjlQo. At higher temperatures there is an exponential relaxation with the rate Ink oc (4riQllnh — l)ln T. Of special interest is the special case t] = nhl4Ql. It turns out that the system exhibits exponential decay with a rate constant which does not depend at all on temperature, and equals k = nAl/2co. Comparing this with (2.37), one sees that the collision frequency turns out to be precisely equal to the cutoff vibration frequency Vo = cojln. 

It explodes on strong friction, and on standing it decomposes and may then explode spontaneously. 

Bishydroxymethyl Peroxide Highly explosive strongly friction-sensitive H. Wieland H. Sutter, Ber 63, 66 (1930)... 

Silver salt, Ag2C2HN j + H2O, powd, explodes on heating or strong friction and Barium salt, Ba3(C2Nn)2 + 8H20, yel pltlts (from w), explodes on mild heating Refs 1) Beil 26, (191) 2) K.A. Hofmann ... 

We are thus led to assume that V and the fiuctuation-dissipation process driving the virtual body depends on the variable 17 so as to simulate the efiects of the H-bond dynamics. For example, a strong interaction potential V accompanied by friction and stochastic torques (forces) of weak intensity simulates the solidlike properties of the environment when the tt ed molecule is characterized by four hydrogen bonds. In this case a reasonable approximation is to simulate such an environment by ice Ih. In the opposite limit, a weak potential V with strong friction and stochastic torques (forces) simulates the difiusional properties of the unbounded molecule (liquid water at high temperature or in very dilute nonpolar solution). 

In order to understand how the algorithm actually works and to construct an explicit expression for the error it is not convenient to work with the metadynamics equations (12) in their full generality. Instead, we notice that the finite temperature dynamics of the collective variables satisfies, under rather general conditions, a stochastic differential equation [54,55]. Furthermore, in real systems the quantitative behavior of metadynamics is perfectly reproduced by the Langevin equation in its strong friction limit [56]. This is due to the fact that all the relaxation times are usually much smaller than the typical diffusion time in the CV space. Hence, we model the CVs evolution with a Langevin t3rpe dynamics ... 

Although the substance is normally non-combustible, strong friction (e.g. grinding) can cause ignition. The measures on this card also apply to sodium bisulfite. Use airtight packaging. ... 

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