Figure 5. The same forces are applied at other points and the stick rotates—in fact, it experiences an accelerated rotation. Here net F = 0 but the system is not at equilibrium. Hence, the net F = 0 is a necessary—but not sufficient—condition for achieving equilibrium. PhET Exploration...
We'll use the second-order differential equation from Example 1.3.2, y″+y=0, which has the two-parameter family of solutions y(t)=c1cost+c2sint. Now let's see what happens if we impose the boundary conditions y(0)=1, y(π)=1. The first condition implies that 1=y(0)...
Their model nests within it the special case of a two-player first-price sealed-bid auction of an item with a commonly known value, to which we add a stochastic head start. Blume (2003) derives the equilibrium in mixed strategies (an equilibrium in pure strategies does not exist) in a ...
In the operating condition of this reactor, the following undesired reaction also takes place: A→UrU=0.003CA1+105CAmolU/L.s The undesired product U is a pollutant and it costs 10 $/mol U to dispose of it, while the desired product D has a value of 35 $/mol D. What size of the...
Although the theory of lattice dynamics was established six decades ago, its accurate implementation for polar solids using the direct (or supercell, small displacement, frozen phonon) approach within the framework of density-function-theory-based first-principles calculations had been a challenge until...
of the first-passage time distribution in the partition function. The corresponding partition function is divided into multipliers, one of which is associated with the equilibrium parameters, and the second one with the parameters of the first-passage time distribution. The thermodynamic parameter ...
The presence of a concentration or chemical potential gradient in the medium is not the only condition under which diffusion occurs. The action of an external electrical field causes the diffusion of charged particles (electrodiffusion), the action of the gravitational field or pressure causes barodi...
3). Winds driven by horizontal gradients of surface thermal properties17 may be the origin of the discrepancies we observe from measurements with respect to the predictions from one-dimensional radiative equilibrium models. Temperature fluctuations are common throughout the sol; these rise after sun...
Thus, due to variable storage conditions, the expiration date is often much shorter than the shelf-life at a given storage condition. The half-life of amoxicillin in the mixture at pH 6.0 and 25°C is (Eq. 2.6): t1/2=0.50[Amox]0k0=0.50·0.1368mol/liter1.17×10−5molliter·h=5.8...
In our numerical experiments, we focus on a bounded interval for the degree of risk aversion. When r becomes too large, the boundary condition (2) cannot be satisfied in general for a positive initial equilibrium bid. This can also be observed in Fig. 1 which shows that as r becomes larg...