Jones unit

Fig. 3.3. Typical results from a density-of-states simulation in which one generates the entropy for aliquid at fixed N and V (i.e., fixed density) (adapted from [29]). The dimensionless entropy. r/ In ( is shown as a function of potential energy U for the 110-particle Lennard-Jones fluid at p = 0.88. Given an input temperature, the entropy function can be reweighted to obtain canonical probabilities. The most probable potential energy U for a given temperature is related to the slope of this curve, d// /dU(U ) = l/k T, and this temperature-energy relationship is shown by the dotted line. Energy and temperature are expressed in Lennard-Jones units...

Fig. 3.8. Transition matrix of move proposal probabilities for the Lennard-Jones fluid at p = 0.88 and N = 110. The energy range of —700 to —500 in Lennard-Jones units has been discretized into 100 bins. Due to the adjustment of the random displacement moves to achieve 50% acceptance, the transition probabilities are highly banded. The tuned moves change the potential energy by only a small amount, and as a result, each energy level is effectively only connected to a few neighbors...

Fig. 10.10. Calculated ,x( U) from a Wang-Landau simulation for the Lennard-Jones fluid at V = 125. The potential energy has been discretized into 1,000 bins and is expressed in Lennard-Jones units. Reprinted figure with permission from [75], 2002 by the American Physical Society...

Figure 7 Comparison of melt structure factor and single-chain structure factor for PB (upper panel, calculated as scattering from the united atoms only) and a bead-spring melt (lower panel, in Lennard-Jones units).

Fig. 16 Time evolution of the director tilt after a step-like start of the shear for two different final shear rates (0.008 and 0.010 in Lennard-Jones units). The lines show the fit to the data using the solution of the averaged linearized form of (27). Fig. 5.12 of [54]...

Absolute integrated intensities given in all tables are in practical units 109, 125), whereas it must be noted that A as defined in the text [Eq. (8)] is the Ramsay and Jones unit. Conversion factors interrelating some of the various commonly used units of intensity to practical units are to be found in Table VIII. 

Here we consider a system of particles interacting through a repulsive Lennard-Jones (LJ) potential E r) = e( ) truncated at a distance of Tc = 2a. We measure temperature and pressure in Lennard-Jones units, T = ksT/e andp =pa respectively. The long-range contribution to the potential was calculated under the assumption of constant density. For this system, the stable nuclei at melting are believed to be face-centered-cubic... 

Figure 16. Plot of (a) a and (b) tq against the logarithm of the velocity for incommensurate walls separated by a monolayer of chain molecules containing six monomers each. Velocities are in Lennard Jones units of (s/tu, which corresponds to roughly 100 m/s. With permission from Ref. 165. Wear 211. 44 (1997).

Figure 6. Depicted is the time-dependence of the volume for three simulations of 2.2 km/sec shock waves in the [110] direction of a perfect 1400 atom Lennard-Jones crystal. Each simulation was performed with a different mass-like parameter Q in Eq. (9), given here in reduced Leimard-Jones units. If Q is chosen too large (top panel), long-lived oscillations can result. If Q is chosen too small (bottom panel) large amplitude oscillations that do not decay with time can result. An optimal value of Q results in fast decay of volume oscillations.

Figure 9 Calculated Hugoniot for shocks in the [110] direction of perfect 25688 atom Leimard-Jones face-centered cubic crystal. The NEMD shock speed and temperature data are from Ref.l3. Here, c = 9.5 in Leimard Jones units. See text for details.

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FIG. 7 Intermediate incoherent scattering function of a bead-spring pol5mer of length 10 beads, approaching the mode coupling temperature which is r=0.45 in Lennard-Jones units [26]. 

FIGURE 7 Cross-sectional view of the local density (left) and local elastic constant (right) distribution of a model polymeric nanostructure. The density is shown in reduced (Lennard-Jones) units, and the elastic constants are shown as a percentage of the bulk value. 

In the following we shall measure all lengths in units of the Lennard-Jones diameter a = app and all energies in units of the Lennard-Jones well-depth e = epp of the polymer. The parameters of the Lennard-Jones potentials of the pure components are identified by matching the critical density crit and temperature Tcrit of pure carbon dioxide and hexadecane. The values from the simulations in reduced Lennard-Jones units and from the experiments are compiled in Table 1. Comparing simulation and experiments we identify a = 4.52 10 m and e = 5.79 10 J. The ratio of the critical densities of CO2 and hexadecane yields ass = 0.816critical temperatures we obtain ess = 0.726c. 

Fig. 22. Pressure (a) and chemical potential (b) against monomer density for chains of 10 monomers. Symbols are nVT simulation data while lines are predictions from TPT1 /m// line, RHNC version dashed line, MSA version. From top to bottom, pressure isotherms at ksT/e = 5, 4, 3, 2.5 and 1.68 in reduced Lennard-Jones units (adapted from [238])...

A different idea that is independent of the atomistic simulation involves mapping of the so-called Lennard-Jones time to real time. If one uses the standard Lennard-Jones units, where we measure lengths in cj (the particle diameter), energies in e (the depth of the Lennard-Jones potential), and masses in m (the monomer mass), a natural time scale appears that is conventionally called the Lennard-Jones time," ... 

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