Sentence examples for maximum energy error from inspiring English sources

Here (Delta E_{max}) is the maximum energy error and (E_{0}) is the initial energy.

In Figure 3, we plot the maximum energy error as a function of θ.

Figure 3 Maximum relative energy error as a function of θ.

Figure 5 Maximum relative energy error and the steps for the Hermite part against η.

Figure 4 Maximum relative energy error as a function of (pmb{Delta r_{mathrm{buff}}}) in unit of (pmb{Delta t_{mathrm{soft}} sigma}).

Top and bottom panels show the maximum relative energy error and the steps for the Hermite part par particle par unit time against η, respectively.

Next, a simple model system consisting of a single source charged particle is studied to show that the maximum electrostatic energy error incurred by anM-order multipole expansion for the Yukawa potential is bounded above by the error of the equivalent multipole expansion for the Coulombic potential.

In Figure 2, we present the maximum relative energy error (|Delta E_{max}/E_{0}|) over 10 N-body time units as a function of (r_{mathrm{cut}}) and (Delta t_{mathrm{soft}}) for several different values of the opening criterion of the tree, θ.

Figure 10 Maximum relative energy errors over 10 N -body time units.

We choose (eta=0.1), (Delta t_{max}=Delta t_{mathrm {soft}}/4) and (Delta r_{mathrm{buff}}=3sigmaDelta t_{mathrm{soft}}), where σ is the global three dimensional velocity dispersion and we adopt (sigma=1/{sqrt{2}}). Figure 2 Maximum relative energy errors as functions of (pmb{r_{mathrm{cut}}}) (left) and (pmb{Delta t_{mathrm{soft}}/r_{mathrm{cut}}sigma}) (right).

The maximum relative energy errors over 10 N-body time units are shown in the top panel of Figure 5 as a function of η and the number of steps for the Hermite part (per particle per unit time, (N_{mathrm{step}})) are presented in the bottom panel.