Mathematical Physics - Volume II - Numerical Methods

6.2 Molecular Dynamics

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Figure 6.7: Temperature evolution for the simulation of the Taylor ballistic test (the (nano)projectile collision with the rigid wall). (a-c) Sequence of deformed nanoprojectile configurations upon v imp = 7 [km/s] rigid-wall collision with the marked positions of the eight averaging areas ("measurement gages") used to evaluate the macroparameters of state: (a-c) 0.2[ps], 6[ps], 12[ps], respectively (Adopted from [46]). (d) An example of time histories of temperature recorded at four measurement locations A − D equidistantly distributed along the longitudinal axis of symmetry of the nanoprojectile at the impact velocity v imp = 4[km/s] (Adopted from [43]). (e-g) Examples of temperature field evolutions during the v imp = 0 . 7[km/s] simulation; the images correspond 10[ps], 20[ps], and 50[ps], respectively. The scale of values on the label refers to the absolute temperature in degree Kelvin. Thermal initialization of the system Assignments of the initial and boundary conditions necessary for an MD simulation imply definition of the initial positions and initial velocities of all atoms of the system. The vibrational part of the initial velocities are generally defined by selecting the velocity intensities for each atom from the Maxwell-Boltzmann distribution for the desired initial sample temperature ( T 0 ) while the velocity directions are assigned randomly. The Maxwell-Boltzmann distribution of the vibrational velocities provides the proba bility density for atoms with the velocity intensity v and has the form pd f ( v ) = 4 π m 2 π k B T 0 3 / 2 v 2 exp − mv 2 2 k B T 0 . (6.17)