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As "Open Internet Access by Molecular Dynamics Simulations", a couple of various codes are shown in https://github.com/Mtanaka77/, which are "Relativistic and Electromagnetic Molecular Dynamics Simulation for Nanoscale Phenomena", "Large-scale Electromagnetic Particle-in-Cell Simulation", and "SIESTA on Vector-Parallel Clusters". This page is discussed on the relativistic and nanoscale molecular dynamics simulations, Computer Physics Communications (2019, Ref. 1). You may visit companion pages other than the "Relativistic and Electromagnetic Molecular Dynamics Simulation".
A molecular dynamics simulation code is implemented for relativistic and electromagnetic fields in three dimensions. It is applied to nanoscale particle phenomena such as nanotube accelerators. Maxwell equations are solved, and momentum equations of relativistic particles are then advanced in time. Four physical CGS units are used in this code: a_unit= 1.00d-08 cm, t_unit= 1.00d-15 sec, electron mass m_unit= 0.9110d-27 g and its charge e_unit= 4.8032d-10 esu. The mass of hydrogen, for example, is 1.6726d-24 g.
One needs files in the simulation: 1) @cnt3-3p8Ca.f03: Molecular dynamics simulation code, 2) param_em3p8_Ca.h: Common parameters of this simulation, 3) Cntemp_config.STARTC: figure parameters, 4) p_config_ss.xyz_D150 and P135 of pellet electrons, H, C and Au ions. The program is written in Fortran 2003 and MPI of ver.3 for parallelization.
The description of each subroutine and important lines of, for example, @a_cnt3-3p8Ca.f03 and @3ddisppC.f03 to be shown later, is written as comments of the simulation code and post-script programs. Initial 70 lines of the file @cnt3-3p8Ca.f03 are devoted to give the title, references, summary of subroutines and remarks of the simulation code. In the major subroutine /moldyn/, (i) the magnetic field is advanced, (ii) current density is calculated and the transverse electric field is advanced, (iii) the correction of the longitudinal electric field is made, (iv) the longitudinal electric field is added, (v) the forces are calculated, and (vi) positions and momenta of particles are advanced toward the next time step.
It is noted, however, that the Gauss's law must be corrected for t>0 time steps as finite errors in the divergence term accumulate. That is the reason why the longitudinal electric field as above is used in the discrete coordinate space in any method. But, the relativistic formulae /vec{v}= \vec{p}/(sqrt(m^2 +(px^2 +py^2 +pz^2)/c^2)) is valid in the nanoscale cases (Ref. 1 and Ref. 2). Also, all the explicit simulation code must satisfy the Courant condition, that is, Dx(length)/Dt(time step) > c, the speed of light. Otherwise, a simulation is overflown quite shortly.
A simulation of the nanotube accelerator is set up by putting pellets of H, C and Au atoms and associated electrons at null velocity. Electromagnetic monochromatic waves at the wavelength 800 nm are travelling from the negative direction toward the origin and then go out to the positive direction. The pellets at the origin are irradiated by these waves and are ejected to ion perpenducular and electron parallel directions toward an open space. The final energies for laser intensity 10^22 W/cm^2 are around 30-40 MeV in 20-40 fs, which is shown by animation movies at my homepage.
(1) Linux (PGI): MPI and FFTW by PGI fortan; configure, make, make install.
mpich-4.0.2: ./configure --prefix=/opt/pgi/mpich-4.0.2 2>&1 | tee conf.txt
fftw3-3.3.10: ./configure --disable-shared --enable-maintainer-mode --enable-threads --prefix=/opt/pgi/fftw3
mpif90 @a_cnt3-3p8Ca.f03 needs param_em3p8_Ca.h, Cntemp_config.STARTC, p_config_ss.xyz_P135 and p_config_ss.xyz_D150.
% mpif90 -byteswapio -mcmodel=medium -fast @a_cnt3-3p8Ca.f03 -I/opt/pgi/fftw3/include -L/opt/pgi/fftw3/lib -lfftw3
(2) Linux (gfortran); configure, make, and make install.
mpich-4.0.2: ./configure --prefix=/opt/mpich-4.0.2 2>&1 | tee conf.txt
fftw3-3.3.10: ./configure --disable-shared --enable-maintainer-mode --enable-threads --prefix=/opt/fftw3
% mpif90 @a_cnt3-3p8Ca.f03 -I/opt/fftw3/include -L/opt/fftw3/lib -lfftw3
Two different fortrans, PGI and gfotran, are incompatible on the processor of the same name of different characters.
Execution: Only for a test. % mpiexec -n 6 a.out &
To analyze simulation results, this program provides the post-processing tool. They are named @3dfdisp.f03 and @3ddisp.f03, for examples. The velocity distributions in parallel and perpendicular directions, @3dfdispC.f03, are plotted in sequential times of ions and electrons. The @3ddisppC.f03 program is time sequential plots of H, C, Au and electrons in side and top views with energy histories as well at the end. These graphic outputs by PDF files are shown on the PC screen, either cntemp.77Cfb.pdf or cntemp.77Csa.pdf. They are discussed in the latter half of the CPC paper in 2019 (Ref. 1 below).
The heavy load of many particles is generally divided on parallel processors which is easily coded. On the other hand, the electromagnetic fields are parallelized for now the one-dimensional case (the z-direction) where the long axis of pellets is open to eject heavy ions in that direction. Finally, the machine run time depends on the physical time and cpu's architecture. For the elapsed time of parallel simulation it executed in 3.2 sec/step for 52 ranks and 4.0 10^5 particles (equal to 1 fs for elapsed 1.8 hours) by Fujitsu FX100 Supercomputer.
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M. Tanaka and M. Murakami, Relativistic and electromagnetic molecular dynamics simulations for a carbon-gold nanotube accelerator, Computer Physics Communications, 241, 56-63 (2019).
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M. Tanaka, A simulation of low-frequency electromagnetic phenomena in kinetic plasmas of three dimensions, J.Comput. Phys., 107, 124-145 (1993).