T - IfB

More documents

Recommendations

Info

Ewald methodoriginal chargescreeningcancelling99Ewald methodThe following sum converges faster.1 erfc( r )!ij nV zizj2 ij nrij n2k21 4 z z e k r z3 L k 042 2i jcos2ijik i„erfc“ is the error function:2erfc( x) e dtxt2100
Particle – Mesh algorithmJ.W. Eastwood, R.W. Hockney and D.N.Lawrence (1980)• Put a fine mesh on top of the system (M ≈ N).• Distribute the charges onto the mesh points.• Calculate electrostatic potential by solving thePoisson equation on the mesh using FFT.• Calculate force on each particle by numericallydifferentiating the potential and interpolatingback from the mesh to the particle position.101Particle – Mesh algorithmCriteria for a good PM scheme:• Errors should vanish at large particledistances. • Momentum conservation: Fij=-Fji• Charges on mesh and interpolatedforces should vary smoothly withparticle position.102
Page 1 and 2: Guidance on Impact AssessmentsDocum
Page 3 and 4: Potentialshard core interaction 0.3
Page 5 and 6: PotentialsLenard Jones potentialε
Page 7 and 8: Contact timeone dimensionenergy:122
Page 9 and 10: Verlet method• One needs to store
Page 11 and 12: Total energy21Small perturbationdiv
Page 13 and 14: TricksMost time consuming loop is c
Page 15 and 16: Verlet tablesThe Verlet table LIST
Page 17 and 18: Linked cell methodexamplecell 1 cel
Page 19 and 20: MoleculesMolecules are composed of
Page 21 and 22: Lagrange multipliersConstraints tha
Page 23 and 24: Lagrange multipliersFirst solve ter
Page 25 and 26: Contact Dynamics (CD)P. Lötstedt (
Page 27 and 28: Example: two particles (1D)Matrix H
Page 29 and 30: Example: two particles (1D)No overl
Page 31 and 32: Contact DynamicsCoulomb-Graph:Frict
Page 33 and 34: Contact Dynamics ext1F 1 1 1
Page 35 and 36: Contact DynamicsPerform direct inve
Page 37 and 38: Non-spherical objectsUp to now: ato
Page 39 and 40: Two dimensionsTime evolution of the
Page 41 and 42: 3d rigid body rotationangular momen
Page 43 and 44: Euler anglesRotations in three dime
Page 45 and 46: AOne can show:Quaternions 2 2
Page 47 and 48: Long-range potentialsLong-range are
Page 49: Ewald summationThe Ewald sum is onl
Page 53 and 54: Particle - Mesh algorithmPM algorit
Page 55 and 56: Multipole expansion„Fast Multipol
Page 57 and 58: Canonical EnsembleTill now we consi
Page 59 and 60: Velocity rescalingThe main problem
Page 61 and 62: Constraint methodThis method is sim
Page 63 and 64: Nosé - Hoover thermostatThis new d
Page 65 and 66: Nosé - Hoover thermostatCoupling t
Page 67 and 68: Nosé - Hoover thermostatnormalener
Page 69 and 70: Constant pressureKeep pressure pfix
Page 71 and 72: givingequationsof motion:NPT ensemb

T - IfB

Create successful ePaper yourself

Delete template?

Save as template?