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EiReaction field methodField of cavity N i generated by the dipol momentsμ j of the particles inside the cavity:2 1 1s32s1 rcjNiTotal force on particle i :j= „reaction field“ F F E i ij i ijNi111Reaction field methodTo avoid a jump in the force each time a particle leavesor enters the cavity one can weaken the influence ofthe particles close to the border by a weight function:1forr rc jwr ( ) for rr rr rj t j c c t 0r t0.95forrcrrcjrrtj112
Canonical EnsembleTill now we considered constant energyand constant volume, i.e. we workedin the microcanonical ensemble.Most commonly, however, experimentsare performed at constant temperature,i.e. in the canonical ensemble. That meansthat the system is coupled to a heat bath.113Canonical EnsembleVarious methods:• Rescaling of velocity• Introduce a constraint (Hoover)• Thermostat (Nosé – Hoover)• Stochastic method (Andersen)114
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Guidance on Impact AssessmentsDocum
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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 and 50: Ewald summationThe Ewald sum is onl
Page 51 and 52: Particle - Mesh algorithmJ.W. Eastw
Page 53 and 54: Particle - Mesh algorithmPM algorit
Page 55: Multipole expansion„Fast Multipol
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
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