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Nosé - Hoover thermostatspurioustemperatureoscillations131Nosé - Hoover thermostatnormaltemperaturefluctuations132
Nosé - Hoover thermostatnormalenergyfluctuations133Nosé - Hoover thermostatHoover proved 1985 that the Nosé – Hooverthermostat is the only method with a singlefriction parameter that gives the correctcanonical distribution. Hoover also showedthat this thermostat satisfies the Liouvilleequation, i.e. that the density of states isconserved in the phase space { x i , p i , s, p s }.134
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Guidance on Impact AssessmentsDocum
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Potentialshard core interaction 0.3
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PotentialsLenard Jones potentialε
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Contact timeone dimensionenergy:122
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Verlet method• One needs to store
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Total energy21Small perturbationdiv
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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
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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 and 56: Multipole expansion„Fast Multipol
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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: Nosé - Hoover thermostatCoupling t
Page 69 and 70: Constant pressureKeep pressure pfix
Page 71 and 72: givingequationsof motion:NPT ensemb
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