The enigma of nonholonomic constraints

Flannery, M. R.

doi:10.1119/1.1830501

Cited by 77 publications

(67 citation statements)

References 5 publications

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“…The equations in Hamiltonian form are useful for determining phase space compressibility and applying linear response theory. 5 However, as the Principle of Least Action is known to give incorrect equations of motions for some constraints, 27 it may not be applicable to obtain a generally valid localized momentum constraint. Gauss's principle of least constraint is used to verify the Principle of Least Action formulation, as in Flannery,30 because it is applicable to holonomic as well as non-holonomic constraints.…”

Section: B Localized Momentum Constraintmentioning

confidence: 99%

“…In this context, the constraint expressed in terms of surface fluxes, as in Eq. (27), is the required starting point to derive an accurate flux coupling. Equation (27) can be interpreted as a constraint on all the surface fluxes, and, therefore, the flux coupling methodology of Flekkøy et al 22 is a special case, where computational fluid dynamics (CFD) pressure and advection are applied at the top CV surface only and no molecular terms are removed.…”

Section: The Constraint Equation In Terms Of Fluxesmentioning

confidence: 99%

“…However, examples in the literature demonstrate that the Principle of Least Action, subject to certain constraints, fails to reproduce the Newtonian equations of motion. 27,28 It is therefore not clear that the Principle of Least Action is formally valid for the semi-holonomic constraints of interest here (see Refs. 17,27,and 29).…”

Section: Introductionmentioning

confidence: 99%

“…27,28 It is therefore not clear that the Principle of Least Action is formally valid for the semi-holonomic constraints of interest here (see Refs. 17,27,and 29). In contrast, Gauss's principle of least constraint is a true minimum principle, which is applicable to any form of constraint.…”

Section: Introductionmentioning

confidence: 99%

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A localized momentum constraint for non-equilibrium molecular dynamics simulations

Smith

Heyes

Dini

et al. 2015

The Journal of Chemical Physics

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Articles you may be interested inEfficient hybrid non-equilibrium molecular dynamics -Monte Carlo simulations with symmetric momentum reversal J. Chem. Phys. 141, 114107 (2014) A term for the advection of molecules appears in the derived constraint and is shown to be essential in order to exactly control the time evolution of momentum in the subvolume. The numerical procedure converges the total momentum in the CV to the target value to within machine precision in an iterative manner. The localized momentum constraint can prescribe essentially arbitrary flow fields in non-equilibrium molecular dynamics simulations. The methodology also forms a rigorous mathematical framework for introducing coupling constraints at the boundary between continuum and discrete systems. This functionality is demonstrated with a boundary-driven flow test case. C 2015 AIP Publishing LLC.[http://dx

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Section: B Localized Momentum Constraintmentioning

confidence: 99%

Section: The Constraint Equation In Terms Of Fluxesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A localized momentum constraint for non-equilibrium molecular dynamics simulations

Smith

Heyes

Dini

et al. 2015

The Journal of Chemical Physics

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“…Although some interpretation problems are associated to non-holonomic constraints [111], and they are known to not accept in general a closed Hamiltonian formalism [112,113,114], they are perfectly valid in the algorithmic sense discussed before (i.e., as a tool to define the integration region in which the integrated quantity is non-negligible in equilibrium statistical mechanics). In fact, when their form is linear in the velocities, as it is the case of eq.…”

Section: Flexible Vs Hard Constraintsmentioning

confidence: 99%

The canonical equilibrium of constrained molecular models

Echenique

Cavasotto

García-Risueño

2011

Eur. Phys. J. Spec. Top.

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Abstract. In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. Since the maximum time step required for the stability of the dynamics is proportional to the shortest period associated with the motions of the system, constraining the fastest vibrations allows to increase it and, assuming that the added numerical cost is not too high, also increase the overall efficiency of the simulation. However, as any other element that affects the physical model, the imposition of constraints must be assessed from the point of view of accuracy: both the dynamics and the equilibrium statistical mechanics are model-dependent, and they will be changed if constraints are used. In this review, we investigate the accuracy of constrained models at the level of the equilibrium statistical mechanics distributions produced by the different dynamics. We carefully derive the canonical equilibrium distributions of both the constrained and unconstrained dynamics, comparing the two of them by means of a "stiff" approximation to the latter. We do so both in the case of flexible and hard constraints, i.e., when the value of the constrained coordinates depends on the conformation and when it is a constant number. We obtain the different correcting terms associated with the kinetic energy mass-metric tensor determinants, but also with the details of the potential energy in the vicinity of the constrained subspace (encoded in its first and second derivatives). This allows us to directly compare, at the conformational level, how the imposition of constraints changes the thermal equilibrium of molecular systems with respect to the unconstrained case. We also provide an extensive review of the relevant literature, and we show that all models previously reported can be considered special cases of the most general treatments presented in this work. Finally, we numerically analyze a simple methanol molecule in order to illustrate the theoretical concepts in a practical case.

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Three‐dimensional behavior of a spherical self‐centering precast prestressed pile isolator

Jünemann

Llera

Besa

et al. 2009

Earthq Engng Struct Dyn

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SUMMARYA 3D analytical formulation of a precast prestressed pile (PPP) seismic isolator with top and bottom spherical rolling kinematic constraints is proposed. The PPP isolator was initially conceived as a low-cost seismic isolation (and foundation) system for housing units of low-income people. Since these structures are usually located at sites with poor soil conditions, the PPP isolator also works as a foundation pile by connecting the superstructure with more competent soil layers. The non-holonomic nature of the rolling constraint is dealt with by a structural formulation. The proposed 3D formulation is validated by numerical results obtained from a previously proposed formulation for the 2D problem, and a contact finite element model in ANSYS (www.ansys.com). Other issues associated with the dynamic response of isolated structures with the PPP are also examined, such as expected response reductions, variation in the axial force of the central prestressed cable, and torsional response amplifications. Finally, guidelines to estimate the actual 3D response using 2D analysis results are investigated.

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The enigma of nonholonomic constraints

Cited by 77 publications

References 5 publications

A localized momentum constraint for non-equilibrium molecular dynamics simulations

A localized momentum constraint for non-equilibrium molecular dynamics simulations

The canonical equilibrium of constrained molecular models

Three‐dimensional behavior of a spherical self‐centering precast prestressed pile isolator

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