Steering forces

If a car is braked whilst negotiating a curve, the steering force is reduced and the car suddenly understeers. 

In this chapter, we focus on the method of constraints and on ABF. Generalized coordinates are first described and some background material is provided to introduce the different free energy techniques properly. The central formula for practical calculations of the derivative of the free energy is given. Then the method of constraints and ABF are presented. A newly derived formula, which is simpler to implement in a molecular dynamics code, is given. A discussion of some alternative approaches (steered force molecular dynamics [35-37] and metadynamics [30-34]) is provided. Numerical examples illustrate some of the applications of these techniques. We finish with a discussion of parameterized Hamiltonian functions in the context of alchemical transformations. 

Several other techniques are available to compute the PMF. In this section we discuss the steered force molecular dynamics (SMD) [35-37] and the metadynamics of Laio and Parrinello [30-34]. 

The first chapter, on Conformational Dynamics, includes discussion of several rather recent computational approaches to treat the dominant slow modes of molecular dynamical systems. In the first paper, SCHULTEN and his group review the new field of steered molecular dynamics (SMD), in which large external forces are applied in order to be able to study unbinding of ligands and conformation changes on time scales accessible to MD... 

In the United States, regulation of emissions from new automotive vehicles has followed the prototype-replicate route. The argument for routine annual automobile inspection is that cars should be regularly inspected for safety (brakes, lights, steering, and tires) and that the additional time and cost required to check the car s emission control system during the same inspection will be minimal. Such an inspection certainly pinpoints cars whose emission control system has been removed, altered, damaged, or deteriorated and force such defects to be remedied. The question is whether... 

Tire traction describes the force transmission between tire and road under aU eventualities. It is the prerequisite for controlled steering, acceleration, and braking of self-propelled vehicles on flat tracks. It finds its upper limit in the frictional force when total sliding occurs. Two aspects have therefore to be considered The mechanics of force transmission of elastic wheels and its relation to rubber friction. 

Consider first the case of cornering, i.e., the plane of the wheel makes an angle with its traveling velocity. This creates a force normal to the plane of the wheel referred to as side force or cornering force. In tires it serves to steer the vehicle. 

However, deep potential wells, including those on the MEP, may be avoided in the reaction mechanism. Forces exerted on the downhill slope of saddle points or ridges on the PES can impart sufficient velocity (both magnitude and direction) to steer the trajectory past a well, just as a skilled kayaker can avoid a whirlpool in the middle of a river by choosing an appropriate velocity well before the whirlpool is encountered. Multiple pathways can arise when the initial conditions upon surmounting the barrier either facilitate or hinder the avoidance of the well. The reaction OH + CH3F discussed in Section V is an example of this phenomenon. 

Reactions without wells can also exhibit multiple pathways due to deviation from the MEP. While many trajectories may follow the MEP over a saddle point, alternative pathways arise when forces on the PES steer away from the saddle point, typically into relatively flat regions of the PES, before finding an additional path to the same exit channel. The roaming mechanisms recently elucidated in the photodissociation of formaldehyde and acetaldehyde, and the reaction of CH3 + O, are examples of this phenomenon, and are discussed in Section V. 

Lu, H. Schulten, K., Steered molecular dynamics simulations of force-induced protein domain unfolding, Proteins Struct. Funct. Gene. 1999, 35, 453 163... 

Park, S. Schulten, K., Calculating potentials of mean force from steered molecular dynamics simulations, J. Chem. Phys. 2004,120, 5946-5961... 

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