Force matching is a research method consisting of test subjects attempting to produce a set forces that are equal to a set of more reliable reference forces.
Types
*Biomechanical force matching –A subject’s
maximum voluntary contraction (MVC) is recorded and used to normalize both reference forces and results between subjects. During the test subjects are assisted in producing a reference force using various types of feedback (static weight or visual display of force generated). This is followed by an attempt of the subject to generate the reference force without assistance. The duration for both reference and matching tasks is usually four seconds. Results are taken as a mean value of force generated over a time interval set by the researcher. Time intervals are generally one second long and near the end of the attempt. Reference forces are typically set as a percentage of a subject’s MVC while error is typically reported as a percentage of a subject’s MVC.
*Atomic force matching – It is one of the effective research method to obtain realistic classical
interatomic potential or
force field for
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...
simulation with high degree of transferability for systems which the
first principles
In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption.
First principles in philosophy are from First Cause attitudes and taught by Aristotelians, and nu ...
or ''
ab initio
''Ab initio'' ( ) is a Latin term meaning "from the beginning" and is derived from the Latin ''ab'' ("from") + ''initio'', ablative singular of ''initium'' ("beginning").
Etymology
Circa 1600, from Latin, literally "from the beginning", from a ...
'' method is capable of treating. This method is based on fitting the forces on individual atoms in a number of reference structures, cohesive energies and stresses on unit cell obtained from
first principles
In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption.
First principles in philosophy are from First Cause attitudes and taught by Aristotelians, and nu ...
calculation with those obtained from classical
interatomic potential. The target of the computational fitting is to determine unknown coefficients in classical
interatomic potential function. This method is developed by F. Ercolessi, and J. B. Adams during 1992 and 1993 at Department of Material Science and Engineering at the University of Urbana-Campaign.
The enormous number of reference structures, which can reach several thousand values, makes it possible to fit large number of parameters needed for potential in binary and ternary systems.
For
Lennard-Jones potential:
:
where ''ε'' is the depth of the
potential well, ''σ'' is the finite distance at which the inter-particle potential is zero, ''r'' is the distance
between the particles. These two unknown parameters can be
fitted to reproduce experimental data or accurate data obtained from
first principle calculations. Differentiating the L-J potential with respect to ''r'' gives an expression for the net inter-molecular force between 2 molecules. This inter-molecular force may be attractive or repulsive, depending on the value of ''r''. When ''r'' is very small, the molecules repel each other. In force matching method the forces from classical potential
: