US 4,908,781 AGranted

Computing device for calculating energy and pairwise central forces of particle interactions

AssigneeThe Trustees of Columbia University in the City of New York

InventorsCyrus Levinthal, Richard M. Fine

Life of this patent

Estimating the term…

Loading patent…

Abstract

This invention provides a computing device which calculates the total energy and total pairwise, central forces between selected pairs of interacting particles within a system. The device comprises (a) a means for generating both (i) a retrievable identifier for the spatial coordinates (x, y, z) of a particle i and (ii) retrievable identifiers of the type of pairwise, central interaction between i and a second particle j; (b) a means for determining r.sup.2, the square of the radius vector between i and j; (c) a means for determining r, the square root of r.sup.2 ; (d) a means for calculating energy and force/r values for each ij pair; (e) means for determining the force on each particle; and (f) means for accumulating energy and force/r values for each ij particle pair.

Claims12

Dependent claims

A computing device which calculates the total energy and total pairwise, central forces between selected pairs of discrete, interacting particles within a system which comprises

a. means for generating as digital outputs both (i) a retrievable identifier of the spatial coordinates (x, y, z) for all selected pairs of particles i and j which interact with one another within the system and (ii) retrievable identifiers of the type of pairs, cental interaction between each ij pair;
b. means for (i) inputting digital outputs from the generating means, (ii) determining therefrom r.sup.2, the square of the radius vector between each i and j, by calculating solutions for the equation
r.sup.2 (x.sub.i -x.sub.j).sup.2 +(y.sub.i -y.sub.j).sup.2 +(z.sub.i -z.sub.j).sup.2,
where (x.sub.i, y.sub.i, z.sub.i) and (x.sub.j, y.sub.j, z.sub.j) are the spatial coordinates for i and j obtained as digital inputs from the generating means, and (iii) outputting r.sup.2 values in digital word form;
c. look-up means for (i) inputting r.sup.2 values in digital word form, (ii) determining therefrom [r, the square root of r.sup.2 ] respective values correspoding to a predetermined function of r.sup.2, and (iii) outputting [r] said respective values in digital word form;
d. means for (i) inputting the digital outputs of the generating means relating to the types of pairwise, central interactions and for inputting the [r] values from the [r determining] look-up means, (ii) calculating therefrom the energy and the force/r values for each ij pair of particles, and (iii) outputting the energy and force/r values for each ij pair of particles in digital word form;
e. means for (i) inputting the force/r values from the force/r calculating means, (ii) determining therefrom the Cartesian components of the force on each particle i within each pair ij, and (iii) outputting the cartesian component values of the force between each particle pair ij in digital output form;
and
f. means for (i) inputting for each particle pair ij the energy values from the energy calculating means and the Cartesian component values of the force from the means for determining the total pairwise, central force values between each ij particle pair, (ii) accumulating the total energy values for each ij particle pair and the total force values between each particle pair ij, and (iii) outputting such total energy and total force values.

6 more elements

A computing device which calculates the total energy and total pairwise, central forces between selected pairs of discrete, interacting atoms comprising:

a. a storage device containing words for forming an ordered list of pairs of atoms (i,j) that can interact with one another, and wherein each word in the list is formed of an i/j bit indicating whether an atom of a pair is an i or a j atom, an atom number uniquely identifying each atom, and a pairtype number pt identifying an interaction that a particular j atom undergoes with an i atom of a pair;
b. means for selectively reading out said atom numbers from said storage device to form said pairs of (i,j) atoms from said atom numbers, wherein j is an atom number greater than i;
c. a plurality of coordinate memories containing cartesian coordinates of all atoms identified in said storage device, said coordinate memories being addressed by said i, j atoms arranged in pairs formed of said atom numbers selectively read out from said storage device for reading out the x, y and z cartesian coordinates of the atoms;
d. arithmetic means for producing the square of the difference between each respective x, y, z cartesian coordinates of the pairs of i,j atoms read out from sai plurality of coordinate memories;
e. summing means for summing said squares of the difference produced by said arithmetic means;
f. look up table means containing values for determining a function of the square of the radial distance between each atom of an i,j pair and being arranged to be addressed by the output of said summing means;
g. a plurality of coefficient memories containing information relating to the electrical charges on each atom and van der Waals interactions and being addressed by said pair type numbers read out from said storage device;
h. a plurality of energy tables containing information relating to the energy of each atom and being addressed by said pair type numbers read out from said storage device and said values for determining a function of the square of the radial distance read out from said look-up table means;
i. a plurality of force divided by radial distance tables containing information relating to the ratio of the atomic forces divided by the radial distance between the atoms of an i,j pair and being addressed by said pair type number read out from said storage device and said values for determining a function of the square of the radial distance read out from said look-up table means;
j. arithmetic means for producing an energy sum of the product of the output from a coefficient table and a respective energy table, said energy sum representing the energy on an i atom created by a j atom of and i,j pair and for producing a force sum of the product of the output from a coefficient table and a respective force divided by radial distance table, said force sum representing the force exerted on an i atom by a j atom of an i,j pair;
k. accumulator means for accumulating the energy values produced by said arithmetic means and producing a total energy value therefrom;
l. coordinate component determining means receiving said force sum and said difference between each respective x, y, z cartesian coordinates from said arithmetic means for producing a Cartesian coordinate force value;
and
m. force accumulator means for accumulating Cartesian coordinate force values from said coordinate component determining means in response to said atom numbers from said storage device and producing an x, y, z component of said force sum.

11 more elements

Dependencies are inferred from the claim text.