Yon can then determine the acceleration, a, of each atom hy dividing the force acting on it by the mass of the atom (cc natioii [Pg.69]

In most real life applications, the evaluation of the forces acting on the classical particles (i.e., the evaluation of the gradient of the interaction potential) is by far the most expensive operation due to the large number of classical degrees of freedom. Therefore we will concentrate on numerical techniques which try to minimize the number of force evaluations. [Pg.399]

Shapes of the ground- and first tln-ee excited-state wavefiinctions are shown in figure AT 1.1 for a particle in one dimension subject to the potential V = which corresponds to the case where the force acting on the [Pg.17]

Settling and sedimentation. In settling processes, particles are separated from a fluid by gravitational forces acting on the particles. The particles can be solid particles or liquid drops. The fluid can be a liquid or a gas. [Pg.68]

In order to solve the classical equations of motion numerically, and, thus, to t)btain the motion of all atoms the forces acting on every atom have to be computed at each integration step. The forces are derived from an energy function which defines the molecular model [1, 2, 3]. Besides other important contributions (which we shall not discuss here) this function contains the Coulomb sum [Pg.79]

Here we have expressed the stress as the sum of the (external) applied pressure PappUed together with a static pressure Pstatic- which arises from the internal forces acting on the uiiit cell. [Pg.311]

Centrifugal separators make use of the common principle that an object whirled about an axis at a constant radial distance from the point is acted on by a force. Use of centrifugal forces increases the force acting on the particles. Particles that do not settle readily in gravity settlers often can be separated from fluids by centrifugal force. [Pg.71]

The second general cause of a variable heat of adsorption is that of adsorbate-adsorbate interaction. In physical adsorption, the effect usually appears as a lateral attraction, ascribable to van der Waals forces acting between adsorbate molecules. A simple treatment led to Eq. XVII-53. [Pg.700]

Fig. 2. Distance classes j = 0,1, 2,... (left) are defined for an atom (central dot) by a set of radii Rj+i the right cnrves sketch the temporal evolntion of the tot il force acting on the selected atom originating from cill atoms in distance class j shown are the exact forces (solid line), their exact valnes to be computed within the multiple time step scheme (filled squares), linear force extrapolations (dotted lines), and resulting force estimates (open sqnares). |

Much of chemistry is concerned with the short-range wave-mechanical force responsible for the chemical bond. Our emphasis here is on the less chemically specific attractions, often called van der Waals forces, that cause condensation of a vapor to a liquid. An important component of such forces is the dispersion force, another wave-mechanical force acting between both polar and nonpolar materials. Recent developments in this area include the ability to measure [Pg.225]

In classical mechanics, the state of the system may be completely specified by the set of Cartesian particle coordinates r. and velocities dr./dt at any given time. These evolve according to Newton s equations of motion. In principle, one can write down equations involving the state variables and forces acting on the particles which can be solved to give the location and velocity of each particle at any later (or earlier) time t, provided one knows the precise state of the classical system at time t. In quantum mechanics, the state of the system at time t is instead described by a well behaved mathematical fiinction of the particle coordinates q- rather than a simple list of positions and velocities. [Pg.5]

Thus, the requirement that the Brownian particle becomes equilibrated with the surrounding fluid fixes the unknown value of, and provides an expression for it in tenns of the friction coefficient, the thennodynamic temperature of the fluid, and the mass of the Brownian particle. Equation (A3.1.63) is the simplest and best known example of a fluctuation-dissipation theorem, obtained by using an equilibrium condition to relate the strengtii of the fluctuations to the frictional forces acting on the particle [22]. [Pg.689]

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