Kinematics equation

The situation is illustrated in Fig. 3.47. The upper part shows a thin film of Ni deposited on a Si substrate. Only particles scattered from the front surface of the Ni film have an energy given by the kinematic equation, Eq. (3.28), Fi = fCNi o- As particles traverse the solid, they lose energy along the incident path. Particles scattered from a Ni atom at the Si-Ni interface therefore have an energy smaller than On the... 

Using the above definitions and integrating over the channel cross section, with some manipulations, Zuber s kinematic equation results (Hsu and Graham, 1976) ... 

The most important question for the calculation of the structure amplitudes from the intensities is that for the validity of the kinematical approximation. Due to the strong interaction of fast electrons with matter the effects of dynamical scattering become more pronounced with increasing size of the microcrystallites in the film. In order to justify application of the kinematical equations it is necessary that the diffracted intensity is much less... 

The z th micro-element is characterized by the position of its center xh velocity vh radius rh monomer concentration ch and by its type tt. The translational movement of each micro-element is governed by kinematic equation and Newton s equation of momentum... 

From this equation, it is possible to discuss further about the general properties of the near-held solution. Noticing that the kinematic equation when substituted in the governing vorticity transport equation... 

The necessary conditions to be fulfilled are the equilibrium conditions, the strain-displacement relationships (kinematic equations), and the stress-strain relationships (constitutive equations). As in linear elasticity theory (12), these conditions form a system of 15 equations that permit us to obtain 15 unknowns three displacements, six strain components, and six stress components. 

The calculation of orientational autocorrelation functions from the free rotator Eq. (14) which describes the rotational Brownian motion of a sphere is relatively easy because Sack [19] has shown how the one-sided Fourier transform of the orientational autocorrelation functions (here the longitudinal and transverse autocorrelation functions) may be expressed as continued fractions. The corresponding calculation from Eq. (15) for the three-dimensional rotation in a potential is very difficult because of the nonlinear relation between and p [33] arising from the kinematic equation, Eq. (7). 

In this chapter, we use the results of numerical infiltration experiments in dual porosity media performed with a three-dimensional lattice-gas model to characterize preferential flow as response to rainfall intensity. From the temporal and spatial evolution of the water content during infiltration and drainage, we evaluate the adequacy of a kinematic wave approximation to describe the flow. We also discuss the conceptual basis of the asymptotic kinematic approach to Richards equation in comparison with the macropore kinematic equation. 

Each nucleus is characterized by a definite atomic number Z and mass number A for clarity, we use the symbol M to denote the atomic mass in kinematic equations. The atomic number Z is the number of protons, and hence the number of electrons, in the neutral atom it reflects the atomic properties of the atom. The mass number gives the number of nucleons (protons and neutrons) isotopes are nuclei (often called nuclides) with the same Z and different A. The current practice is to represent each nucleus by the chemical name with the mass number as a superscript, e.g., 12C. The chemical atomic weight (or atomic mass) of elements as listed in the periodic table gives the average mass, i.e., the average of the stable isotopes weighted by their abundance. Carbon, for example, has an atomic weight of 12.011, which reflects the 1.1% abundance of 13C. 

Fig. 9.1. Different representations of a rigidly rotating spiral wave, (a) Involute of a hole, (b) Solution of the kinematical equation with linear velocity-curvature relationship, (c) Archimedean spiral, (d) Superposition of the three wave fronts where the dotted, dashed and solid lines correspond to (a), (b), and (c), respectively. Far from the rotation center the fronts practically coincide.

The mass-conserving kinematic equation for this system is of the form [32]... 

The kinematic equation, which should be added to the system of (2.2)-(2.15), determines the location of the jet axis in space in accordance with the velocity field... 

A fiiee surface boundary condition was imposed on the glass gob sur ce in POLYFLOW. Since the fiiee surface boundary position is not known in advance, the fiee-sur ce problems have additional degrees of freedom and additional equations to solve as coitqrared widi fixedboundary flow problems. For a transient flow problem, the position of moving boundaries is determined by solving a kinematic equation ... 

Denavit-Hartenbei Parameters Used for Derivation of Forward Kinematic Equations for the Tracker... 

Similarly, an imaginary frame theo is formed using the theoretical locations of points 1,2, and 3, which are obtained using the forward kinematics equations [17]. Thus, the axes and of the frame theo are defined in the same way... 

Articulated arm model for implementing forward-kinematics equations. 

An equation between stress and strain can be obtained for any mechanical model by using equilibrium and kinematic equations for the system and constitutive equations for the elements. For a Maxwell fluid, equilibrium... 

The objective is to find the constitutive equation (governing differential equation) for the three-parameter model. The kinematic equation for the three-parameter solid is,... 

A spatially localized periodic stimulus generates a train of impulses which propagates into the medium away from the stimulus site. Let xj (t), k = 1,2,, be the position of the upstroke of the kth impulse. We consider its inverse function t (x), 0 X L, which represents the trajectory of the impulse In the x-t plane. If the above approximations are applied, the speed dx (t)/dt of the impulse when it passes the location x is given by c(T (x)), where T (x) E t (x) - t (x) is the time since the predecessor impulse passed the same location. In this way, by using dt (x)/dx = dt/dxj (t), we obtain the following kinematic equation for the trajectories t (x) [1] ... 

The zero flux condition is assumed at the other boundary. The Crank-Nicholson method with spatial and temporal mesh Ax = 0.75 and At = 1.0 is used to solve (1).) The dashed curves, which almost perfectly coincide with the dotted curves, are solutions of the kinematic equation (2) (subject to the initial conditions t (0) = (k-l)T-j) based upon the dispersion relation of Fig.1-B. The curves in Fig.2-B show the speeds c (x) E dx/dt (x) of the impulses in the x-c plane. 

First, the kinematic equation is constructed by obtaining the direction of cosines tables. Direction of cosines is obtained by using Euler Rotational Series which is a series of three rotations used to define uniquely the orientation of rigid body in 3-dimensional space. Table 1 summarize the direction of cosines for reference frame of scapula (N) acting on reference frame of humerus (A). 

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