Translational and rotational equations of motion are derived for ligament's points and special cases of translational displacements of the tooth root are analysed.
In particular, for gene regulatory networks, i.e., transcriptional and translational processes, the Hill equation is applied.
For gene regulatory networks, i.e., transcriptional and translational processes, the Hill equation is applied [ 13, 26].
The equation for translational motility of the nucleus in the cell geometry can be approximated as γ = 9 π 2 2 η cell r nucleus 4 ϵ 5 / 2 where ε= rcell−rnucleus )/rnucleus is the cell clearance.
Accounting for translational invariance, the elastodynamic equations of prestressed helical structures yield a 2D problem posed on the cross-section, corresponding to a so-called semi-analytical finite element (SAFE) formulation.
Bubble radial oscillation was simulated by a modified Keller Miksis equation and bubble translational motion was derived from an equation obtained by applying Newton's second law to a bubble in a liquid medium.
The Stokes Einstein equation for the translational diffusion coefficient of spherical objects (eq 3 ) was used in this study to calculate an effective hydrodynamic diameter (HD).
Even though it is widely used, the cited experimental justification for the translational misreading probability scheme in equation 2 is weak, especially in that translational misreading is more transition-biased in misreading of the second codon position than in the first.
The equations of motion for the particles are given by the momentum equations for the translational velocity u p = (u p,v p,w p ) T m_{p} : frac{mathrm{d}mathbf{u}_{p}}{mathrm{d} t} = underbrace{oint_{Gamma_{p}} boldsymbol{tau} cdot mathbf{n}: {mathrm{d}A}}_{=mathbf{F}_{h}} + underbrace{V_{p}:(rho_{p}-rho_{f}): mathbf{g}}_{=mathbf{F}_{g}} + mathbf{F}_{l} + mathbf{F}_{c}, (25).
The governing equations for the translational and rotational motion of particles are outlined, and simulation results for ellipsoidal particles with minimum diameters from 1 to 50 μm and aspect ratios from one to ten are presented.
To obtain the system of equations describing the translational motion of the tooth root along the z-axis, it is necessary to equalize displacements u 0x and u 0y and all angles of rotation in (9) to zero.
