Local force

The aim of the model is to find the relation between the energy dissipated in growing the crack tip craze, as that is the macroscopic toughness and the local force at the fibril closest to the crack tip which controls the molecular level failure... 

Resistance to puncture is another type of loading. It is of particular interest in applications involving sheet and film as well as thin-walled tubing or molding and other membrane type loaded structures. Hie surface skins of sandwich panels are another area where it is important. A localized force is applied by a relatively sharp object perpendicular to the plane of the sheet of material being stressed. If the material is thick compared to the area of application of the stress, it is effectively a localized compression stress with some shear effects as the material is deformed below the surface of the sheet. 

From simple considerations of the local force balance near the triple line, or of free energy changes, the global driving force for dewetting per unit length of triple line, F , is... 

Any or all of these forces may result in local stresses within the fluid. Stress can be thought of as a (local) concentration of force, or the force per unit area that bounds an infinitesimal volume of the fluid. Now both force and area are vectors, the direction of the area being defined by the normal vector that points outward relative to the volume bounded by the surface. Thus, each stress component has a magnitude and two directions associated with it, which are the characteristics of a second-order tensor or dyad. If the direction in which the local force acts is designated by subscript j (e.g., j = x, y, or z in Cartesian coordinates) and the orientation (normal) of the local area element upon which it acts is designated by subscript i, then the corresponding stress component (ay) is given by... 

In the Lagrangian approach, individual parcels or blobs of (miscible) fluid added via some feed pipe or otherwise are tracked, while they may exhibit properties (density, viscosity, concentrations, color, temperature, but also vorti-city) that distinguish them from the ambient fluid. Their path through the turbulent-flow field in response to the local advection and further local forces if applicable) is calculated by means of Newton s law, usually under the assumption of one-way coupling that these parcels do not affect the flow field. On their way through the tank, these parcels or blobs may mix or exchange mass and/or temperature with the ambient fluid or may adapt shape or internal velocity distributions in response to events in the surrounding fluid. 

Solid surfaces of single crystals provide to some extent the realization of a well-defined two-dimensional (2D) periodic array of atoms. However, the loss of vertical translational invariance at the surface changes the local force held with respect to the bulk forces. As seen in section 3 the charge redistribution is... 

Because of the symmetry conditions integration of the local forces (160) results in vanishing electric and magnetic volume forces Fe and Fm as given by Eqs. (13). Of the Poynting vector S and the electromagnetic momentum vector g... 

In many cases of transport in solids, the atoms (ions) of one sublattice of the crystal are (almost) immobile. Here, we can identify the crystal lattice with the external (laboratory) frame and define the fluxes relative, to this immobile sublattice (to = 0). v° is bk-Xk (Eqn. (4.51)) where Xk is the sum of all local forces which can be applied externally (eg., an electric field), or which may stem from fields induced by the, (Fickian) diffusion process itself (eg., self-stresses). An example of such a diffusion process that leads to internal forces is the chemical interdiffusion of A-B. If the lattice parameter of the solid solution changes noticeably with concentration, an elastic stress field builds up and acts upon the diffusing particles, it depends not only on the concentration distribution, but on the geometry of the bounding crystal surfaces as well. 

Conceptually, predecessors of the scanning force microscope are the surface force apparatus (SFA) [73,74] and the stylus profilometer [75,76]. The SFA enables measurement of normal and friction forces between molecularly smooth surfaces as small as 1 nN as a function of distance with a resolution of 0.1 nm. In addition to the local force measurement, the profilometer provides a topographic map of the surface by scanning the surface with a sharp probe. However, the profilometer is not suitable for structure characterisation because of the large radius of the tip (about 1 pm) and the low sensitivity of the force sensor (in the range of 1(T2 to 1(T5 N). 

Complementary to the SFA experiments, SFM techniques enabled direct, non-destructive and non-contact measurement of forces which can be as small as 1 pN. Compared to other probes such as optical tweezers, surface force balance and osmotic stress [378-380], the scanning force microscope has an advantage due to its ability in local force measurements on heterogeneous and rough surfaces with excellent spatial resolution [381]. Thus, a force-distance dependence measured from a small surface area provides a microscopic basis for understanding the macroscopic interfacial properties. Furthermore, lateral mapping... 

Pyranine has been used to study the proton dissociation and diffusion dynamics in the aqueous layer of multilamellar phospholipid vesicles [101], There are 3-10 water layers interspacing between the phospholipid membranes of a multilamellar vesicle, and their width gets adjusted by osmotic pressure [102], Pyranine dissolved in these thin layers of DPPC and DPPC+cholesterol multilamellar vesicles were used as a probe for the study. Before the photoreleased proton escapes from the coulombic cage, the probability of a proton excited-anion recombination was found to be higher than in bulk. This was attributed to the diminished water activity in the thin layer. It was found that the effect of local forces on proton diffusion at the timescale of physiological processes is negligible. 

Kjerfve, B J., Greer, J.E., and Crout, R.L. (1978) Low-frequency response of estuarine sea level to non-local forcing. In Estuarine Interactions (Wiley, M.L., ed.), pp. 497-513, Academic Press, New York. 

Wang, D.P., and Elliott, A.J. (1978) Non-tidal variability in the Chesapeake Bay and Potomac River evidence for non-local forcing. J. Phys. Oceanogr. 8, 225-232. 

A method to calculate J]j, based on the local approximation to spin density functional theory has been developed by Liechtenstein et al. [51, 52]. Using spherical charge and spin densities and a local force theorem, expression for Jjj is... 

To attain their purpose, all sides employ all kinds of methods to mobilize local forces, which in the current new order oppose and undermine the Indonesian republican government overtly and covertly. Among these forces are remnants of the G-30-S PKI and groups which are defending the political principles of the old order. 

A certain boiler employs one hundred 2-cm-diameter tubes I m long. The boiler is designed to produce local forced-convection boiling of water at 3 MPa pressure with AT, = I0°C. Estimate the total heat-transfer rate and the amount of saturated vapor which can be produced at 3 MPa. 

A thermodynamic driving force occurs when a difference in potential exists, and its direction is the maximal decrease in pr Consequently, at the point x. y, z, the local force X causing the flow of component i is expressed by... 

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