Elastic spring

Figure Bl.20.1. Direct force measurement via deflection of an elastic spring—essential design features of a direct force measurement apparatus.

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

The press temperature influences the possible press time and therefore the capacity of the production line. The minimal press time has to guarantee that the bond strength of the still hot board can withstand the internal steam pressure as well as the elastic spring back of the board when the press opens or when the board leaves the continuous press. 

Federmesser, n. penknife, fedem, v.i. be elastic, spring lose feathers, molt. 

Bueche (16,152) had earlier proposed a related theory based on a spring-bead model (springs with a rubberlikc elasticity spring constant coupled in a linear chain by beads whose friction factor supplies the viscous resistance). This theory as extended by Fox and co-workers (28,153) gives... 

Elastic recovery, 19 744 in olefin fibers, 11 227—228 Elastic scattering, 24 88-89 Elastic springs, in virtual two-way SMA devices, 22 346-347 Elastic waves, 17 422 Elastohydrodynamic (EHD) lubrication regime, 15 211-212 Elastomer-coated dies, in bar soap manufacture, 22 752 Elastomer designations, ASTM, 9 552t Elastomeric fibers, dyeing, 9 204 Elastomeric polycarboranylsiloxanes,... 

The cantilevers can be modelled as elastic springs (Fig. 4), generally characterised by spring constants calculated from the resonant frequency of the spring as follows ... 

It is convenient to use a simple weightless Hookean, or ideal, elastic spring with a modulus G and a simple Newtonian (fluid) dashpot or shock absorber having a liquid with a viscosity of 17 as models to demonstrate the deformation of an elastic solid and an ideal liquid, respectively. The stress-strain curves for these models are shown in Figure 14.1. 

Models are used to describe the behavior of materials. The fluid or liquid part of the behavior is described in terms of a Newtonian dashpot or shock absorber, while the elastic or solid part of the behavior is described in terms of a Hookean or ideal elastic spring. The Hookean spring represents bond flexing, while the Newtonian dashpot represents chain and local segmental movement. 

The analogous case of an elastic spring satisfying Hooke s law (t = kt) was treated previously in (2.63a). 

Figure H3.3.4 Mechanical models are often used to model the response of foods in creep or stress relaxation experiments. The models are combinations of elastic (spring) and viscous (dashpot) elements. The stiffness of each spring is represent by its compliance (J= strain/stress), and the viscosity of each dashpot is represent by a Newtonian viscosity (ri). The form of the arrangement is often named after the person who originally proposed the model. The model shown is called a Burgers model. Each element in the middle—i.e., a spring and dashpot arranged in parallel—is called a Kelvin-Voigt unit.

Freiburg, A., Trombitas, K., and Hell, W. (2000). Series of exon-skipping events in the elastic spring region of titin as the structural basis for myofibrillar elastic diversity. Circ. Res. 86, 1114-1121. 

In this communication we will give a description of the vibronic E-e interaction in an optical center in a crystal near one of the minima of the trough of the deformed (due to the quadratic vibronic coupling) Mexican-hat-type AP. We will also present a derivation of the nonperturbative formula describing the temperature dependence of the ZPL in the case of an arbitrary change of the elastic springs on the electronic transition. Then we will study a case when the excited state is close to the dynamical instability. Finally, we will apply the obtained general results to the ZPLs in N-V centers in diamond. 

Here wi and w2 are the positive elastic springs (wli2 > 0), qh 1=1, 2 is the symmetrized difference of the central displacements of the central atom and its nearest neighboring atoms, i denotes the row of the -representation, Qni are all the other displacements of the crystal, being orthogonal to q and q2,1 is the second-order unit matrix, configurational coordinates q and q2 can be expanded into the normal coordinates xn and x2j of the -representation as follows ... 

To describe the effect of the change of the elastic springs on the optical spectrum of an impurity center, we use the adiabatic approximation. In this approximation, phonons are described by different phonon Hamiltonians in different electronic states. The optical spectrum, which corresponds to a transition between different electronic states is determined by the expression /( >) = const X oj1 1 I(oj) [28], where the — sign corresponds to the absorption spectrum and the + sign stands for the emission spectrum,... 

Here we consider the case when the elastic springs in the excited state are remarkably weakened (the weakening of the springs in the ground state can be regarded analogously). 

In real systems a number of coordinates usually contribute to y and 8 not all of them can be related to softening modes. Therefore, one should expect that at low temperatures and I(w — u cr)/wcr << 1 the ZPL width can be described by the equations y y0 + aT3 + bT1. where the oc T1 term accounts for the contribution of hard modes (a and b are positive parameters). The temperature dependence of the position of the ZPL can be approximated by the equation 8T /xT2 — vT4, where the sign of /i may be positive or negative. The term oc T4 accounts for the contribution of hard modes. The sign of v is positive if the elastic springs are reduced with excitation. 

Consequently both the temperature broadening and the main part of the shift of the ZPL of the N-V centers at 637 nm ZPL are well described by presented theory supposing that strong softening of the elastic springs in the excited state takes place (see Figs 2a and b). Only relatively small blue shift at T < 40 K most probably has another origin it can be explained by repopulation between strain-induced sublevels of the excited 3E state [32]. 

The Maxwell model can be represented by a purely viscous damper and a purely elastic spring connected in series, as shown in the diagram. The model can be represented by the following equation ... 

The Kelvin-Voigt model, also known as the Voigt model, consists of a Newtonian damper and Hookean elastic spring connected in parallel, as shown in the picture. It is used to explain the stress relaxation behaviors of polymers. 

An elastic spring tethers the two beads together and exerts a force on the beads tends to restore the system to its equilibrium coil-like shape. If the spring is taken to e a force constant, K (l R ), the spring force is... 

Single-molecule theories originated in early polymer physics work (45) to describe the flow behavior of very dilute polymer solutions, which are free of interpolymer chain effects. Most commonly, the macromolecular chain, capable of viscoelastic response, is represented by the well-known bead-spring model or cartoon, shown in Fig. 3.8(a), which consists of a series of small spheres connected to elastic springs. 

A reasonable approximation for the force between two adjacent particles is given by the so-called FENE (finitely extendable non-linear elastic) spring force law (Bird et al. 1987a)... 

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