Strings of beads

The basic concepts of shock and particle velocities are well illustrated by an example first introduced by Duvall and Band (1968). Here we assume that a string of beads of diameter d, mass m, and spaced a fixed distance / apart on a smooth (frictionless) wire is impacted by a rigid, massive piston at velocity v. Each bead is assumed to undergo perfectly elastic, rigid-body motion upon impact with its neighbor. 

This simple example Illustrates the important kinematic properties of shock waves, particularly the concepts of particle velocity and shock velocity. The particle velocity is the average velocity acquired by the beads. In this example, it is the piston velocity, v. The shock velocity is the velocity at which the disturbance travels down the string of beads. In general, at time n//2v, the disturbance has propagated to the nth bead. The distance the disturbance has traveled is therefore n d -b /), and the shock velocity is... 

If the string of beads is considered to be a single entity, the part behind the disturbance has a kinetic energy per bead of... 

The difference between these two energies can be identified with an agitation energy of the beads that does not participate in translating the string of beads as a whole. This is analogous to the internal energy of a real material. This... 

Perlen-glanz, m. pearly (or nacreous) luster, -probe, /. bead test, -schnur, /. string of beads or pearls. 

Perl-mutterpapier, n, naereous paper, -rohr, n, -rohre, /. bead tube (tube filled with glass beads), -sago, m. pearl sago, -salz, n. micro-eosmic salt, -samen, m. seed pearl, -schicht, /. nacreous layer, -schnur, /. string of beads or pearls row of droplets, -seide, /. embroidery silk ardassine, -spat, m, pearl spar (pearly dolomite), -stein, m, perlite adu-laria. -sucht, /. bovine tubereulosis. -weisa, n. pearl white. 

These also are non-sporing, spherical organisms which grow characteristically in chains like strings of beads, and can grow aerobically or anaerobically. 

Further refinements of the model (Ganguly and Magee, 1956) include interspur overlap in the same track. The track is seen as a string of beads. The beads are spurs, the average spacing of which corresponds to the local LET of the particle. The free path of the incident particle between spur centers is distributed exponentially with a mean value given by... 

The focus of this chapter is on an intermediate class of models, a picture of which is shown in Fig. 1. The polymer molecule is a string of beads that interact via simple site-site interaction potentials. The simplest model is the freely jointed hard-sphere chain model where each molecule consists of a pearl necklace of tangent hard spheres of diameter a. There are no additional bending or torsional potentials. The next level of complexity is when a stiffness is introduced that is a function of the bond angle. In the semiflexible chain model, each molecule consists of a string of hard spheres with an additional bending potential, EB = kBTe( 1 + cos 0), where kB is Boltzmann s constant, T is... 

Actin filaments are thought to exist in a double-stranded, right-hand helix with 14 subunits (per strand) per complete turn (Fig. 4.4), and a crossover distance of 38 nm. This strings of beads appearance is 70 A in diameter and thought to represent the structure of thin filaments. As the new fila-... 

We are now in a position to ask a more sophisticated question related to protein structure what is the three-dimensional structure of the protein This question assumes something that is by no means obvious that a protein has a unique three-dimensional structure. Think of the protein ribonuclease A as 124 beads on a string. You can imagine that it could fold up in a great many ways, just like you can fold up a string of beads in a great many ways. 

When peptides containing four cysteine residues in the molecule are randomly oxidized, three different disulfide isomers can be formed (Scheme 1), isomer 1 with the disulfides aligned in parallel manner, isomer 2 with crossed disulfides and isomer 3 with sequential disulfides these isomers are also named in a more descriptive manner as the ribbon, globule and string-of-beads isomers. 28 The preferred formation of one of the isomers strongly depends upon the sequential topology of the cysteine residues, but also upon the sequence composition that may favor more or less globular structures with hydrophobic cores. 

Strings of beads that are modeled on real proteins fold much better than random sequences in the computer.45... 

Actin is a protein that polymerizes at physiologic ionic strength levels into thin filaments. The monomers in actin are oriented to one another by a rotation of 166° and a translation of 275 nm. This gives an assembly that resembles a double-stranded string of beads. 

In fact, the proteins used by hydra in their nervous systems are identical to some of the proteins that our brains use to help us think and feel. These proteins are called neuropeptides. A neuropeptide is like a string of beads, and each bead is an amino acid. Neuropeptides may be assembled from only a few... 

The polymer is then treated as a string of beads where the frictional force on each bead is described by Stokes law. However, this results in a relationship between [77] and molecular weight, M, of the form [77] AF+Jl, where A is a small fraction. Experimentally, we have seen that [77] AP, where a usually has values between 0.5 and 0.8. Obviously, the assumption that the polymer beads do not perturb the solvent is not a good one. 

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