Rigid-body critical

When the previously described intersections lie along the straight line on the critical speed map with a slope of 0.5, the critical speed is bearing controlled. This condition is often referred to as a rigid-body critical. ... 

In principle, every conformer of a set of flexible ligands could be stored in a database, and then each conformation could be evaluated with rigid-body docking algorithms. The size of the ensemble is critical since the computing time increases linearly with the number of conformations and the quality of the result drops with larger differences between the most similar conformation of the ensemble and the actual complex conformation. Thus a balance must be struck between computing time requirements and the desire to cover all of conformational space. 

An important problem is to analyze the stability of fluid flows. With the exception of the Taylor-Couette and Saffman Taylor problems, this chapter has focused on stability questions when the base state of the system was one with no motion (or rigid-body motion), so that instability addresses the conditions for spontaneous onset of flow. An equally valid question is whether a particular flow, such as Poiseuille flow in a pipe (or any of the other flows that we have analyzed in previous chapters of this book), is stable, especially to infinitesimal perturbations as linear instability determines whether the particular flow is actually realizable in experiments. This question was first mentioned back in Chapter 3 when we analyzed simple unidirectional flow problems and noted that solutions such as Poiseuille s solution for flow through a tube was a valid solution of the Navier-Stokes equations for all Reynolds numbers, even though common experience tells us that beyond some critical Reynolds number there is a transition to turbulent flow in the tube. 

The efficiency of widely used programs for rigid body minimization of crystal structures was criticized by Gibson and Scheraga. They introduced a new algorithm, based on secant methods (computationally fast methods to compute derivative matrices ) that efficiently calculate the energy gradient with respect to the minimization variables. 

Kharlamov, M. P. Topologic analysis of classical integrable systems in rigid-body dynamics. Dokl. Akad. Nauk SSSR. 278 (1983), No. 6, 1322-1325. Pogosyan, T. I. Critical Integral Surfaces in the Clebsch Problem. Mekhanika Tverdogo Tela 16, 19-24. Kiev. 

The treatment which follows is based on that in E. B. Wilson, Jr., and J. B, Howard,. ]. Chem. Phys., 4 260 (1936), but has been corrected to conform to the criticism of B. T. Darling and D. M. Dennison, Phys. Rev., 57 128 (1940). The -ector technique used was adapted from the similar treatment of rigid bodies by b. Page, Introduction to Theoretical Physics, 2d ed., Chap. 2, Van Nostrand, New York, 1934. See also H. Margenaii and G. M. Murphy, The Mathematics of Physics and Chemistry, Chap. 9, an Xostrand, New York, 1943. 

Using MD simulations [82,83], we studied three models, each of which has a LL critical point. Two (the TIP5P and the ST2) treat water as a multiple-site rigid body that interacts via electrostatic site-site interactions complemented by a Lennard-Jones potential. The third is the spherically symmetric two-scale Jagla potential with attractive and repulsive ramps. In all three models the loci of maxima of the relevant response functions, Ki and Cp, which coincide close to the critical point and give rise to the Widom line, were evaluated. The hypothesis that, for all three potentials, a dynamic crossover occurs when the Widom line is crossed, was carefully explored. 

In order to increase the critical speed of the rotor a number of different modifications can be made to the rotor system. By supporting one or both main bearings in a flexible pillow block the first critical speed of the rotor can be turned into a low speed rigid-body motion for the rotor. It can then be operated supercritically with respect to this critical speed. Other modifications are the floating conveyor and the separately supported gearbox. 

At low ij), the cmve is linear. At high values of < >, there is a critical value, where no fiirther shrinks e takes place, corresponding to liquid just filling the pores at the leatherhard point. This critical volume fraction, <, occurs when the mechanical properties of the particle network is sufficiently rigid to resist the compressive capillary pressure. The liquid expansion of a ceramic green body, a, is defined by... 

A goal of this essay is to contribute to this body of critical literature on chemical kinds, but from a different direction. It considers the impact of chemical synthesis on the natural/non-natural divide. The point is simply that the properties of synthesized compounds can satisfy criteria just as easily as naturally occurring compounds, and thus that the intuitive connection between essences (or necessities or rigidities) and natural kinds is not in fact warranted. For example, take naturally synthesized proteins versus artificially synthesized proteins that are in every other way identical to the former. Is one a natural kind, the other not What is the basis for categorization ... 

First, we shall illustrate this remark by studying the form function of a rigid rod in various cases then, afterwards, we shall consider the form factors associated with convex solid bodies of dimension D. Finally, we shall determine the asymptotic behaviour of the form factor of critical continuous polymer chains (Brownian chains and Kuhnian chains). 

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