Perturbations uniform

Figure 3 The collapse of the peptide Ace-Nle30-Nme under deeply quenched poor solvent conditions monitored by both radius of gyration (Panel A) and energy relaxation (Panel B). MC simulations were performed in dihedral space 81% of moves attempted to change angles, 9% sampled the w angles, and 10% the side chains. For the randomized case (solid line), all angles were uniformly sampled from the interval —180° to 180° each time. For the stepwise case (dashed line), dihedral angles were perturbed uniformly by a maximum of 10° for 4>/ / moves, 2° for w moves, and 30° for side-chain moves. In the mixed case (dash-dotted line), the stepwise protocol was modified to include nonlocal moves with fractions of 20% for 4>/ J/ moves, 10% for to moves, and 30% for side-chain moves. For each of the three cases, data from 20 independent runs were combined to yield the traces shown. CPU times are approximate, since stochastic variations in runtime were observed for the independent runs. Each run comprised of 3 x 107 steps. Error estimates are not shown in the interest of clarity, but indicated the results to be robust.

When correlation is included, jxc(q) depends upon Vg as well as (q/2kp), in a way that is known from Quantum Monte Carlo studies [62] of the weakly-perturbed uniform gas. 

The elements q(i,j) of 3. defined by the way trial configurations j are generated. Usually one of the N molecules is selected at random, and each of its coordinates is given a perturbation uniformly on some fixed interval [-A,A] (for a spherically symmetric molecule). Thus the state j lies in some domain D(i) in configuration space centered on state i, with volume V(D) = N(2A). More concisely. 

The value o+l <0.4 found for H2 shows that even in the lowest state the molecules are rotating freely, the intermolecular forces producing only small perturbations from uniform rotation. Indeed, the estimated (3vq<135° corresponds to Fo <28 k, which is small compared with the energy difference 164 k of the rotational states j = 0 and j= 1, giving the frequency with which the molecule in either state reverses its orientation. The perturbation treatment shows that with this value of Fo the eigenfunctions and energy levels in all states closely approximate those for the free spatial rotator.9... 

Equation 5.1.13 shows how heat release acts a volume source. Assuming that the combustion takes place in a uniform medium at rest (Mach < 0), and writing for small perturbations, a = a + a a = p, p, v), the linearized conservation equations for mass and momentum can be used to eliminate the density in 5.1.13 to obtain a wave equation for the pressure in the presence of local heat release ... 

The foundation of our approach is the analytic calculations of the perturbed wave-functions for a hydrogenic atom in the presence of a constant and uniform electric field. The resolution into parabolic coordinates is derived from the early quantum calculation of the Stark effect (29). Let us recall that for an atom, in a given Stark eigenstate, we have ... 

An expression for e(k) in the case of a Fermi gas of free electrons can be obtained by considering the effect of an introduced point charge potential, small enough so the arguments of perturbation theory are valid. In the absence of this potential, the electronic wave functions are plane waves V 1/2exp(ik r), where V is the volume of the system, and the electron density is uniform. The point charge potential is screened by the electrons, so that the potential felt by an electron, O, is due to the point charge and to the other electrons, whose wave functions are distorted from plane waves. The electron density and the potential are related by the Poisson equation,... 

In a shooting move a trial path is generated from an old path as follows. First, one of the L states of the old path z(° 8) is selected at random with a uniform probability, i.e., all states on the path have the same probability to be selected.3 The selected state consists of the positions qsmall perturbation (ip to the old momenta... 

While batch dissolution methods are simple to set up and to operate, are widely used, and may be carefully and reproducibly standardized, they suffer from the following disadvantages (1) the hydrodynamics are usually poorly characterized, with the notable exception of the rotating disc method, (2) a small change in dissolution rate will often create an undetectable and therefore an immeasurable perturbation in the dissolution time curve, and (3) the solute concentration cb may not be uniform throughout the solution volume V. 

Rao and Singh32 calculated relative solvation free energies for normal alkanes, tetra-alkylmethanes, amines and aromatic compounds using AMBER 3.1. Each system was solvated with 216 TIP3P water molecules. The atomic charges were uniformly scaled down by a factor of 0.87 to correct the overestimation of dipole moment by 6-31G basis set. During the perturbation runs, the periodic boundary conditions were applied only for solute-solvent and solvent-solvent interactions with a non-bonded interaction cutoff of 8.5 A. All solute-solute non-bonded interactions were included. Electrostatic decoupling was applied where electrostatic run was completed in 21 windows. Each window included 1 ps of equilibration and 1 ps of data... 

The assumption that the water is adsorbed in uniform layers on all the clay surfaces for a wide range of mixtures has been criticized (2, 20). The argument is that the individual clay particles in the clay-water mixture do not expand beyond a certain distance regardless of the quantity of water which is added. The clay layers group themselves into tactoids resulting in two populations of water those molecules which are found between the tactoids and those directly perturbed by the clay layers. If true, this would invalidate the procedure used to calculate the thermodynamic properties of the adsorbed water. However, other workers have reported complete delamination of certain smectites (21., 22). It is not clear under what conditions tactoids will form, or not, and this uncertainty is underlined in (21) (see remarks by Nadeau and Fripiat, pages 146-147). 

Our questions broadened to consider how the transport and metabolic capabilities of these aquatic species compare with those of mammalian species. One reason for asking such a question is to assess whether the presence or absence of these capabilities alters the ability of fish to survive in toxic environments. Survival mechanisms fall into two catagories - behavioral and physiologic. An example of a behavioral mechanism could be as simple as a fish avoiding that area of a stream which contains toxic quantitites of phenol. When external perturbations caused by pollutants are small, homeostatic mechanisms such as those of the liver and kidney, allow fish to adapt to the body of water in which they exist. The problem then is related to defining the limits to which homeostatic phenomena can be stressed in aquatic species. An important reason to establish such information in fish is that bodies of water are the "ultimate sink" for a number of pollutants (12). Thus, while a behavioral response such as removing itself from a toxic environment is invariably available to a mammalian species, this type of response is impossible for a fish if a toxic xenobiotic occurs uniformly throughout an entire body of water. 

The introduction of branching in the Kirkwood formula and the KR calculations can be accomplished in a relatively easy way if Gaussian statistics corresponding to ideal chains are maintained. This description cannot, however, be very accurate in molecules with centers of high functionality because of the presence of cores with a high density of polymer units, which profoundly perturbs the internal distribution of distances. Stockmayer and Fixman [81 ] employed the Kirwood formula and Gaussian statistics to calculate h in the case of uniform stars, obtaining an analytical formula. They also performed a KR evaluation of the viscosity and proposed that g could be evaluated from the approximation... 

Table 1. First-order relativistic one-electron perturbation operators from the introduction of a uniform...

The C-terminal domain (85 amino acid residues, not completely denatured at 90 °C) of the so-called a subunit of the RNAP from the extremely thermophilic eubacterium T. thermophilus (Tt) has been expressed uniformly N/ C-labelled and structurally characterized by the NMR spectroscopy. The tertiary structure of the domain, comprising a helical turn and four helices, was found to be almost identical to that of the corresponding domain from the mesophilic E. coli, despite 32% sequence homology. The interaction of the Tt domain with a variety of DNAs at 37 °C and 50 °C was investigated by chemical shift perturbation of the NMR signals and the DNA binding site was localized. ... 

---