3,645 research outputs found
Secondary Structures in Long Compact Polymers
Compact polymers are self-avoiding random walks which visit every site on a
lattice. This polymer model is used widely for studying statistical problems
inspired by protein folding. One difficulty with using compact polymers to
perform numerical calculations is generating a sufficiently large number of
randomly sampled configurations. We present a Monte-Carlo algorithm which
uniformly samples compact polymer configurations in an efficient manner
allowing investigations of chains much longer than previously studied. Chain
configurations generated by the algorithm are used to compute statistics of
secondary structures in compact polymers. We determine the fraction of monomers
participating in secondary structures, and show that it is self averaging in
the long chain limit and strictly less than one. Comparison with results for
lattice models of open polymer chains shows that compact chains are
significantly more likely to form secondary structure.Comment: 14 pages, 14 figure
Internal rotor friction instability
The analytical developments and experimental investigations performed in assessing the effect of internal friction on rotor systems dynamic performance are documented. Analytical component models for axial splines, Curvic splines, and interference fit joints commonly found in modern high speed turbomachinery were developed. Rotor systems operating above a bending critical speed were shown to exhibit unstable subsynchronous vibrations at the first natural frequency. The effect of speed, bearing stiffness, joint stiffness, external damping, torque, and coefficient of friction, was evaluated. Testing included material coefficient of friction evaluations, component joint quantity and form of damping determinations, and rotordynamic stability assessments. Under conditions similar to those in the SSME turbopumps, material interfaces experienced a coefficient of friction of approx. 0.2 for lubricated and 0.8 for unlubricated conditions. The damping observed in the component joints displayed nearly linear behavior with increasing amplitude. Thus, the measured damping, as a function of amplitude, is not represented by either linear or Coulomb friction damper models. Rotordynamic testing of an axial spline joint under 5000 in.-lb of static torque, demonstrated the presence of an extremely severe instability when the rotor was operated above its first flexible natural frequency. The presence of this instability was predicted by nonlinear rotordynamic time-transient analysis using the nonlinear component model developed under this program. Corresponding rotordynamic testing of a shaft with an interference fit joint demonstrated the presence of subsynchronous vibrations at the first natural frequency. While subsynchronous vibrations were observed, they were bounded and significantly lower in amplitude than the synchronous vibrations
Microcanonical versus Canonical Analysis of Protein Folding
The microcanonical analysis is shown to be a powerful tool to characterize
the protein folding transition and to neatly distinguish between good and bad
folders. An off-lattice model with parameter chosen to represent polymers of
these two types is used to illustrate this approach. Both canonical and
microcanonical ensembles are employed. The required calculations were performed
using parallel tempering Monte Carlo simulations. The most revealing features
of the folding transition are related to its first-order-like character,
namely, the S-bend pattern in the caloric curve, which gives rise to negative
microcanonical specific heats, and the bimodality of the energy distribution
function at the transition temperatures. Models for a good folder are shown to
be quite robust against perturbations in the interaction potential parameters.Comment: 4 pages, 4 figure
Unbiased sampling of globular lattice proteins in three dimensions
We present a Monte Carlo method that allows efficient and unbiased sampling
of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit
each lattice site exactly once. They are often used as simple models of
globular proteins, upon adding suitable local interactions. Our algorithm can
easily be equipped with such interactions, but we study here mainly the
flexible homopolymer case where each conformation is generated with uniform
probability. We argue that the algorithm is ergodic and has dynamical exponent
z=0. We then use it to study polymers of size up to 64^3 = 262144 monomers.
Results are presented for the effective interaction between end points, and the
interaction with the boundaries of the system
Evolution of the potential-energy surface of amorphous silicon
The link between the energy surface of bulk systems and their dynamical
properties is generally difficult to establish. Using the activation-relaxation
technique (ART nouveau), we follow the change in the barrier distribution of a
model of amorphous silicon as a function of the degree of relaxation. We find
that while the barrier-height distribution, calculated from the initial
minimum, is a unique function that depends only on the level of distribution,
the reverse-barrier height distribution, calculated from the final state, is
independent of the relaxation, following a different function. Moreover, the
resulting gained or released energy distribution is a simple convolution of
these two distributions indicating that the activation and relaxation parts of
a the elementary relaxation mechanism are completely independent. This
characterized energy landscape can be used to explain nano-calorimetry
measurements.Comment: 5 pages, 4 figure
Nonuniversal power law scaling in the probability distribution of scientific citations
We develop a model for the distribution of scientific citations. The model
involves a dual mechanism: in the direct mechanism, the author of a new paper
finds an old paper A and cites it. In the indirect mechanism, the author of a
new paper finds an old paper A only via the reference list of a newer
intermediary paper B, which has previously cited A. By comparison to citation
databases, we find that papers having few citations are cited mainly by the
direct mechanism. Papers already having many citations ('classics') are cited
mainly by the indirect mechanism. The indirect mechanism gives a power-law
tail. The 'tipping point' at which a paper becomes a classic is about 21
citations for papers published in the Institute for Scientific Information
(ISI) Web of Science database in 1981, 29 for Physical Review D papers
published from 1975-1994, and 39 for all publications from a list of high
h-index chemists assembled in 2007. The power-law exponent is not universal.
Individuals who are highly cited have a systematically smaller exponent than
individuals who are less cited.Comment: 7 pages, 3 figures, 2 table
Markov processes follow from the principle of Maximum Caliber
Markov models are widely used to describe processes of stochastic dynamics.
Here, we show that Markov models are a natural consequence of the dynamical
principle of Maximum Caliber. First, we show that when there are different
possible dynamical trajectories in a time-homogeneous process, then the only
type of process that maximizes the path entropy, for any given singlet
statistics, is a sequence of identical, independently distributed (i.i.d.)
random variables, which is the simplest Markov process. If the data is in the
form of sequentially pairwise statistics, then maximizing the caliber dictates
that the process is Markovian with a uniform initial distribution. Furthermore,
if an initial non-uniform dynamical distribution is known, or multiple
trajectories are conditioned on an initial state, then the Markov process is
still the only one that maximizes the caliber. Second, given a model, MaxCal
can be used to compute the parameters of that model. We show that this
procedure is equivalent to the maximum-likelihood method of inference in the
theory of statistics.Comment: 4 page
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