5,220 research outputs found
Transcription and the Pitch Angle of DNA
The question of the value of the pitch angle of DNA is visited from the
perspective of a geometrical analysis of transcription. It is suggested that
for transcription to be possible, the pitch angle of B-DNA must be smaller than
the angle of zero-twist. At the zero-twist angle the double helix is maximally
rotated and its strain-twist coupling vanishes. A numerical estimate of the
pitch angle for B-DNA based on differential geometry is compared with numbers
obtained from existing empirical data. The crystallographic studies shows that
the pitch angle is approximately 38 deg., less than the corresponding
zero-twist angle of 41.8 deg., which is consistent with the suggested principle
for transcription.Comment: 7 pages, 3 figures; v2: minor modifications; v3: major modifications
compared to v2. Added discussion about transcription, and reference
Twisting Uneven Ropes
A classical two-stranded rope can be made by twisting two identical strands
together under strain. Despite being conceptually simple, the contact-equations
for helically twisted identical strands have only been solved within the last
20 years. Our goal here is basic: to understand the twisting of two circular
strands, where one is thicker than the other. This is what we call an uneven
rope. The geometry of the uneven rope depend on the ratio, , between the
diameters of the two strands. In particular, the maximally twisted geometry may
be determined as a function of by solving the contact-equations for the two
strands numerically.Comment: 6 pages, 4 figure
TMB: Automatic Differentiation and Laplace Approximation
TMB is an open source R package that enables quick implementation of complex
nonlinear random effect (latent variable) models in a manner similar to the
established AD Model Builder package (ADMB, admb-project.org). In addition, it
offers easy access to parallel computations. The user defines the joint
likelihood for the data and the random effects as a C++ template function,
while all the other operations are done in R; e.g., reading in the data. The
package evaluates and maximizes the Laplace approximation of the marginal
likelihood where the random effects are automatically integrated out. This
approximation, and its derivatives, are obtained using automatic
differentiation (up to order three) of the joint likelihood. The computations
are designed to be fast for problems with many random effects (~10^6) and
parameters (~10^3). Computation times using ADMB and TMB are compared on a
suite of examples ranging from simple models to large spatial models where the
random effects are a Gaussian random field. Speedups ranging from 1.5 to about
100 are obtained with increasing gains for large problems. The package and
examples are available at http://tmb-project.org
Experimental evaluation of combustor concepts for burning broad property fuels
A baseline CF6-50 combustor and three advanced combustor designs were evaluated to determine the effects of combustor design on operational characteristics using broad property fuels. Three fuels were used in each test: Jet A, a broad property 13% hydrogen fuel, and a 12% hydrogen fuel blend. Testing was performed in a sector rig at true cruise and simulated takeoff conditions for the CF6-50 engine cycle. The advanced combustors (all double annular, lean dome designs) generally exhibited lower metal temperatures, exhaust emissions, and carbon buildup than the baseline CF6-50 combustor. The sensitivities of emissions and metal temperatures to fuel hydrogen content were also generally lower for the advanced designs. The most promising advanced design used premixing tubes in the main stage. This design was chosen for additional testing in which fuel/air ratio, reference velocity, and fuel flow split were varied
Predictions for the First Parker Solar Probe Encounter
We examine Alfv\'en Wave Solar atmosphere Model (AWSoM) predictions of the
first Parker Solar Probe (PSP) encounter. We focus on the 12-day closest
approach centered on the 1st perihelion. AWSoM (van der Holst et al., 2014)
allows us to interpret the PSP data in the context of coronal heating via
Alfv\'en wave turbulence. The coronal heating and acceleration is addressed via
outward-propagating low-frequency Alfv\'en waves that are partially reflected
by Alfv\'en speed gradients. The nonlinear interaction of these
counter-propagating waves results in a turbulent energy cascade. To apportion
the wave dissipation to the electron and anisotropic proton temperatures, we
employ the results of the theories of linear wave damping and nonlinear
stochastic heating as described by Chandran et al. (2011). We find that during
the first encounter, PSP was in close proximity to the heliospheric current
sheet (HCS) and in the slow wind. PSP crossed the HCS two times, namely at
2018/11/03 UT 01:02 and 2018/11/08 UT 19:09 with perihelion occuring on the
south of side of the HCS. We predict the plasma state along the PSP trajectory,
which shows a dominant proton parallel temperature causing the plasma to be
firehose unstable.Comment: 16 pages, 5 figures; accepted for publication in the Astrophysical
Journal Letter
On topological phases of spin chains
Symmetry protected topological phases of one-dimensional spin systems have
been classified using group cohomology. In this paper, we revisit this problem
for general spin chains which are invariant under a continuous on-site symmetry
group G. We evaluate the relevant cohomology groups and find that the
topological phases are in one-to-one correspondence with the elements of the
fundamental group of G if G is compact, simple and connected and if no
additional symmetries are imposed. For spin chains with symmetry
PSU(N)=SU(N)/Z_N our analysis implies the existence of N distinct topological
phases. For symmetry groups of orthogonal, symplectic or exceptional type we
find up to four different phases. Our work suggests a natural generalization of
Haldane's conjecture beyond SU(2).Comment: 18 pages, 7 figures, 2 tables. Version v2 corresponds to the
published version. It includes minor revisions, additional references and an
application to cold atom system
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