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, $r$, between the diameters of the two strands. In particular, the maximally twisted geometry may be determined as a function of $r$ 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