Nonlinear dynamics of self-sustained supersonic reaction waves: Fickett's detonation analogue

The present study investigates the spatio-temporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. The model is an extension of Fickett's detonation model with a state dependent energy addition term. Stable and pulsating supersonic waves are predicted. With increasing sensitivity of the reaction rate, the reaction wave transits from steady propagation to stable limit cycles and eventually to chaos through the classical Feigenbaum route. The physical pulsation mechanism is explained by the coherence between internal wave motion and energy release. The results obtained clarify the physical origin of detonation wave instability in chemical detonations previously observed experimentally.Comment: 4 pages, 3 figure

Genome Wide Association Studies for Identification of Markers Linked to Sucrose Traits in Sugarcane

Sugarcane, being a complex aneu-polyploid, poses unique challenges to fine mapping of quantitative trait loci (QTL) controlling agronomic traits of interest. Genome-wide association studies (GWAS) could be a better alternative to identify molecular markers associated with specific traits due to high linkage disequilibrium in sugarcane. In the first study, marker-trait associations (MTAs) were evaluated for three sucrose traits, Brix, total recoverable sugar (TRS), and percent sucrose on 48 elite and historic Louisiana breeding clones using 1,062 alleles. These sucrose traits were highly correlated (P-value \u3c 0.0001) at \u3e0.96. TASSEL 5.1 and JMP Genomics 8.0 were compared with eight models run in each program. Two identity by state (IBS) K-matrices were paired with four different Q-matrices: a Q-matrix from STRUCTURE 2.3.4, a principal component analysis each from TASSEL and JMP Genomics, and a maximum distance separable matrix from JMP Genomics. The Q-matrix contributed the majority of variation in the results, with minor differences between the software. Additionally, three markers were identified to be associated with sucrose traits. The second study was the first study to use genotyping by sequencing for MTA in sugarcane. It used JMP Genomics to evaluate MTAs on a Louisiana core collection for 10 cane yield-component (CYC) and sucrose traits: stalk count, stalk height, stalk diameter, stalk weight, TRS, Brix, percent sucrose, fiber, Pol, and purity using 6,299 single nucleotide polymorphisms (SNPs) and 235 insertions-deletions (InDels). There were some significant (P-value \u3c 0.05) and highly significant (P-value \u3c 0.0001) correlations among CYC traits, and between fiber and CYC traits. All sucrose traits except fiber were highly correlated. A total of 154 and 209 MTAs were identified for CYC and sucrose traits, respectively. These associations were from 238 distinct markers with 56 markers associated with more than one trait. The third study assessed the genetic diversity among 1,236 clones from the World Collection of Sugarcane and Related Grasses (WCSRG) and 249 clones from the Louisiana breeding programs using 423 alleles. A 309-clone sugarcane diversity panel (SDP1) was developed for GWAS to identify markers associated with agronomic trait(s) of interest for their use in marker-assisted breeding in Louisiana and elsewhere

The refined inviscid stability condition and cellular instability of viscous shock waves

Combining work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and Texier and Zumbrun, we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite-cross-section duct the violation of the refined planar stability condition of Zumbrun--Serre, a viscous correction of the inviscid planar stability condition of Majda. More precisely, we show for a model problem involving flow in a rectangular duct with artificial periodic boundary conditions that transition to multidimensional instability through violation of the refined stability condition of planar viscous shock waves on the whole space generically implies for a duct of sufficiently large cross-section a cascade of Hopf bifurcations involving more and more complicated cellular instabilities. The refined condition is numerically calculable as described in Benzoni-Gavage--Serre-Zumbrun

Structural fingerprints of transcription factor binding site regions

Fourier transforms are a powerful tool in the prediction of DNA sequence properties, such as the presence/absence of codons. We have previously compiled a database of the structural properties of all 32,896 unique DNA octamers. In this work we apply Fourier techniques to the analysis of the structural properties of human chromosomes 21 and 22 and also to three sets of transcription factor binding sites within these chromosomes. We find that, for a given structural property, the structural property power spectra of chromosomes 21 and 22 are strikingly similar. We find common peaks in their power spectra for both Sp1 and p53 transcription factor binding sites. We use the power spectra as a structural fingerprint and perform similarity searching in order to find transcription factor binding site regions. This approach provides a new strategy for searching the genome data for information. Although it is difficult to understand the relationship between specific functional properties and the set of structural parameters in our database, our structural fingerprints nevertheless provide a useful tool for searching for function information in sequence data. The power spectrum fingerprints provide a simple, fast method for comparing a set of functional sequences, in this case transcription factor binding site regions, with the sequences of whole chromosomes. On its own, the power spectrum fingerprint does not find all transcription factor binding sites in a chromosome, but the results presented here show that in combination with other approaches, this technique will improve the chances of identifying functional sequences hidden in genomic data

A model for shock wave chaos

We propose the following model equation: $$u_{t}+1/2(u^{2}-uu_{s})_{x}=f(x,u_{s}),$$ that predicts chaotic shock waves. It is given on the half-line $x<0$ and the shock is located at $x=0$ for any $t\ge0$. Here $u_{s}(t)$ is the shock state and the source term $f$ is assumed to satisfy certain integrability constraints as explained in the main text. We demonstrate that this simple equation reproduces many of the properties of detonations in gaseous mixtures, which one finds by solving the reactive Euler equations: existence of steady traveling-wave solutions and their instability, a cascade of period-doubling bifurcations, onset of chaos, and shock formation in the reaction zone.Comment: 4 pages, 4 figure

Molecular Dynamics Simulations of Detonation Instability

After making modifications to the Reactive Empirical Bond Order potential for Molecular Dynamics (MD) of Brenner et al. in order to make the model behave in a more conventional manner, we discover that the new model exhibits detonation instability, a first for MD. The instability is analyzed in terms of the accepted theory.Comment: 7 pages, 6 figures. Submitted to Phys. Rev. E Minor edits. Removed parenthetical statement about P^\nu from conclusion

Hydrodynamic instabilities in gaseous detonations: comparison of Euler, Navier–Stokes, and large-eddy simulation

A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier–Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier–Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier–Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier–Stokes computations, which appear to be fully combusted when large-eddy simulation is employed

I. Walden Inversions Involving the Isomeric 2,3-Butanediamenes and Related Compounds. II. An Experimental Test of Kirkwood's Theory of Optical Rotatory Power. III. Zero-Point Vibrational Contributions to the Optical Activity of Isotopically Asymmetric Molecules

It has been demonstrated that reaction of ammonia with 1,2-dimethylethyleneimine is attended by single Walden inversion and that the analogous reaction of ammonia with 2,3-epoxybutane very probably proceeds in the same way. This result and other evidence have been used to assign configurations to the 3-amino-2-butanols and to draw certain conclusions about the courses of the reactions in which they are involved. Optically active 1,2-dichloropropane has been prepared and its relative configuration determined. Measurements of its optical rotatory power in different solvents and at different temperatures permit an approximate determination of the optical rotations of the two forms of the molecule corresponding to the two lowest potential minima for internal rotation about the 1,2-carbon-carbon bond. These values are compared with the results of a theoretical calculation; the resulting assignment of absolute configuration is consistent with a previous result for 2,3-epoxybutane. Kirkwood's theory of optical rotation has been modified so as to take into account contributions arising from zero-point vibrational effects. The theory is used to calculate the optical rotations of compounds of the type R1R2CHD. The result for α-deuteroethylbenzene is found to be comparable in magnitude with an experimental value and consistent in sign with previous assignments of absolute configuration.</p

Gravitational Wave Emission from the Single-Degenerate Channel of Type Ia Supernovae

The thermonuclear explosion of a C/O white dwarf as a Type Ia supernova (SN Ia) generates a kinetic energy comparable to that released by a massive star during a SN II event. Current observations and theoretical models have established that SNe Ia are asymmetric, and therefore--like SNe II--potential sources of gravitational wave (GW) radiation. We perform the first detailed calculations of the GW emission for a SN Ia of any type within the single-degenerate channel. The gravitationally-confined detonation (GCD) mechanism predicts a strongly-polarized GW burst in the frequency band around 1 Hz. Third-generation spaceborne GW observatories currently in planning may be able to detect this predicted signal from SNe Ia at distances up to 1 Mpc. If observable, GWs may offer a direct probe into the first few seconds of the SNe Ia detonation.Comment: 8 pages, 4 figures, Accepted by Physical Review Letter

Wind Energy: Applying New Technology to an Old Idea

Special PaperPg. 89-100Wind energy has been used by man since the first ships sailed the Mediterranean Sea more than four thousand years ago. In the last two thousand years, wind has been used as a motive force to pump water for the cultivation of arid regions of the world. Within the last one hundred years, the generation of electricity from the wind has had limited use in remote areas of the world. Since 1978, federal and state laws have encouraged investment in alternative energy technology. This investment has advanced wind power technology to a new level, involving innovative mechanical design and application. Through the application of entrepreneurial and engineering innovation, a new electric power generation industry has been created. Over the last six years nearly 10, 000 wind turbine generators, comprising well over 30 different designs, have been installed in California. These machines range in generator size from less than 1 kW to over 3200 kW; the rotor diameters range from less than 2 ft to over 300 ft. Since 1973, this technology has taken two distinct development paths-a few large machines (100 kW or greater) developed with federal funds, and thousands of small machines (less than 100 kW) developed by the private sector. While both large and small machines have encountered technical and economic problems, only the small machine industry has progressed to commercialization under recent limited federal and state financial assistance. An overview of the wind industry is presented, along with a review of the commercialization process. The operating history of a 15 MW project run by a power corporation is discussed. This project demonstrates a typical commercialization process for any new technology, where problems are assessed, designs evaluated and improved, and modified machines are deployed and successfully operated. If federal financial assistance abruptly ends in 1985 (as presently planned), it could retard the rapid deployment of larger second generation machines (200 kW to 400 kW). If this occurs, it would be unfortunate, because these second generation machines, while a nonfirm resource, will cost less and can be constructed faster than most conventional oil, gas, nuclear, and coal resources through the end of this century. As a result, these second generation machines will continue to reduce future energy costs and, therefore, become an important part of utility resource plans