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

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

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

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

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

Equilibrium and stability properties of detonation waves in the hydrodynamic limit of a kinetic model

A shock wave structure problem, like the one which can be formulated for the planar detonation wave, is analyzed here for a binary mixture of ideal gases undergoing the symmetric reaction A1+A1=A2+A2 . The problem is studied at the hydrodynamic Euler limit of a kinetic model of the reactive Boltzmann equation. The chemical rate law is deduced in this frame with a second-order reaction rate, in a hemical regime such that the gas flow is not far away from the chemical equilibrium. The caloric and the thermal equations of state for the specific internal energy and temperature are employed to close the system of balance laws. With respect to other approaches known in the kinetic literature for detonation problems with a reversible reaction, this paper aims to improve some aspects of the wave solution. Within the mathematical analysis of the detonation model, the equation of the equilibrium Hugoniot curve of the final states is explicitly derived for the first time and used to define the correct location of the equilibrium Chapman–Jouguet point in the Hugoniot diagram. The parametric space is widened to investigate the response of the detonation solution to the activation energy of the chemical reaction. Finally, the mathematical formulation of the linear stability problem is given for the wave detonation structure via a normal-mode approach, when bidimensional disturbances perturb the steady solution. The stability equations with their boundary conditions and the radiation condition of the considered model are explicitly derived for small transversal deviations of the shock wave location. The paper shows how a second-order chemical kinetics description, derived at the microscopic level, and an analytic deduction of the equilibrium Hugoniot curve, lead to an accurate picture of the steady detonation with reversible reaction, as well as to a proper bidimensional linear stability analysis.Brazilian Research Council (CNPq), by Italian Research Council GNFM-INdAM, and by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds of FCT, project PEstOE/MAT/UI0013/2014

A reduced model for shock and detonation waves. II. The reactive case

We present a mesoscopic model for reactive shock waves, which extends a previous model proposed in [G. Stoltz, Europhys. Lett. 76 (2006), 849]. A complex molecule (or a group of molecules) is replaced by a single mesoparticle, evolving according to some Dissipative Particle Dynamics. Chemical reactions can be handled in a mean way by considering an additional variable per particle describing a rate of reaction. The evolution of this rate is governed by the kinetics of a reversible exothermic reaction. Numerical results give profiles in qualitative agreement with all-atom studies

An Unusual 500,000 Bases Long Oscillation of Guanine and Cytosine Content in Human Chromosome 21

An oscillation with a period of around 500 kb in guanine and cytosine content (GC%) is observed in the DNA sequence of human chromosome 21. This oscillation is localized in the rightmost one-eighth region of the chromosome, from 43.5 Mb to 46.5 Mb. Five cycles of oscillation are observed in this region with six GC-rich peaks and five GC-poor valleys. The GC-poor valleys comprise regions with low density of CpG islands and, alternating between the two DNA strands, low gene density regions. Consequently, the long-range oscillation of GC% result in spacing patterns of both CpG island density, and to a lesser extent, gene densities.Comment: 15 pages (figures included), 5 figure

Laterally Propagating Detonations in Thin Helium Layers on Accreting White Dwarfs

Theoretical work has shown that intermediate mass (0.01Msun<M_He<0.1Msun) Helium shells will unstably ignite on the accreting white dwarf (WD) in an AM CVn binary. For more massive (M>0.8Msun) WDs, these helium shells can be dense enough (5x10^5 g/cc) that the convectively burning region runs away on a timescale comparable to the sound travel time across the shell; raising the possibility for an explosive outcome. The nature of the explosion (i.e. deflagration or detonation) remains ambiguous. In the case of detonation, this causes a laterally propagating front whose properties in these geometrically thin and low density shells we begin to study here. Our calculations show that the radial expansion time of <0.1 s leads to incomplete helium burning, in agreement with recent work by Sim and collaborators, but that the nuclear energy released is still adequate to realize a self-sustaining detonation propagating laterally at slower than the Chapman-Jouguet speed. Our simulations resolve the subsonic region behind the front and are consistent with a direct computation of the reaction structure from the shock strength. The ashes are typically He rich, and consist of predominantly Ti-44, Cr-48, along with a small amount of Fe-52, with very little Ni-56 and with significant Ca-40 in carbon-enriched layers. If this helium detonation results in a Type Ia Supernova, its spectral signatures would appear for the first few days after explosion. (abridged)Comment: 7 pages, 5 figure, accepted to the Astrophysical Journa