256 research outputs found
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
A model for shock wave chaos
We propose the following model equation:
that predicts chaotic shock waves.
It is given on the half-line and the shock is located at for any
. Here is the shock state and the source term 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
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
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
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
Comparative gene prediction in human and mouse.
The completion of the sequencing of the mouse genome promises to help predict human genes with greater accuracy. While current ab initio gene prediction programs are remarkably sensitive (i.e., they predict at least a fragment of most genes), their specificity is often low, predicting a large number of false-positive genes in the human genome. Sequence conservation at the protein level with the mouse genome can help eliminate some of those false positives. Here we describe SGP2, a gene prediction program that combines ab initio gene prediction with TBLASTX searches between two genome sequences to provide both sensitive and specific gene predictions. The accuracy of SGP2 when used to predict genes by comparing the human and mouse genomes is assessed on a number of data sets, including single-gene data sets, the highly curated human chromosome 22 predictions, and entire genome predictions from ENSEMBL. Results indicate that SGP2 outperforms purely ab initio gene prediction methods. Results also indicate that SGP2 works about as well with 3x shotgun data as it does with fully assembled genomes. SGP2 provides a high enough specificity that its predictions can be experimentally verified at a reasonable cost. SGP2 was used to generate a complete set of gene predictions on both the human and mouse by comparing the genomes of these two species. Our results suggest that another few thousand human and mouse genes currently not in ENSEMBL are worth verifying experimentally
The Erpenbeck high frequency instability theorem for ZND detonations
The rigorous study of spectral stability for strong detonations was begun by
J.J. Erpenbeck in [Er1]. Working with the Zeldovitch-von Neumann-D\"oring (ZND)
model, which assumes a finite reaction rate but ignores effects like viscosity
corresponding to second order derivatives, he used a normal mode analysis to
define a stability function V(\tau,\eps) whose zeros in
correspond to multidimensional perturbations of a steady detonation profile
that grow exponentially in time. Later in a remarkable paper [Er3] he provided
strong evidence, by a combination of formal and rigorous arguments, that for
certain classes of steady ZND profiles, unstable zeros of exist for
perturbations of sufficiently large transverse wavenumber \eps, even when the
von Neumann shock, regarded as a gas dynamical shock, is uniformly stable in
the sense defined (nearly twenty years later) by Majda. In spite of a great
deal of later numerical work devoted to computing the zeros of V(\tau,\eps),
the paper \cite{Er3} remains the only work we know of that presents a detailed
and convincing theoretical argument for detecting them.
The analysis in [Er3] points the way toward, but does not constitute, a
mathematical proof that such unstable zeros exist. In this paper we identify
the mathematical issues left unresolved in [Er3] and provide proofs, together
with certain simplifications and extensions, of the main conclusions about
stability and instability of detonations contained in that paper.
The main mathematical problem, and our principal focus here, is to determine
the precise asymptotic behavior as \eps\to \infty of solutions to a linear
system of ODEs in , depending on \eps and a complex frequency as
parameters, with turning points on the half-line
Ignition of thermally sensitive explosives between a contact surface and a shock
The dynamics of ignition between a contact surface and a shock wave is investigated using a
one-step reaction model with Arrhenius kinetics. Both large activation energy asymptotics and
high-resolution finite activation energy numerical simulations are employed. Emphasis is on comparing
and contrasting the solutions with those of the ignition process between a piston and a shock,
considered previously. The large activation energy asymptotic solutions are found to be qualitatively
different from the piston driven shock case, in that thermal runaway first occurs ahead of
the contact surface, and both forward and backward moving reaction waves emerge. These waves
take the form of quasi-steady weak detonations that may later transition into strong detonation
waves. For the finite activation energies considered in the numerical simulations, the results are
qualitatively different to the asymptotic predictions in that no backward weak detonation wave
forms, and there is only a weak dependence of the evolutionary events on the acoustic impedance
of the contact surface. The above conclusions are relevant to gas phase equation of state models.
However, when a large polytropic index more representative of condensed phase explosives is used,
the large activation energy asymptotic and finite activation energy numerical results are found to
be in quantitative agreement
Steady non-ideal detonations in cylindrical sticks of expolsives
Numerical simulations of detonations in cylindrical rate-sticks of highly
non-ideal explosives are performed, using a simple model with a weakly pressure
dependent rate law and a pseudo-polytropic equation of state. Some numerical issues
with such simulations are investigated, and it is shown that very high resolution
(hundreds of points in the reaction zone) are required for highly accurate (converged)
solutions. High resolution simulations are then used to investigate the qualitative
dependences of the detonation driving zone structure on the diameter and degree of
confinement of the explosive charge. The simulation results are used to show that,
given the radius of curvature of the shock at the charge axis, the steady detonation
speed and the axial solution are accurately predicted by a quasi-one-dimensional
theory, even for cases where the detonation propagates at speeds significantly below
the Chapman-Jouguet speed. Given reaction rate and equation of state models, this
quasi-one-dimensional theory offers a significant improvement to Wood-Kirkwood
theories currently used in industry
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