467 research outputs found
Effect of thermal expansion on the linear stability of planar premixed flames for a simple chain-branching model: The high activation energy asymptotic limit
The linear stability of freely propagating, adiabatic, planar premixed
ames is investigated in the context of a simple chain-branching
chemistry model consisting of a chain-branching reaction step and a completion reaction step. The role of chain-branching is governed
by a crossover temperature. Hydrodynamic effects, induced by thermal expansion, are taken into account and the results compared and
contrasted with those from a previous purely thermal-di�usive constant density linear stability study. It is shown that when thermal
expansion is properly accounted for, a region of stable
ames predicted by the constant density model disappears, and instead the
ame
is unstable to a long-wavelength cellular instability. For a pulsating mode, however, thermal expansion is shown to have only a weak
e�ect on the critical fuel Lewis number required for instability. These e�ects of thermal expansion on the two-step chain-branching
ame
are shown to be qualitatively similar to those on the standard one-step reaction model. Indeed, as found by constant density studies, in
the limit that the chain-branching crossover temperature tends to the adiabatic
ame temperature, the two-step model can be described
to leading order by the one-step model with a suitably de�ned e�ective activation energy
Magnetic Field Dependent Tunneling in Glasses
We report on experiments giving evidence for quantum effects of
electromagnetic flux in barium alumosilicate glass. In contrast to expectation,
below 100 mK the dielectric response becomes sensitive to magnetic fields. The
experimental findings include both, the complete lifting of the dielectric
saturation by weak magnetic fields and oscillations of the dielectric response
in the low temperature resonant regime. As origin of these effects we suggest
that the magnetic induction field violates the time reversal invariance leading
to a flux periodicity in the energy levels of tunneling systems. At low
temperatures, this effect is strongly enhanced by the interaction between
tunneling systems and thus becomes measurable.Comment: 4 pages, 4 figure
Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier-Stokes equations
Two-dimensional compressible Reactive Navier-Stokes numerical simulations of intrinsic planar, premixed flame instabilities are performed. The initial growth of a sinusoidally perturbed planar flame is first compared with the predictions of a recent exact linear stability analysis, and it is shown the analysis provides a necessary but not sufficient test problem for validating numerical schemes intended for flame simulations. The long-time nonlinear evolution up to the final nonlinear stationary cellular flame is then examined for numerical domains of increasing width. It is shown that for routinely computationally affordable domain widths, the evolution and final state is, in general, entirely dependent on the width of the domain and choice of numerical boundary conditions. It is also shown that the linear analysis has no relevance to the final nonlinear cell size. When both hydrodynamic and thermal-diffusive effects are important, the evolution consists of a number of symmetry breaking cell splitting and re-merging processes which results in a stationary state of a single very asymmetric cell in the domain, a flame shape which is not predicted by weakly nonlinear evolution equations. Resolution studies are performed and it is found that lower numerical resolutions, typical of those used in previous works, do not give even the qualitatively correct solution in wide domains. We also show that the long-time evolution, including whether or not a stationary state is ever achieved, depends on the choice of the numerical boundary conditions at the inflow and outflow boundaries, and on the numerical domain length and flame Mach number for the types of boundary conditions used in some previous works
Correlated Persistent Tunneling Currents in Glasses
Low temperature properties of glasses are derived within a generalized
tunneling model, considering the motion of charged particles on a closed path
in a double-well potential. The presence of a magnetic induction field B
violates the time reversal invariance due to the Aharonov-Bohm phase, and leads
to flux periodic energy levels. At low temperature, this effect is shown to be
strongly enhanced by dipole-dipole and elastic interactions between tunneling
systems and becomes measurable. Thus, the recently observed strong sensitivity
of the electric permittivity to weak magnetic fields can be explained. In
addition, superimposed oscillations as a function of the magnetic field are
predicted.Comment: 4 page
Magnetic field effect on the dielectric constant of glasses: Evidence of disorder within tunneling barriers
The magnetic field dependence of the low frequency dielectric constant
(H) of a structural glass a - SiO2 + xCyHz was studied from 400 mK to 50
mK and for H up to 3T. Measurement of both the real and the imaginary parts of
is used to eliminate the difficult question of keeping constant the
temperature of the sample while increasing H: a non-zero (H) dependence is
reported in the same range as that one very recently reported on multicomponent
glasses. In addition to the recently proposed explanation based on
interactions, the reported (H) is interpreted quantitatively as a
consequence of the disorder lying within the nanometric barriers of the
elementary tunneling systems of the glass.Comment: latex Bcorrige1.tex, 5 files, 4 figures, 7 pages [SPEC-S02/009
Low temperature acoustic properties of amorphous silica and the Tunneling Model
Internal friction and speed of sound of a-SiO(2) was measured above 6 mK
using a torsional oscillator at 90 kHz, controlling for thermal decoupling,
non-linear effects, and clamping losses. Strain amplitudes e(A) = 10^{-8} mark
the transition between the linear and non-linear regime. In the linear regime,
excellent agreement with the Tunneling Model was observed for both the internal
friction and speed of sound, with a cut-off energy of E(min) = 6.6 mK. In the
non-linear regime, two different behaviors were observed. Above 10 mK the
behavior was typical for non-linear harmonic oscillators, while below 10 mK a
different behavior was found. Its origin is not understood.Comment: 1 tex file, 6 figure
Linear stability of planar premixed flames: reactive Navier-Stokes equations with finite activation energy and arbitrary Lewis number
A numerical shooting method for performing linear stability analyses of travelling waves is described and applied to the problem of freely propagating planar premixed flames. Previous linear stability analyses of premixed flames either employ high activation temperature asymptotics or have been performed numerically with finite activation temperature, but either for unit Lewis numbers (which ignores thermal-diffusive effects) or in the limit of small heat release (which ignores hydrodynamic effects). In this paper the full reactive Navier-Stokes equations are used with arbitrary values of the parameters (activation temperature, Lewis number, heat of reaction, Prandtl number), for which both thermal-diffusive and hydrodynamic effects on the instability, and their interactions, are taken into account. Comparisons are made with previous asymptotic and numerical results. For Lewis numbers very close to or above unity, for which hydrodynamic effects caused by thermal expansion are the dominant destablizing mechanism, it is shown that slowly varying flame analyses give qualitatively good but quantitatively poor predictions, and also that the stability is insensitive to the activation temperature. However, for Lewis numbers sufficiently below unity for which thermal-diffusive effects play a major role, the stability of the flame becomes very sensitive to the activation temperature. Indeed, unphysically high activation temperatures are required for the high activation temperature analysis to give quantitatively good predictions at such low Lewis numbers. It is also shown that state-insensitive viscosity has a small destabilizing effect on the cellular instability at low Lewis numbers
Effect of Nuclear Quadrupole Interaction on the Relaxation in Amorphous Solids
Recently it has been experimentally demonstrated that certain glasses display
an unexpected magnetic field dependence of the dielectric constant. In
particular, the echo technique experiments have shown that the echo amplitude
depends on the magnetic field. The analysis of these experiments results in the
conclusion that the effect seems to be related to the nuclear degrees of
freedom of tunneling systems. The interactions of a nuclear quadrupole
electrical moment with the crystal field and of a nuclear magnetic moment with
magnetic field transform the two-level tunneling systems inherent in amorphous
dielectrics into many-level tunneling systems. The fact that these features
show up at temperatures , where the properties of amorphous materials
are governed by the long-range interaction between tunneling systems,
suggests that this interaction is responsible for the magnetic field dependent
relaxation. We have developed a theory of many-body relaxation in an ensemble
of interacting many-level tunneling systems and show that the relaxation rate
is controlled by the magnetic field. The results obtained correlate with the
available experimental data. Our approach strongly supports the idea that the
nuclear quadrupole interaction is just the key for understanding the unusual
behavior of glasses in a magnetic field.Comment: 18 pages, 9 figure
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