220 research outputs found
Existence conditions and drift velocities of adiabatic flame-balls in weak gravity fields
Combining activation energy asymptotics, suitable scalings and numerical methods, we study how flame-balls move under the action of the free convection that they themselves generate in the presence of a weak, uniform gravity field. Attention is focused on steady configurations (in a suitable reference frame), on an isolated flame-ball of size comparable to what is obtained in the absence of gravity, and on deficient reactants that are characterized by a low Lewis number. For the sake of simplicity, we consider an adiabatic combustion process, in the sense that the radiative exchanges are neglected. This work provides one with:
(a) a description of the free-convection field around the flame-ball, along with an asymptotic estimate of the drift velocity;
(b) a relationship between the flame-ball radius, strength of gravity and physico-chemical properties of the reactive premixture;
(c) extinction conditions, caused by the net effect of heat extraction from the flame-ball to its surroundings by the free-convection field.
Hints on generalizations currently under consideration are also given
Flame front propagation IV: Random Noise and Pole-Dynamics in Unstable Front Propagation II
The current paper is a corrected version of our previous paper
arXiv:adap-org/9608001. Similarly to previous version we investigate the
problem of flame propagation. This problem is studied as an example of unstable
fronts that wrinkle on many scales. The analytic tool of pole expansion in the
complex plane is employed to address the interaction of the unstable growth
process with random initial conditions and perturbations. We argue that the
effect of random noise is immense and that it can never be neglected in
sufficiently large systems. We present simulations that lead to scaling laws
for the velocity and acceleration of the front as a function of the system size
and the level of noise, and analytic arguments that explain these results in
terms of the noisy pole dynamics.This version corrects some very critical
errors made in arXiv:adap-org/9608001 and makes more detailed description of
excess number of poles in system, number of poles that appear in the system in
unit of time, life time of pole. It allows us to understand more correctly
dependence of the system parameters on noise than in arXiv:adap-org/9608001Comment: 23 pages, 4 figures,revised, version accepted for publication in
journal "Combustion, Explosion and Shock Waves". arXiv admin note:
substantial text overlap with arXiv:nlin/0302021, arXiv:adap-org/9608001,
arXiv:nlin/030201
On the small-scale stability of thermonuclear flames in Type Ia supernovae
We present a numerical model which allows us to investigate thermonuclear
flames in Type Ia supernova explosions. The model is based on a finite-volume
explicit hydrodynamics solver employing PPM. Using the level-set technique
combined with in-cell reconstruction and flux-splitting schemes we are able to
describe the flame in the discontinuity approximation. We apply our
implementation to flame propagation in Chandrasekhar-mass Type Ia supernova
models. In particular we concentrate on intermediate scales between the flame
width and the Gibson-scale, where the burning front is subject to the
Landau-Darrieus instability. We are able to reproduce the theoretical
prediction on the growth rates of perturbations in the linear regime and
observe the stabilization of the flame in a cellular shape. The increase of the
mean burning velocity due to the enlarged flame surface is measured. Results of
our simulation are in agreement with semianalytical studies.Comment: 9 pages, 7 figures, Uses AASTEX, emulateapj5.sty, onecolfloat.sty.
Replaced with accepted version (ApJ), Figures 1 and 3 are ne
Nonlinear equation for curved stationary flames
A nonlinear equation describing curved stationary flames with arbitrary gas
expansion , subject to the
Landau-Darrieus instability, is obtained in a closed form without an assumption
of weak nonlinearity. It is proved that in the scope of the asymptotic
expansion for the new equation gives the true solution to the
problem of stationary flame propagation with the accuracy of the sixth order in
In particular, it reproduces the stationary version of the
well-known Sivashinsky equation at the second order corresponding to the
approximation of zero vorticity production. At higher orders, the new equation
describes influence of the vorticity drift behind the flame front on the front
structure. Its asymptotic expansion is carried out explicitly, and the
resulting equation is solved analytically at the third order. For arbitrary
values of the highly nonlinear regime of fast flow burning is
investigated, for which case a large flame velocity expansion of the nonlinear
equation is proposed.Comment: 29 pages 4 figures LaTe
Flame front propagation I: The Geometry of Developing Flame Fronts: Analysis with Pole Decomposition
The roughening of expanding flame fronts by the accretion of cusp-like
singularities is a fascinating example of the interplay between instability,
noise and nonlinear dynamics that is reminiscent of self-fractalization in
Laplacian growth patterns. The nonlinear integro-differential equation that
describes the dynamics of expanding flame fronts is amenable to analytic
investigations using pole decomposition. This powerful technique allows the
development of a satisfactory understanding of the qualitative and some
quantitative aspects of the complex geometry that develops in expanding flame
fronts.Comment: 4 pages, 2 figure
Dynamic Key-Value Memory Networks for Knowledge Tracing
Knowledge Tracing (KT) is a task of tracing evolving knowledge state of
students with respect to one or more concepts as they engage in a sequence of
learning activities. One important purpose of KT is to personalize the practice
sequence to help students learn knowledge concepts efficiently. However,
existing methods such as Bayesian Knowledge Tracing and Deep Knowledge Tracing
either model knowledge state for each predefined concept separately or fail to
pinpoint exactly which concepts a student is good at or unfamiliar with. To
solve these problems, this work introduces a new model called Dynamic Key-Value
Memory Networks (DKVMN) that can exploit the relationships between underlying
concepts and directly output a student's mastery level of each concept. Unlike
standard memory-augmented neural networks that facilitate a single memory
matrix or two static memory matrices, our model has one static matrix called
key, which stores the knowledge concepts and the other dynamic matrix called
value, which stores and updates the mastery levels of corresponding concepts.
Experiments show that our model consistently outperforms the state-of-the-art
model in a range of KT datasets. Moreover, the DKVMN model can automatically
discover underlying concepts of exercises typically performed by human
annotations and depict the changing knowledge state of a student.Comment: To appear in 26th International Conference on World Wide Web (WWW),
201
Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach
Five types of blow-up patterns that can occur for the 4th-order semilinear
parabolic equation of reaction-diffusion type
u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1,
\quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, are discussed. For
the semilinear heat equation , various blow-up patterns
were under scrutiny since 1980s, while the case of higher-order diffusion was
studied much less, regardless a wide range of its application.Comment: 41 pages, 27 figure
Preliminary definitions for the sonographic features of synovitis in children
Objectives Musculoskeletal ultrasonography (US) has the potential to be an important tool in the assessment of disease activity in childhood arthritides. To assess pathology, clear definitions for synovitis need to be developed first. The aim of this study was to develop and validate these definitions through an international consensus process. Methods The decision on which US techniques to use, the components to be included in the definitions as well as the final wording were developed by 31 ultrasound experts in a consensus process. A Likert scale of 1-5 with 1 indicating complete disagreement and 5 complete agreement was used. A minimum of 80% of the experts scoring 4 or 5 was required for final approval. The definitions were then validated on 120 standardized US images of the wrist, MCP and tibiotalar joints displaying various degrees of synovitis at various ages. Results B-Mode and Doppler should be used for assessing synovitis in children. A US definition of the various components (i.e. synovial hypertrophy, effusion and Doppler signal within the synovium) was developed. The definition was validated on still images with a median of 89% (range 80-100) of participants scoring it as 4 or 5 on a Likert scale. Conclusions US definitions of synovitis and its elementary components covering the entire pediatric age range were successfully developed through a Delphi process and validated in a web-based still images exercise. These results provide the basis for the standardized US assessment of synovitis in clinical practice and research
Resolvent methods for steady premixed flame shapes governed by the Zhdanov-Trubnikov equation
Using pole decompositions as starting points, the one parameter (-1 =< c < 1)
nonlocal and nonlinear Zhdanov-Trubnikov (ZT) equation for the steady shapes of
premixed gaseous flames is studied in the large-wrinkle limit. The singular
integral equations for pole densities are closely related to those satisfied by
the spectral density in the O(n) matrix model, with n = -2(1 + c)/(1 - c). They
can be solved via the introduction of complex resolvents and the use of complex
analysis. We retrieve results obtained recently for -1 =< c =< 0, and we
explain and cure their pathologies when they are continued naively to 0 < c <
1. Moreover, for any -1 =< c < 1, we derive closed-form expressions for the
shapes of steady isolated flame crests, and then bicoalesced periodic fronts.
These theoretical results fully agree with numerical resolutions. Open problems
are evoked.Comment: v2: 29 pages, 6 figures, some typos correcte
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