145 research outputs found
Stabilization by Unbounded-Variation Noises
In this paper, we claim the availability of deterministic noises for
stabilization of the origins of dynamical systems, provided that the noises
have unbounded variations. To achieve the result, we first consider the system
representations based on rough path analysis; then, we provide the notion of
asymptotic stability in roughness to analyze the stability for the systems. In
the procedure, we also confirm that the system representations include
stochastic differential equations; we also found that asymptotic stability in
roughness is the same property as uniform almost sure asymptotic stability
provided by Bardi and Cesaroni. After the discussion, we confirm that there is
a case that deterministic noises are capable of making the origin become
asymptotically stable in roughness while stochastic noises do not achieve the
same stabilization results.Comment: 22 pages, 5 figure
On the probabilistic approach for Gaussian Berezin integrals
We present a novel approach to Gaussian Berezin correlation functions. A
formula well known in the literature expresses these quantities in terms of
submatrices of the inverse matrix appearing in the Gaussian action. By using a
recently proposed method to calculate Berezin integrals as an expectation of
suitable functionals of Poisson processes, we obtain an alternative formula
which allows one to skip the calculation of the inverse of the matrix. This
formula, previously derived using different approaches (in particular by means
of the Jacobi identity for the compound matrices), has computational advantages
which grow rapidly with the dimension of the Grassmann algebra and the order of
correlation. By using this alternative formula, we establish a mapping between
two fermionic systems, not necessarily Gaussian, with short and long range
interaction, respectively
Wrinkled flames and geometrical stretch
Localized wrinkles of thin premixed flames subject to hydrodynamic
instability and geometrical stretch of uniform intensity (S) are studied. A
stretch-affected nonlinear and nonlocal equation, derived from an inhomogeneous
Michelson-Sivashinsky equation, is used as a starting point, and pole
decompositions are used as a tool. Analytical and numerical descriptions of
isolated (centered or multicrested) wrinkles with steady shapes (in a frame)
and various amplitudes are provided; their number increases rapidly with 1/S >
0. A large constantS > 0 weakens or suppresses all localized wrinkles (the
larger the wrinkles, the easier the suppression), whereasS < 0 strengthens
them; oscillations of S further restrict their existence domain. Self-similar
evolutions of unstable many-crested patterns are obtained. A link between
stretch, nonlinearity, and instability with the cutoff size of the wrinkles in
turbulent flames is suggested. Open problems are evoked
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