247 research outputs found
Burgers' Flows as Markovian Diffusion Processes
We analyze the unforced and deterministically forced Burgers equation in the
framework of the (diffusive) interpolating dynamics that solves the so-called
Schr\"{o}dinger boundary data problem for the random matter transport. This
entails an exploration of the consistency conditions that allow to interpret
dispersion of passive contaminants in the Burgers flow as a Markovian diffusion
process. In general, the usage of a continuity equation , where stands for the
Burgers field and is the density of transported matter, is at variance
with the explicit diffusion scenario. Under these circumstances, we give a
complete characterisation of the diffusive transport that is governed by
Burgers velocity fields. The result extends both to the approximate description
of the transport driven by an incompressible fluid and to motions in an
infinitely compressible medium. Also, in conjunction with the Born statistical
postulate in quantum theory, it pertains to the probabilistic (diffusive)
counterpart of the Schr\"{o}dinger picture quantum dynamics.Comment: Latex fil
Instanton filtering for the stochastic Burgers equation
We address the question whether one can identify instantons in direct
numerical simulations of the stochastically driven Burgers equation. For this
purpose, we first solve the instanton equations using the Chernykh-Stepanov
method [Phys. Rev. E 64, 026306 (2001)]. These results are then compared to
direct numerical simulations by introducing a filtering technique to extract
prescribed rare events from massive data sets of realizations. Using this
approach we can extract the entire time history of the instanton evolution
which allows us to identify the different phases predicted by the direct method
of Chernykh and Stepanov with remarkable agreement
Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation
Tese de doutoramento. Ciências da Engenharia. 2006. Faculdade de Engenharia. Universidade do Porto, Instituto Superior Técnico. Universidade Técnica de Lisbo
Symmetries of Discrete Systems
In this series of lectures presented at the CIMPA Winter School on Discrete
Integrable Systems in Pondicherry, India, in February, 2003 we give a review of
the application of Lie point symmetries, and their generalizations to the study
of difference equations. The overall theme of these lectures could be called
"continuous symmetries of discrete equations".Comment: 58 pages, 5 figures, Lectures presented at the Winter School on
Discrete Integrable Systems in Pondicherry, India, February 200
Solving Fractional Damped Burgers' Equation Approximately by Using The Sumudu Transform (ST) Method
في هذا البحث , يتم حل معادلة بيركر دامبت الكسرية من الصيغة In this work, the fractional damped Burger's equation (FDBE) formula = 0
Non-commutative NLS-type hierarchies: dressing & solutions
We consider the generalized matrix non-linear Schrodinger (NLS) hierarchy. By
employing the universal Darboux-dressing scheme we derive solutions for the
hierarchy of integrable PDEs via solutions of the matrix
Gelfand-Levitan-Marchenko equation, and we also identify recursion relations
that yield the Lax pairs for the whole matrix NLS-type hierarchy. These results
are obtained considering either matrix-integral or general order
matrix-differential operators as Darboux-dressing transformations. In this
framework special links with the Airy and Burgers equations are also discussed.
The matrix version of the Darboux transform is also examined leading to the
non-commutative version of the Riccati equation. The non-commutative Riccati
equation is solved and hence suitable conserved quantities are derived. In this
context we also discuss the infinite dimensional case of the NLS matrix model
as it provides a suitable candidate for a quantum version of the usual NLS
model. Similarly, the non-commutitave Riccati equation for the general dressing
transform is derived and it is naturally equivalent to the one emerging from
the solution of the auxiliary linear problem.Comment: 29 pages, LaTex. Minor modification
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